Multi-Objective Optimization of Squeeze Casting ...

International Journal of Swarm Intelligence Research Volume 7 • Issue 1 • January-March 2016

Multi-Objective Optimization of Squeeze Casting Process using Evolutionary Algorithms Manjunath Patel G C, Department of Mechanical Engineering, National Institute of Technology Karnataka, Surathkal, India Prasad Krishna, Department of Mechanical Engineering, National Institute of Technology Karnataka, Surathkal, India Mahesh B. Parappagoudar, Department of Mechanical Engineering, Chhatrapati Shivaji Institute of Technology, Bhilai, India Pandu Ranga Vundavilli, School of Mechanical Sciences, Indian Institute of Technology, Bhubneswar, India

ABSTRACT The present work focuses on determining optimum squeeze casting process parameters using evolutionary algorithms. Evolutionary algorithms, such as genetic algorithm, particle swarm optimization, and multi objective particle swarm optimization based on crowing distance mechanism, have been used to determine the process variable combinations for the multiple objective functions. In multi-objective optimization, there are no single optimal process variable combination due to conflicting nature of objective functions. Four cases have been considered after assigning different combination of weights to the individual objective function based on the user importance. Confirmation tests have been conducted for the recommended process variable combinations obtained by genetic algorithm (GA), particle swarm optimization (PSO), and multiple objective particle swarm optimization based on crowing distance (MOPSO-CD). The performance of PSO is found to be comparable with that of GA for identifying optimal process variable combinations. However, PSO outperformed GA with regard to computation time. Keywords Genetic Algorithm (GA), Multi-Objective Optimization, Multiple Objective Particle Swarm Optimization Based on Crowing Distance (MOPSO-CD), Particle Swarm Optimization (PSO), Squeeze Casting Process

INTRODUCTION Hybrid squeeze casting process has been developed by combining the distinguished features such as strength, integrity, economic, and design flexibility of conventional casting (gravity and die casting) and forging processes (Rajgopal, 1981). The technical benefit of the squeeze casting process over conventional casting and forging process cited in the literature (Rajgopal, 1981; Ghomashchi & DOI: 10.4018/IJSIR.2016010103 Copyright © 2016, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited.

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Vikhrov, 2000) are near net-shape castability, simpler tooling construction, high productivity, refined structure, improved surface finish, heat-treatability, minimum porosity and segregations, ability to cast ferrous, non-ferrous and wrought alloys. Hence, the squeeze cast parts are used in automobile parts, namely piston, cylinder, clutch housing, brake drum, engine block, connecting rod, wheels, suspension arm, hubbed flanges, barrel heads, truck hubs, and so on (Rajgopal, 1981; Ghomashchi & Vikhrov, 2000; Krishna, 2001). These diverse applications have led the researchers’ attention towards squeeze casting process throughout the globe during the 1990s and 2000s. It is interesting to note that major class of research work was reported using analytical, numerical, and classical engineering experimental approaches. Solidification time was determined using one dimensional analytical model such as Gracias virtual and steady state heat flow models respectively, by (Yang, 2007). It should be noted that casting density and mechanical properties were improved with low solidification time. Chattopadhyay (2007) carried out the solidification simulation using numerical approach by solving Navier-Stokes equation coupled with energy equation. It is important to note that solidification time is inversely proportional to the interfacial heat transfer coefficient. Krishna (2001) reported heat transfer coefficient in metal castings depends mainly on geometry, size, casting shape, mould materials, physical, chemical and interfacial conditions and major interactions among them. Jacob and Michael (2012) reported several assumptions to be made while estimating heat transfer coefficient under experimentations during squeeze casting of aluminium alloys. Aweda and Adeyemi (2009) studied the effect of casting temperature and squeeze pressure on heat transfer coefficients using numerical and classical engineering experimental approaches. It is important to note that experiments were conducted for fixed pressure duration. The effect of squeeze pressure variations on density, secondary dendrite arm spacing and mechanical properties were investigated by Fan et al., (2010). It is noted that pressure duration and temperature influencing parameters variations were not considered during their experiments. Furthermore, the properties were found to increase steadily, with applied squeeze pressure up to 120 MPa and thereafter remained constant. The influence of squeeze pressure, die and pouring temperature on density, mechanical, micro and macrostructure properties were studied using classical engineering experimental approach of varying one factor at a time by Maleki, Niroumand and Shafyei (2006; 2009). Hong, Lee and Shen (2000) analysed squeeze pressure, waiting time, inoculants, degassing, pouring and die temperature effects on formation of macro-segregation. It should be noted that experiments were conducted using classical engineering experimental approaches. Rajagopal and Altergott (1985) identified many direct squeeze casting defects and suggested wide scope to determine the appropriate choice of the process parameter combinations to eliminate most of these defects. The above literature confirmed that casting quality in squeeze casting process is majorly influenced by its process variables and the practical guidelines suggested/followed by authors using analytical, classical engineering experimental and numerical approaches may lead to many sub-optimal solutions and are not considered to be globally optimal. The above traditional approaches can only estimate the main process parameter effects and might fail to estimate the interaction factor effects with minimum experiments and computational burden. Furthermore, interaction factor estimation requires varying process parameters simultaneously under experimental approach. In recent years, statistical methods have been used to model, identify, analyze, and establish input-output relationship of the squeeze casting process. The process parameters were simultaneously studied to estimate the main, square and interaction factor effects with minimum number of experiments using statistical Taguchi and conventional regression analysis. Statistical Taguchi method has been employed to study the effect of squeeze pressure, die and pouring temperature effects on hardness and tensile strengths of cast aluminium alloys by Souissi et al., (2014). It should be noted that the influence of pressure duration effects were neglected in their analysis. Die temperature, squeeze pressure and pressure duration effects on hardness and mechanical strengths were investigated using Taguchi method by Vijian and Arunachalam (2007). It is noteworthy that the influence of waiting time

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and pouring temperature effects were neglected in their analysis. Further, no work reported to develop mathematical input-output relationship and check their prediction accuracy with random test cases. Predicting response could help the foundry personnel in selecting the most influential process variable combinations without conducting experiments and energy consumptions. Later, research work directed towards addressing the limitations of statistical Taguchi method to provide complete insight information of both individual and interaction effects of the process variables using response surface methodology (RSM) and design of experiments (DOE). Moreover, two non-linear DOE models such as Box-Behnken design (BBD) and central composite design (CCD) have been employed to study the influence of squeeze casting process variables on some properties of aluminium based alloys by Patel, Krishna and Parappagoudar, (2015). In the above work authors have made an attempt by considering pressure duration, squeeze pressure, die and pouring temperature as input parameters, and density, hardness and secondary dendrite arm spacing as outputs. Among the two non-linear regression models, CCD based model was found better for hardness and secondary dendrite arm spacing predictions, whereas BBD based model outperformed CCD to accurately predict the casting density. Improving the casting quality by identifying appropriate process variable combinations and providing improved casting properties is of great relevance to industry. To identify the optimal process parameter combinations using the above traditional techniques may fail when number of process variables increases and their corresponding interaction effect of the process becomes complex and non-linear in behaviour. In addition, use of traditional optimization methods such as analytical, numerical, classical engineering experimental, statistical design of experiments, and response surface methodology may lead to local optimum solutions. Traditional optimization techniques use deterministic search procedure with specific rules to move one solution with respect to other leads to many sub optimal solutions. Alternatively, global optimum solutions can be obtained using popular non-traditional search techniques such as genetic algorithm (GA), particle swarm optimization (PSO), simulated annealing (SA), ant colony optimization (ACO), differential evolution (DE), harmonic search (HS), bacterial foraging optimization (BFO), artificial bee colony algorithm (ABC), teacher learner base algorithm (TLBO) and so on. Rao and Savsani (2012) reported non-traditional search techniques are considered to be stochastic in nature with certain combination of probabilistic transition rules. Process optimization can be performed either for single or multi responses. In single response optimization the optimal solutions can be clearly defined based on the problem domain (global minima or maxima). In squeeze casting identifying the best process variable combinations for all the responses such as hardness, secondary dendrite arm spacing and density is difficult due to the conflicting requirements. Patel et al., (2015) found density and hardness have direct relation and those responses with secondary dendrite arm spacing identified inverse relation using statistical analysis and this problem requires multi-objective optimization. Multi-objective optimization is the process of determining a set of optimum process variables that result in best combination of responses. Multi-objective optimization problems can be effectively solved by using heuristic search procedure of evolutionary algorithms. Population based search techniques, namely GA and PSO, are proved as cost effective tools in searching near optimal solutions, through its heuristic search mechanisms at many distinct locations simultaneously. The early use of evolutionary computational search was first reported by Rosenberg in 1960 (Rosenberg, 1967). Later, Schaffer (1985) proposed multi-objective evolutionary optimization to optimize two or more responses simultaneously. Multi-objective optimization can be solved using two general approaches. The first approach deals with combining two or more individual objective functions to form single composite function after assigning suitable weights to each objective function. The second approach deals with generating set of Pareto optimal solutions depending on the trade-offs (weights). In recent past weight methods has been utilized to determine the optimum process parameters of different manufacturing processes like wire electrical discharge machining (Mahapatra & Patnaik, 2007), tube spinning process (Vundavilli, Kumar & Parappagoudar, 2013) and green sand molding process (Surekha et al., 2012). The present research work also focused on the first approach i.e. multi-response optimization using evolutionary 57


algorithms namely GA, PSO and MOPSO-CD. The heuristic search abilities of GA and PSO identify the global minima or maxima more quickly through competitive solutions among potential populations. In recent years, GA and PSO have been used for multi-objective optimization of different problems related to squeeze casting (Vijian & Arunachalam, 2007), green sand moulding (Surekha et al., 2012), machining (Mahapatra & Patnaik, 2007), drilling (Ting & Lee, 2012), tube spinning process (Vundavilli, Kumar, & Parappagoudar, 2013), welding (Pashazadeh, Gheisari, & Hamedi 2014), and so on. Multi-objective evolutionary optimization algorithms (MEOAs) have been used during recent years in several domains of science and engineering applications (Zhou et al., 2011). Evolutionary algorithm parameters are to be suitably modified using different niching techniques to handle conflict multiple objective functions (Das et al., 2011). Therefore major modifications are made to the simple PSO algorithm to select the best guides for updating position and velocity based on the non-dominated solutions stored in the external repository through the use of crowding distance (CD) method (Sierra & Coello, 2005). It is to be noted that the multi objective particle swarm optimization based on crowding distance (MOPSO-CD) method outperformed other modification methods such as Dynamic niching PSO (DNPSO), Cross searching strategy MOPSO (CSS-MOPSO), MOPSO and MOPSO based crowding distance and local search (MOPSO-CDLS) for solving multi-objective optimization problems (Santana, Pontes, & Bastos-Filho, 2009). It is important to note that, the authors Vijian and Arunachalam (2007) used only linear terms in their objective function. In addition, Vijian and Arunachalam (2007) conducted optimization for hardness and ultimate tensile strength which does not have conflicting requirements. To the best of author’s knowledge, not much work has been reported on structure to property (density, hardness and SDAS) optimization of process parameters in a squeeze casting process. In the present work, Patel et al., (2015) obtained the non-linear regression equations based on CCD and BBD which have been used as the objective functions for multi-response optimization. PSO, MOPSO-CD and GA have been used to determine the best combination of process variables for high values of density and hardness, and low values of secondary dendrite arm spacing, respectively. Density, hardness and secondary dendrite arm spacing are considered as outputs (objective functions), whereas squeeze pressure, pressure duration, die temperature and pouring temperatures are treated as inputs (process variables). It is to be noted that, using mathematical formulation all objective functions are suitably modified to form a single objective function. In addition, the predicted optimal process parameter combinations using PSO, MOPSO-CD and GA are compared among themselves experimentally. MATHEMATICAL FORMULATION OF THE PROBLEM In squeeze casting process, the casting properties (density, hardness and secondary dendrite arm spacing) depends mainly on the influence of process variables such as squeeze pressure, pressure duration, die and pouring temperatures. The input-output model of the squeeze casting process is shown in Figure 1. Figure 1. Squeeze casting input-output process model

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The selection of process variable and their corresponding levels is of primary importance since too narrow range might result in poor or incomplete information about the process. Conversely, too wide range may lead to infeasible solution for the response surface (Parappagoudar, Prathihar, & Datta, 2007). Hence, squeeze casting process variables and their operating levels have been selected after conducting trial experiments in the research laboratory and consulting literature (Refer to Table 1). It should be noted that experiments were conducted for different process variable combinations and levels using standard matrices of central composite design (CCD) and box behnken designs (BBD). Statistical analysis of experimental data and non-linear input-output relationship were established in accordance with design of experiments and response surface methodology (Montgomergy, 2001). For each casting conditions, three replicates were considered and the responses namely density, hardness and secondary dendrite arm spacing were measured. The non-linear input-output relations were developed for the responses namely, density, secondary dendrite arm spacing and hardness by utilizing response surface methodology. The statistical adequacy and significance were tested by utilizing ANOVA test. It is to be noted that, all three nonlinear regression (input-output) models were found to be statistically adequate. It is important to note that, prediction performances of the developed non-linear models were tested with the help of fifteen test cases. It is interesting to note in Patel et al., (2015), CCD model performed better for hardness and secondary dendrite arm spacing prediction. Whereas BBD model outperformed the CCD based model for density prediction. It is important to note that best response model has been selected for process parameter optimization. The relationship between process variables and the responses are shown in Equations 1, 2 and 3. These response equations have been developed by utilizing the experimental data collected as per DOE and applying response surface methodology (refer Parappagoudar et al., (2007)): Density, ρBBD = 0.926894 - 0.00162963A + 0.00140417B + 0.00468148C + 0.000867778D -1.14815 × 10−5 A2

-4.19271 ×10−6 B 2 - 3.37449 ×10−6C 2 - 1.5037 ×10−6 D 2 + 8.33333 × 10−7 AB +2.59259 ×10−6 AC (1) +3.11111 ×10−6 AD - 5.55556 ×10−7 BC + 3.33333 ×10−7 BD -5.92593 ×10−7CD

Secondary Dendrite Arm Spacing , SDASCCD = 558.023 + 0.203851A - 0.186898B -1.45184C - 0.212065 D - 0.00147737 A2 - 3.90046 × 10−5 B 2 +0.00102844C 2 + 0.000189794 D 2 + 7.70833 × 10−5 AB -8.51852 ×10−5 AC - 3.65556 ×10−4 AD + (2)

0.000168056 BC -1.50417 ×10−4 BD + 0.000252593CD

Table 1. Squeeze casting process parameters and their respective levels Process Variables

Levels

Description

Symbols

Low (-1)

Middle (0)

High (+1)

Pressure duration, PD, (s)

A

20

35

50

Squeeze pressure, SP, (MPa)

B

40

80

120

Pouring temperature, PT, (°C)

C

630

675

720

Die temperature, DT, (°C)

D

150

225

300

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Hardness, BHN CCD = -380.453 - 0.267973 A - 0.219502 B + 1.27475C + 0.179611D - 0.00166255 A2 + 0.000766204 B 2 -9.00777 ×10−4 C 2 - 2.20576 ×10−5 D 2 + 0.0005 AB +0.000407407 AC + 7.77778 ×10−5 AD + 0.000284722 BC + 0.0001BD -2.88889 × 10−4 CD

(3)

Density is influenced by internal casting defects such as porosity, voids, segregations and shrinkages. The internal casting defects decrease the available load area, provoke stress concentration and initiate crack formation resulting in poor tensile strengths, ductility and hardness. Finer arm spacing in a casting is desirable to enhance mechanical properties. It should be noted that primary dendrites once developed does not change during or after solidification, whereas the secondary dendrite arms in the primary dendrites undergo ripening process. Thus secondary dendrite arm spacing is of paramount importance to optimize with respect to the process variables to enhance micro structure and hence mechanical properties. In the present work (Patel et al., 2015), attempts are made to optimize the squeeze casting process that could maximize the throughput in improving the casting quality (properties) using evolutionary algorithms. For better casting properties, the responses such as density and hardness are to be maximize, meanwhile secondary dendrite arm spacing should be minimized. It is difficult to determine the single optimal combinations of process variables for density, hardness and secondary dendrite arm spacing, respectively. Thus, there is a need for multi-objective optimization method to determine the optimal solutions for this problem. Therefore, the multiple performances of conflicting responses (one is minimization (refer to Equation 5) and the rest is maximization (refer to Equation 4 and 6)) are converted into single objective function of maximization using suitable mathematical formulation (refer to Equation 7). The weighted method has been adapted for the outputs to form single objective function, similar to the work carried out earlier by (Mahapatra & Patnaik, 2007; Vundavilli et al., 2013; Surekha et al., 2012). The formulated weighted objective function for maximization is shown in Equation 7:

Objective function ( R 1 ) = Density Objective function ( R 2 ) =

1 SDAS

(4)

(5)

Objective function ( R 3 ) = Hardness

(6)

Maximize Y = (W1R 1 +W2 R 2 +W3 R 3 )

(7)

Subject to constraints:

20 ≤ A ≤ 50

(8)

40 ≤ B ≤ 120

(9)

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630 ≤ C ≤ 720

(10)

150 ≤ D ≤ 300

(11)

where, R1, R2 and R3 the objective functions of the responses such as density (ρ), secondary dendrite arm spacing (SDAS) and hardness (BHN) respectively. W1, W2 and W3 are the weights considered for the responses ρ, SDAS and BHN, respectively. Moreover, the terms A, B, C and D are the process variables representing pressure duration, squeeze pressure, pouring temperature and die temperature, respectively. In multi-objective optimization, there exist a multiple combination of optimal solutions. Selection of single process variable combination from multiple optimal solutions is difficult for foundry personnel. Therefore, four cases have been considered with different combination of weights assigned to the responses by user. Weighted factors are selected in such a way that their corresponding summation must be equal to one (Mahapatra & Patnaik, 2007; Vundavilli et al., 2013; Surekha et al., 2012). Moreover higher weight factors indicate more importance assigned for the particular objective function. Four different cases have been selected in such a way that, Case 1 deals with equal importance for all the responses (W1 = 0.3333, W2 = 0.3333 and W3 = 0.3333), Case 2 deals with maximum importance for the response, density (W1 = 0.8, W2 = 0.1 and W3 = 0.1), Case 3 deals with maximum importance for the response, secondary dendrite arm spacing (W1 = 0.1, W2 = 0.8 and W3 = 0.1) and Case 4 deals with maximum importance for the response, hardness (W1 = 0.1, W2 = 0.1 and W3 = 0.8). METHODOLOGY OF MULTI–OBJECTIVE EVOLUTIONARY OPTIMIZATION In the present work, multi-objective evolutionary algorithms such as binary coded PSO, MOPSO-CD and GA have been utilized to optimize the squeeze casting process using mathematically formulated single objective function. The working principle of population based search and optimization techniques of GA and PSO algorithms will be discussed in the following sections. Genetic Algorithms (GA) Genetic algorithm was first proposed by Prof. John Holland at University of Michigan during 1975. GA works with the well-known principles of Charles Darwin theory of the survival of fittest among the individuals over successive generations to simulate natural system necessary for evolution. GA has been applied in the past to solve various manufacturing related problems (Schaffer, 1985; Mahapatra & Patnaik, 2007; Vundavilli et al., 2013; Pashazadeh et al., 2014). Unlike traditional search techniques, GA searches the optimum solutions at many distinct locations simultaneously. The schematic diagram represents the methodology adopted to optimize the process parameter with working procedure of evolutionary genetic algorithm (see Figure 2.). Tournament selection and bit-wise mutations are adopted to avoid local solutions if any. Particle Swarm Optimization (PSO) Particle swarm optimization was introduced by Dr. Russel C. Eberhart and Dr. James Kennedy during 1995. The PSO has gained prime importance for solving various domains of manufacturing (Vundavilli et al., 2013; Surekha et al., 2012; Ting and Lee, 2012) due to few tuning parameters, easy implementation, and fast convergence rate in comparison to GA. PSO algorithm mimic the movement of foraging behaviour of the bird flock. In particle swarm optimization, the swarm is a community composed of many individuals referred as particles and all particles fly around in a multidimensional search space. It is important to note that based on self-flying experience and neighboring particles experience, each particle adjusts its own flight path reported in Sierra and Coello (2005). The schematic diagram of working cycle of particle swarm optimization is shown in Figure 3. Unlike evolutionary 61


Figure 2. Methodology followed for process optimization and working cycle of GA

genetic algorithm parameters such as selection and crossover, PSO utilize the particles, wherein each individual move with certain velocity and is dynamically adjusted during its search space. The parameters are adjusted by updating its positions and velocity of the particles using Equations 12 and 13 (Surekha et al., 2012):

New Velocity :Vi K +1 = w × Vi k + Rand1  Pbestik - Pi k  + Rand 2 Gbestik - Pi k 

(12)

New Position : Pi k +1 = Pi k + Vi k +1

(13)

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Figure 3. Schematic diagram of working cycle of PSO

The terms; w refers to inertia weight,

Vi k is the current velocity of the individual particle i at

Vi K +1 indicate the modified velocity of the individual i at iteration k+1, Rand1, Rand2: k k random numbers vary in the range of [0 and 1]. Pbesti , Gbesti indicate the best positions of

iteration k,

individual particle i have reached and group until iteration k. It is important to note that the second term in Equation 12 refers to the cognitive part where the particle changes its velocity based on self experience and the third term is the social part where the particle changes its velocity through their neighbor particle experience.

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Multi-Objective Particle Swarm Optimization: Crowding Distance (MOPSO-CD) Multi objective particle swarm optimization based on crowding distance mechanism coupled with mutation operator is incorporated for simple PSO, to keep the variety of non-dominated solutions in an external repository, discussed in the work by Raquel and Naval (2005). The major modifications employed for the basic PSO algorithm are selection process of cognitive leader ( Pbest ) and social leader ( Gbest ) using the Pareto dominance and crowding distance methods. The MOPSO uses the peripheral repository of non-dominated solutions found in earlier iterations and the mutation operator enhance the search capability of the algorithm to prevent the premature convergence (local minima) by Raquel and Naval (2005). The schematic diagram illustrate the working cycle of the MOPSO-CD is shown in Figure 4. Thus, MOPSO-CD is considered as an effective tool to handle the complex multi objective optimization problems which are conflict in nature. Figure 4. Schematic diagram of working cycle of MOPSO-CD

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RESULTS AND DISCUSSIONS Results of parametric study and the optimized process variable combinations for four different cases are discussed in the present section. Genetic Algorithms (GA) The performance of GA depends mainly on the appropriate choice of algorithm parameters. It is to be noted that there are no universal standards available to select the GA parameters such as population size (Pop), probability of mutation (PM), probability of cross over (PC), and generation number (Gen). Thus in the present work, selections are made using parameter study (i.e, varying one parameter at a time and keeping the rest at fixed values). Selection of weight factor is also of paramount importance on the performance of the casting properties. Weight factor has been selected based on the decision maker requirements. Therefore, four different cases have been considered after varying the weighing factors based on the importance assigned for objectives. The parametric study has been conducted to determine maximum fitness values of GA and the corresponding parameters responsible for better casting properties are shown in Figure 5. In the first stage, probability of crossover was varied in the range of 0.5 to 1, after keeping probability of mutation, population size and number of generations fixed as 0.1, 0.8 and 100 respectively. It is interesting to note that the probability of crossover (PC*) with 0.55 showed best performance in terms of maximum fitness value. Therefore for the second stage and further, the probability of crossover is fixed at 0.55. Similarly the maximum fitness values have been determined for PM, Pop and Gen in successive stages (refer to Figure 5). In each stage the GA parameters, responsible for maximum fitness, have been identified. The optimum GA parameter values obtained using parametric study are shown below: Figure 5. Genetic algorithm parameter study: (a) Fitness vs. probability of cross over; (b) Fitness vs. probability of mutation; (c) Fitness vs. population size; and (d) Fitness vs. generations

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Probability of Crossover (PC*) = 0.55 Probability of Mutation (PM*) = 0.15 Population Size (Pop*) = 80 Generation Number (Gen*) = 85 The optimum casting conditions obtained for multiple outputs with different weight factor combinations are given in Table 2. Maximum fitness value obtained for case 1 to case 4 are found to be equal to 26.93, 9.907, 8.089 and 62.88 respectively. Case 4 is recommended for the present work since it has maximum fitness value compared to the other cases and yield maximum density, hardness and minimum values of secondary dendrite arm spacing. Particle Swarm Optimization (PSO) The performance of the heuristic search method PSO depends mainly on the parameters such as inertia weight, swarm size and number of generations. Therefore a detailed systematic study has been conducted to determine the best PSO parameters responsible for better casting properties. The systematic study has been conducted by varying one parameter at a time after keeping the other parameters at fixed values. Swarm size in particle swarm optimization greatly affect the computational time. Smaller swarm size results in faster convergence rate but may have higher probability in getting trapped at local minima. Conversely, improvement in the performance with large swarm size must compensate for larger computational time. The systematic study has been conducted to determine the maximum fitness of PSO parameters responsible to yield the best casting properties (refer to Figure 6). The study has been carried out in three stages. In the first stage, the inertia weights are varied between zero and one, after keeping both the swarm size and number of generations fixed to 50. It is interesting to note that the inertia weight (W*) with 0.6 showed the best performance in terms of maximum fitness (see Figure 6 (a)). Thus from second stage onwards, the inertia weight is kept fixed to 0.6. Similarly maximum fitness values are determined for swarm size (SS*) and maximum generation (G*) in successive stages. Finally the optimized PSO parameters responsible for the better performance are as follows: Inertia Weight (W*) = 0.6 Swarm Size (SS*) = 50 Number of Generations (G*) = 50 Table 2. Optimum casting conditions for multiple outputs with different combination of weight factors via GA, PSO and MOPSO-CD methods Optimum Values of Casting Conditions and Casting Properties Process Variables and Outputs

Case 1 (W1 = 0.333, W2 = 0.333 and W3 =0.333) GA

PSO

MOPSOCD

Case 2 (W1 = 0.8, W2 = 0.1 and W3 =0.1) GA

PSO

MOPSOCD

Case 3 (W1 = 0.1, W2 = 0.8 and W3 =0.1) GA

PSO

MOPSOCD

Case 4 (W1 = 0.1, W2 = 0.1 and W3 =0.8) GA

PSO

MOPSOCD

A:PD, sec

27.81

43.24

27.65

24.07

38.27

38.27

24.42

45.98

21.34

27.81

27.88

28.64

B:SP, MPa

119.6

119.8

120

119.8

118.1

119.9

119.5

117.1

119.99

120.0

119.9

120

C:PT, ˚C

708.6

696.4

708.5

698.0

698.1

698.4

705.4

660.8

709.13

708.4

708.3

705.4

D:DT, ˚C

150.3

157.7

150.0

169.4

222.4

208.5

158.2

167.7

150.05

150

150.5

150.1

ρ, g/cm3

2.663

2.665

2.663

2.665

2.668

2.668

2.663

2.663

2.661

2.663

2.663

2.663

SDAS, µm

35.16

34.35

35.11

34.50

35.0

34.64

34.90

34.33

35.00

35.14

35.11

34.95

BHN

78.19

77.52

78.27

77.72

76.5

77.06

78.00

74.78

78.20

78.27

78.26

78.26

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Figure 6. Parameter study of PSO: (a) Fitness vs. inertia weight; (b) Fitness vs. swarm size; and (c) Fitness vs. generations

Similar to GA four different cases has been considered to determine the optimal process variable combinations responsible for multiple output performances (refer to Table 2). The maximum fitness obtained from case 1 to case 4 is found to be equal to 26.79, 10.06, 7.78 and 63.16 respectively. Case 4 is recommended for PSO as its maximum fitness values over performed the other cases to give better casting properties. Multi-Objective Particle Swarm Optimization – Crowding Distance (MOPSO-CD) In MOPSO-CD also, systematic study has been conducted to determine the optimum PSO parameters (refer to Figure 7). The final best PSO parameters responsible for maximum fitness values are determined using parameter study as follows: Inertia Weight (W*) = 0.1 Swarm Size (SS*) = 50 Number of Generations (G*) = 40 The same four different case studies considered in the previous approaches are considered to estimate the extreme values of the multiple conflicting responses and there corresponding process variable combinations (refer to Table 2). It is worth noting that the fitness values obtained for case 1 to case 4 are found equal to 27.04, 10.13, 8.13 and 63.16 respectively. Further, the case 4 is selected as the corresponding optimum casting conditions which are responsible to gain the maximum fitness values.

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Figure 7. Parameter study of MOPSO-CD: (a) Fitness vs. inertia weight; (b) Fitness vs. swarm size; and (c) Fitness vs. generations

Confirmation Test Confirmation tests have been conducted with three replicates for the recommended process variable combinations of PSO and GA. It is important to note that the confirmation tests have been conducted for the case 4, as its corresponding fitness value is found to be maximum compared to other cases. It is also important to note that the responses have been measured under similar conditions that are used for model developing (CCD and BBD). The density has been measured using Archimedes principle with a weighing balance accuracy of 0.1 mg, secondary dendrite arm spacing is measured using linear intercept method and hardness is measured using optical brinell hardness tester as per ASTM standard. The average density, secondary dendrite arm spacing and hardness values obtained for the optimized process variable combinations are given in Table 3. It is important to note that the applied squeeze pressure brings a sudden large under cooling in the liquid metal, which increases the solubility of the silicon particles to refine silicon particles. Further, the dendritic structure is refined due to drastic increase in the cooling rate resulted from the improved interfacial contact between metal and mould surface. These reasons might have resulted in enhanced casting microstructure (see Figure Table 3. Results of confirmation test for the optimal casting conditions Optimal Process Variables Models

Pressure Duration, s

Squeeze Pressure, MPa

Responses

Pouring Temperature, °C

Die Temperature, °C

Density, g/ cm3

SDAS, µm

BHN

GA and PSO

28

120

708

150

2.672

33.12

82.3

MOPSO-CD

29

120

705

150

2.672

32.28

82.6

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8). It is to be noted that the microstructure obtained for the determined optimal casting conditions by MOPSO-CD (refer to Figure 8 (b)) found to be more refined with regard to small dendrites and arm spacing compared to that of GA and PSO (refer to Figure 8 (a)). This might have happened due to better casting conditions of MOPSO-CD and the reasons for this are explained above. Comparison of PSO, MOPSO-CD and GA Evolutionary algorithms such as GA, PSO and MOPSO-CD are applied to optimize the multiple outputs of the squeeze casting process that are responsible for better casting properties. It is to be noted that all population based search techniques determine the optimal process variable combinations in multi-dimensional space at many distinct locations simultaneously. It is also important to note that the speed of convergence depends mainly on the appropriate choice of algorithm parameters. The optimal GA, PSO and MOPSO-CD parameters are determined after conducting the systematic study by varying one parameter at a time and keeping the rest at fixed value. It is to be note that optimal GA parameters such as probability of crossover (PC*), probability of mutation (PM*), population size (Pop*) and number of generations (Gen*) are found to be 0.55, 0.15, 80, and 85, respectively. Similarly for PSO, the optimal parameters such as inertia weight (W*), swarm size (SS*) and number of generations (G*) are found to be {0.6, 50, 50} and {0.1, 50, 40} for simple PSO and MOPSO-CD, respectively. In the present case the speed of convergence to reach the maximum fitness value using PSO is found to be faster than that of GA. Moreover, the fitness values as obtained for case 1 to 4 are found to be {26.93, 9.907, 8.089, 62.88}, {26.79, 10.06, 7.78, 63.16} and {27.04, 10.13, 8.13, 63.16} for GA, simple PSO and MOPSO-CD, respectively. It is interesting to note that MOPSO-CD outperforms the other optimization algorithms to determine the maximum fitness values responsible for better casting conditions. Therefore by considering different cases the casting properties are comparable for the density and secondary dendrite arm spacing, whereas drastic improvement was observed for determining the hardness values. Furthermore, confirmation tests have been conducted for the obtained maximum fitness value corresponding to the different case studies of PSO, MOPSO-CD and GA. It is important to note that case 4 is recommended since its corresponding fitness value is found to be maximum and better for PSO, MOPSO-CD and GA. MOPSO-CD determines the extreme values of secondary dendrite arm spacing and hardness values as compared to GA and PSO (refer Table 3). The determined optimal casting conditions obtained by GA, PSO and MOPSO-CD are compared experimentally. Here also, MOPSO-CD showed slightly better results with density, hardness and SDAS values. Moreover, the speed of convergence to reach the maximum fitness function with the number of generations is found to be 85 for GA (refer to Figure 4 (d)), 50 for PSO (refer to Figure 5(c))

Figure 8. Microstructure obtained for optimal squeeze casting condition: (a) GA and PSO; and (b) MOPSO-CD

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and 40 for MOPSO-CD (refer to Figure 6 (c)). This indicates that PSO performed better in terms of computational time and identifying the better global process variable combination. Better performance of PSO algorithm might be due to the exhaustive search carried out in multi-dimensional search space at many distinct locations simultaneously and the simple structure with few tuning parameters. CONCLUSION An attempt has been made to optimize the input-output parameters of the squeeze casting process using the popular evolutionary algorithms, namely PSO, MOPSO-CD, and GA. The input-output mathematical relationship developed based on central composite and box-behnken design models was used as the fitness functions for all the evolutionary algorithms. Three individual objective functions (density, hardness and secondary dendrite arm spacing) were converted in to a single objective function with different combination of weight factors. Exhaustive heuristic search was carried out by evolutionary algorithms in multi-dimensional search space at many distinct locations simultaneously to determine the optimal casting conditions. It was noted that all algorithms, GA, PSO and MOPSOCD, performed effectively to optimize squeeze casting process parameters. Experiments have been conducted to measure the responses namely, density, secondary arm spacing and hardness for the optimum process parameters obtained after applying GA, PSO and MOPSO-CD. The particle swarm optimization algorithm was found to perform better than genetic algorithm in terms of computational efficiency. The improved performance of particle swarm optimization might be due to the simple structure with few tuning parameters. The present research work is of great importance to casting industry, since the extreme values of conflicting requirements of the multiple performance outputs are determined. Moreover, the present research work might help to overcome few shortcomings of the existing traditional approaches (like classical engineering experimental, analytical, numerical, costly simulation, expert reliant try error method and so on) in determining the best process variable combinations, which will result in improved casting quality and reduced computational burden and energy consumption. ACKNOWLEDGMENT The authors would like to sincerely thank the Department of Applied Mechanics and Hydraulics, National Institute of Technology Karnataka, Surathkal for providing research facilities.

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REFERENCES Aweda, J. O., & Adeyemi, M. B. (2009). Experimental determination of heat transfer coefficients during squeeze casting of aluminium. Journal of Materials Processing Technology, 209(3), 1477–1483. doi:10.1016/j. jmatprotec.2008.03.071 Aweda, J.O., & Adeyemi, M.B. (2012). Experimental determination of heat transfer coefficients during squeeze casting of aluminium. In S.N. Kazi (Ed.), An overview of heat transfer phenomena (pp. 35-66). doi:10.5772/52038 Chattopadhyay, H. (2007). Simulation of transport processes in squeeze casting. Journal of Materials Processing Technology, 186(1-3), 174–178. doi:10.1016/j.jmatprotec.2006.12.038 Das, S., Maity, S., Qu, B. Y., & Suganthan, P. N. (2011). Real-parameter evolutionary multimodal optimization — A survey of the state-of-the-art. Swarm and Evolutionary Computation, 1(2), 71–88. doi:10.1016/j. swevo.2011.05.005 Fan, C. H., Chen, Z. H., Chen, J. H., & Chen, D. (2010). Effects of applied pressure on density, microstructure and tensile strength of Al–Zn–Mg–Cu alloy prepared by squeeze casting. International Journal of Cast Metals Research, 23(6), 349–353. doi:10.1179/136404610X12693537270253 Ghomashchi, M. R., & Vikhrov, A. (2000). Squeeze casting: An overview. Journal of Materials Processing Technology, 101(1), 1–9. doi:10.1016/S0924-0136(99)00291-5 Hong, C. P., Lee, S. M., & Shen, H. F. (2000). Prevention of macro defects in squeeze casting of an Al-7 wt pct Si alloy. Metallurgical and Materials Transactions. B, Process Metallurgy and Materials Processing Science, 31(2), 297–305. doi:10.1007/s11663-000-0048-5 Krishna, P. (2001). A study on interfacial heat transfer and process parameters in squeeze casting and low pressure permanent mold casting [Ph.D. Thesis]. University of Michigan, Ann Arbor, Michigan. Mahapatra, S. S., & Patnaik, A. (2007). Optimization of wire electrical discharge machining (WEDM) process parameters using Taguchi method. International Journal of Advanced Manufacturing Technology, 34(9-10), 911–925. doi:10.1007/s00170-006-0672-6 Maleki, A., Niroumand, B., & Shafyei, A. (2006). Effects of squeeze casting parameters on density, macrostructure and hardness of LM13 alloy. Materials Science and Engineering A, 428(1-2), 135–140. doi:10.1016/j. msea.2006.04.099 Maleki, A., Shafyei, A., & Niroumand, B. (2009). Effects of squeeze casting parameters on the microstructure of LM13 alloy. Journal of Materials Processing Technology, 209(8), 3790–3797. doi:10.1016/j. jmatprotec.2008.08.035 Montgomery, D. C. (2001). Design and analysis of experiments. New York: John Wiley & Sons. Parappagoudar, M. B., Pratihar, D. K., & Datta, G. L. (2007). Linear and non-linear statistical modelling of green sand mould system. International Journal of Cast Metals Research, 20(1), 1–13. doi:10.1179/136404607X184952 Pashazadeh, H., Gheisari, Y., & Hamedi, M. (2014). Statistical modeling and optimization of resistance spot welding process parameters using neural networks and multi-objective genetic algorithm. Journal of Intelligent Manufacturing, 1–11. doi:10.1007/s10845-014-0891-x Patel, G. C. M., Krishna, P., & Parappagoudar, M. B. (2015). (Manuscript submitted for publication). Modelling of squeeze casting process: Conventional statistical regression analysis approach. Applied Mathematical Modelling. Rajagopal, S. (1981). Squeeze casting: A review and update. Journal of Applied Metalworking, 14(4), 3–14. doi:10.1007/BF02834341 Rajagopal, S., & Altergott, W. H. (1985). Quality control in squeeze casting of aluminium. AFS Transactions, 93, 145–154. Rao, R. V., & Savsani, V. J. (2012). Mechanical design optimization using advanced optimization techniques. Springer London Dordrecht Heidelberg New York. doi:10.1007/978-1-4471-2748-2

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Raquel, C. R., & Naval, P. C. Jr. (2005). An effective use of crowding distance in multiobjective particle swarm optimization. Proceedings of the 2005 conference on Genetic and evolutionary computation (pp. 257-264). ACM. doi:10.1145/1068009.1068047 Rosenberg, R. S. (1967). Simulation of genetic populations with biochemical properties [Ph.D. Thesis]. University of Michigan, Ann Arbor, Michigan. Santana, R. A., Pontes, M. R., & Bastos-Filho, C. J. A. (2009). A multiple objective particle swarm optimization approach using crowding distance and roulette wheel. Proceedings of the 2009 Ninth international conference on intelligent systems design and applications (pp. 93–100). doi:10.1109/ISDA.2009.73 Schaffer, J. D. (1985). Multiple objective optimization with vector evaluated genetic algorithm. Proceedings of 1st International Conference on Genetic Algorithms (pp. 93–100). Sierra, M. R., & Coello, C. A. C. (2005). Improving PSO-based multi-objective optimization using crowding, mutation and ∈-dominance (pp. 505–519). Evolutionary Multi-Criterion Optimization. doi:10.1007/978-3540-31880-4_35 Souissi, N., Souissi, S., Niniven, C. L., Amar, M. B., Bradai, C., & Elhalouani, F. (2014). Optimization of squeeze casting parameters for 2017A wrought Al alloy using Taguchi method. Metals, 4(2), 141–154. doi:10.3390/ met4020141 Surekha, B., Kaushik, L. K., Panduy, A. K., Vundavilli, P. R., & Parappagoudar, M. B. (2012). Multi-objective optimization of green sand mould system using evolutionary algorithms. International Journal of Advanced Manufacturing Technology, 58(1-4), 9–17. doi:10.1007/s00170-011-3365-8 Ting, T. O., & Lee, T. S. (2012). Drilling optimization via particle swarm optimization. International Journal of Swarm Intelligence Research, 3(1), 43–54. doi:10.4018/jsir.2012010103 Vijian, P., & Arunachalam, V. P. (2007). Modelling and multi objective optimization of LM24 aluminium alloy squeeze cast process parameters using genetic algorithm. Journal of Materials Processing Technology, 186(1), 82–86. doi:10.1016/j.jmatprotec.2006.12.019 Vundavilli, P. R., Kumar, J. P., & Parappagoudar, M. B. (2013). Weighted average-based multi-objective optimization of tube spinning process using non-traditional optimization techniques. International Journal of Swarm Intelligence Research, 4(3), 42–57. doi:10.4018/ijsir.2013070103 Yang, L. J. (2007). The effect of solidification time in squeeze casting of aluminium and zinc alloy. Journal of Materials Processing Technology, 192-193, 114–120. doi:10.1016/j.jmatprotec.2007.04.025

Manjunath Patel G. C. received his Bachelor Degree in Mechanical Engineering from Jawaharlal Nehru National College of Engineering, Shimoga, and his MTech in Production Management from Gogte Institute of Technology, Belgaum, affiliated to Visvesvaraya Technological University, Belgaum, India, in 2009 and 2011 respectively. He is currently working towards his PhD in Mechanical Engineering, National Institute of Technology Karnataka, Surathkal, India. His area of interests includes Casting and Solidification, Modelling and Optimization of Manufacturing Processes. Prasad Krishna obtained his Bachelor Degree in Mechanical Engineering from NITK, Surathkal, India in 1983, Master’s Degree in Manufacturing from IIT Madras, India and Doctoral Degree in Manufacturing (DEng Manufacturing) from the University of Michigan, Ann Arbor, USA. Prof. Krishna has more than thirty-one years of professional experience in manufacturing, precision machine tool design & development and teaching a variety of courses in the field of manufacturing and materials engineering. His research interests are in the areas of Metal Casting, Additive Manufacturing and CNC Machine Tools. Currently, Prof. Krishna is working as Professor and Head, Department of Mechanical Engineering and Coordinator of the World Bank funded TEQIP Project at NITK Surathkal, India. 72


Mahesh B. Parappagoudar completed his engineering graduation in Industrial & Production Engineering from B.V. Bhoomaraddi College of Engineering and Technology, Hubli, affiliated to Karnataka University, Dharwad. He obtained his Master of Engineering degree in Production Management from Gogte Institute of Technology, affiliated to Karnataka University, Dharwad, India, in 1996. He joined Indian Institute of Technology, Kharagpur in 2004 as a research scholar, in the mechanical engineering department under the quality improvement program funded by MHRD, Govt. of India. Further, he obtained his PhD degree in Mechanical Engineering from Indian Institute of Technology, Kharagpur - 721302, India in 2008. Presently he is working as the principal and professor in Chhatrapati Shivaji Institute of Technology, Durg (C.G) 491001, India. His total experience (Industry, Teaching, Research, and Administration) extends over a period of 24 years. His biography (distinguished personality) is published in the 30th edition of Marquis Who’s Who in the world 2013. His research interests include application of statistical and soft computing tools in manufacturing and industrial engineering. Pandu R Vundavilli received his BTech in Mechanical Engineering from Jawaharlal Nehru Technological University, Kakinada-533003, India and MTech. in Computer Integrated Manufacturing from National Institute of Technology,Warangal-506004, India in 2000 and 2003, respectively. From 2003 to 2005, he worked as a faculty member at the Koneru Lakshmaiah College of Engineering, Vaddeswaram-522502, India. He received his PhD in Mechanical Engineering from Indian Institute of Technology, Kharagpur-721302, India in 2009. He is working at present as Asst. Professor in the School of Mechanical Sciences of IIT Bhubaneswar - 751013, India. His research interests include modeling and simulation of manufacturing systems, robotics and soft computing. He has published around 50 publications in various International and National Journals and Conferences.

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ABBREVIATIONS GA: Genetic Algorithm PSO: Particle Swarm Optimization MOPSO-CD: Multi Objective Particle Swarm Optimization based on Crowing Distance RSM: Response Surface Methodology DOE: Design of Experiments CCD: Central Composite Design BBD: Box-Behnken Design DNPSO: Dynamic Niching Particle Swarm Optimization CSS-MOPSO: Cross Searching Strategy Multi Objective Particle Swarm Optimization ANOVA: Analysis of Variance

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Author's personal copy

MODELING OF PRESSURE DIE CASTING PROCESS: AN ARTIFICIAL INTELLIGENCE APPROACH Jayant K. Kittur and G. C. Manjunath Patel KLS Gogte Institute of Technology, Belgaum, Karnataka, India Mahesh B. Parappagoudar Chhatrapati Shivaji Institute of Technology, Durg, Chhattisgarh, India

Copyright Ó 2015 American Foundry Society DOI 10.1007/s40962-015-0001-7

Abstract In the present work, both forward and reverse modeling is carried out for the high pressure die casting process by utilizing back-propagation neural network (BPNN) algorithm. The pressure die casting process is considered as an input–output model with the fast shot velocity, intensification pressure, phase change over point and holding time as the input parameters, whereas surface roughness, hardness and porosity as the output of the system. Batch mode of training had been provided to the networks with the help of one thousand input–output training data. These training data were generated artificially from the regression equations, which were obtained earlier by the same authors. The

regression equations used in the present work were obtained by applying design of experiments and response surface methodology techniques. The performance of BPNN in forward and reverse modeling has been tested with the help of test cases. Further, the performance of BPNN in forward modeling was compared with statistical regression models. The results showed that the BPNN approach is able to carry out both the forward as well as reverse mappings effectively and can be used in the foundries.

Introduction

but also has a negative effect on the machinability and surface properties of aluminum parts.

High pressure die casting (HPDC) is one of the fastest and most cost-effective methods for producing a wide range of components, which are widely used in many industries, such as automotive, aerospace, computer, telecommunication. This is mainly due to high quality, low cost and high strength to weight ratio of pressure die-cast components. Typical reasons for the selection of the die casting process include high production volume along with good consistency, part accuracy and dimensional stability. Die castings made today have complicated features and maintain very high dimensional accuracy. The porosity in die casting has always been a problem, and in spite of considerable research, design and development, it is virtually impossible to eliminate porosity altogether. In cold-chamber die casting, the acceptability of casting is often dependent upon the location, size, distribution and total volume of gas porosity. Porosity formation in aluminum alloys not only affects the mechanical properties

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Keywords: high pressure die casting (HPDC), forward and reverse mappings, NN, BPNN

Design of experiments (DOE) technique has been used in the past by various investigators to study the effect of process parameters on porosity and other mechanical properties of diecast component. Analytical, experimental and numerical studies were carried out by Schneiderbauer et al.1 to understand the flow and filling characteristics during injection of aluminum in a HPDC process. Mathematical and numerical models were proposed by Sowa et al.2 to determine the influence of parameters on quality of casting in HPDC. It was shown that temperature and pressure were critical in obtaining good quality casting. Verran et al.3 applied DOE for investigating the influence of the injection parameters and upset pressure over quality of castings, in aluminum alloys. Analysis of variance (ANOVA) was used to study the effect of parameters on the process. Gunasegaram et al.4 investigated the effect of parameters on the size and location of a shrinkage pore in a die-cast aluminum alloy. They used the DOE approach and varied section thickness in their study. Chiang

International Journal of Metalcasting/Volume 10, Issue 1, 2016

Author's personal copy et al.5 used statistical modeling and analysis to study the effects of machining parameters on the performance characteristics in the HPDC process of Al–Si alloys. Sycros6 analyzed various significant process parameters of the die casting of AlSi9cu13 aluminum alloy. The process parameters considered were slow shot velocity, fast shot velocity, metal temperature, filling time and hydraulic pressure. The effects of the selected process parameters on the casting density and optimal settings of the parameters have been accomplished using Taguchi’s method. Kittur et al.7 analyzed the effect of three injection parameters (slow shot, fast shot and upset pressure) on two critical internal quality factors (porosity and density) of an aluminum alloy die casting using DOE method. Sun et al.8 studied the effect of pore size and pore volume fraction on ductility. It was observed that lower pore size and lower volume fraction had reduced the ductility of the cast component. Finite element approach was used for this purpose. Yarlagadda9 developed a neural network-based approach to model the HPDC process. The neural network was developed based on the governing equations of the filling stage for the die casting process, and the network was trained with data collected from experts in this field and data generated from simulation studies. Their investigation showed that the casting conditions, e.g., melt temperature, die temperature, injection pressure and injection time, dominate the quality of the casting. Zhang et al.10 showed that artificial neural network (ANN) combined with genetic algorithm (GA) is an effective tool for the process optimization of low pressure die casting (LPDC). Further, it was shown that the methodology adopted was useful in choosing the right process parameters of LPDC thin-walled aluminum alloy casting. Reilly et al.11 used computational process modeling to minimize the defects in LPDC of aluminum alloy automotive wheels. Rai et al.12 developed a neural network-based model for real-time estimation of optimal HPDC process parameters. Four process parameters, namely inlet melt temperature, mold initial temperature, inlet first phase velocity and inlet second phase velocity, were used. The mold cavity filling time, solidification time and porosity were considered as the system output, and the neural network was trained using data generated by finite element modeling-based flow simulation software. Zhang et al.13 developed an ANN model for the surface defect of casting. They used neural network (NN) to generalize the correlation between surface defects and die casting parameters, such as mold temperature, pouring temperature, and injection velocity. Hassan et al.14 used the feed-forward backpropagation neural network in prediction of some physical properties and hardness of aluminum–copper/silicon carbide composites, synthesized by compo-casting method. Yin et al.15 used a back-propagation neural network (BPNN) 5-2020-1 model for warpage prediction in injected plastic parts, based on key process variables, namely mold temperature, melt temperature, packing pressure, packing time and cooling time. The neural network was trained by the input and output data obtained from the finite element simulations, which were performed on Moldflow software platform. Back-propagation neural network has been used successfully as a forward and


reverse mapping tool for modeling different molding sand system by Parappagoudar et al.16–18 The geometry of the die cavity, location of associated gates and vents are the major factors influencing air entrapment in die casting. Further, the machine parameters like slow shot (pre-fill) velocity and transition time from slow shot to fast shot velocity (phase change over point) along with the other factors, such as intensification pressure, holding time and melt temperature, will influence the formation of the porosity. The low value of fast shot speed results in cold shuts, whereas very high speed leads to porosities and increase the amount of flash. Intensification pressure (IP) is responsible for the compacting of casting during the solidification and preventing the entrapped gases expansion. The phase change over point is a stage in cavity filling process from slow shot to fast shot and is normally activated by a limit switch, which affects the cavity filling and possible metal freeze at the gate. To produce a sound casting, the melt temperature must be controlled within a particular range depending on the type of alloy to be cast. The holding time influences the ultimate tensile strength, yield strength and elongation of the casting. The holding time also affects the average grain size and hence the mechanical properties. Hence, for given geometry and design of cast component, an appropriate combination of machine-related injection parameters should be employed to minimize the porosity and improve mechanical properties. DOE coupled with response surface methodology can be used to make accurate predictions. However, separate models are required to be developed to predict each of the responses as a function of input variables. It is to be noted that, in actual practice, all the responses are measured for a particular set of input parameters. Moreover, it is required to obtain a set of input parameters, which will produce a set of desired outputs. This is an important practical requirement, especially for the online control of a process. Reverse mapping (i.e., to predict the inputs for a set of desired outputs) might be difficult to carry out by using response equations obtained through statistical analysis. As the models are developed independently, the interdependency of the output responses might be lost in statistical models. To the best of the authors’ knowledge, not much of the work has been reported in the literature on reverse mapping of the die casting process using a neural network. Hence, an attempt was made to develop a BPNN for modeling the influence of die casting machine parameters on the quality characteristics. In forward mapping, the responses have been predicted for a given set of input parameters, whereas in case of reverse mapping, the machine parameters are predicted for the desired quality characteristics. The performance of NN is influenced by many factors, such as the network structure (i.e., number of hidden layers and number of neurons in each layer) and learning parameters (i.e., learning rate, momentum constant and thresholds of system and pattern errors), which form components of the generalized delta rule. The

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Author's personal copy optimum values of the above factors are determined by a parametric study. In practice, it is not feasible to conduct experiments to collect the huge amount of data required to train the neural network. Hence, the training data have been generated at random by using the response equations derived through experiments and modeling. BPNN was developed to predict all three responses in one go. As the training data were collected off-line, a batch mode of training was used to optimize the neural network. Modeling of Die Casting Process Using Neural Networks

Figure 1. Structure of neural network used for forward mapping.

The objective of modeling of die casting process is to establish the input–output relationship. The modeling was carried out, based on the important machine-related process parameters, like fast shot velocity, phase change over point, intensification pressure and holding time on porosity and mechanical properties of the cast component. The input parameters and their levels used in this study (refer to Table 1) were set in consultation with the foundry industries and a detailed literature survey conducted on the pressure die casting of aluminum alloys. Back-propagation neural network was developed for modeling of the die casting process. It is to be noted that BPNN requires a large amount of training data. Hence, regression models developed earlier by the same authors have been utilized to generate the training data.7 The central composite design (CCD) was used for the responses hardness and surface roughness, whereas BoxBehnken Design (BBD) model was used for porosity. In case of forward mapping, performances of neural network-based approach were compared with those of the statistical model.

provided by the input–output layers. Figure 1 shows the neural network used in modeling (forward mapping) the pressure die casting process. Vij and Wjk represented in the figure are the connecting weights used in the training process. These weights act as connection strength between the input–output neurons, and these weights contain information about the input signal. Suffixes i, j and k represent the input, hidden and output neurons. The input parameters and their range considered in the present study are shown in Table 1.

Forward Mapping

where Xnorm is the normalized value of a variable, X indicates the value before normalization, and Xmin and Xmax are the minimum and maximum values of the variable, respectively. A linear transfer function y = m 9 x was used in the neurons of input layer. The value of m was decided through a number of trials. The log sigmoid transfer function [refer Eqn. 2] was used in the neurons of output layers, while modeling different responses. 1 Y¼ Eqn: 2 1 þ eax

In the present work, neural network is assumed to be consisting of three layers of neurons, i.e., input, hidden and output layers. The input layer receives external information, such as adjustable process parameters. The output layer generates the data corresponding to the properties of cast component. The above structure also incorporates hidden layer of neurons that do not interact with the outside world, but assist in performing a nonlinear feature extraction on the data Table 1. Parameters and Their Levels Sl. no.

Parameters

Levels

Description

Notation

Low

High

1

Fast shot velocity (m/s)

A

0.4

0.6

2

Intensification pressure (Kg/cm2)

B

180

220

3

Phase change over (mm)

C

110

150

4

Holding time (s)

D

8

12

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Four neurons were considered in the input layer and three neurons in the output layer to represent the number of input parameters and the number of responses, respectively. The optimal number of neurons in hidden layer was obtained through a parametric study. The data used in the network training and testing processes were normalized using the expression (1) Xnorm

ðX Xmin Þ ðXmax Xmin Þ

Eqn: 1

where ‘a’ is activation function constant and ‘x’ is the input of the neuron. The same sigmoid transfer function was used for all the neurons lying in the hidden layer. Back-Propagation Neural Network19 The back-propagation neural network was trained by utilizing a batch mode of supervised learning. A batch mode of training consists of passing all test cases, before the updating of network parameter occurs. This mode of training is generally used for off-line training. A neural network needs to be trained to obtain an optimal network


Author's personal copy by updating its weights, bias values architecture, etc. Backpropagation algorithm utilizes steepest descent method to minimize error. Networks were adaptively trained to reduce the mean-squared error (MSE). The error considered in this work was the difference between the network predicted value and the actual value of the responses. The error function used in the present work was the MSE as given below in expression (3). MSE ¼

R X N 2 1 X 1 Tij Oij R N i¼1 j¼1 2

Eqn: 3

In the above equation, Tij and Oij represent the target and predicted values of the responses, respectively, and R indicates the number of responses, whereas N represents the number of training scenarios. Back-propagation algorithm works on a steepest descent method with a momentum term a which was used to update the weights of the neural network, as given in expression (4). DWjk ðtÞ ¼ g

oE ðtÞ þ aDWjk ðt 1Þ oWjk

Eqn: 4

where g indicates the learning rate, a represents the momentum constant, t indicates the iteration number, E error corresponding to a particular training scenario and oE oWjk can be determined by using the chain rule of differentiation as given in expression (5). oE oE oYk oUk ¼ oWjk oYk oUk oWjk

Eqn: 5

where Yk and Uk represent the output and input, respectively, of kth neuron lying on the output layer. Reverse Mapping Reverse mapping aims to determine the set of input process parameters, corresponding to a set of desired output parameters. The statistical method7 might fail to carry out the said reverse mapping because the transformation matrix might not be invertible at all. This problem of reverse mapping could be handled effectively by using NN. Figure 2

shows the structure of a neural network used in reverse mapping. The responses namely surface roughness, hardness and porosity were treated as an input to NN, whereas process parameters such as fast shot velocity, intensification pressure, phase change over point and holding time were considered as output in reverse mapping. Hence, the NN structure in reverse mapping consists of three neurons for the input layer and four neurons in output layer. Data Collection A batch mode of training was adopted for the neural network, which requires a huge amount of training data. The number of training scenarios should be more than network parameters; otherwise, the trained network will be mathematically undetermined. The training data were generated artificially with the help of statistical regression models, developed earlier by the same authors. On the other hand, test data were collected through the experiments. Training Data The training data for the responses—surface roughness, hardness and porosity—were generated artificially using the response equations. These response equations were developed by the authors earlier, using response surface methodology based on statistical design of experiment. For each of the responses, two nonlinear models namely CCD and BBD were developed. Their performances were compared with the help of 20 randomly generated test cases, and the best model was chosen for each of the responses.7 In the present work, only the best response equation for each of the response was used to generate input–output data required for the training of neural network. CCD provided the best response for hardness and surface roughness, whereas the Box-Behnken model showed the best performance for the responses porosity. i: Surface roughness ðCCDÞ ¼ 33:8549 4:6917 A þ 0:3571 B 0:017775 C þ 0:554829 D þ 2:90745 A2 8:43564 104 B2 þ 8:89363 105 C2 0:0323564 D2 0:00508438 A B þ 0:0422906 A C 0:168344 A D 1:97297 104 B C þ 0:000177031 B D þ 0:00158953 C D ii: Hardness ðCCDÞ ¼ 35:2758 590:691 A þ 3:86974 B 2:85761 C þ 3:44465 D þ 848:876 A2 0:00548686 B2 þ 0:0174031 C2 þ 0:0424389 D2 0:917638 A B 0:958638 A C

Figure 2. Structure of neural network used for reverse mapping.


þ 6:60675 A D 0:00595725 B C 0:0327881 B D 0:00805062 C D

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Author's personal copy iii: Percent Porosity ðBBDÞ ¼ 160:93 þ 50:0969 A þ 0:92389 B þ 0:428678 C þ 6:1058 D 56:2375 A2

die casting machine and the cast component are shown in Figures 3 and 4, respectively. Various combinations of the input variables were generated at random by considering the different levels lying within their respective ranges.

0:00213697 B2 0:00129213 C 2 0:220253 D2 0:01165 A B 0:0038125 A C þ 0:931 A D 6:6 105 B C 0:00564875 B D 0:007755 C D One thousand training data were generated artificially by selecting the values of the input variables lying within their respective ranges and determining the response values by utilizing the above equations. Test Data The experiments have been conducted in a local die casting industry on a horizontal cold-chamber pressure die casting machine for the production of cast component (mounting flange encoder) using aluminum alloy LM 20. The pressure

Surface roughness parameter Ra was measured using Taylor Hobson (UK) make Surtronic 3?Talysurf (refer Figure 5). The surface roughness value (Ra) is mean of absolute values of the profile heights, measured from a mean line averaged over the profile. The Ra value is determined using the n P relationship, Ra 1n jYij. The sample (cutoff) length was taken as 0.8 mm.

i¼1

A Brinell hardness tester is used for measuring the hardness of specimen with 5-mm-diameter diamond ball indenter and a load set of 250 kg. The experimental setup of measuring the hardness of the cast component is shown in Figure 6. The diameter of indentation on the component was measured using Brinell microscope. Hardness value was then calculated by using the formula (6):

Figure 3. Pressure die casting machine.

Figure 4. Mounting flange encoder.

74


Author's personal copy For each combination of input parameters, three observations were made to minimize the error of variation and the average value was considered. Thus, a set of 20 test cases was generated at random (input parameters), and tests were carried out to record the responses (refer to Appendix).

Results and Discussion In this section, the results obtained through BPNN have been discussed and compared with those obtained from regression model as well as experimental results. Results of Forward Mapping Figure 5. Taylor Hobson Surtronic 3?Talysurf.

BHN ¼

2P pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pD D D2 d2

Eqn: 6

where, BHN = Brinell hardness number, P = load in kg (250 kg), D = diameter of the diamond ball indenter in mm (5 mm) and d = diameter of the indenter impression in mm. Percentage porosity in the components was found using Archimedes principle in terms of density of the components using Eqns. 7 and 8. Percentage porosity ¼

qapparent qtheoritical qtheoritical

Eqn: 7

Apparent densityðqapparent Þ mass of casting in air qwater ¼ mass of cating in air mass of casting in water Eqn: 8 where qwater = density of water (1 gm/cm3), and qtheoritical is the density of alloy LM 20 = 2.68 gm/cm3.

Back-propagation neural network is developed to predict casting properties such as surface roughness, hardness and percentage porosity from the process parameters, namely fast shot velocity, intensification pressure, phase change over and holding time of die casting process. Back-Propagation Neural Network (BPNN) A parametric study was carried out to optimize the network parameters. The results of the parametric study are shown in Figure 7. The training of neural network needs huge training data for accurate modeling. Hence, the required training data have been generated at random by utilizing the regression models developed by the authors earlier.5 Parametric Study of Forward Mapping The detailed parametric study has been carried out, and the results are presented in Figure 7. The optimal parameters, such as the number of hidden layer neurons, learning rate

Figure 6. Brinell hardness tester.


75


Figure 7. Results of parametric study to determine the optimal neural network parameters for forward mapping: (a) Error versus number of neurons in the hidden layer. (b) Error versus learning rate—hidden layer. (c) Error versus learning rate—output layer. (d) Error versus momentum constant. (e) Error versus activation constant—hidden layer. (f) Error versus activation constant—output layer. (g) Error versus bias value.

76


Author's personal copy (g), momentum constant (a), activation constant of hidden layer (a1), activation constant of output layer (a2) and the bias value, are listed below: 1. 2. 3. 4. 5. 6. 7.

Number of hidden neurons—18 Value of learning rate—hidden layer (g)—0.5 Value of learning rate—output layer (g)—0.6 Value of momentum constant (a)—0.5 Value of activation constant—hidden layer (a1)— 2.0 Value of activation constant—output layer (a2)— 2.5 Value of bias—0.00007

A batch mode of training has been provided to the network with the help of one thousand training data sets. To test the performance of the trained neural network, 20 randomly generated test cases are passed through it and the average absolute % deviation in prediction is found to be equal to 4.37 %.

Figure 8. Comparison of two models in terms of % deviation in prediction of surface roughness for the test cases.

Comparison of BPNN and Statistical Models

summarized in Table 2. Figure 8 shows that the BPNN model outperformed the other model in terms of accuracy in prediction of surface roughness. The values of percentage deviation for the response—surface roughness—are found to lie in the range of ?14. 51 to -13.2 and ?7.62 to -9.31 % for CCD and BPNN models, respectively.

The performances of the NN-based approach and statistical model were compared for 20 test cases, and the results are

Figure 9 shows the % deviation values in prediction for the response—hardness, as obtained by models, CCD-based

Table 2. Summary of the Results of Test Cases for the Response—Surface Roughness Test no.

Measured surface roughness

CCD

BPNN

Predicted

Deviation

% Devn.

Abs % devn.

Predicted

Deviation

% Devn.

Abs % devn.

1

2.49

2.41

0.07

2.95

2.95

2.42

0.07

2.88

2.88

2

2.35

2.23

0.12

5.31

5.31

2.17

0.18

7.67

7.67

3

2.23

2.45

-0.21

-9.72

9.72

2.49

-0.04

-1.73

1.73

4

2.42

2.26

0.16

6.79

6.79

2.31

0.11

4.59

4.59

5

2.46

2.34

0.12

4.98

4.98

2.47

-0.01

-0.24

0.23

6

2.12

1.81

0.3

14.51

14.51

2.02

0.1

4.67

4.66

7

2.31

2.35

-0.04

-1.8

1.8

2.38

-0.07

-3.19

3.19

8

2.22

2.36

-0.13

-6.09

6.09

2.37

-0.15

-6.77

6.76

9

2.45

2.2

0.24

10.14

10.14

2.24

-0.12

-5.76

5.75

10

2.24

2.05

0.18

8.34

8.34

2.18

0.06

2.8

2.8

11

2.43

2.31

0.12

5.08

5.08

2.3

-0.2

-9.31

9.31

12

2.3

2.22

0.08

3.78

3.78

2.35

-0.05

-2.04

2.03

13

2.23

2.3

-0.06

-3.03

3.03

2.19

0.04

1.8

1.8

14

2.31

2.28

0.028

1.23

1.23

2.29

0.02

0.76

0.76

15

2.16

2.45

-0.28

-13.2

13.24

2.52

-0.09

-3.64

3.63

16

2.1

2.02

0.08

4.08

4.08

2.04

0.06

2.73

2.73

17

2.51

2.45

0.06

2.39

2.39

2.45

0.06

2.47

2.47

18

2.47

2.46

0.01

0.26

0.26

2.45

0.02

0.6

0.6

19

2.33

2.21

0.11

5.02

5.02

2.32

0.02

0.66

0.66

20

2.35

2.1

0.24

10.25

10.25

2.11

0.24

10.26

10.25

Average absolute % deviation = 5.94



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Figure 9. Comparison of two models in terms of % deviation in prediction of hardness for the test cases.

regression analysis and BPNN. For the two models, the values of % deviation in prediction are found to lie on both the positive and negative sides. Figure 8 shows that the % deviation values are varying in the ranges of -3.01 to ?1.84 and -4.013 to ?4.997 % for CCD-based regression analysis and BPNN, respectively. Table 3 provides the summary of the results of test cases for the response— hardness.

Figure 10. Comparison of two models in terms of % deviation in prediction of porosity for the test cases.

The % deviations of the model predicted values, from the corresponding actual porosity values for both the models (BBD and BPNN), are shown in Figure 10. The said values are seen to lie in the ranges of -7.223 to ?16.25 and-11.96 to ?26.22 % for BBD-based regression analysis and BPNN models, respectively. Table 4 shows the summary of the test results for the response— porosity.

Table 3. Summary of the Results of Test Cases for the Response—Hardness Test no.

1

Measured hardness (BHN)

CCD

BPNN

Predicted

Deviation

% Devn.

Abs % devn.

Predicted

Deviation

% Devn.

Abs % devn.

121.31

121.8

-0.50

-0.41

0.41

122.82

-1.50

-1.23

1.23

2

118.24

118.7

-0.45

-0.38

0.38

119.63

-1.38

-1.17

1.17

3

116.00

116.5

-0.49

-0.43

0.43

119.31

-3.25

-2.80

2.80

4

117.60

118.1

-0.50

-0.42

0.42

121.00

-3.39

-2.88

2.88

5

114.48

117.7

-3.26

-2.84

2.84

119.08

-4.59

-4.01

4.01

6

125.63

128.1

-2.49

-1.98

1.98

119.36

6.27

4.99

4.99

7

118.95

119.5

-0.50

-0.42

0.42

121.93

-2.97

-2.49

2.49

8

127.90

128.4

-0.51

-0.39

0.39

125.18

2.72

2.12

2.12

9

118.62

118.4

0.18

0.15

0.15

121.11

-2.49

-2.10

2.10

10

123.47

122.4

1.09

0.88

0.88

124.13

-0.65

-0.53

0.53

11

121.07

122.1

-1.06

-0.88

0.88

123.54

-2.46

-2.03

2.03

12

116.89

118.1

-1.24

-1.06

1.06

120.06

-3.17

-2.71

2.71

13

117.40

120.9

-3.53

-3.01

3.00

119.42

-2.02

-1.72

1.72

14

115.86

119.2

-3.38

-2.91

2.91

118.02

-2.15

-1.86

1.86

15

123.76

122.3

1.46

1.18

1.18

121.57

2.19

1.76

1.77

16

123.44

121.2

2.27

1.84

1.84

121.55

1.88

1.52

1.52

17

114.86

116.8

-1.92

-1.67

1.67

118.95

-4.09

-3.56

3.56

18

120.50

121.2

-0.73

-0.60

0.60

119.94

0.55

0.46

0.46

19

118.39

121.5

-3.10

-2.62

2.62

120.47

-2.08

-1.70

1.75

20

120.67

118.5

2.14

1.77

1.77

120.03

0.64

0.53

0.53

Average of absolute % deviation = 1.29

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Author's personal copy Table 4. Summary of the Results of Test Cfor the Response—Porosity Test no.

Measured % porosity

BBD

BPNN

Predicted

Deviation

% Devn.

Abs % devn.

Predicted

Deviation

% devn.

Abs % devn.

1

1.52

1.37

0.15

9.74

9.74

1.48

0.04

2.48

2.48

2

1.38

1.15

0.22

16.25

16.25

1.38

0.00

0.35

0.35

3

1.30

1.31

-0.01

-1.05

1.05

1.32

0.03

2.15

2.15

4

1.12

1.18

-0.06

-5.53

5.53

1.25

-0.13

-11.96

11.96

5

1.45

1.42

0.04

2.45

2.45

1.48

-0.03

-2.012

2.01

6

1.43

1.27

0.16

10.85

10.85

1.41

0.02

1.17

1.17

7

1.62

1.63

-0.01

-0.53

0.53

1.58

0.04

2.54

2.54

8

1.27

1.37

-0.09

-7.22

7.22

1.35

-0.08

-6.18

6.18 1.51

9

1.26

1.29

-0.03

-2.28

2.28

1.28

-0.02

-1.51

10

1.53

1.51

0.02

1.02

1.024

1.46

0.07

4.50

4.504

11

1.59

1.75

-0.16

-10.22

10.22

1.35

0.24

15.06

15.06

12

0.95

0.96

-0.00

-0.41

0.419

1.02

0.06

6.58

6.58

13

1.86

1.98

-0.13

-6.91

6.917

1.43

0.42

22.67

22.67

14

2.13

2.00

0.13

5.93

5.93

1.57

0.56

26.22

26.22

15

1.72

1.65

0.07

3.96

3.96

1.67

0.05

2.61

2.615

16

1.41

1.47

-0.06

-4.06

4.06

1.36

0.04

3.15

3.15

17

1.87

1.98

-0.11

-5.65

5.65

1.47

0.33

17.57

18.32

18

1.67

1.74

-0.07

-4.09

4.09

1.64

0.03

2.08

2.08

19

1.45

1.65

-0.20

-13.57

13.57

1.50

0.05

3.52

3.52

20

1.20

1.16

0.04

3.46

3.46

1.08

0.13

10.41

10.41

Average of absolute % deviation = 5.76

Results of Reverse Mapping Reverse mapping has been developed to predict process parameters, such as fast shot velocity, intensification pressure, phase change over and holding time of die casting process from the responses (i.e., die-cast component properties). The BPNN approach has been used for the said purpose. The architecture of neural network is maintained the same as that of forward mapping, whereas the training data consist of die-cast component properties as the inputs and process parameters as the outputs of the system. A parametric study was carried out, and the values for the number of hidden neurons, learning rate—hidden layer (g), learning rate—output layer (g), momentum constant (a), activation constant—hidden layer (a1), activation constant— output layer (a2) and bias are found to be equal to 20, 0.5885, 0.01, 0.14355, 9.1, 3.25 and 0.00001585, respectively. Twenty test cases are passed through the optimized network, and the average of absolute % deviation is found to be equal to 8.09 %. Table 5 compares BPNN predicted values with actual values of fast shot velocity. The graph of fast shot velocity



and BPNN predicted values for the different test cases are shown in Figure 11. It can be noted that output—fast shot velocity—and BPNN predictions are very close to each other, and the average absolute percentage deviation value is found to be equal to 9.91. Table 6 shows the comparison of experimental results and neural network prediction, using twenty test cases for response intensification pressure. Figure 12 shows graphically the comparison of actual values of intensification pressure with those predicted by BPNN. It can be noted that the output intensification pressure and BPNN predictions are comparable, and the average absolute percentage deviation value is found to be equal to 3.95. Table 7 shows the comparison of experimental results and neural network prediction, using twenty test cases for response phase change over point. Figure 13 shows that the output phase change over point and BPNN predictions are in good relation to each other and the average absolute percentage deviation is found to be equal to 5.87. The comparison of actual holding time values with those of the BPNN predicted values for the twenty test cases is shown in Table 8. Graphical comparison for the same is

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Author's personal copy Table 5. Summary Results of Test Cases for Response—Fast Shot Velocity Test cases

Fast shot velocity

BPNN prediction

Deviation

% Deviation

Absolute % deviation

1

0.55

0.53

0.01

2.85

2.85

2

0.44

0.51

-0.07

-16.37

16.37

3

0.48

0.51

-0.03

-7.22

7.22

4

0.55

0.50

0.04

7.34

7.34

5

0.52

0.50

0.01

3.00

3.00

6

0.41

0.45

-0.04

-12.04

12.04

7

0.54

0.50

0.03

7.22

7.22

8

0.58

0.47

0.10

17.43

17.43

9

0.55

0.44

0.10

18.60

18.60

10

0.48

0.48

0.00

-1.44

1.44

11

0.53

0.44

0.08

16.51

16.51

12

0.57

0.48

0.08

14.85

14.85

13

0.42

0.45

-0.03

-8.65

8.65

14

0.47

0.44

0.02

4.40

4.40

15

0.58

0.52

0.05

9.55

9.55

16

0.43

0.45

-0.02

-4.83

4.83

17

0.47

0.50

-0.03

-6.89

6.89

18

0.54

0.52

0.01

2.03

2.03

19

0.41

0.50

-0.09

-23.86

23.86

20

0.45

0.50

-0.05

-13.07

13.07

Summation of absolute percentage deviation = 198.25 Average absolute percentage deviation = 9.91

Summary Results of Test Cases In the forward mapping, the surface roughness, hardness and porosity have been predicted for given input parameters—fast shot velocity, intensification pressure, phase change over point and holding time. In case of reverse mapping, the process parameters are predicted for the desired output parameters.

Summary of Forward Mapping

Figure 11. Validation of experimental results for fast shot velocity using BPNN.

made in Figure 14. The output holding time and BPNN predictions are in good relation to each other for many of the test cases, and the average absolute percentage deviation value is found to be equal to 12.64.

80

Forward mapping is done to predict the responses from the known input parameters. In the present work, forward mapping is developed to predict the surface roughness, hardness and porosity from the known set of input process parameters like fast shot velocity, intensification pressure, phase change over point and holding time. The results of forward mapping are summarized in Table 9, and it is to be noted that the mean absolute percentage deviation is found to be 4.37. These results indicate that the model is quite accurate and can be used in foundry practice.


Author's personal copy Table 6. Summary Results of Test Cases for Response—Intensification Pressure Test cases

Intensification pressure

BPNN

Deviation

% Deviation


1

199

193.03

5.96

2.99

2.99

2

201

196.13

4.87

2.42

2.42

3

198

186.51

11.40

5.79

5.79

4

194

188.76

5.23

2.69

2.69

5

185

184.30

0.69

0.37

0.37

6

210

218.39

-8.30

-3.99

3.99

7

206

202.26

3.77

1.83

1.83

8

200

216.96

-16.96

-8.45

8.48

9

201

215.23

-14.23

-7.07

7.07

10

217

213.84

3.16

1.45

1.45

11

201

217.18

-16.18

-8.05

8.05

12

186

193.34

-7.34

-3.94

3.94

13

203

201.50

1.50

0.73

0.73

14

200

191.51

8.48

4.24

4.24

15

208

191.51

16.48

7.92

7.92

16

212

218.17

-6.17

-2.91

2.91

17

198

185.46

12.53

6.32

6.32

18

196

194.44

1.55

0.79

0.79

19

210

198.53

11.46

5.46

5.46

20

197

200.18

-3.18

-1.61

1.61


roughness, hardness and porosity as the input parameters and the process parameters namely fast shot velocity, intensification pressure, phase change over point and holding time as the output of the network. The results of reverse mapping are summarized in Table 10, and it is to be noted that the mean absolute percentage deviation is found to be equal to 8.09 which is within the permissible range for the foundry practice.

Concluding Remarks

Figure 12. Validation of experimental results for intensification pressure using BPNN.

Summary of Reverse Mapping Reverse mapping is developed to predict the process parameters like fast shot velocity, intensification pressure, phase change over point and holding time from the known set of responses like the surface roughness, hardness and porosity. The procedure remains similar to forward mapping, whereas the training data consist of surface


An attempt was made to carry out both the forward as well as reverse mappings in pressure die casting process by using back-propagation neural network approach. A batch mode of training was adopted, which requires a large amount of data. In the present work, regression equations already developed by the same authors were utilized to generate the training data. It is to be noted that the regression equations were developed based on the experimental data collected as per the DOE. These regression equations were used to artificially generate a huge data for training the NN by selecting the values of the input variables (at random) lying within their respective ranges. The response equations with better fit will predict the response more accurately. Two nonlinear response equations based on CCD and BBD have been developed for each of the

81

Author's personal copy Table 7. Summary Results of Test Cases for Response—Phase Change Over Point Test case

Phase changeover point

BPNN

Deviation

% Deviation


1

120

134.45

-14.45

-12.04

12.04

2

130

130.56

-0.56

-0.43

0.43

3

139

134.43

4.57

3.28

3.28

4

139

132.97

6.03

4.33

4.33

5

146

135.22

10.78

7.38

7.38

6

145

114.13

30.86

21.28

21.28

7

125

127.74

-2.74

-2.19

2.19

8

115

115.52

-0.52

-0.45

0.45

9

131

123.70

7.29

5.56

5.56

10

116

119.22

-3.22

-2.77

2.77

11

116

121.76

5.76

-4.97

4.97

12

136

126.80

9.19

6.76

6.76

13

135

131.22

3.77

2.80

2.79

14

144

135.22

8.77

6.09

6.09

15

137

129.58

7.42

5.41

5.41

16

133

115.44

17.50

13.20

13.20

17

139

136.55

2.44

1.76

1.76

18

148

133.51

14.40

9.78

9.78

19

127

129.41

2.41

-1.89

1.89

20

122

128.19

-6.19

-5.07

5.07


obtained through the conventional regression analysis, but the BPNN outperformed the latter in case of predicting the surface roughness, whereas in the other two cases, the performance of the conventional regression was found to be slightly better. The better performance of BPNN might be due to the adoptability of NN. The NN approaches were able to carry out the reverse mapping effectively.

Figure 13. Validation of experimental results for phase change over point using BPNN.

response. It is to be noted that the selection of CCD for the responses hardness and surface roughness, whereas BBD for the response porosity is based on results of R2 value (coefficient of determination). In case of forward mapping, the performance of BPNN was compared with that of the conventional regression analysis for 20 randomly generated test cases. It is interesting to note that the neural networks were trained by using the data

82

The average absolute deviation in prediction is found to be equal to 4.37 and 8.09 for forward and reverse mapping, respectively. The average deviations as well as prediction for some of the test cases are found to be high for the fast shot velocity and holding time (reverse mapping). The holding time is varied from 8 to 12 s. The deviation for holding is found to be more, since the output of BPNN is rounded to whole number and comparison is made. Apart from this, there might be possibility of getting the solution trapped in local minima due nature of error surface. The combined effect of small variability in experimental data and limitation of BPNN (local minima) might have resulted in poor prediction results in few cases. Forward modeling will help to make the prediction of hardness, porosity and surface roughness for any combination of machine parameters in pressure die casting process. Moreover, the requirement of casting properties depends upon the application. For some applications,


Author's personal copy Table 8. Summary Results of Test Cases for Response—Holding Time Test cases

Holding time

BPNN prediction

Deviation

Percentage deviation

Absolute percentage deviation

1

10

11

-1

-10.00

10.00

2

09

10

-1

-11.11

11.11

3

12

11

1

08.33

08.33

4

08

11

-3

-37.50

37.50

5

09

11

-2

-22.22

22.22

6

08

09

-1

-12.5

12.50

7

10

10

0

00.00

00.00

8

09

09

0

00.00

00.00

9

08

08

0

00.00

00.00

10

10

09

1

10.00

10.00

11

09

08

1

11.11

11.11

12

08

10

-2

-25.00

25.00

13

10

09

1

10.00

10.00

14

09

10

-1

-11.11

11.11

15

11

10

1

09.09

09.09

16

09

08

1

11.11

11.11

17

11

11

0

00.00

00.00

18

09

11

-2

-22.22

22.22

19

12

10

2

16.66

16.66

20

08

10

-2

-25.00

25.00


Table 9. Summary Results of Forward Mapping Sl. No.

Responses

Average absolute percentage deviation

1

Surface roughness

3.73

2

Hardness

2.11

3

Percentage porosity

7.27

Summation of average absolute percentage deviation = 13.12 Mean absolute percentage deviation = 4.37

Table 10. Summary Results of Reverse Mapping

Figure 14. Validation of experimental results for holding time using BPNN.

porosity might be critical, whereas for some other requirements, it may be the surface finish or hardness. The reverse modeling will help to know the machine parameters (input parameters) that will produce the casting with desired surface roughness, porosity and hardness. The present work will help to avoid costly trial and error methods. Further, the work can be extended and used in automated machines for the online control and setting of parameters by incremental training of NN.


Sl. no

Process parameters

Average absolute percentage deviation

1

Fast shot velocity

2

Intensification pressure

3.95

3

Phase change over point

5.87

4

Holding time

9.91

12.64

Summation of average absolute percentage deviation = 32.39 Mean absolute percentage deviation = 8.09

Appendix See Table 11.

83

Author's personal copy Table 11. Input–Output Data of the Test Cases Test no.

Process parameters

Responses

Fast shot velocity (m/s)

Intensification pressure (Kg/cm2)

Phase change over point (mm)

Holding time (s)

Surface roughness (Ra)

Hardness (BHN)

T1

0.55

199

120

T2

0.44

201

130

T3

0.48

198

T4

0.55

T5

0.52

T6 T7

% Porosity

10

2.49

121.32

2.21

9

2.36

118.24

2.10

139

12

2.24

116.01

1.30

194

139

8

2.43

117.60

1.12

185

146

9

2.47

114.49

1.46

0.41

210

145

8

2.13

125.64

0.99

0.54

206

125

10

2.31

118.96

2.00

T8

0.58

200

115

9

2.23

127.90

1.28

T9

0.55

201

131

8

2.45

118.62

1.27

T10

0.48

217

116

10

2.24

123.48

1.53

T11

0.53

201

116

9

2.44

121.07

1.59

T12

0.57

186

136

8

2.31

116.89

0.59

T13

0.42

203

135

10

2.24

117.40

1.86

T14

0.47

200

144

9

2.31

115.86

2.13

T15

0.58

208

137

11

2.17

123.76

1.72

T16

0.43

212

133

9

2.11

123.44

1.89

T17

0.47

198

139

11

2.52

114.86

1.80

T18

0.54

196

148

9

2.47

120.50

1.68

T19

0.41

210

127

12

2.34

118.39

0.59

T20

0.45

197

122

8

2.35

120.68

1.21

REFERENCES 1.

2.

3.

4.

5.

6.

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S. Schneiderbauer, S. Pirker, C. Chimani, R. Kretz, Studies on Flow Characteristics at High-Pressure DieCasting. The 3rd International Conference on Advances in Solidification Processes, IOP Conf. Series: Materials Science and Engineering, vol. 27 (2011), pp. 1–6 L. Sowa, Numerical modeling the pressure die casting process of an angle plate. Arch. Mech. Technol. Autom. 32(1), 55–63 (2012) G.O. Verran, R.P.K. Mendes, L.V.O. Dalla Valentina, DOE applied to optimization of aluminum alloy die castings. J. Mater. Process. Technol. 200(1), 120–125 (2008) D.R. Gunasegaram, D.J. Farnsworth, T.T. Nguyen, Identification of critical factors affecting shrinkage porosity in permanent mold casting using numerical simulations based on design of experiments. J. Mater. Process. Technol. 209, 1209–1219 (2009) K. Chiang, N. Liu, T. Tsai, Modeling and analysis of the effects of processing parameters on the performance characteristics in the high pressure die casting process of Al–SI alloys. Int. J. Adv. Manuf. Technol. 41(11–12), 1076–1084 (2009) G.P. Syrcos, Die casting process optimization using Taguchi methods. J. Mater. Process. Technol. 135, 68–74 (2003)

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J.K. Kittur, M.N. Choudhari, M.B. Parappagoudar, Modeling and multi-response optimization of pressure die casting process using response surface methodology. Int. J. Adv. Manuf. Technol. (2014). doi: 10.1007/s00170-014-6451-x X. Sun, K.S. Choi, D.S. Li, Predicting the influence of pore characteristics on ductility of thin-walled high pressure die casting magnesium. Mater. Sci. Eng. A 572, 45–55 (2013) C. Reilly, J. Duan, L. Yao, D.M. Maijer, S.L. Cockcroft, Process modeling of low-pressure die casting of aluminum alloy automotive wheels. JOM 65(9), 1111–1121 (2013) P.K. Yarlagadda, Development of an integrated neural network system for prediction of process parameters in metal injection moulding. J. Mater. Process. Technol. 130, 315–320 (2002) L. Zhang, L. Li, S. Wang, B. Zhu, Optimization of LPDC process parameters using the combination of artificial neural network and genetic algorithm method. J. Mater. Eng. Perform. 21, 492–499 (2012) J.K. Rai, A.M. Lajimi, P. Xirouchakis, An intelligent system for predicting hpdc process variables in interactive environment. J. Mater. Process. Technol. 203, 72–79 (2008) J. Zhang, Q. Wang, P. Zhao, C. Wu, Optimization of high pressure die-casting process parameters using


Author's personal copy artificial neural network. Int. J. Adv. Manuf. Technol. 44, 667–674 (2009) 14. A.M. Hassan, A. Alrashdan, M.T. Hayajneh, A.T. Mayyas, Prediction of density, porosity and hardness in aluminum–copper-based composite materials using artificial neural network. J. Mater. Process. Technol. 209, 894–899 (2009) 15. F. Yin, H. Mao, L. Hua, W. Guo, M. Shu, Back propagation neural network modeling for warpage prediction and optimization of plastic products during injection molding. Mater. Des. 32, 1844–1850 (2011) 16. M.B. Parappagoudar, D.K. Pratihar, G.L. Datta, Neural network-based approaches for forward and reverse

mappings of sodium silicate-bonded, carbon dioxide gas hardened moulding sand system. Mater. Manuf. Process. 24, 59–67 (2009) 17. M.B. Parappagoudar, D.K. Pratihar, G.L. Datta, Forward and reverse mappings in green sand mould system using neural networks. Appl. Soft Comput. 8(1), 239–260 (2008) 18. M.B. Parappagoudar, D.K. Pratihar, G.L. Datta, Modelling of input-output relationships in cementbonded moulding sand system using neural networks. Int. J. Cast Met. Res. 20, 265–274 (2007) 19. D.K. Pratihar, Soft Computing (Narosa Publishing House Pvt. Ltd., New Delhi, 2008)

Technical Review and Discussion

responses were measured on each cast sample, the variability associated with the measured responses is estimated, and obtained average value of all the responses is presented in the paper. The ANOVA test (test of variance) was conducted, and statistical adequacy was checked (Reference 7).

Modeling of Pressure Die Casting Process: An Artificial Intelligence Approach Jayant K. Kittur, G.C. Manjunath Patel; KLS Gogte Institute of Technology, Belgaum, Karnataka, India Mahesh B. Parappagoudar; Chhatrapati Shivaji, Institute of Technology, Durg, Chhattisgarh, India Reviewers: It is not clear in the paper where and how the training data were produced. Authors: The performance of neural network (NN) depends on training data. Huge amount of training data are required to train NN properly. It is not feasible to conduct tests to generate large amount of training data. However, training data can be generated either by simulations or by regression models. It is shown in the literature 17, 18 that the regression equations (input/output relations) developed by applying DOE (design of experiments) and RSM (response surface methodology) can be effectively utilized to generate huge amount of training data (input/output data). In the present work, regression equations already developed by the same authors (Reference 7) were utilized to generate the training data. It is to be noted that the regression equations were developed based on the experimental data collected as per DOE. These regression equations were used to artificially generate a huge amount of data for training the NN by selecting the values of the input variables (at random) lying within their respective ranges. Reviewers: The experimental data appear to be based on a single casting at each condition. It would be better to have a statistically relevant batch size at each test condition. Without that, it is hard to determine how much variability should be expected across the 20 test cases. Authors: Three (3) replicates were conducted at each casting condition (i.e., the experiments conducted to develop input–output relations and 20 test cases). The


Reviewers: The data do not appear to support the usefulness of the reverse mapping. In each case, the percentage deviation from the experimental data is approximately one-third of the total deviation in that process parameter. For example, the fast shot velocity varies experimentally by 29 %, and the reverse mapping deviation is 9.9 % on average. The maximum deviation for the fast shot velocity is 23.9 %. At any given test case, the BPNN could predict process parameters 1–2 experimental conditions away from the required setting. It is not clear whether this is a limitation of the BPNN or whether that is a reflection of variability in the experimental data. Please clarify. Authors: Please note that the average absolute percentage deviation in predicting fast shot velocity, intensification pressure, phase change over point, and holding point is found to be 9.91, 3.95, 5.87, and 12.67, respectively. Hence, the grand average absolute percentage deviation will be 8.09. As it is pointed out by the reviewer, the average deviation as well as prediction for some of the test cases is found to be high for the fast shot velocity and holding time. The holding time is varied from 8 to 12 s. The deviation for holding is found to be more, since the output of BPNN is rounded to whole number and comparison is made. Apart from this, there might be a possibility of getting the solution trapped in local minima due to the nature of error surface. The combined effect of small variability in experimental data and limitation of BPNN (local minima) might have resulted in poor prediction of results in few cases. Reviewers: How do you ensure that your response equations are correct?

85

Author's personal copy Authors: After conduction of experiments based on the design matrix obtained using Minitab software, the responses were measured on each casted samples with three replicates, and the average value was used for developing the regression equation. Once the regression model is developed, the next step is to check the statistical adequacy of the developed model. The statistical adequacy of the regression model is tested through the analysis of variance (ANOVA) test and the R2 value (coefficient of determination). ANOVA is used to analyze the variances present in the experiment. To ensure the response equations are correct or not, we can use the value of coefficient of determination or R2 value. The value of R2 normally ranges from 0 to 100 %. If the model fits the observed dependent variable values perfectly, R2 is 1.0. In the present study, the higher R2 value for the response porosity under Box–Behnken design of experiments (BBD) is 95.9 % or 0.959. R2 value for the response surface roughness under central composite design (CCD) is R2 93.3 % or 0.933 and for hardness is 99.8 % or 0.998. Higher R2 value indicates better fit. All the response equations were found statistically adequate. Further, the response equations were tested for their prediction accuracy with the help of 20 test cases. Reviewers: What is the practical application of this research work? Authors: Forward modeling will help to make the prediction of hardness, porosity, and surface roughness for any combination of machine parameters in pressure die casting process. Moreover, the requirement of casting properties depends upon the application. For example, for some applications, porosity might be critical, whereas for some other requirements it may be the surface finish or hardness. The reverse modeling will help to know the machine parameters (input parameters) that will produce the casting with desired surface roughness, porosity, and hardness. The present work will help to avoid costly trial-and-error methods. Further, the work can be extended and used in automated machines for the online control and setting of parameters by incremental training of NN. Reviewers: Regarding modeling of die casting process using neural network, why have you specifically chosen the four process parameters: fast shot velocity, phase change over point, intensification pressure, and holding time? (Apart from DOE results) Authors: The component quality of the pressure die casting process depends on the process variables. The above four parameters are affecting the product quality by affecting surface roughness, porosity, and hardness of the cast component in pressure die casting. Hence, an attempt is made to investigate the effects of process parameters considering these process variables.

86

Reviewers: Explain the term ‘‘fast shot velocity’’? Isn’t it just ‘‘shot velocity?’’ Authors: There are normally slow shot velocity and fast shot velocity in the pressure die casting process which critically affects the final parts. The purpose of the slow shot is to fill the sleeve with the metal and start to push the metal from the runner system towards the gate and finally through the part. The point from the slow shot to fast shot usually occurs in the runner and prior to the gating system where the metal starts to enter into the part. Very low fast shot speeds result in cold shuts, and very high speeds lead to porosities and increase the amount of flash. So we specifically named fast shot velocity to distinguish from slow shot velocity. Reviewers: Why is CCD used as responses for hardness and surface roughness? Similarly, why is BBD used as a response for porosity? Please explain. Authors: RSM is method of fitting a polynomial to the true input–output relationship. Once the response equation is developed and its statistical adequacy is checked, R2 value (coefficient of determination) is used to test the fit of the response equation. Once the regression model is developed, the next step is to check the statistical adequacy of the developed model. The response equations with R2 value equal to 1 indicate perfect correlation, whereas 0 indicates lack of relationship. The response equations with better fit will predict the response more accurately. In the present work, two nonlinear response equations based on CCD and BBD have been developed for each of the response. The regression model CCD was selected for the responses hardness and surface roughness, whereas BBD was selected for the response porosity. It is to be noted that R2 values (that is, coefficient of determination) were used for the said purpose. Response-wise and design-wise (CCD/BBD) R2 values are presented in the following table.

Sl. no.

1 2 3

Response parameter

Coefficient of determination CCD

BBD

Porosity Surface roughness Hardness

0.657 0.933 0.998

0.959 0.927 0.865

Reviewers: The ‘‘average absolute deviation’’ (and its summation) of the predictions is calculated and discussed, but the utility of this measure is unclear. I suppose it gives a single number that can be used to quantify the prediction method and compare to another method, but this may not be an ideal comparison. Typically, an objective function with parameter weights would be used. Here, the assumption (I think) is that all parameters have equal weights. If so, this should at least be defined or addressed.


Author's personal copy Authors: The summation of actual deviation will be very low and close to zero in many cases due to the addition of positive and negative terms (i.e., actual deviation values obtained from test case comparison). Thus, the average of actual deviation will be low and misleading. Hence, average absolute percent deviation is obtained by dividing the summation of absolute percentage deviations by the number of test cases. This number along with the range of deviation and plot of actual percent deviation will provide good basis for making comparison. This type of comparison is available in the literature. However, parameter weights in objective function provide information on significance and sensitivity of the parameter (process variable) with reference to the particular response. Reviewers: More physical test data could be used than the 20 samples. This would improve breadth of the test data and statistical confidence.


Authors: Please note that more number of experiments were conducted to develop the response equations. The confidence level, statistical adequacy, ANOVA test are performed, and the results are presented in Reference 7. The experiments for testing the models were different from the experiments performed for developing the regression models (response equations). Moreover, these test data are also not used for training the neural network. The experiments were conducted with different combinations of process parameter values (process parameter values are generated at random, within the operating range considered). Hence, the same 20 test cases which were used to test regression model (Reference 7) are used for testing, so that comparison is possible between statistical- and NN-based models (results are compared in the present paper).

87

AUTHOR'S PROOF!

JrnlID 170_ArtID 8416_Proof# 1 - 30/01/2016

Int J Adv Manuf Technol DOI 10.1007/s00170-016-8416-8

1 3 2

4 5 Q1 6

ORIGINAL ARTICLE

An intelligent system for squeeze casting process—soft computing based approach Manjunath G. C. Patel 1 & Prasad Krishna 1 & Mahesh B. Parappagoudar 2

Received: 2 November 2014 / Accepted: 20 January 2016 # Springer-Verlag London 2016

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

Abstract The present work deals with the forward and reverse modelling of squeeze casting process by utilizing the neural network-based approaches. The important quality characteristics in squeeze casting, namely surface roughness and tensile strength, are significantly influenced by its process variables like pressure duration, squeeze pressure, and pouring and die temperatures. The process variables are considered as input and output to neural network in forward and reverse mapping, respectively. Forward and reverse mappings are carried out utilizing back propagation neural network and genetic algorithm neural network. For both supervised learning networks, batch training is employed using huge training data (input-output data). The input-output data required for training is generated artificially at random by varying process variables between their respective levels. Further, the developed model prediction performances are compared for 15 random test cases. Results have shown that both models are capable to make better predictions, and the models can be used by any novice user without knowing much about the mechanics of materials and the process. However, the genetic algorithm tuned neural network (GA-NN) model prediction

performance is found marginally better in forward mapping, whereas BPNN produced better results in reverse mapping.

31 32

Keywords Squeeze casting process . Forward mapping . Reverse mapping . BPNN and GA-NN

33 34

1 Introduction

35

The near net-shape manufacturing capability of the squeeze casting process has greater potential to yield good-quality castings. In squeeze casting, the casting quality is mainly affected by cold laps, segregations (types such as v-type, minor, macro, pipe, centreline, extrusion), hot tears, sticking, over filling, under filling, case de-bonding, shrinkage and so on [1, 2]. It is noteworthy that accurate control of process variables is one of the possible solutions to reduce defects and to obtain the desirable quality in castings (surface finish and tensile strengths). A great deal of research work was carried out in this arena, during the 1990s and 2000s throughout the world. However, majority of work reported in the literatures during that period was on use of numerical, analytical, and classical experimental approaches. The effects of casting temperature on the mechanical properties were investigated by Yang [3]. The influence of die temperature, squeeze pressure and pressure durations were kept constant in their study. Further, analytical models, such as gracia’s virtual and steady state heat flow models were utilized to estimate the influence of solidification time towards the mechanical properties [4]. A major drawback of their model is that the analysis was carried out with many assumptions. The pouring temperature and squeeze pressure influences on the mechanical properties were studied [5, 6]. It is to be noted that pressure duration and die temperature effects were not considered in their analysis. The influencing process variables such as squeeze pressure and pouring and die temperatures were

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N C O R R EC TE D

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PR O O

F

7

* Mahesh B. Parappagoudar [email protected] Manjunath G. C. Patel [email protected] Prasad Krishna [email protected]

1

Department of Mechanical Engineering, National Institute of Technology Karnataka, Surathkal 575025, India

2

Department of Mechanical Engineering, Chhatrapati Shivaji Institute of Technology, Durg, C. G. 491001, India

AUTHOR'S PROOF! JrnlID 170_ArtID 8416_Proof# 1 - 30/01/2016

Int J Adv Manuf Technol

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&

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PR O O

F

neural networks (ANNs) have been utilized to predict the temperature difference of the squeeze cast part using back propagation algorithms [17]. Later on, the authors extended their research work to predict the solidification time using ANNs [18]. The mechanical properties of the squeeze cast parts were predicted for different squeeze casting conditions using radial basis functions of ANNs [19]. More recently [20], ANNs were used to predict the outputs (i.e. density and secondary dendrite arm spacing) and process parameters (time delay, squeeze pressure, pressure duration, melt and die-preheat temperature) using forward and reverse mapping tools. It is to be noted that the training data had been collected, where the interaction terms in the response equations were neglected. This might have resulted in large average absolute percent deviation in prediction. In the recent past, few authors had used neural networks as forward mapping tool to predict the casting properties for the known set of process parameters [21–24]. Few researchers made an attempt to predict the responses as well as process variables using forward and reverse mappings of neural network approaches [25–29]. Neural network (NN) trained with back propagation (BP) algorithm has been successfully applied in the past for prediction. Since the BP algorithm works on the steepest descent method, it has a greater probability of getting trapped in local optimum solutions. However, an evolutionary genetic algorithm (GA) starts searching the solutions in huge space at many distinct locations, simultaneously. Thus, GA has greater probability to hit the global minima. An attempt is being made in the present study to carry out both forward and reverse mappings utilizing BP algorithm tuned neural network (BPNN) and GA tuned NN (GA-NN), separately. The following two objectives are aimed in the present work:

N C O R R EC TE D

studied to investigate their effects on the mechanical and microstructure properties [7]. It must be duly noted that experiments were conducted with the constant pressure duration. Although much work is reported earlier in the literature to improve the casting quality, the practical guidelines followed by the researchers may not be sufficient to the foundry men in selecting the most influential parameters. The Taguchi method and statistical design of experiments have been used in the past, wherein the process parameters were simultaneously varied. The main and combined process parameter effects were identified and analyzed. The complex input-output relationships were established at reduced cost and energy consumption. The Taguchi method was adopted to study the effects of die materials, die temperature and squeeze pressure on the surface roughness of the LM24 alloy [8]. It is to be noted that experiments were carried out by keeping the pressure duration and pouring temperature as a constant. To study the effects on mechanical properties of aluminium and magnesium-based alloys [9, 10], the influence of die temperature, applied pressure and its durations were considered. It is to be noted that pouring temperature contributions were left out in their research work. Squeeze pressure and pouring and die temperature effects were studied to estimate the percent contribution of process variables on surface roughness (SR), density, hardness and ultimate tensile strengths (UTS) of aluminium alloys [11, 12]. It is also important to mention that experiments are conducted for the fixed pressure duration. Bin et al. [13] studied the strength and ductility of the cast components under the different squeeze pressure, filling velocity, pouring, and mould temperature. It is noteworthy that the pressure duration effects were not considered in their analysis. Yield strength (YS) of the cast parts were studied under different squeeze casting conditions [14]. An attempt was made by authors [15] to improve the ductility by optimizing melt, die-preheat temperature and squeeze pressure parameters using the statistical Taguchi method. However, the paramount information regarding the duration of holding and waiting time has not reported. The practical requirement for industry personnel is to know the required process variable combinations that will produce the desired output, particularly for online process control. An attempt was made in the past using statistical regression tool to predict the welding parameters through reverse mapping [16]. Reverse mapping via statistical regression tools requires the transformation matrix to be a square one. Hence, the model predictions can be determined only for the response equation includes linear terms, whereas transformation matrix might not be invertible with interaction terms in response equation. Thus, statistical design of experiments and the Taguchi method fails to perform reverse modelling accurately. Soft computation tools have been proven to be the cost effective to meet the industrial requirements, analyze the complex non-linear input-output relationships and predict multi-outputs simultaneously. Artificial

U

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&

Forward mapping: Forward mapping is carried out to predict the casting properties (surface roughness, yield strength and ultimate tensile strength) for the known set of process variables (squeeze pressure, pressure duration, pouring temperature and die temperature). For the 15 test cases, neural network models prediction performances are compared among themselves and those with the statistical regression models. Reverse mapping: Reverse mapping is carried out to predict the required process variable combination, which will yield the desired surface roughness, yield and ultimate tensile strength. It is noteworthy that the prediction performances are compared among the neural network-based approaches.

2 Modelling of squeeze casting system

160

Modelling has been employed to map the complex non-linear system by utilizing neural network-based models. To establish

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AUTHOR'S PROOF!



the input-output relationships, four process variables have been considered, namely, pressure duration, squeeze pressure, pouring temperature, die temperature as input and three conflicting (minimization and maximization) responses such as surface roughness, yield and ultimate tensile strength as output. The process variables and their respective levels considered for the present work is presented in Table 1.

Reverse mapping The requirement to predict the process parameters for the desired output is carried out utilizing reverse mapping. BPNN and GA-NN have been used to carry out the abovementioned task. In the reverse modelling system, the outputs (casting properties) of the forward mapping are treated as inputs, and inputs (process variables) are expressed as a function of outputs.

212 213 214 215 216 217 218

170

2.1 Forward mapping

2.2 Back propagation algorithm tuned neural network (or) BP algorithm tuned NN

219 220

The supervised learning capability of back propagation algorithm has been adaptively trained with batch mode to reduce the error in successive iterations. The network predictions obtained by the forward pass calculation is compared with the target values in order to determine the error. The mean squared error (MSE) is used as an error function in the present work is shown in Eq. 4

221 222 223 224 225 226

199

1 Surface roughness; y ¼ ð1 þ expðaxÞÞ

198 197

Yield strength; ultimate tensile stength; y ¼

202 201 200 203 204

1 ð1 þ expð−bxÞÞ

ð1Þ

ð2Þ

Log-sigmoid transfer function is employed for all the hidden neurons lying in that layer (see Eq. 3) y¼

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PR O O

R 1 X M SE ¼ R N i¼1

1 ð1 þ expð−cxÞÞ

ð3Þ

The terms a, b and c are the constants of activation function; y represents the neuron output and x is the neuron input. The steps followed in modelling the squeeze casting process for BPNN is shown in Appendix B.

ð4Þ

The terms Tij and Oij depicts the desired (experimental or target), and the network predicted output values; R denotes the number of outputs, and N represents the number of network training scenarios. It is to be noted that network weights are updated for minimum error using Eq. 5.

N C O R R EC TE D

The three-layer feed forward neural network with input, hidden and output layers is considered (refer to Fig. 1). In the forward mapping, four and three neurons are used in the input and output layers to represent the process variables and responses, respectively. The detailed parametric study has been carried out to optimize NN parameters by varying individual network parameter at once after keeping other network parameters at midvalues. During the first stage of parameter study, hidden neurons are varied in the range of 4 to 25, and the optimum number of hidden neuron has been selected corresponding to the minimum mean squared error. Optimization of other NN parameters, namely, learning rate, momentum constant, constants of activation function hidden layer, constants of activation function output layer-1, constants of activation function output layer-2, and bias value has been carried out in the subsequent stages of parametric study. The training and testing data are normalized between zero and one to avoid numerical overflows due to very low and high values. It is noteworthy that the process parameter effect on the measured responses has been studied by using surface plots, and interdependency among the outputs is also checked [30]. A linear transfer function, y = mx, is employed for the input layer. The value of m (0 < m > 1) is determined through number of trial runs. It has been observed that the influence of process variables on surface roughness is opposite to that of the tensile strengths. Hence, for the output layer, the following log-sigmoid transfer functions are used while modelling the responses (Eqs. 1 and 2)

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ΔW jk ðt Þ ¼ −η

∂E ðt Þ þ αΔW jk ðt−1Þ ∂W jk

ð5Þ

The term η represents the learning rate, t indicates the iteration number and α is the momentum constant. ∂E/∂Wjk estimated utilizing the chain rule of differentiation (see Eq. 6). Yk and Uk represent output and input, respectively, of kth neuron lying in the output layer. ∂E ∂E ∂Y k ∂U k ¼ ∂W jk ∂Y k ∂U k ∂W jk

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237 236 235 238 239 240 241 242

ð6Þ 245 244 243

2.3 GA tuned NN

246

The population-based search method i.e. GA has been used in the past to optimize the complex manufacturing processes. In the present work, GA has been used to tune the network parameters, wherein the optimal solutions are searched in multidimensional space at many distinct locations simultaneously. The auxiliary hybrid working system has been used in the integral GA-NN model. In GA-NN, the network parameters such as synaptic weights, bias and transfer function constant values are supplied through GA-string, and the network computes the expected output. The optimum number of hidden

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t1:3 t1:4 t1:5 t1:6 t1:7

268 267 266

Source Pressure duration Squeeze pressure Pouring temperature Die temperature

Levels Un-coded A B C D

neurons, which is determined through a parametric study using BPNN, is kept the same in combined GA-NN approach. The mean square error is calculated by comparing the network predicted and target values. The determined mean squared error is used as the fitness function for GA-string (refer to Eq. 7). The schematic diagram of working cycle GA-NN model is shown in Appendix C. The solutions are altered using the selected GA parameters namely, bit wise mutation, uniform cross over and tournament selection. R N 2 1 X X 1 T i j −Oi j Fitness ¼ R N i¼1 j¼1 2

ð7Þ

Units S MPa °C °C

269

2.4 Data collection

270 271

The training of NN requires huge input-output data base, and collection of such data through actual experiments is impractical.

U

Fig. 1 Artificial neural network structure used for forward mapping

Low (−1) 20 40 630 150

Middle (0) 35 80 675 225

High (+1) 50 120 720 300

Hence, training data is generated at random by utilizing response equations derived through actual experiments via statistical modelling. It is important to note that the test case data have been collected through actual experimentations.

2.5 Training data

Experiments are conducted using standard matrices of statistical design of experiments and response surface methodology (RSM). The non-linear input-output relations (response equations) have been obtained by conducting experiments and applying statistical DOE and RSM techniques. These response equations have been used to artificially generate the training data, related to the responses such as, surface roughness, yield and ultimate tensile strengths. To derive, the response equations two non-linear regression models are used namely boxbehnken design (BBD) and central composite design (CCD) [30]. Further, the best model for each response has been

N C O R R EC TE D

257 258 259 260 261 262 263 264 265

Process variables

F

Table 1 Process variables and their respective levels

PR O O

t1:1 t1:2

272 273 274 275

276 277 278 279 280 281 282 283 284 285 286 287

AUTHOR'S PROOF!



288 289 290 291 296 297

selected based on the average absolute percent deviation determined by utilizing the test cases [30]. It is noteworthy that CCD-based model performs best when modelling for surface roughness and yield strength, whereas BBD showed a better

SRCCD ¼

result for ultimate tensile strength predictions. Hence, the input-output data has been artificially generated using the best regression equations obtained for different responses using two non-linear regression models is shown in Eqs. 8–10:

292 293 294 295

15:2320−0:0215093A−0:0249583B−0:0376636C þ 0:00577407D þ 2:22222 10−05 A2 þ 6:875 10−05 B2 þ 2:71605 10−05 C 2 −8:88889 10−06 D2 þ 2:70833 10−05 AB þ 2:40741 10−05 AC−2:22222 10−06 AD þ 2:08333 10−06 BC þ 1:0833 3 10−05 BD −5:92593 10−06 CD ð8Þ

302 303 304 305

U T S BBD ¼

306 307 308 310 309

−1071:38−1:26601A−0:797501B þ 3:36494C þ 0:902819D þ 0:0123095A2 þ 0:00276227B2 −0:00238537C 2 −8:58733 10−04 D2 þ 0:00253125AB þ 0:000101852AC þ 0:000627778AD þ 0:000746528BC þ 0:00034375BD −8:87037 10−04 CD

N C O R R EC TE D

Y S CCD ¼

PR O O

F

298 299 300 301

−1176:2−4:71685A−1:29458B þ 3:97148C þ 0:932667D−0:00137037A2 þ 0:00234635B2 −0:00293004C 2 −8:21481 10−04 D2 þ 0:00354167AB þ 0:00651852AC þ 4:44444 10−05 AD þ 0:00155556BC þ 0:001025BD −0:00102693CD

2.6 Test data

312 313 314 315 316 317 318 319 320 321 322

Fifteen test cases are randomly generated after selecting the process variables between their corresponding levels. The experiments have been conducted to measure the outputs namely, surface roughness, yield strength and ultimate tensile strength. Three replicates are considered for each casting condition. Average values of nine surface roughness and six tensile strengths are used to minimize the error variations and to check the prediction performance. The 15 random test cases which have been utilized to test the prediction performance of neural network (BPNN and GA-NN) models in forward and reverse mapping is shown in Appendix A.

323

3 Results and discussions

324 325 326

In forward mapping case, the prediction performances of neural network-based approaches have been compared among themselves and with those of the statistical

U

311

ð9Þ

ð10Þ

design of experiments. The neural network performances are compared among themselves in reverse mapping. It is important to note that the same network training and testing data are used for both forward and reverse mappings of neural network-based approaches. The forward and reverse mappings results will be discussed in the following sections.

327 328 329 330 331 332 333

3.1 Results of forward mapping

334

The neural network (BPNN and GA-NN) models have been used to predict the surface roughness, yield and ultimate tensile strengths for the known set of process variable combinations namely squeeze pressure, pressure duration, pouring temperature and die temperature.

335 336 337 338 339

3.2 BP algorithm tuned NN

340

Thousands of combinations of input-output data have been generated artificially by utilizing the regression

341 342



U

N C O R R EC TE D

PR O O

F

Fig. 2 BPNN parametric study: a MSE vs. no. of hidden neurons, b MSE vs. learning rate-hidden layer, c MSE vs. learning rateoutput layer, d MSE vs. momentum constant, e MSE vs. activation function constanthidden layer, f error MSE vs. activation function constant 1output layer, g MSE vs. activation function constant 2-output layer and g MSE vs. bias value

343 344

equations, and the same is used to train the network through batch mode. To determine the optimum network

parameters, a detailed parametric study has been conducted as shown in Fig. 2. The results of the parametric

345 346

AUTHOR'S PROOF!


Int J Adv Manuf Technol t2:1

Table 2

t2:2

Neural network parameters

Optimum parameter values

GA-NN parameters


t3:2

t2:3 t2:4 t2:5 t2:6 t2:7 t2:8 t2:9 t2:10

Hidden neurons Learning rate-hidden layer, η Learning rate-output layer, η Momentum constant, α Activation constant-hidden layer Activation constant-output layer-1 Activation constant-output layer-2 Bias

23 0.455 0.4995 0.4995 4.15 3.25 5.5 0.00009505

Mutation probability Population size Generations number

0.0001106 274 510

t3:3 t3:4 t3:5

GA-NN parametric study results of forward mappings

t3:1

354

The GA-NN performance depends mainly on the GA parameters namely size of population, probability of mutation and number of generations. GA parameters are optimized by conducting the detailed parametric study (refer to Fig. 3). Uniform cross over with a probability value of 0.5 is used. The optimized GA parameter values obtained using the parametric study is shown in Table 3. The network training completed with the reduced mean squared error found equal to 0.001338. The average absolute percent deviation in prediction of test cases considering all the responses is found to be equal to 3.54 %.

355 356 357 358 359 360 361 362 363 364 365

PR O O

F

3.3 GA tuned NN

N C O R R EC TE D

study obtained for an optimum network parameters are presented in Table 2. The network training is completed with the minimized mean squared error equal to 0.002961. The trained neural models are tested for 15 test cases, and the results obtained in terms of average absolute percent deviation in prediction considering all outputs are found to be equal to 4.87 %.

Table 3

U

347 348 349 350 351 352 353

BPNN parametric study results of both forward mapping

Fig. 3 GA-NN parametric study a MSE vs. mutation probability (Pm), b MSE vs. population size and c MSE vs. generation number


N C O R R EC TE D

PR O O

F


Fig. 4 Models comparison in terms of PD in prediction a surface roughness, b yield strength and c ultimate tensile strength

3.4 Comparison of forward mapping of neural network and statistical models

368 369 370 371 372 373 374

The GA-NN and BPNN prediction performances are compared among themselves and those with statistical models for 15 test cases. Figure 4a compares the percent deviation (PD) in prediction of surface roughness utilizing the three models. Prediction performances of non-linear regression-based CCD model and GA-NN are found to be of almost similar. The prediction of

t4:1 t4:2

t4:4 t4:5 t4:6 t4:7

U

366 367

Table 4 Models comparison for prediction of responses (forward mapping)

Response

Surface roughness Ultimate tensile strength Yield strength Average of all responses

surface roughness in terms of PD values using CCD, BPNN and GA-NN are found to vary in the range of −14.86 to +9.59 %, −39.13 to +11.2 % and −15.22 to +13.7 %, respectively. Similarly, the prediction of yield strength in terms of percent deviation values using CCD, BPNN and GA-NN models are found to lie in the range of −6.67 to +2.3 %, −6.13 to +4.76 % and −6.35 to +2.67 %, respectively (see Fig. 4b). The nonlinear regression-based BBD model performed better for predicting the ultimate tensile strengths. The PD in pre-

375 376 377 378 379 380 381 382 383 384

Average absolute percent deviation in prediction BPNN

GA-NN

CCD [30]

BBD [30]

10.05 1.998 2.57 4.87

6.36 2.11 2.16 3.54

6.48 1.94 2.21 3.54

7.94 1.76 3.27 4.32

t4:3

AUTHOR'S PROOF!


Int J Adv Manuf Technol Table 5

Optimum network parameter values

t5:2

Hidden neurons Learning rate-hidden layer, η Learning rate-output layer, η Momentum constant, α Activation constant-hidden layer Activation constant-output layer Bias

23 0.6775 0.455 0.455 7.3 5.5 0.0000505

t5:3 t5:4 t5:5 t5:6 t5:7 t5:8 t5:9

430 431 432 433

3.5 Results of reverse mapping

434

The stringent requirement for the industrial personnel to know the required process parameters setting in order to obtain the desired responses is carried out through the reverse mappings, using neural network-based approaches. It is to be noted that during training, surface roughness, ultimate tensile strength and yield strength are used as the network inputs to predict the process parameters such as pressure duration, squeeze pressure, and pouring and die temperatures as outputs.

435 436 437 438 439 440 441 442 443

3.6 BP algorithm tuned NN

444

A detailed parametric study is conducted to determine the optimum network parameters for better predictions. The result of the parametric study is presented in Table 5. It should be noted that after the network parameters are optimized, 15 test cases were passed in batch mode to the optimized NN to obtain the process parameters. The BPNN training completed with the mean squared error of 0.022292. Further, the average

445 446 447 448 449 450 451 452

F

response at a time). Hence, it fails to capture interdependency among the outputs (if any) since all the responses are measured on the same sample under particular casting conditions.

N C O R R EC TE D

diction of ultimate tensile strength using BBD, BPNN and GA-NN models are found to vary in the range of −4.61 to +2.68 %, −2.94 to +4.07 % and −4.15 to +3.72 %, respectively (refer Fig. 4c). Table 4 compares the neural network (BPNN and GA-NN) models and statistical (CCD and BBD) models for 15 test cases in terms of average absolute PD in prediction of the individual and combined responses. Considering all responses, the average absolute PD in prediction made by BPNN, GA-NN, CCD and BBD models are found to be equal to 4.87, 3.54, 3.54 and 4.32 %. However, GA-NN performance is comparable with CCD-based non-linear model and outperformed other models for predicting the combined responses in terms of average absolute percent deviation (refer to Fig. 5). The results have shown that all the models are capable of making effective prediction; however, GA-NN performs slightly better compared to BPNN. The reasons might be the ability of the GA to search the global solutions in multi-dimensional space at many distinct locations simultaneously and its ability to capture non-linear information of the process accurately. The nature of error surface and more importantly due to the lesser chances of optimum solution getting trapped in local minima with GA might have resulted in better performance of GA-NN. In making accurate predictions, although non-linear regression-based CCD model is comparable with GA-NN model, the main weakness of the non-linear regression-based CCD model is that predictions are made response wise (i.e. one

U

385 399 398 397 396 395 394 393 392 391 390 389 388 387 386 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429

t5:1

Neural network parameters

PR O O

Fig. 5 Models comparison for predicting the combined responses in terms of average absolute percent deviation (Forward mapping)

BPNN parametric study results of reverse mappings

Table 6

GA-NN parametric study results of reverse mappings

t6:1

GA-NN parameters


t6:2

Mutation probability Population size Generations number

0.0001515 260 510

t6:3 t6:4 t6:5



N C O R R EC TE D

PR O O

F

Fig. 6 Model comparison in terms of PD in prediction a pressure duration and b squeeze pressure

Fig. 7 Model comparison in terms of PD in prediction a pouring temperature and b die temperature

absolute percent deviation in prediction of combined responses is found to be equal to 5.18 %.

455

3.7 GA tuned NN

456 457

The input parameters (process variables) and outputs (casting properties) of forward mapping are treated as

t7:1 t7:2

t7:4 t7:5 t7:6 t7:7 t7:8

U

453 454

Table 7 Models comparison for predicting the process parameters (reverse mapping)

Process parameters

Pressure duration Squeeze pressure Pouring temperature Die temperature Average of all process parameters

the outputs and inputs, respectively, in reverse mapping. GA parameters are optimized after conducting a detailed parametric study, and the obtained results are presented in Table 6. The GA-NN training ends with the mean squared error of 0.022632, and the average absolute PD in predictions of all the network outputs is found equal to 5.46 %.

458 473 472 471 470 469 468 467 466 465 464 463 462 461 460 459 474 475 476 477 478 479

Average absolute deviation in prediction (%) BPNN

GA-NN

7.33 6.49 1.76 5.13 5.18

6.67 7.14 1.76 6.26 5.46

t7:3

AUTHOR'S PROOF!



3.8 Comparison of reverse mappings of neural network models

482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509

Fifteen random test case results while predicting the process parameters via revere mappings by utilizing the neural network (BPNN and GA-NN) models are discussed below, The BPNN and GA-NN model for pressure duration prediction in terms of percent deviation is shown in Fig. 6a. The PD prediction values are found to vary in the range of −13.96 to 14.39 % for BPNN and −6.62 to 12.16 % for GA-NN models. Figure 6b shows the plot representing the BPNN and GA-NN models prediction of squeeze pressure in terms of PD. It is noteworthy that neural (BPNN and GA-NN) models yielded similar trend in PD in prediction. However, BPNN showed slightly better performance than GA-NN. The PD in prediction is seen to vary in the levels of −23.03 to 12.17 % for BPNN and −23.89 to 12.66 % for GA-NN model (refer to Fig. 6b). Figure 7a compares the BPNN and GA-NN models prediction performance in terms of PD for the pouring temperature. The plot indicates that both models follow a similar pattern; however, GA-NN has shown slightly better performance as compared to BPNN. Moreover, the PD in the prediction of pouring temperature is found to be lying in the range of −4.36 to 2.55 % for BPNN and −4.01 to 2.5 % for GA-NN. Figure 7b represents the plot of PD in prediction for die temperature NN models. It is worth noting that the BPNN prediction performance is found to be better than GA-NN towards this response. Furthermore, the PD in

513

Table 7 compares the average absolute percent deviation in prediction of the individual and the combined responses of BPNN and GA-NN models in reverse mapping. The percent deviation from the zero line showed larger deviation for both models as compared to forward prediction. This might be due to the fact that in most of the manufacturing processes, the behaviour of the responses varies non-linearly with respect to the independent variables. Increase of one parameter and decrease of the other and vice versa may result in a similar output effect. Thus, the neural network model performances are considered as data dependent. The results have shown that the BPNN model is found to make better prediction than GA-NN in most of the cases. The reason might be due to adaptability of the model to capture complex non-linearity in the process and error surface. Thus, it can be concluded that the evolutionary GA tuned NN performs better only when the BP algorithm tuned NN get trapped in local minima. However, the practical requirements in predicting the process parameters can be effectively tackled using neural network based approaches via reverse mapping. Although both models are capable of making effective reverse mapping predictions, BPNN is the finally preferred one due to a better average absolute PD in prediction (considering all responses) as shown in Fig. 8.

514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539

4 Conclusions

540

The neural network-based approaches have been used to carry out the input-output modelling of the squeeze casting process in both forward and reverse directions. The batch mode training requires huge data sets which are generated artificially through the regression equations. The following conclusions are drawn from the present study:

541 542 543 544 545 546 547

1. In the present work, different responses are measured on the same casting specimen. It is noteworthy that all responses need to be estimated simultaneously, or else interdependency among the outputs (if any) might be lost. Since the analysis is carried out response wise, conventional regression analysis

548 549 550 551 552 553

F

3.9 Comparison of the models

U

N C O R R EC TE D

480 481

510 511 512

PR O O

Fig. 8 NN models comparison in terms of PD in prediction considering all process parameters (reverse mapping)

prediction of die temperature using neural models is found to fall in the range of −12.24 to 11.42 % for BPNN and −17.48 to 11.77 % for GA-NN.



Appendix I t8:1

Table 8

Summary of input-output results of the test cases

t8:2

Exp. no.

Squeeze cast process variables

t8:3

U

A

580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601

Acknowledgments The authors greatly acknowledge the Dept. of Applied Mechanics and Hydraulics, National Institute of Technology Karnataka, India, for their kind support in carrying out the experiments.

602 603 604

F

3. By utilizing the neural network-based approaches, the process parameters for the desired quality can be obtained. Furthermore, the performances of the neural network models have been compared among themselves by utilizing 15 test cases. It is interesting to note that BPNN outperformed GA-NN in predicting most of the responses. The overall performance of BPNN is slightly better as compared to GA-NN. The reason might be the fact that the nature of error surface. BPNN results are found to be better for uni-modal error surfaces. The grand average absolute percent deviation in prediction of combined process variables is found equal to 5.18 % for BPNN and 5.46 % for GA-NN. 4. The NN-based approaches are capable of making effective forward and reverse mapping predictions. The reverse mapping predictions are more useful for a foundry man in online monitoring of the process. Furthermore, reverse mapping also helps to reduce the cost incurred in the selection of the most influential process parameters, material wastages, energy consumption, casting simulation software.

PR O O

approach might fail to capture the interdependency among the responses. Neural networks are capable of predicting multi-outputs simultaneously, resulting in integral approach. 2. In forward mapping, the quality characteristics (i.e. yield strength, surface roughness and ultimate tensile strength) are predicted for the known set of process variables (i.e. pressure duration, squeeze pressure, pouring temperature and die temperature). The BPNN, GA-NN and statistical models prediction performances have been compared for 15 test cases. Although the neural network approaches are trained with the data collected from the regression models, the results have shown that GA-NN slightly outperformed the other models while predicting the responses, surface roughness and yield strength. Furthermore, the non-linear regression models outperformed neural network models in prediction of ultimate tensile strength. Moreover, GA-NN results are comparable with the non-linear regression based CCD model in predicting the responses. The average absolute deviation in prediction in terms of percentage obtained for the combined responses using different models is found equal to 4.87 % for BPNN, 3.54 % for GA-NN, 3.54 % for CCD and 4.32 % BBD, respectively.

N C O R R EC TE D

554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579

Q3

Responses

B

C

D

Ra, (μm)

UTS, MPa

YS, MPa

t8:4 t8:5

1 2

36 41

96 57

682 646

211 231

0.73 1.02

194 178

126 117

t8:6 t8:7 t8:8 t8:9 t8:10 t8:11 t8:12 t8:13 t8:14 t8:15 t8:16 t8:17 t8:18

3 4 5 6 7 8 9 10 11 12 13 14 15

33 27 35 42 42 29 32 38 39 36 33 28 34

55 69 54 117 106 61 68 114 105 55 43 44 41

661 692 677 684 673 707 680 642 663 684 685 712 702

213 203 215 230 251 232 256 241 213 202 163 199 203

1.08 0.94 0.98 0.46 0.53 0.92 0.74 0.55 0.56 1.08 1.33 1.25 1.16

180 188 183 213 207 188 191 208 206 180 179 177 178

116 114 114 138 135 116 121 136 135 116 116 108 112

AUTHOR'S PROOF!



Appendix II Flow chart illustrating methodology followed in squeeze casting process modelling via DOE based BPNN Back propagation neural network

Generate input-output training data through response equations Start An integrate system development to co-relate input and outputs Examine experimental needs

F

PR O O

Define objective(s)

Initialize random weights, network parameters, error goal and training epochs Load training data via batch mode

Identify control and noise factors influencing response(s)

Forward calculation to estimate network output Determine error by comparing network output and target values

N C O R R EC TE D

Determine the controllable variable ranges of a process

Backward calculation to update synaptic weights

Select particular design of experiments and design the experimental matrix

End of epoch

I = I +1

Yes

Error goal Reached?

Perform experiments as per design and collect experimental data with three replicates

Save weights No

No

U

Establish either linear or non-linear input-output relationships using software

Analyze the collected data to estimate the performances

Significance and ANOVA test

Estimate individual, combined effect on the responses

Load test cases

Exceed Max. Iteration? Yes

Predict network results

Declare network failure

Test the developed model performances with random test cases

End



Appendix III Steps followed in GA-NN modelling [29] 605

609 GA Starts

Initial Population Generation = 0

No

GA string =0

F

Gen > Max gen

End Yes

GA string >Pop

Assign fitness to all strings

PR O O

Yes

Start case=0

No

N C O R R EC TE D

Case> max Case

Reproduction

Determine output using NN

Cross over

Mutation

No

Case= Case+1

Gen. = Gen+1

U

GA String = GA String + 1

606

607 608

Yes

Calculate fitness of a string

AUTHOR'S PROOF!



3.

4.

5.

6. 7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

F

2.

Britnell DJ, Neailey K (2003) Macrosegregation in thin walled castings produced via the direct squeeze casting process. J Mater Process Technol 138(1):306–310 Hong CP, Lee SM, Shen HF (2000) Prevention of macrodefects in squeeze casting of an Al-7 wt pct Si alloy. Metall Mater Trans B 31(2):297–305 Yang LJ (2003) The effect of casting temperature on the properties of squeeze cast aluminium and zinc alloys. J Mater Process Technol 140(1):391–396 Yang LJ (2007) The effect of solidification time in squeeze casting of aluminium and zinc alloys. J Mater Process Technol 192:114– 120 Raji A, Khan RH (2006) Effects of pouring temperature and squeeze pressure on Al-8 % Si alloy squeeze cast parts. AU J T 9(4):229–237 Yue TM (1997) Squeeze casting of high-strength aluminium wrought alloy AA7010. J Mater Process Technol 66(1):179–185 Maleki A, Niroumand B, Shafyei A (2006) Effects of squeeze casting parameters on density, macrostructure and hardness of LM13 alloy. Mater Sci Eng A 428(1):135–140 Vijian P, Arunachalam VP (2006) Optimization of squeeze cast parameters of LM6 aluminium alloy for surface roughness using Taguchi method. J Mater Process Technol 180:161–166 Vijian P, Arunachalam VP (2007) Modelling and multi objective optimization of LM24 aluminium alloy squeeze cast process parameters using genetic algorithm. J Mater Process Technol 186(1):82–86 Guo ZH, Hou H, Zhao YH, Qu SW (2012) Optimization of AZ80 magnesium alloy squeeze cast process parameters using morphological matrix. Trans Nonferrous Metals Soc China 22(2):411–418 Patel GCM, Krishna P, Parappagoudar MB (2014) Optimization of squeeze cast process parameters using Taguchi and grey relational analysis. Procedia Technol 14:157–164 Souissi N, Souissi S, Niniven CL, Amar MB, Bradai C, Elhalouani F (2014) Optimization of squeeze casting parameters for 2017A wrought Al alloy using Taguchi method. Metals 4(2):141–154 Bin SB, Xing SM, Zhao N, Lan LI (2013) Influence of technical parameters on strength and ductility of AlSi9Cu3 alloys in squeeze casting. Trans Nonferrous Metals Soc China 23(4):977–982 Senthil P, Amirthagadeswaran KS (2014) Experimental study and squeeze casting process optimization for high quality AC2A aluminium alloy castings. Arab J Sci Eng 39(3):2215–2225 Souissi N, Souissi S, Lecompte J-P, Amar MB, Bradai C, Halouani F (2015) Improvement of ductility for squeeze cast 2017A wrought aluminium alloy using the Taguchi method. Int J Adv Manuf Technol 78(9–12):2069–2077 Benguluri S, Vundavilli PR, Bhat RP, Parappagoudar MB (2011) Forward and reverse mappings in metal casting—a step towards

PR O O

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quality casting and automation, (11–009). Trans Am Foundry Soc 119(19):1–15 17. Wang RJ, Zeng J, Zhou DW (2012) Determination of temperature difference in squeeze casting hot work tool steel. Int J Mater Form 5(4):317–324 18. Wang RJ, Tan WF, Zhou DW (2013) Effects of squeeze casting parameters on solidification time based on neural network. Int J Mater Prod Technol 46(2):124–140 19. Fuhua S, Fuhua S (2007) Aluminum-zinc alloy squeeze casting technological parameters optimization based on PSO and ANN. China Foundry 4(3):202–205, Article ID: 1672-6421(2007)03 20. Patel GCM, Krishna P and Parappagoudar MB (2014), Forward and reverse process models for the squeeze casting process using neural network based approaches. App Comput Intell Soft Comput, (2014), Article ID 293976, 12 pages 21. Patel GCM, Mathew R, Krishna P, Parappagoudar MB (2014) Investigation of squeeze cast process parameters effects on secondary dendrite arm spacing using statistical regression and artificial neural network models. Procedia Technol 14:149–156 22. Krimpenis A, Benardos PG, Vosniakos GC, Koukouvitaki A (2006) Simulation-based selection of optimum pressure diecasting process parameters using neural nets and genetic algorithms. Int J Adv Manuf Technol 27(5–6):509–517 23. Yarlagadda PKDV, Chiang ECW (1999) A neural network system for the prediction of process parameters in pressure die casting. J Mater Process Technol 89:583–590 24. Zhang L, Wang R (2013) An intelligent system for low-pressure die-cast process parameters optimization. Int J Adv Manuf Technol 65(1–4):517–524 25. Parappagoudar MB, Pratihar DK, Datta GL (2007) Modelling of input–output relationships in cement bonded moulding sand system using neural networks. Int J Cast Met Res 20(5):265–274 26. Mollah AA, Pratihar DK (2008) Modeling of TIG welding and abrasive flow machining processes using radial basis function networks. Int J Adv Manuf Technol 37(9–10):937–952 27. Parappagoudar MB, Pratihar DK, Datta GL (2008) Neural networkbased approaches for forward and reverse mappings of sodium silicate-bonded, carbon dioxide gas hardened moulding sand system. Mater Manuf Process 24(1):59–67 28. Reddy DY, Pratihar DK (2011) Neural network-based expert systems for predictions of temperature distributions in electron beam welding process. Int J Adv Manuf Technol 55(5–8):535–548 29. Parappagoudar MB, Pratihar DK, Datta GL (2008) Forward and reverse mappings in green sand mould system using neural networks. Appl Soft Comput 8(1):239–260 30. Patel GCM, Krishna P, Parappagoudar MB (2015) Modelling of squeeze casting process using design of experiments and response surface methodology. Int J Cast Met Res 28(3):167–180

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References

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Modelling of squeeze casting process using design of experiments and response surface methodology M. Patel G C1, P. Krishna1 and M. B. Parappagoudar*2 The present work makes an attempt to model and analyse squeeze casting process by utilising design of experiments and response surface methodology. The input–output data for developing regression models and test cases is obtained by conducting the experiments. Surface roughness, ultimate tensile strength and yield strength have been measured for different combinations of process variables, namely, squeeze pressure, pressure duration, pouring temperature and die temperature. Two non-linear regression models based on central composite design (CCD) and Box-Behnken design (BBD) of experiments have been developed to establish the input–output relationships. The effects of process variables on the measured responses have been studied using surface plots. The performances of the two non-linear models have been tested for their prediction accuracy with the help of 15 test cases. It is observed that, both CCD and BBD, the non-linear regression models are statistically adequate and capable of making accurate predictions. Keywords: Squeeze casting, CCD, BBD, ANOVA, RSM

Introduction Squeeze casting is one of the near net-shape casting processes, developed with the desirable features of both conventional forging and casting process. Hence squeeze casting is also known as extrusion casting, pressurised crystallisation, liquid metal forging, liquid pressing and squeeze forming.1 A lot of research work has been carried out throughout the world, using conventional engineering approach, where one parameter at a time is varied to study the effect of variables. Experiments have been conducted by the researchers2,3 to study the effects of pouring temperatures and squeeze pressure on some properties of squeeze cast aluminium alloys. It is important to note that the die temperature and pressure duration effect were not considered in their analysis. The applied squeeze pressure effects on the mechanical and microstructure properties of Al–Cu alloys4 and bronze5 components were studied. It should be observed that the die temperature, pouring temperature and pressure duration were not included in their investigation. The effects of applied pressure, time delay, degassing, inoculants, die and pouring temperatures on the formation of the macrosegregation of Al–Si alloys were investigated.6 Oxide inclusion, segregations, under filling

1

Department of Mechanical Engineering, National Institute of Technology Karnataka, Surathkal 575025, India Department of Mechanical Engineering, Chhatrapati Shivaji Institute of Technology, Durg (C.G) 491001, India

2

*Corresponding author, email [email protected]

ß 2015 W. S. Maney & Son Ltd. Received 18 August 2014; accepted 23 December 2014 DOI 10.1179/1743133614Y.0000000144

or over filling, cold laps, sticking, hot tear, case debonding, extrusion and extrusion segregation have a large impact on the quality of squeeze casting.7 Accurate control of the process variables is one of means to reduce the probability of occurrence of the above-said defects. The relationship among properties and process variables is complex in nature. The use of conventional engineering approach may not help the foundry men in selection of most influencing process variables unless the input–output relationships are expressed in mathematical form. This has led the researchers to search for an alternative tool to study, identify, control, analyse and establish the complex input–output relationships for better quality and improved productivity in manufacture of cast components. Statistical design of experiments (DOE) refers to the method of planning the experiments, collecting the appropriate set of data from the planned experiments, and analysing the data using regression analysis to draw meaningful conclusion on the developed input–output relationship of the system.8 Considerable research has been carried out by the distinguished researchers using design of experiments and statistical Taguchi method to tackle problems related to the squeeze casting process. The squeeze cast process variable effects on the surface roughness of the LM6 cast components were investigated.9,10 However, the effect of influencing parameters such as pressure duration and pouring temperature was not considered in their analysis. Later on, the authors extended their work to study the effects of pressure duration on the mechanical properties of LM24 squeeze

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cast components.11,12 Further, the pouring temperature, which influences the mechanical properties, was not considered in their work. The Taguchi matrix of squeeze casting conditions was utilised to study the major quality characteristics namely wear-resistance, tensile strength and hardness of the squeeze cast AC2A alloy.13–15 The effect of process parameters on strength and ductility of the aluminium silicon alloys cast components was studied using Taguchi method.16 More recently, the effects of squeeze pressure, pouring and die temperature were also studied using Taguchi method to analyse the impact on surface roughness, density,17 ultimate tensile strength and hardness18 of squeeze cast components. It is to be noted that, the effect of pressure duration was not considered in their analysis. It is proved from the above literature that statistical Taguchi method can be used to tackle the various problems related to squeeze casting process. However, the following key observations have been made from the published work: (i) the Taguchi recommended orthogonal array designs are limited in number and may fail to test all interaction effect of the process variables under investigation19 (ii) the knowledge of behaviour of the response is a pre-requisite for accurate control of the process and this can be effectively analysed and understood with the help of response surface plots (iii) the developed response equations derived through real experiments may fail to provide all main, square and interaction effects (combined) of the process variables (iv) it is also important to note that the practical utility of (that is, testing of the model prediction capability with the help test cases) the developed response equations were not tested by many of the researchers. The limitations of Taguchi experimental design can be tackled effectively by using the full factorial design (FFD) of experiments and response surface methodology. The effects of squeeze pressure, die temperature and strontium modifier on strength and ductility of AlSi7Mg components were studied with two-level FFD of experiment.20 It is important to note that two-level FFD has the capability to provide complete information of individual and the combined effect of process variables on the response. However, with this approach it is possible to develop only linear input–output relationships (regression models). Hence, though the number of experiments is less it fails to detect the curvature effect (if any) in the response function. The curvature effect in the response surface can be detected by conducting experiments with process parameters set at minimum of three levels. The number of experiments increases with the increase in number of parameters and their levels (Refer equation [1]) Number of experiments~(Levels)Factors

which require the input variables to be set at three or more number of levels. The CCD refers to rotatable, if the prediction accuracy of the output is the same on the sphere around the design centre. However, rotatable designs require the input variables to be set at five levels. On the other hand, non-rotatable design requires the input variables to be set at three levels. It is of primary importance to note that use of either rotatable or nonrotatable designs depends on the geometric nature of the practical constraints on the design region. The rotatable designs should not be followed strictly unless the practical consideration dictates.8,21 Hence, in the present work, the non-rotatable CCD is employed, wherein the input variables are set at three levels. Box-Behnken design, considered to either rotatable or nearly rotatable design, is formed by combining 2k factorials with incomplete block designs, where k is the number of input parameters.21 Response surface methodology has been successfully implemented by various investigators to model different processes, namely, machining,22 casting,23 welding24 and sand moulds.25–27 It is to be noted that, a lot of research work, with the application of response surface methodologies in various manufacturing processes is reported in the literature. It is also important to mention that not much work has been reported to model the squeeze casting process using nonlinear regression models. Surface roughness and tensile strength are considered to be the major quality characteristics in the present study. Better surface finish is desirable for foundry men, as the product can be readily used in service without any secondary manufacturing process (plating, polishing, machining, shot blasting, etc.). The tensile strength in a cast component depends on material internal characteristics, such as porosity, segregations, shrinkages, etc. These defects, when present in the casting decrease the available load area, promote stress concentrations, and crack initialisations. This results in reduced tensile strength and the component may catastrophically fail during its service.28 In general, the fatigue properties are related to surface roughness, tensile strength and microstructure. The cast defects like porosity and formation of aluminium skin are of paramount importance, since these defects are usually larger at the outer surface than other microstructural features.29 Surface roughness should be very low and tensile strengths should be as high as possible in order to ensure better quality. It is to be noted that, the relationships between these responses are normally conflicting in nature. For foundry men, selection of most influential process parameters is of paramount importance in order to maximise throughput with reduced cost and energy consumption. Hence, the present work focuses on establishing the complex non-linear input–output relationships by utilising statistical tools like DOE and RSM. In addition to this, attempts have been made to analyse complex relationships of input variables on surface roughness, ultimate tensile and yield strengths with the help of surface plots. The present work consists of developing regression models for the squeeze casting process. Design of experiments along with RSM based on CCD and BBD have been used for the said purpose. The influence and relation of each process variable on responses have been studied with the help of surface plots. Both CCD and

(1)

Response surface methodology is a collection of mathematical and statistical techniques used to establish the input–output relationships and identifies the curvature effects in the response function. Box-Behnken design (BBD) and central composite design (CCD) are the major classes of response surface methodologies,

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BBD models have been tested for their statistical adequacy and further, their prediction accuracy is tested utilising test cases.

the amount of flash and cycle time.32 The process parameters and their corresponding levels used in the present study are shown in Table 1.

Methodology

Step 2: conduction of experiments

The present work consists of following steps.

Step 1: selection of process variables and their corresponding levels The selection of process parameters and decision on their operating range is of primary importance for the systematic study and to establish good control over the process. In the present work, the process variables and their operating range have been selected based on some trial experiments conducted in the research laboratory and consulting available literature. For trial experiments, the squeeze casting process variables such as squeeze pressure, pressure duration, time delay, die temperature and pouring temperature are selected with wide range and analysed there effects on different responses using statistical analysis.30 The results showed the pressure and temperature related parameters have a large influence on the quality of component in squeeze casting. Moreover, time delay of four seconds in bringing the punch to come in contact with the molten metal gives better tensile strengths and surface finish.30 Therefore in the present work, the following process parameters were considered for experimentation: (i) squeeze pressure (ii) pressure duration (iii) pouring temperature (iv) die temperature. Applied squeeze pressure may have direct influence on porosity, segregation, microshrinkage, mechanical and microstructure properties. Low squeeze pressure may not be sufficient to eliminate all possible gasses, resulting in gas porosity. Whereas, high pressure eliminates all possible gasses, resulting in improved heat transfer rate and leading to better mechanical and microstructure properties.31 However, high pressure requires large tonnage equipment facilities and also leads to reduction in the die life. It is to be noted that, squeeze cast component properties will not significantly improve beyond certain value of squeeze pressure.31 Short pressure duration leads to unsatisfactory results, since the punch has been withdrawn before the complete solidification occurs. On the other hand, long pressure duration affects the die life and increases the problem of punch retraction and cycle time. Too low pouring and die temperature results in premature solidification whereas, higher die and pouring temperature results in hot tears, shrinkage pores and problems with die sticking/welding.31,32 Low die temperature will result in fatigue failure of the dies and high temperature increases

The yield strength, ultimate tensile strength and surface roughness of the squeeze cast components have been measured for the different combinations of process variables. The experiments have been conducted to develop non-linear regression models as per the design matrices and to test the developed models (test cases). The design matrix for CCD and BBD used to collect the experimental data is presented in Table 2. Experimental work and data collection is explained in the subsequent section of the paper.

Step 3: developing non-linear models The non-linear regression models based on CCD and BBD have been developed for the responses – surface roughness, yield strength and ultimate tensile strength.

Step 4: statistical analysis and comparison of developed models Analysis of variance (ANOVA) is performed to check the statistical adequacy of each response separately. The prediction accuracy of the developed models is compared with the help of fifteen test cases and the best model is selected for each response.

Step 5: testing of models The non-linear regression models developed were further tested for their prediction capability with the help of test cases.

Experimental details Materials Inherent properties, such as excellent fluidity, pressure tightness, free from hot tears, wear and corrosion resistance led to the wide use of LM20 aluminium alloys as casting material. These properties find major applications in water jackets, marine applications, casting subjected to atmosphere exposure, street lighting, automobile, general purpose engineering application, office equipments and domestic appliances. The LM20 alloy has been used in automobile component mounting flange encoder.33 H13 chromium molybdenum based hot die steel heat treated to 45–48 Rc was used to withstand die wall cracking, thermal fatigue, corrosion, erosion and indentation.2 The chemical analysis of the casting and die material has been made with the help of optical emission spectrometer (OES). The chemical analysis results obtained through OES are shown in Table 3.

Table 1 Process parameters and their respective levels Process parameters

Levels

Description

Uncoded

Coded

Units

Low (21)

Middle (0)

High (z1)

Pressure duration DP Squeeze pressure SP Pouring temperature Pt Die temperature Dt

A B C D

X1 X2 X3 X4

S MPa uC uC

20 40 630 150

35 80 675 225

50 120 720 300


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Table 2 Design matrix for non-linear regression models* Central composite design (CCD) Process parameters

Box-Behnken design (BBD) Responses

Ex. no.

A

B

C

D

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27

21 1 21 1 21 1 21 1 21 1 21 1 21 1 21 1 21 1 0 0 0 0 0 0 0 0 0

21 21 1 1 21 21 1 1 21 21 1 1 21 21 1 1 0 0 21 1 0 0 0 0 0 0 0

21 21 21 21 1 1 1 1 21 21 21 21 1 1 1 1 0 0 0 0 21 1 0 0 0 0 0

21 21 21 21 21 21 21 21 1 1 1 1 1 1 1 1 0 0 0 0 0 0 21 1 0 0 0

SR

Process parameters

YS

UTS

Responses

A

B

C

D

0 0 21 0 21 1 0 0 0 1 0 1 21 1 21 0 0 21 0 0 0 21 0 0 0 1 1

1 0 1 0 0 1 21 1 21 0 0 0 0 21 0 1 0 21 0 0 21 0 0 21 1 0 0

1 0 0 0 0 0 1 21 0 0 0 21 1 0 21 0 21 0 1 1 21 0 21 0 0 0 1

0 0 0 0 1 0 0 0 1 21 0 0 0 0 0 1 21 0 1 21 0 21 1 21 21 1 0

SR

YS

UTS

*SR, surface roughness; YS, yield strength; UTS, Ultimate tensile strength.

Experimental procedure

that, test specimen for yield strength and ultimate tensile strength is prepared as per ASTM E8 standard. For each casting condition, six tensile specimens were prepared to measure the yield and ultimate tensile strength. The tensile specimens and electronic tensometer used are shown in Fig. 1b and c, respectively. Surface roughness of squeeze cast specimen has been measured at three different locations (see Fig. 1d ) using Mitutoyo surftest SJ301. To reduce the variation, average of nine different surface roughness values are taken for each casting condition. The surface roughness measurement is performed as per JIS 2001 standard. The device used for measurement of surface roughness is shown in Fig. 1e.

Metered quantity of the molten metal is poured into the pre-heated cylindrical die cavity, pressure is then applied through punch fitted at the middle of the cross head of a 40 tonne universal testing machine. The punch is withdrawn and the solidified casting is ejected. The experiments have been conducted as per the CCD and BBD matrices and three replicates have been considered for each casting condition. Determination of yield strength, ultimate tensile strength and surface roughness

Experiments have been carried out to measure the surface roughness, yield and ultimate tensile strength of the squeeze casting sample. The specimens were prepared for different values of process variables as per standard experimental design matrix (Refer Table 2). The cylindrical castings (108 mm height and 36 mm diameter) are sectioned on both sides and the casting structure used for characterisation is shown in Fig. 1a. Yield strength and ultimate tensile strength were measured using electronic tensometer. It is to be noted

Results and discussion The present section discusses development and analysis of non-linear regression models based on CCD and BBD approaches. It is to be noted that, experimental data has been collected to develop the non-linear regression models and to test them by conducting experiments. Minitab

Table 3 Chemical composition of LM 20 Alloy Element

Cu

Mg

Si

Fe

OES analysis 0.18 0.17 10.41 0.29 Chemical composition of H13 Hot die steel Element C Mn Si Cr OES analysis 0.39 0.38 1.0 4.9

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Mn

Ni

Zn

Pb

Sn

Ti

Al

Others

0.5

0.02

0.20

0.005

0.005

0.17

87.84

0.017Cr

P 0.019

Mo 1.17

V 0.79

Fe 90.91

S 0.008

Others 0.433

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1 a casting structure (all dimensions are in mm), b tensile specimen, c electronic tensometer, d surface roughness measurement locations, and e surface roughness tester

software is utilised to develop the non-linear regression models and analyse the input–output relationships.

SRCCD ~0:643333{0:02X1 {0:345X2 { 0:034167X3 {0:125833X4 z

Development of mathematical model and statistical analysis

0:065833X12 z0:158333X22 z

The non-linear models based on CCD and BBD were developed based on the experimental data and analysis has been made response-wise using significance and ANOVA tests. In addition, the developed input–output relationships were studied by utilising main and interaction effect plots (surface plots) for the responses – surface roughness, yield and ultimate tensile strength.

0:037083X32 z0:087083X42 z

(3)

0:0725X1 X2 z0:01X1 X3 z0:0125X1 X4 z0:03X2 X3 z 0:0625X2 X4 {0:0075X3 X4

Response surface roughness

The non-linear regression models based on CCD and BBD have been developed for the response surface roughness with the process parameters set at three levels. The input–output relationship for the response surface roughness was derived based on the collected experimental data, using MINITAB software. The non-linear input–output relationship has been developed for the response, surface roughness as per CCD and BBD and is expressed in coded form in equations (2) and (3) respectively. The detailed procedure of obtaining the regression equations is included in the Appendix 2.

SRCCD ~0:785556{0:030556X1 {0:366667X2 { 0:059444X3 {0:107778X4 z0:005X12 z 0:11X22 z0:055X32 {0:05X42 z0:01625X1 X2 z (2) 0:01625X1 X3 {0:0025X1 X4 z0:00375X2 X3 z 0:0325X2 X4 {0:02X3 X4

Table 4 Significance test results, coefficients, standard error coefficients, T statistics and P values obtained using CCD model for response surface roughness (SR)

Constant X1 X2 X3 X4 X12 X22 X32 X42 X1 X2 X1 X3 X1 X4 X2 X3 X2 X4 X3 X4

Coefficient

SE Coefficient

T

P

0.785556 20.030556 20.366667 20.059444 20.107778 0.005000 0.110000 0.055000 20.050000 0.016250 0.016250 20.002500 0.003750 0.032500 20.020000

0.010740 0.006869 0.006869 0.006869 0.006869 0.018174 0.018174 0.018174 0.018174 0.007286 0.007286 0.007286 0.007286 0.007286 0.007286

73.146 24.448 253.38 28.654 215.69 0.275 6.053 3.026 22.751 2.23 2.23 20.343 0.515 4.461 22.745

0.000 0.001 0.000 0.000 0.000 0.788 0.000 0.011 0.018 0.046 0.046 0.737 0.616 0.001 0.018


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2 Surface plots of surface roughness with a pressure duration and Squeeze pressure, b pressure duration and pouring temperature, c pressure duration and die temperature, d squeeze pressure and pouring temperature, e squeeze pressure and die temperature and f pouring temperature and die temperature

held at constant will reduce the surface roughness drastically (Refer Fig. 2a). This is because the applied squeeze pressure at higher level pushes the molten metal close to the die walls and does not allow the punch to retract from the die surface

The significance test results for the response surface roughness using CCD model are presented in Table 4. The information on the significance of process parameters, their square terms and all two parameter interactions is provided in the above-said table. The significance test has been conducted for all terms mentioned in equation (2) at 95% confidence level. The terms, X1, X2, X3, X4, X22, X32, X42, X1X2, X1X3, X2X4 and X3X4 are found to make significant contribution towards the response, as their corresponding P values are found to be less than 0?05 (Refer Table 4). It is also important to note that, the square terms of X2, X3 and X4 are found to have less than P values of 0?05, indicating that the relationship between the squeeze pressure, pouring and die temperature with the response surface roughness might be non-linear in nature, whereas, the square term of X1 is found to be insignificant, indicating linear relationship of the pressure duration and surface roughness. It is important to mention that, the results obtained in significant test are found to match with those obtained in surface plots. Surface plot for the response surface roughness is presented in Fig. 2. Following observations have been made from the study of surface plots obtained for the response surface roughness based on CCD approach: (i) increase in squeeze pressure and pressure duration with the pouring and die temperature

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Table 5 Significance test results, coefficients, standard error coefficients, T statistics and P values obtained using BBD model for response surface roughness (SR)

Constant X1 X2 X3 X4 X12 X22 X32 X42 X1 X2 X1 X3 X1 X4 X2 X3 X2 X4 X3 X4

NO

3

Coefficient

SE Coefficient

T

P

0.643333 20.020000 20.345000 20.034167 20.125833 0.065833 0.158333 0.037083 0.087083 0.072500 0.010000 0.012500 0.030000 0.062500 20.007500

0.02113 0.01057 0.01057 0.01057 0.01057 0.01585 0.01585 0.01585 0.01585 0.01830 0.01830 0.01830 0.01830 0.01830 0.01830

30.445 21.8930 232.653 23.2340 211.910 4.154 9.990 2.340 5.495 3.962 0.546 0.683 1.639 3.415 20.410

0.000 0.043 0.000 0.007 0.000 0.001 0.000 0.037 0.000 0.002 0.595 0.508 0.127 0.005 0.689

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Table 6 Coefficient of multiple corelation and insignificant terms of non-linear models for response SR Model

Corelation coefficient with all R terms

Corelation coefficient without insignificant terms

Insignificant terms

CCD BBD

0.9964 0.9913

0.9922 0.9811

AA, AD, BC AC, AD, BC, CD

(ii) increase in pouring temperature drastically reduces the surface roughness up to the midvalues; however, further increase in pouring temperature will not have much impact on surface roughness (Refer Fig. 2b). This is due to the fact that increase in pouring temperature results in improved fluidity of aluminium alloys (iii) surface roughness decreases drastically with increasing pressure duration and die temperature (Refer Fig. 2c), while keeping squeeze pressure and pouring temperature at their respective mid-values (iv) surface roughness decreases drastically with increasing squeeze pressure and pouring temperature. The resulting surface plot (Fig. 2d ) is found to be almost flat, indicating a strong linear relationship with surface roughness (v) Fig. 2e shows almost similar trend as that of Fig. 2d, that is, increase in squeeze pressure decreases surface roughness rapidly and linearly whereas, die temperature, shows slight curvature effect (vi) surface roughness decreases with increasing pouring temperature. However, surface roughness values are found to decrease rapidly with the increasing die temperature (Refer Fig. 2f ). Major conclusions drawn from the study of surface plots are listed below: (i) squeeze pressure, pouring and die temperature have shown significant contribution towards surface roughness (ii) pressure duration is found to have negligible effect on surface roughness (iii) the squeeze pressure shows dominating contribution on surface roughness as compared to the rest of the parameters. The significance test has been conducted at 95% confidence level for all terms used in equation (3) (refer Table 5). The terms, X1, X2, X3, X4, X12, X22, X32, X42, X1X2 and X2X4 are found to be significant for the nonlinear regression model based on BBD. Further, surface plots obtained for this response using BBD is found to almost similar in nature as that of CCD. The process parameters can be coded using the following relationships

A{35 B{80 , X2 ~ , 15 40 C{675 D{225 , X4 ~ X3 ~ 45 75 X1 ~

X1, X2, X3 and X4 indicates the process parameters namely pressure duration A, squeeze pressure B, pouring temperature C and die temperature D in coded form respectively. The response equations (refer equations (2) and (3)) for surface roughness, have been expressed in uncoded form and presented below SRCCD ~15:2320{0:0215093A{0:0249583B{ 0:0376636Cz0:00577407Dz2:22222 |10{5 A2 z6:875|10{5 B2 z2:71605|10{5 C 2 { 8:88889|10{6 D2 z2:70833|10{5

(4)

ABz2:40741|10{5 AC{2:22222|10{6 ADz 2:08333|10{6 BCz1:08333|10{5 BD{5:92593|10{6 CD SRBBD ~14:1026{0:0439815A{0:044625B{ 0:0268333C{0:0092Dz0:000292593A2 z9:89583|10{5 B2 z1:83128|10{5 C 2 z 1:54815|10{5 D2 z0:000120833AB z1:48148|10

{5

ACz1:11111|10

(5)

{5

ADz

1:66667|10{5 BCz2:08333|10{5 BD {2:22222|10{6 CD where A, B, C and D represents the process parameters namely pressure duration, squeeze pressure, pouring temperature and die temperature respectively in uncoded (real) form. The significance test has been carried out for both CCD and BBD based regression models separately and the insignificant terms are identified for the response surface roughness (Refer Table 6). Moreover, the coefficient of multiple correlations have been determined to statistically test the

Table 7 ANOVA results for response surface roughness Design

Central composite

Box-Behnken

Source

DF

Seq. SS

Adj. SS

Adj. MS

F

P

Seq. SS

Adj. SS

Adj. MS

F

P

Regression Linear Square Interaction Residual error Lack of fit Pure error Total

14 4 4 6 12 10 2 26

2.83448 2.70950 0.09290 0.03207 0.01019 0.01013 0.00007 2.84467

2.83448 2.70950 0.09290 0.03207 0.01019 0.01013 0.00007

0.202463 0.677375 0.023225 0.005346 0.000849 0.001013 0.000033

238.39 797.56 27.35 6.29

0.000 0.000 0.000 0.003

0.130267 0.015607 0.036279 0.006917 0.001340 0.001401 0.001033

0.000 0.000 0.000 0.008

0.032

1.82373 0.06243 0.14512 0.04150 0.01608 0.01401 0.00207

97.24 11.65 27.08 5.16

30.38

1.82373 1.63712 0.14512 0.04150 0.01608 0.01401 0.00207 1.83981

1.36

0.497


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3 Surface plots of yield strength with a pressure duration and squeeze pressure, b pressure duration and pouring temperature, c pressure duration and die temperature, d squeeze pressure and pouring temperature, e squeeze pressure and die temperature and f pouring temperature and die temperature

accuracy of the developed models. The ANOVA has been performed to test the significance of the main, square and interaction parameters of the developed models. The results of ANOVA tests for both CCD and BBD based non-linear regression models are presented in Table 7 for the response surface roughness. It is important to note that all linear, square and interactions terms are found to be significant as their corresponding P values are found to be less than 0?05 for both the models. However, lack of fit is found to be significant for BBD model. It is to be noted that, removal of insignificant terms from the model makes the regression equation simpler but reduces the prediction accuracy of the model. The significance and ANOVA test results along with the coefficient of correlation values indicate that both regression models based on CCD and BBD are statistically adequate for the response surface roughness.

Response yield strength

The non-linear regression equations derived for the response yield strength using CCD and BBD approach are as follows

YSCCD ~{1071:38{1:26601A{0:797501Bz 3:36494Cz0:902819Dz0:0123095A2 z0:00276227B2 {0:00238537C 2 { 8:58733|10{4 D2 z0:00253125AB z0:000101852ACz0:000627778ADz 0:000746528BCz0:00034375BD {8:87037|10{4 CD

Table 8 Coefficient of multiple corelation and insignificant terms of non-linear models for response yield strength

174

Model

Corelation coefficient with all terms R


Insignificant terms

CCD BBD

0.9793 0.9861

0.9551 0.9699

A, AA, AC, AD, BD AA, AB, AD, BD


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Table 9 Results of ANOVA – yield strength (non-linear models) Design

Central composite

Box-Behnken

Source

DF

Seq. SS

Adj. SS

Adj. MS

F

P

Seq. SS

Adj. SS

Adj. MS

F

P


14 4 4 6 12 10 2 26

3363.89 2957.45 172.17 234.27 71.13 50.25 20.88 3435.02

3363.89 287.83 172.17 234.27 71.13 50.25 20.88

240.28 71.958 43.043 39.045 5.928 5.025 10.442

40.54 12.14 7.26 6.59

0.000 0.000 0.003 0.003

112.378 33.543 33.951 9.079 1.848 1.750 2.333

0.000 0.000 0.000 0.009

0.824

1573.29 134.17 135.80 54.48 22.17 17.50 4.67

60.83 18.16 18.38 4.91

0.48

1573.29 1383.01 135.80 54.48 22.17 17.50 4.67 1595.46

0.75

0.693

YSBBD ~{732:29{2:29333A{0:60625Bz 2:49204Cz0:505444Dz0:00394444A2 {9:60938|10{4 B2 {0:00187037C 2 { 5:17778|10{4 D2 z0:000541667AB

(7)

z0:00259259ACz0:000755556ADz 0:00141667BCz0:000166667BD {5:11111|10{4 CD The insignificant terms identified and coefficient of correlation values for both CCD and BBD based nonlinear models are presented in Table 8. Following observations have been made from the surface plots of yield strengths based on BBD approach: (i) yield strength was found to increase rapidly with increasing pressure duration as shown in Fig. 3a. Response surface is found to be almost flat indicating a strong linear relationship with these input parameters for the said response. It is also observed that contribution of squeeze pressure towards this response is more compared to that of pressure duration (ii) yield strength has shown non-linear relationship with pouring temperature, whereas its effect with pressure duration seems to be linear (Fig. 3b). However, compared to the pressure duration, pouring temperature shows major contribution (iii) increase in die temperature shows slight increase in yield strength up to the mid-values and there after decreases drastically (Refer Fig. 3c), whereas, with increasing pressure duration, there is negligible change in the yield strength (iv) yield strength is found to increase with increasing squeeze pressure and seems to increase initially with die temperature and remains unchanged after the mid-values of pouring temperature (see Fig. 3d ). It is also observed

that the effect of squeeze pressure is more significant than die temperature for this response (v) an increase in squeeze pressure would increase the yield strength linearly, whereas, there is negligible change in yield strength with increase in die temperature as shown in Fig. 3e (vi) with the increase in both die and pouring temperature, the yield strength increases initially and later decreases with further increasing pouring and die temperature (refer Fig. 3f ). The reason might be due to premature solidification at low temperature and on the other hand, high temperature paves way for formation of segregations, shrinkages and increased solidification time. Thus, reducing heat transfer rate result in decreased yield strength. The results of ANOVA test of the non-linear models for the response yield strength is presented in Table 9. It is important to note that the linear, interaction and square terms are considered to be significant (as the P value is less than that of the confidence level 0?05). However lack of fit exists for both non-linear models is found to be insignificant, as the P value is seen to be more than 0?05. Thus the models are statistically adequate for making prediction of yield strength. Response ultimate tensile strength

The non-linear regression equations developed by using CCD and BBD approaches are presented below UTSCCD ~{2310:46z0:678584A{1:09405Bz 6:99702Cz1:24816Dz0:00652181A2 z0:00622963B2 {0:0048556C 2 { (8)

6:0135|10{4 D2 z0:00426667AB {0:00235185ACz0:000122222ADz 0:000569444BCz0:000241667BD {0:00154741CD

Table 10 Coefficient of multiple co-relation and insignificant terms of non-linear models for response ultimate tensile strength Model

Corelation coefficient with all R terms


Insignificant terms

CCD BBD

0.9736 0.9870

0.9429 0.9719

A, AA, DD, AC, AD, BC, BD AA, AB, AD


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a central composite design; b Box-Benkhen design 4 Comparison of model predicted surface roughness with actual surface roughness

Response-wise performance of the model is presented below.

UTSBBD ~{1176:2{4:71685A{1:29458Bz 3:97148Cz0:932667D{0:00137037A2

Response surface roughness

z0:00234635B2 {0:00293004C 2 { 8:21481|10{4 D2 z0:00354167AB

Experiments have been conducted for the 15 randomly generated test cases and the performances of the developed non-linear regression models are compared for the response surface roughness. The line of best fit is used to make the said comparison (Refer Fig. 4).That is, the measured values of the response are compared with those of the corresponding model predicted values. It has been observed that, the best fit line obtained for the BBD model shown in Fig. 4b, is found to have a slight deviation from the ideal, y5x line. However, majority of the data points are seen to lie close to the ideal line for CCD indicating better prediction when compared to the BBD for the response, surface roughness (see Fig. 4a). The values of percent deviation in prediction are found to lie in the range of 214?86 to z9?89 for CCD, and 26?52 to z24?66 for BBD based regression models respectively (see Fig. 5a). In BBD model, most of the data points are found to be lie on the positive side, whereas, the data points are distributed on either side of the reference lines for CCD model. It is also important to note that CCD model has shown better prediction, in terms of average absolute percent deviation, for the response surface roughness (see Fig. 6b).

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z0:00651852ACz4:44444|10{5 ADz 0:00155556BCz0:001025BD {0:00102693CD The coefficient of multiple correlation and the insignificant terms identified for the response ultimate tensile strength for both the non-linear models is presented in Table 10. The results of ANOVA tests showed that all linear, interaction and square terms are significant at 95% confidence level as their P value is found to be less than 0?05 (Refer Table 11). Although lack of fit exists, it is found to be in-significant, since; their P values are found to be more than 0?05 for both models. The results of ANOVA and coefficient of correlation values indicate that, the non-linear regression models based on CCD and BBD are statistically adequate.

Testing and comparison of models

Response ultimate tensile strength

It is to be noted that both non-linear models based on CCD and BBD have been tested for their statistical adequacy in the previous section. The performances of the developed models for their prediction capability have been tested with the help of fifteen test cases.

Comparison of the model predicted values with their respective target values through the best fit line, is shown in Fig. 7. Since the data points are evenly distributed on either sides of the ideal trend line, the BBD performs

Table 11 Results of ANOVA – ultimate tensile strength (non-linear models) Design

176

Central composite

Box-Behnken

Source

DF

Seq. SS

Adj. SS

Adj. MS

F

P

Seq. SS

Adj. SS

Adj. MS

F

P


14 4 4 6 12 10 2 26

8312.85 7273.83 431.93 607.09 225.12 194.11 31.01 8537.97

8312.85 7273.83 431.93 607.09 225.12 194.11 31.01

593.78 1818.46 107.98 101.18 18.76 19.41 15.50

31.65 96.93 5.76 5.39

0.000 0.000 0.008 0.006

420.551 105.435 124.648 35.500 6.455 6.542 6.023

0.000 0.000 0.000 0.006

0.523

5887.71 421.74 498.59 213.00 77.46 65.42 12.05

65.15 16.33 19.31 5.50

1.25

5887.71 5176.12 498.59 213.00 77.46 65.42 12.05 5965.17

1.09

0.570


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a surface roughness; b ultimate tensile strength 5 Standard deviation in prediction of test cases

6 a standard deviation in prediction of yield strength for 15 test cases and b comparison of models in terms of average absolute percent deviation in prediction of test cases for different responses

a central composite design; b Box-Benkhen design 7 Comparison of model predicted ultimate tensile strength with actual ultimate tensile strength

slightly better as compared to the CCD. Furthermore, the percent deviation in prediction is found to lie in the range of 24?3 to z2?93 for CCD and 24?61 to z2?68 for BBD models. It is also important to mention that most of the data points as predicted by the CCD model lie below the line of best fit, as shown in Fig. 5b. Moreover the BBD model shows slightly better performance in terms of mean absolute percent deviation in predicting this response (refer Fig. 6b).

The values of yield strength as predicted by the nonlinear models based on CCD and BBD are compared with their respective experimental values using best fit line as shown in Fig. 8. The best fit line is found to be close to ideal line for the regression model based on CCD. Further, most of the data points are found to be closer to the best fit line for CCD model as compared to BBD. The percent deviation in prediction of the test cases for this response is found to vary in the range of


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a central composite design; b Box-Benkhen design 8 Comparison of model predicted yield strength with actual yield strength

26?67 and z2?3 for CCD model, and 28?89 to z6?65 for BBD model respectively (Refer Fig. 6a). The response-wise absolute percent deviation for the CCD and BBD based non-linear regression models is shown in Fig. 6b. The average absolute percent deviation in prediction using CCD model is found to be better for the responses of surface roughness and yield strength, whereas BBD model showed slightly better performance in prediction of the response, ultimate tensile strength. The better performance might be due to the ability to accurately capture the non-linearity of the process.

know the more influencing process parameters in the squeeze casting process. The regression models can be used to predict the response values without conducting experiments for the set of process parameters.

Acknowledgement The authors acknowledge with gratitude the kind help and support received from the Department of Applied Mechanics and Hydraulics of NIT Karnataka, Surathkal, India, in carrying out the actual experiments.

References Concluding remarks

1. M. R. Ghomashchi and A. Vikhrov: ‘Squeeze casting: an overview’, J. Mater. Process. Technol., 2000, 101, (1), 1–9. 2. A. Raji and R. H. Khan: ‘Effects of pouring temperature and squeeze pressure on Al-8%Si alloy squeeze cast parts’, AU JT, 2006, 9, (4), 229–237. 3. T. M. Yue: ‘Squeeze casting of high-strength aluminium wrought alloy AA7010’, J. Mater. Process. Technol., 1997, 66, (1), 179–185. 4. M. Zhang, W. W. Zhang, H. D. Zhao, D. T. Zhang and Y. Li: ‘Effect of pressure on microstructures and mechanical properties of Al-Cu-based alloy prepared by squeeze casting’, Trans. Nonferrous Met. Soc. China, 2007, 17, (3), 496–501. 5. P. Vijian and V. P. Arunachalam: ‘Experimental study of squeeze casting of gunmetal’, J. Mater. Process. Technol., 2005, 170, 32–36. 6. C. P. Hong, S. M. Lee and H. F. Shen: ‘Prevention of macrodefects in squeeze casting of an Al-7 wt pct Si alloy’, Metall. Mater. Trans. B, 2000, 31B, (2), 297–305. 7. D. J. Britnell and K. Neailey: ‘Macrosegregation in thin walled castings produced via the direct squeeze casting process’, J. Mater. Process. Technol., 2003, 138, (1), 306–310. 8. D. C. Montgomery: ‘Design and analysis of experiments’, 5th edn; 2001, New York, John Wiley & Sons. 9. P. Vijian and V. P. Arunachalam: ‘Optimization of squeeze cast parameters of LM6 aluminium alloy for surface roughness using Taguchi method’, J. Mater. Process. Technol., 2006, 180, 161–166. 10. P. Vijian, V. P. Arunachalam and S. Charles: ‘Study of surface roughness in squeeze casting LM6 aluminium alloy using taguchi method’, Ind. J. Eng. Mater. Sci., 2007, 14, 7–11. 11. P. Vijian and V. P. Arunachalam: ‘Modelling and multi objective optimization of LM24 aluminium alloy squeeze cast process parameters using genetic algorithm’, J. Mater. Process. Technol., 2007, 186, (1), 82–86. 12. P. Vijian and V. P. Arunachalam: ‘Optimization of squeeze casting process parameters using taguchi analysis’, Int. J. Adv. Manuf. Technol., 2007, 33, 1122–1127. 13. Senthil P and Amirthagadeswaran KS: ‘Optimization of squeeze casting parameters for non symmetrical AC2A aluminium alloy castings through Taguchi method’, J. Mater. Process. Technol., 2012, 26, (4), 1141–1147. 14. P. Senthil and K. S. Amirthagadeswaran: ‘Experimental study and squeeze casting process optimization for high quality AC2A

Modelling has been carried out to determine the input– output relationships of the squeeze casting process utilising the two non-linear regression models namely CCD and BBD of experiments. The effect of each of the process parameters on responses have been studied with the help of response surface plots. It is found that surface roughness decreases, whereas tensile strength will improve with increasing squeeze pressure. It has been observed that, the surface roughness has more or less linear relationship with squeeze pressure, pouring and die temperature, whereas a non-linear relation with pressure duration. However, tensile strength is found to increase linearly with the squeeze pressure and its duration. Further, tensile strength increases initially and then decreases with an increase in pouring and die temperatures. The result showed that pressure duration parameter has minimum contribution towards all the response. Non-linear regression models based on CCD and BBD have been tested for their statistical adequacy and prediction capability with the help of ANOVA and test cases respectively. It has been observed that all models are found to be statistically adequate. The performances of CCD and BBD have been compared response-wise by utilising test cases. The average absolute percent deviation is used as the criterion to select the best model for each response. It is important to note that, performance of CCD is found to be better in predicting surface roughness and yield strength, whereas, BBD is better for predicting ultimate tensile strength. The present work presents a methodology to model and analyse squeeze casting process utilising statistical tools. Further, it will help foundry men to

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24. V. Gunaraj and N. Murugan: ‘Application of response surface methodology for predicting weld bead quality in submerged arc welding of pipes’, J. Mater. Process. Technol., 1999, 88, (1), 266– 275. 25. M. B. Parappagoudar, D. K. Pratihar and G. L. Datta: ‘Linear and non-linear modeling of cement-bonded moulding sand system using conventional statistical regression analysis’, J. Mater. Eng. Perform., 2008, 17, (4), 472–481. 26. M. B. Parappagoudar, D. K. Pratihar and G. L. Datta: ‘Linear and non-linear statistical modelling of green sand mould system’, Int. J. Cast Met. Res., 2007, 20, (1), 1–13. 27. M. B. Parappagoudar, D. K. Pratihar and G. L. Datta: ‘Modeling and analysis of sodium silicate-bonded moulding sand system using design of experiments and response surface methodology’, J. Manuf. Sci. Prod., 2011, 11, (1–3), 1–14. 28. H. D. Zhao, F. Wang, Y. Y. Li and W. Xia: ‘Experimental and numerical analysis of gas entrapment defects in plate ADC12 die castings’, J. Mater. Process. Technol., 2009, 209, (9), 4537–4542. 29. J. Linder, M. Axelsson and H. Nilsson: ‘The influence of porosity on the fatigue life for sand and permanent mould cast aluminium’, Int. J. Fatigue, 2006, 28, (12), 1752–1758 30. G. C. M. Patel, P. Krishna and M. B. Parappagoudar: ‘Modelling and multi-objective optimization of squeeze casting process using regression analysis and genetic algorithm’, Aust. J. Mech. Eng., in press. 31. W. P. Chen, Y. Y. Li, G. W. Guo, D. T. Zhang, Y. Long and T. L. Nagi: ‘Squeeze casting of Al-Cu alloy’, J. Cent. South Univ. Tech., 2002, 9, (3), 159–164. 32. S. Rajagopal: ‘Squeeze casting: a review and update’, J. Appl. Met. Work., 1981, 14, 3–14. 33. J. K. Kittur and M. B. Parappagoudar: ‘Forward and reverse mappings in die casting process by neural network-based approaches’, J. Manuf. Sci. Prod., 2012, 12, (1), 65–80.

aluminium alloy castings’, Arab. J. Sci. Eng., 2014, 39, (3), 2215– 2225. P. Senthil and K. S. Amirthagadeswaran: ‘Enhancing wear resistance of squeeze cast AC2A aluminum alloy’, Int. J. Eng. Trans. A: Basics, 2013, 26, (4), 365–374. S. B. Bin, S. M. Xing, N. Zhao and L. Li: ‘Influence of technical parameters on strength and ductility of AlSi9Cu3 alloys in squeeze casting’, Trans. Nonferrous. Met. Soc. China, 2013, 23, (4), 977– 982. G. C. M. Patel, P. Krishna and M. B. Parappagoudar: ‘Optimization of squeeze cast process parameters using taguchi and grey relational analysis’, Proc. Tech., 2014, 14, 157–164. N. Souissi, S. Souissi, C. L. Niniven, M. B. Amar, C. Bradai and F. Elhalouani: ‘Optimization of squeeze casting parameters for 2017 A wrought Al alloy using taguchi method’, Metals, 2014, 4, (2), 141–154. I. Mukherjee and P. K. Ray: ‘A review of optimization techniques in metal cutting processes’, Comput. Indust. Eng., 2006, 50, (1), 15– 34. A. Zyska, Z. Konopka, M. La˛giewka and M. Nadolski: ‘Optimization of squeeze parameters and modification of AlSi7Mg alloy’, Arch. Foundry Eng., 2013, 13, (2), 113–116. C. F. J. Wu and M. Hamada: ‘Experiments planning, analysis, and parameter design optimization’, 1st edn; 2000, New York, John Wiley & Sons. K. Maji and D. K. Pratihar: ‘Modeling of electrical discharge machining process using conventional regression analysis and genetic algorithms’, J. Mater. Eng. Perform., 2011, 20, (7), 1121– 1127. K. T. Chiang, N. M. Liu and T. C. Tsai: ‘Modeling and analysis of the effects of processing parameters on the performance characteristics in the high pressure die casting process of Al–SI alloys’, Int. J. Adv. Manuf. Technol., 2009, 41, (11–12), 1076–1084.

Appendix 1 Summary of input–output results of the test cases Squeeze cast process variables

Responses

Exp. no.

DP

SP

Pt

Dt

Ra/mm

UTS/MPa

YS/MPa

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

36 41 33 27 35 42 42 29 32 38 39 36 33 28 34

96 57 55 69 54 117 106 61 68 114 105 55 43 44 41

682 646 661 692 677 684 673 707 680 642 663 684 685 712 702

211 231 213 203 215 230 251 232 256 241 213 202 163 199 203

0.73 1.02 1.08 0.94 0.98 0.46 0.53 0.92 0.74 0.55 0.56 1.08 1.33 1.25 1.16

194 178 180 188 183 213 207 188 191 208 206 180 179 177 178

126 117 116 114 114 138 135 116 121 136 135 116 116 108 112

Appendix 2 The general form representing Y (response) expressed as a function of process variables (X1, X2, X3 and X4) is shown below Y ~f (X1 ,X2 ,X3 ,X4 ) Y ~b0 zb1 X1 zb2 X2 zb3 X3 zb4 X4 z b5 X12 zb6 X22 zb7 X32 zb8 X42 z b9 X1 X2 zb10 X1 X3 zb11 X1 X4 z b12 X2 X3 zb13 X2 X4 zb14 X3 X4

(10)

The term X1, X2, X3 and X4 denote the input parameters in coded form. Here X1, X2, X3 and X4 are the linear terms, X12 , X22 , X32 and X42 are the square terms, X1X2, X1X3, X1X4, X2X3, X2X4 and X3X4 are two-factor interaction terms the non-linear regression model developed by utilising three levels. The term, b0, b1, b2, b3,…, b14 are the coefficients of the regression equations and are calculated using the least square techniques explained in subsequent sections. The term b0 is the free term of the regression equation and defines the intercept of the plane. b1, b2, b3 and b4 are the coefficients of linear (main effect) terms, b5, b6, b7 and b8 are the quadratic term coefficients and b9, b10, b11,


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b12, b13 and b14 are the interaction term coefficients. However, b1, b2, b3 and b4 are sometimes referred as partial regression coefficients because, b1 measures the expected change in Y per unit change in X1, when X2, X3 and X4 are held constants. Similarly for b2, b3,…, b14 other regression coefficients are estimated. Three important terms namely main effect, square and interaction terms were commonly used in the developed regression equation utilising response surface methodology (refer equation (2)–(9)). The first order model with only main effect terms is represented for m observations as shown in equation (11) Ym ~b0 zb1 xm1 zb2 xm2 z:::zbk xmk zem

(11)

The first order model with main and interaction terms are appear as shown in equation (12) Ym ~b0 zb1 xm1 zb2 xm2 z:::zbk xmk z b12 xm1 xm2 z:::zbm{1,m xmk{1 xmk zem

(12)

" # N k k X X X XX LLS ~{2 Ym {b0 { bi xmi { bii x2mi { bij xmi xmj x2mi ~0 (19) (19) Lbii m~1 i~1 i~1 ivj " # N k k X X X XX LLS ~{2 Ym {b0 { bi xmi { bii x2mi { bij xmi xmj xmi xmj ~0 (20) (20) Lbij m~1 i~1 i~1 ivj

The above equations can be solved easily when the equations are expressed in matrix form Y ~f ðxÞbze 2

2 3 y1 1 x11 6 7 6 6 y2 7 6 1 x12 6 7 6 6 7 6 6 7 Y ~6 : 6 : 7, f ~6 : 6 7 6 6 : 7 6: : 4 5 4 yN 1 x1N 2 3 2 3 b0 e0 6 7 6 7 6 b1 7 6 e1 7 6 7 6 7 6 7 6 7 6 7 7 b~6 6 : 7,e~6 : 7 6 7 6 7 6 : 7 6 : 7 4 5 4 5 bk eN

The general form of second order polynomial representing includes linear, square and interactions terms in the regression equation shown in equation (13)

(13)

b12 xm1 xm2 z:::zbm{1,m xmk{1 xmk zem The above equation can be re-written in the standard form as shown below (refer equation (14)) Ym ~b0 z

k X

bi xmi z

k X

i~1

bii x2mi z

i~1

XX

bij xmi xmj zem

ivj

LS~ (14)

e2m

LS~

m~1

Ym {b0 {

i~1

bi xmi {

k X

bii x2mi {

i~1

XX

x212

...

x2k2

x12 x22

...

:

:

...

:

:

...

:

:

...

:

:

x21N

...

x2kN

x1N x2N

. . . xkN

3

7 xk2{1 xk2 7 7 7 7, ... : 7 7 7 ... : 5 . . . xkN{1 xkN ...

e2m ~e1 e~ðY {xbÞ1 ðY {xbÞ

0

0

0

0

0

0

0

0

0

#2

(16) (16)

Solving the above expression the coefficient of regression equations can be estimated

bij xmi xmj

ivj

0

VOL

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x xb~x Y 0

b~

xY x0 x

0 {1 0 b~x Y x x

" # N k k X X X XX LLS ~{2 Ym {b0 { bi xmi { bii x2mi { bij xmi xmj xmi ~0 (18) (18) Lbi m~1 i~1 i~1 ivj

2015

xk2

xk1{1 xk1

b x Y indicates (161) matrix, its corresponding trans0 pose bxY is also a matrix of (161), it is also important to note that least square estimator must satisfy the following equations :LLS ~{2x0 Y z2x0 xb~0 Lb b

" # N k k X X X XX LLS (17) ~{2 Ym {b0 { bi xmi { bii x2mi { bij xmi xmj ~0 (17) Lb0 m~1 i~1 i~1 ivj


N X

0

The least square function aims at minimising the response with respect to b0, bi, bii and bij using the following equation (17)–(20)

180

...

...

~Y Y {2b x Y zb x xb

(15)

k X

x11 x21

0

Therefore equation (15) can be written as follows "

x2k1

LS~Y 1 Y {b x Y {Y xbzb x xb

m~1

N X

...

The equation shown above can be expressed as

0

LS~

x211

m~1

where m51, 2, 3,…, N, xmi represents the mth observation of the variable xi and N denotes the total observations. Least square principle was used to estimate the coefficients of the regression equation obtained using RSM. The least square function can be expressed using equation (15) N X

xk1

where, x represents the independent (process) variables, f term indicates the response function, e represents experimental error, b indicates the regression coefficients and Y is the response. It is to be note that, Y is the response corresponds to N61 matrix of observations, x represents the independent (process) variables of (N6P) matrix of levels, P 5 Kz1, b (N61) indicates the multiple regression coefficients and e is an (N61) is an matrix of random experimental errors. Solving the aforementioned equations the regression coefficients are estimated

Ym ~b0 zb1 xm1 zb2 xm2 z:::zbk xmk z b11 x2m1 z:::zbkk x2mk z

...

NO

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J. Manuf. Sci. Prod. 2014; 14(2): 125 – 140

Manjunath Patel G. C., Prasad Krishna and Mahesh B. Parappagoudar*

Prediction of Squeeze Cast Density Using Fuzzy Logic Based Approaches Abstract: In the present work, efforts are made to develop the input-output relationships for squeeze casting pro cess by utilizing the fuzzy logic based approaches. Cast ing density in Squeeze casting is expressed as function of process parameters, such as time delay before pres surizing the metal, pressure durations, squeeze pressure, pouring temperature and die temperature. It is to be noted that, Mamdani based model and Takagi and Sugeno’s model have been developed to model density in squeeze casting process. Manually constructed Mamdani based fuzzy logic controller and Takagi and Sugeno’s based fuzzy logic controller have been used in approach 1 and approach 2 respectively. Training of FLC is carried with the help of five hundred input-output data set generated artificially through regression equations, obtained earlier by the same authors. The performance of the developed models was tested for both the linear and non-linear membership function distributions with the help of ten test cases. Moreover, the test data was collected by conducting the experiments and not used in training of FLCs. It is interesting to note that both approaches are capable to make accurate predictions. However, the performance of approach 2 with G bell shape membership function distribution is found to outperform approach 1 and other type of membership function distributions. The findings are useful to foundry-men, since it provides information on casting density in squeeze casting process for the different combination of process parameters without conducting any experiments. Keywords: squeeze casting process, density, fuzzy logic, adaptive network based fuzzy interface system (ANFIS) PACS® (2010). 83.50.Uv, 81.20.Hy DOI 10.1515/jmsp-2014-0011 Received March 19, 2014; accepted June 15, 2014.

*Corresponding author: Mahesh B. Parappagoudar: Department of Mechanical Engineering, Chhatrapati Shivaji Institute of Technology, Durg (C.G.) 491001, India. E-mail: [email protected] Manjunath Patel G. C., Prasad Krishna: Department of Mechanical Engineering, National Institute of Technology, Karnataka-Surathkal 575025, India

1 Introduction Squeeze casting process is one of the hybrid metal cast ing process developed using the pressurized solidification concept suggested by D. K. Chernov (1878). Squeeze casting is known for producing castings with high yield and dense structure. However, it is required to have precise control of process parameters. The major drawbacks of conventional casting processes such as porosity, shrinkage and segregations are addressed by combining the desirable features of gravity, pressure die casting and forging processes in a single step process in squeeze casting. During squeeze casting process the quality of the parts depends largely on the process variables such as die temperature, pouring temperature, applied pressure, pressure duration and time delay before pressurization. Inappropriate choice of the said process variables may lead to the possible squeeze casting defects, such as oxide inclusions, under/over filling, cold laps, poor surface finish, dimensional accuracy, hot tearing, sticking, extrusion, segregations and case de-bonding [1]. It is important to note that the aforementioned defects finally affects the casting density, which can be minimized by proper control of the squeeze cast process variables. Higher casting density is always desirable because the casting density is directly decides the mechanical and the micro-structure properties. Hence it is of paramount importance to develop the squeeze cast process model and analyse the input- output relationships of the process. The rapid development of the squeeze casting process had drawn much attention for researchers towards the improvement of the mechanical and micro-structure properties during 1990’s and 2000’s across the globe. How ever, most research works carried out during that period was theoretical analysis and conventional engineering experimental approach. The effect of different casting temperatures on density, impact and tensile strength of LM6 alloy and ZA3 alloys processed under gravity and squeeze casting method were studied by Yang [2]. Fur ther, it was mentioned that, the experiments conducted by keeping the die temperature, compression holding time and applied pressure as constant. Later, Yang [3] studied the effects of solidification time on the density, fracture energy, tensile strengths, yield and ultimate

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Manjunath Patel G. C. et al., Prediction of Squeeze Cast Density Using Fuzzy Logic Based Approaches

tensile strengths of LM6 and ZA3 alloys by using two analytical models, namely steady state heat flow model and gracia’s virtual model. The analytical models showed an average deviation of 27% for LM6 and 20% for ZA3 alloys, when compared with test cases. In addition it was observed that shorter solidification time was re sponsible to achieve better mechanical properties. Maleki et al. [4] used a classical approach to study the effects of squeeze pressure, melt temperature and die temperature on density, macrostructure, hardness and tensile strengths of LM13 alloy, by varying one process variable at a time and keeping the rest of the parameters at their mid values. However, it is important to note that the effects of pressure duration and time delay before pressurization was left out in their research work. It is to be noted that, conventional approaches, discussed need more number of experiments and the combined (interaction) effect of parameters is lost. Optimizing squeeze casting process requires the input-output relationships expressed in the mathematical form. The statistical regression analyses allow the researchers to study effect of process variables, estimates significant contributions on the measured responses and develop input-output relationship with less number of experiments [5]. To the best of the authors’ knowledge, limited research work has been reported in the literature on squeeze casting process using statistical regression and taguchi tools. Vijian and Arunachalam [6] utilized taguchi method to study the effect of squeeze pressure, pressure duration and die temperature on hardness and tensile strengths of LM24 alloy. In addition they established separate multi variable linear regression equations for hardness and tensile strength. The developed regression equations included only linear terms and neglected the square and interaction terms. Moreover, they did not considered pouring temperature variations in their analysis. Senthil and Amirthagadeswaran [7] used taguchi method to con duct experiments and developed mathematical input- output relationship, which included all linear, square and interaction terms. Later on Senthil and Amirthagades waran [8] extended their research efforts to study the yield strengths via taguchi method and developed the input-output relationships. However, the time delay before pressurizing the metal and percentage contribution estimation of square and interaction terms towards the responses was left out in their analysis. More recently, Bin et al. [9] investigated the influence of squeeze casting parameters on the strength and ductility of AlSi9Cu3 alloys. However, they did not develop the model to predict the responses and they did not consider the important machine related parameter like pressure duration, in their

analysis. Soft computing modelling approaches can be used to effectively handle the complex problems and to overcome the limitations of Parappagoudar and Vundavilli [10]. The major soft computing tools namely artificial neural networks (ANNs), genetic algorithms (GA) and fuzzy logic (FL) approaches and their different combinations were used in various manufacturing processes. Vijian and Arunachalam utilized GA to solve the multiobjective optimization problems related to squeeze casting process, however they fail to include the square and interaction terms in their objective functions [6]. ANNs employed to predict the effects of process parameters on temperature difference of the squeeze cast part [11]. It is important to note that some research efforts were made to develop the hybrid systems (combining the desirable features of two or more approaches) Genetic algorithm based neural network (GA-NN) and back propagation neural network (BPNN) models were developed for foundry applications, namely, different moulding sand systems and pressure die casting [12–15]. The authors made efforts to to model and analyse important manufacturing processes with the help of fuzzy logic based approaches [16–20]. It is to be noted that fuzzy logic based approaches can be successfully implemented in various manufacturing processes and proved as a cost effective tool to analyze, control and model the complex non-linear input-output relationship. To the authors’ best knowledge, not much of the work is reported to address the problems related to the squeeze casting process utilizing fuzzy logic based approaches. Casting density is the important quality characteristic, since; it is directly related to the internal casting de fects such as micro-porosity, segregation, shrinkages and micro-voids. The amount of porosity present in the castings decreases the available load area, provoke stress concentration, crack initialization leads to poor tensile strength and ductility of the alloy [21]. In the present work, an attempt has been made to predict the casting density using two fuzzy models, namely Mamdani based fuzzy logic and Takagi Sugeno based fuzzy logic. Approach 1: Development of manually constructed Mamdani based fuzzy logic system deals with construction of rule base, consequent and antecedent parts with the help of human expertise. Approach 2: Development of adaptive network based fuzzy interface system (ANFIS) a Takagi and Sugeno’s model deals with automatic evolution of rule base, consequent and antecedent parts.



127

Fig. 1: Input-output model for squeeze casting process

Table 1: Squeeze cast process parameters and their respective levels Process parameters

Notation

Unit

Level-1

Level-2

Level-3

Level-4

Level-5

Squeeze pressure (Sp ) Pressure duration (Dp ) Time delay ( Td) Pouring temperature (Pt ) Die temperature (Dt )

A B C D E

MPa s s °C °C

0.1 10 03 630 100

50 20 05 660 150

100 30 07 690 200

150 40 09 720 250

200 50 11 750 300

2 Modelling of squeeze casting process using fuzzy logic Modelling refers to the method of identifying, analysing and establishing the input-output relationship of the phy sical system. Squeeze casting is one of the most economical routes to process from liquid metal stage to the final solidification stage. However, density of the components in squeeze casting is largely influenced by squeeze cast technical parameters. Figure 1 shows the inputs (time delay, pressure duration, squeeze pressure, pouring and die temperature) and output (density) of the squeeze casting process. The input parameters of squeeze casting process and their respective levels used in the current study are shown in Table 1.

2.1 Data collection The prediction capabilities of any training algorithm rely on the accuracy of the data collected and the amount of data used for training. The collection of huge data through real experiments is impractical, because it leads to material wastage, high labour costs and time consuming. It is to be noted that five hundred input-output data sets used for training generated artificially through regression equation obtained earlier by the same authors [22]. The performance of the developed models has been tested with the help of ten test cases. It is also important to mention that the test cases used to check the model performances are separate from those used in training.

The non-linear regression equation for casting density in terms of squeeze cast process parameters is shown in Eq. (1). Density = 1.21121 − 0.0120733Td + 8.80233E − 05Pd

+ 0.000270477S p + 0.00354289Pt + 0.001781D t + 6.77354E − 05Td2 + 4.03295E − 06Pd2 − 1.32509E − 07S2p − 2.47673E − 06Pt2 − 3.89751E − 06D 2t .

(1)

Five hundred sets of input-output data have been gen erated at random using the above equation by selecting the squeeze cast process variables within their respective ranges.

2.2 Fuzzy modelling The fuzzy concept was used to develop the input-out relationship for the squeeze casting process as shown in the Fig. 2. The aim of the fuzzy modelling is to predict the output for the known set of inputs. In the present work, squeeze cast process casting density is expressed as a function of input parameters. Takagi and Sugeno’s approach of FLC and Mamdani approach of FLC has been developed to model the squeeze casting process.

3 Fuzzy logic controller In manufacturing processes the researchers/investigators are more interested to establish accurate input-output relationships. The human brain behaviour (thinking and


128


Fig. 2: Model representation of squeeze casting process using fuzzy interface system

reasoning) can be used to develop such input-output relationship using the concept of fuzzy set theory namely fuzzy logic controller (FLC). Fuzzy logic controller widely used in many applications might be due to many ad vantages, such as, easy to understand and implement, capable of handling uncertainty and imprecise data and exact mathematical formulation is not required to develop the FLC [23]. The performance of the developed models rely on the use of knowledge base approach, majorly consists of both data bases and rule base. In data base approach, the membership function is decided, based on the variability of distributed data in the process. Triangular and trapezoidal membership function is used if the data distributions are assumed to be linear, whereas sigmoid, gaussian and bell-shaped membership functions are used for non-linear. In FLC the variables are expressed in the form of linguistic terms (low, medium, high, etc.) and the input-output relationships are expressed in the form of rules. Since the rules were expressed in the form of linguistic terms and number of rules increases with the increase in linguistic terms and the process variables. Fuzzy logic controllers are majorly categorized into two types as shown in Table 2.

3.1 Approach 1: Development of manually constructed Mamdani based FLC In the present work, Mamdani based fuzzy logic approach has been developed to perform forward mapping Table 2: Fuzzy logic controller modelling approaches [23] Type

Linguistic fuzzy modelling

Precise fuzzy modelling

Approach Advantage Limitation

Mamdani approach Better interpretability Low accuracy

Takagi sugeno’s approach High accuracy Low interpretability

of squeeze casting process. The squeeze cast process parameters considered includes five inputs (time delay, pressure duration, squeeze pressure, pouring temperature and die temperature) and one output (density). It is interesting to note that in fuzzy logic the inputoutput parameters need to be expressed as a function of linguistic terms. Three linguistic terms are used for the input-output variables namely low, medium and high. For simplicity, the linear type triangular membership function distributions of input-output variables of the fuzzy logic system are shown in Fig. 3. It is important to note that most of the casting processes are complex in nature and output may behaves non-linear with respect to change in the input. So both linear and non-linear (Gaussian and bell shaped) membership function distributions were tried and the performances of the developed models are compared. In Fig. 3 the ‘a’ values indicates the half base widths of isosceles triangles and base width of right angled triangles. As there are five input variables and each input variable is expressed as a function of three linguistic terms. The number of rules to be defined for current study is found to be equal to 35 = 243. The Mamdani based manually constructed rule base of the fuzzy logic system is shown in Table 3. One typical manually constructed rule of the fuzzy logic system will appear as follows: IF A is M AND B is H AND C is L AND D is H AND E is M, THEN ρ is M However the knowledge base is comprised of both rule and data base of the fuzzy logic system and the manually constructed rule base is purely rely on the experience of the designer, which is not considered to be optimal in most of the cases. Thus attempts required to automatically determine the rule and data base using better learning capabilities of artificial neural networks (ANNs).



129

Fig. 3: Manually constructed membership function distribution for input-output variables

3.2 Approach 2: Development of adaptive network based fuzzy interface system to automatically retrieve the data and derive the rule base Artificial neural networks considered being an excellent modelling tool for mapping the complex manufacturing processes [10]. The use of fuzzy set theory finds major applications in the field of production as well as in operation management [24]. ANNs have potential advantages to model complex non-linear relationship but associated with few limitations namely getting stuck with local op timal solution instead of global one, output precisions are limited, huge training data which covers entire range of different process variables is required and large number of training epochs [25]. There is no systematic procedure

available to define the fuzzy membership function is the major drawback found in the fuzzy logic controller [26]. The hybrid systems developed by combining the desirable features of learning capabilities of ANNs and reasoning capability of fuzzy logic to limit the weak points of one technology with the strengths of the other. In recent years an embedded type adaptive network based fuzzy interface system (ANFIS) developed and shown better prediction in high pressure water jet cleaning [27], surface roughness in end milling process [28, 29] and Al- and weld bead in submerged arc welding process [30]. ANFIS uses the hybrid learning algorithm which combines gradient descent method and method of least square principles to model input-output relationship. Here, the developed rule composed of fuzzy antecedent which includes the membership function parameters and its shape and functional consequent parameter which describe the


130


Table 3: Manually constructed rule base of the fuzzy logic system Rule No.

A

B

C

D

E

ρ

Rule No.

A

B

C

D

E

ρ

Rule No.

A

B

C

D

E

ρ

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56

L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L

L L L L L L L L L L L L L L L L L L L L L L L L L L L M M M M M M M M M M M M M M M M M M M M M M M M M M M H H

L L L L L L L L L M M M M M M M M M H H H H H H H H H L L L L L L L L L M M M M M M M M M H H H H H H H H H L L

L L L M M M H H H L L L M M M H H H L L L M M M H H H L L L M M M H H H L L L M M M H H H L L L M M M H H H L L

L M H L M H L M H L M H L M H L M H L M H L M H L M H L M H L M H L M H L M H L M H L M H L M H L M H L M H L M

L M M L M M L M M M M M M H M M H H M H M M H H M H H M M M M M M M M M M M M M H M M H H M H H M H H M H H M M

57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112

L L L L L L L L L L L L L L L L L L L L L L L L L M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M

H H H H H H H H H H H H H H H H H H H H H H H H H L L L L L L L L L L L L L L L L L L L L L L L L L L L M M M M

L L L L L L L M M M M M M M M M H H H H H H H H H L L L L L L L L L M M M M M M M M M H H H H H H H H H L L L L

L M M M H H H L L L M M M H H H L L L M M M H H H L L L M M M H H H L L L M M M H H H L L L M M M H H H L L L M

H L M H L M H L M H L M H L M H L M H L M H L M H L M H L M H L M H L M H L M H L M H L M H L M H L M H L M H L

M M M M M M M M M M M H H M H H M H H M H H M H H L M M L M M L M M L M M M M M M M M M M M M M M M M M L M M L

113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168

M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M H H H H H H

M M M M M M M M M M M M M M M M M M M M M M M H H H H H H H H H H H H H H H H H H H H H H H H H H H L L L L L L

L L L L L M M M M M M M M M H H H H H H H H H L L L L L L L L L M M M M M M M M M H H H H H H H H H L L L L L L

M M H H H L L L M M M H H H L L L M M M H H H L L L M M M H H H L L L M M M H H H L L L M M M H H H L L L M M M

M H L M H L M H L M H L M H L M H L M H L M H L M H L M H L M H L M H L M H L M H L M H L M H L M H L M H L M H

M M M M M L M M M M M M M M M M M M M M M M M L M M L M M L M M M M M M M M M M M M M M M M M M M M L L L L L L


131


Table 3 (cont.) Rule No.

A

B

C

D

E

ρ

Rule No.

A

B

C

D

E

ρ

Rule No.

A

B

C

D

E

ρ

169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193

H H H H H H H H H H H H H H H H H H H H H H H H H

L L L L L L L L L L L L L L L L L L L L L M M M M

L L L M M M M M M M M M H H H H H H H H H L L L L

H H H L L L M M M H H H L L L M M M H H H L L L M

L M H L M H L M H L M H L M H L M H L M H L M H L

L L L L L L M M M L M M L M M L M M L M M L L L L

194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218


M M M M M M M M M M M M M M M M M M M M M M M H H

L L L L L M M M M M M M M M H H H H H H H H H L L

M M H H H L L L M M M H H H L L L M M M H H H L L

M H L M H L M H L M H L M H L M H L M H L M H L M

L L L L L L L L L M M L M M L M M L M M L M M L L

219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243



L L L L L L L M M M M M M M M M H H H H H H H H H

L M M M H H H L L L M M M H H H L L L M M M H H H

H L M H L M H L M H L M H L M H L M H L M H L M H

L L M L L M L L M M L M M L M M L M M L M M L M M

network output. During training cycle, in forward calculation the antecedent parameters are fixed and the consequent parameters are determined using least square principle. The obtained ANFIS output using the consequent parameters is compared with the target value to determine the error. The objective is to minimize the error by up dating the network parameters in the backward step. In backward step, the consequent parameters were fixed and the output error is back propagated and the antecedent parameters are updated using the gradient descent method [26]. The procedure adapted in ANFIS model is shown in Fig. 4. The ANFIS model developed for the squeeze casting process is capable to predict the casting density at different squeeze casting conditions. Squeeze cast process parameters, namely, time delay (Td ), pressure duration (Dp ), squeeze pressure (Sp ), pouring temperature (Pt ) and die temperature (Dt ) are considered as input parameters in the input layer and casting density is the output param eter in the output layer (see Fig. 5). Each squeeze cast process parameters are represented using three linguistic terms, since five input parameters used in the current study 35 = 243 combination of rules exists. According to

first order Takagi and Sugeno’s model of FLC, the typical output of each rule is expressed in Eqs. (2) to (4): Rule 1: If (Td is A1) and (Dp is B1) and (Sp is C1) and (Pt is D1) and (Dt is E1), then f1 = p1Td + q1 D p + r1 S p + s1 Pt + t 1 Dt + u1

(2)

Rule 2: If (Td is A2) and (Dp is B2) and (Sp is C2) and (Pt is D2) and (Dt is E2), then f2 = p2Td + q 2 D p + r2 S p + s2 Pt + t 2 Dt + u2

(3)

Rule 3: If (Td is Ai) and (Dp is Bi) and (Sp is Ci) and (Pt is Di) and (Dt is Ei), then fi = piTd + qi D p + ri S p + si Pt + t i Dt + ui

(4)

where i = 1, 2, 3, . . . , 243, pi, qi, ri, si, ti and ui are the coefficients, f is the output parameter, Ai, Bi, Ci, Di and Ei are the linguistic terms used to divide the membership function. The network architecture of adaptive network based fuzzy interface system is shown in Fig. 5. The entire


132


O2,i = μAi(Td) for i = 1, 2, 3

(5)

O2,i = μBi−3(Dp) for i = 4, 5, 6

(6)

O2,i = μCi−6(Sp) for i = 7, 8, 9

(7)

O2,i = μDi−9(Pt) for i = 10, 11, 12

(8)

O2,i = μEi−12(Dt) for i = 13, 14, 15

(9)

The most commonly used membership functions are triangular, bell shaped and gaussian membership functions and the values are always lies between maximum of 1 and a minimum of zero corresponding to the input parameter setting. Layer 3: The layer 3 contains the 35 = 243 nodes, which determines the number of possible rules and is usually labelled using the term Π. For the particular set of input pairs a maximum of 32 nodes will be activated in the third layer and each node is a possible combination of input variables. In this layer the information received from the layer 2 is multiplied and the obtained output as a firing strength shown in Eq. (10). O3,=i w=i µ Ai (Td ). µ Bi−3 ( D p ). µCi−6 ( S p ). µ Di−9 ( Pt ). µ E i−12 ( Dt ) (10)

Fig. 4: Flow chart representing methodology followed for predicting casting density using ANFIS

network architecture is a combination of 6 layers namely, input layer, fuzzification layer, product layer, normalization layer, de-fuzzification layer and the output layer. The systematic procedure in developing the input-output relationship is described as follows: Layer 1: The network architecture of layer 1 is expressed as a function of squeeze cast process variables, since five inputs used in the current study and this layer consists of five nodes only. The output nodes of the layer 1 are same as the input of the corresponding layer and are directly passed to the input layer 2. Layer 2: The function of the layer 2 is to determine the membership values for the given set of inputs corresponding to the assigned linguistic terms shown in Eqs. (5) to (9). Td, Dp, Sp, Pt and Dt are the input nodes expressed as membership functions in terms of Ai, Bi, Ci, Di and Ei of layer 2. O2,i is the output of ith node of layer 2.

Layer 4: Each node present in the layer 4 is labelled as N. The function of this layer is to normalize the weight functions using Eq. (11). The calculation of the ith node is the ratio of ith rule firing strength to the summation of all the fired rules. O4,i = wi = wi /( w1 + w 2 + w 3 +  + w 243 )

(11)

Layer 5: 243 nodes present in the layer 5 and maximum of 32 nodes will be activated for the particular input variables combination. This layer considered as the defuzzification (centroid area method) layer and the output node is calculated using the product of the normalized firing strength and the output of the corresponding fired rule shown in Eq. (12). O5,i = wi fi = wi ( piTd + qi D p + ri S p + si Pt + t i Dt + ui )

(12)

Layer 6: Since only one output used in the present case the output layer has only one node and is denoted by a symbol Σ, hence the present output is the combination of summation of all the received signals from the 5th layer shown in Eq. (13). = O6,i


wf ∑= i

i i

∑wf ∑w

i i

i

i

i

(13)


133

Fig. 5: ANFIS network architecture for predicting the casting density

4 Results and discussion The performance of the developed models to predict the casting density at different squeeze casting conditions is carried using the forward mappings. Ten different squeeze casting conditions were taken to evaluate the model performances using both linear and non-linear type membership function distributions. The following section presents the information regarding results ob-

tained and comparison of the developed models used in the current study.

4.1 Approach 1 The rule base and data base of the fuzzy logic system is constructed manually with the help of experience of human experts. For simplicity, the linear type triangular


134


Table 4: Summary results of test cases for the response density Test case no.

1 2 3 4 5 6 7 8 9 10 MAPE R2

Approach 1 Triangular

G bell shape

Approach 2 Gaussian

Triangular

G bell shape

Gaussian

Pre‑ dicted

Abs.% deviation

Pre‑ dicted

Abs.% deviation

Pre‑ dicted

Abs.% deviation

Pre‑ dicted

Abs.% deviation

Pre‑ dicted

Abs. % deviation

Pre‑ dicted

Abs. % deviation

2.608 2.623 2.625 2.640 2.613 2.622 2.615 2.621 2.649 2.635

0.231 0.038 0.114 0.901 0.495 0.306 0.771 0.114 1.009 1.051 0.503 0.856

2.620 2.621 2.622 2.635 2.609 2.622 2.620 2.622 2.662 2.646

0.692 0.038 0.228 1.089 0.648 0.307 0.963 0.153 0.523 0.638 0.528 0.693

2.617 2.621 2.622 2.637 2.614 2.621 2.618 2.622 2.651 2.638

0.577 0.038 0.228 1.013 0.457 0.268 0.886 0.152 0.934 0.939 0.549 0.828

2.576 2.608 2.632 2.671 2.615 2.609 2.591 2.601 2.674 2.651

0.999 0.534 0.152 0.263 0.419 0.191 0.154 0.649 0.075 0.451 0.388 0.928

2.588 2.617 2.629 2.681 2.611 2.607 2.594 2.604 2.677 2.662

0.538 0.191 0.038 0.638 0.571 0.268 0.039 0.535 0.037 0.038 0.289 0.949

2.589 2.619 2.624 2.728 2.61 2.607 2.594 2.606 2.682 2.676

0.499 0.114 0.152 2.402 0.609 0.268 0.039 0.458 0.224 0.488 0.523 0.843

membership function distribution is shown in Fig. 3. The values of a1, a2, a3, a4, a5 and a6 are kept equal to 4, 20, 75, 60, 100 and 0.8 respectively. It is interesting to note that three different membership functions were used and the results were compared with the experimental values as shown in Table 4. The construction of the rules plays vital role in accurate prediction of the responses, since it purely rely on the knowledge of the human expertise. The developed manually constructed rule base is presented in Table 3.

4.2 Approach 2 Five hundred data sets have been collected from the regression equation carried out by earlier authors. The steps followed to predict the casting density via ANFIS is shown in Fig. 4. Five inputs namely, squeeze pressure, pressure duration, time delay, pouring temperature and die temperature and one output such as density have been considered for the present study as shown in Fig. 5. Table 5 presents ten different test cases used for the present study to compare the predicted and the observed values. Linear type, triangular membership function distribution and non-linear type gaussian and generalized bell shaped membership function distributions have been adopted and the performance of the developed models are compared with experimental values as shown in Table 4. The root mean squared error (RMSE) obtained at the end of the training for different membership functions are shown in Fig. 6.

Table 5: Summary results of input-output results of the test cases Exp. no. 1 2 3 4 5 6 7 8 9 10

Squeeze casting process parameters

Responses

Td

Pd

Sp

Pt

Dt

SDAS

ρ

11 7 6 5 5 9 9 11 4 4

30 14 37 40 10 33 48 32 21 23

101 110 63 142 71 110 96 172 196 89

671 635 674 731 723 738 637 712 646 742

263 192 236 254 142 261 174 189 213 284

48.43 49.74 47.64 33.78 46.86 48.33 50.63 44.86 35.66 41.34

2.602 2.622 2.628 2.664 2.626 2.614 2.595 2.618 2.676 2.663

4.3 Comparison of the developed models The performances of the developed models are compared with different membership function distributions in predicting the casting density, as shown in Figs. 7 and 8.

4.3.1 Approach 1 It is interesting to note that for approach 1 shown in Fig. 7(a), the best-fit line of triangular shape membership function distributions are close to the ideal line as compared to Fig. 7(b) and Fig. 7(c) and many data points falls close to the trend line. The summary results of test cases in predicting the casting density is shown in Table 4. The accuracy and prediction capability of the developed



135

Fig. 6: Convergence of ANFIS training (RMSE v/s Number of training epoch) for response-density: (a) Triangular membership function, (b) bell shaped membership function, and (c) Gaussian membership function

models have been evaluated using coefficient of cor relation determination (R2) and mean absolute percent error (MAPE) using Eqs. (14) and (15) respectively. The co-efficient of determination is expressed as the square ratio of covariance and the multiplied standard deviation between the observed and predicted values. The R2 values always fall in the range of 0 to 1. Higher R2 value indicates a strong co-relation between the observed and the predicted values and there is no co-relation, if R2 value is zero. However it is interesting to note that for approach 1, R2 value is found to be equal to 0.856 for triangular membership function, 0.693 for bell shape membership function and 0.828 for gaussian function distribution and is shown in Table 4. The mean absolute percentage error (MAPE) in prediction of casting density for the approach 1 is found to be 0.503 for triangular membership function, 0.528 for bell shaped membership function and 0.549 for gaussian membership distribution (see Table 4).  n  ∑ i=1 (Oi − O )( Pi − P ) 2 R = n n  (Oi − O )2 ∑ i 0 ( Pi − P )2 =  ∑i 1 =

    

2

(14)

MAPE =

1 n Oi − Pi ∑ n i=1 Oi

(15)

where P is the predicted, n is the number of data sets and O is the observed values.

4.3.2 Approach 2 The artificial neural networks are fused together in the second approach in order to improve the prediction performance of the developed models. In this approach the better learning capabilities of artificial neural networks is utilized to automatically define the rule and the membership function distributions of the data bases. As reported in the previous literatures the performance of the developed models can be further enhanced with different membership function distributions [16, 17]. It is also important to note that the performance of the developed models rely on the number of training data used and closeness of the actual and the predicted network values and is usually determined by the root mean squared


136


Fig. 7: Comparison of predicted and actual density values using approach 1: (a) Triangular membership function distributions, (b) bell shape membership function distributions, and (c) Gaussian membership function distributions

error at the end the end of the training. Five hundred data sets used for training the network and the network training were terminated once the error value becomes steady. The network convergence during the ANFIS training is studied for different membership function distri butions and the minimum root mean square values are found to be equal to 0.00209 for triangular membership function distributions, 0.00205 for bell shaped membership function and 0.00211 for gaussian membership function distributions (see Fig. 6). It is interesting to note that the initial input-output membership function distributions at the beginning of the training phase of the fuzzy logic system are seen similar to Fig. 3. How ever, a small change in the input-output membership function distributions of the fuzzy logic system has been observed at the end of training. The optimized “a” values of six variables such as a1, a2, a3, a4, a5 and a6 are found to be equal to 2.9941, 19.5594, 74.3348, 59.4485, 99.6776 and 2.61385 respectively for bell shaped mem bership function distributions. Similarly for gaussian membership function distributions the “a” values are found to be equal to 3.3835, 19.6299, 74.3831, 59.3588,

98.9817 and 2.61385 respectively. It is interesting to note that there is no significant change in the input mem bership distributions for triangular shape. However, the slight change in the output membership distribution and the corresponding a6 value is found to be equal to 2.60415. The performance of the developed models with dif ferent membership function distributions in predicting the casting density using approach 2 is shown in Fig. 8. The best fit line method is used to compare the model predicted and the actual values. However it is interesting to note that line of best fit for all the models is found to be close to the ideal line. However, bell shape membership function distribution shown in Fig. 8(b) outperforms the triangular (see Fig. 8(a)) and gaussian membership dis tributions (see Fig. 8(c)). It is interesting to observe that majority of the data points of bell shape membership function of the fuzzy logic system falls on the best fit line compared to gauss and triangular shaped membership distribution of fuzzy logic system. Summary results of the results of the test cases for predicting the casting density is shown in Table 4.



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Fig. 8: Comparison of predicted and actual density values using approach 2: (a) Triangular membership function distributions, (b) bell shape membership function distributions, and (c) Gaussian membership function distributions

In addition, the performance of the developed models is evaluated using MAPE and R2 values. It is interesting to note that R2 value is found to be equal to the 0.949 for bell shape membership function distribution. This indicates, the model can map with actual values accurately with a probability equal to 94.9%. For triangular and gauss shaped membership function distribution the R2 value is found to be equal to 0.928 and 0.843 respectively (see Table 4). However, the MAPE value is also calculated for the developed membership function distributions and the values are found to be equal to 0.388 for triangular shape membership function distribution, 0.289 for bell shape membership function distribution and 0.523 for gaussian membership function distributions of fuzzy logic system (see Table 4).

4.4 Comparison of the developed approaches The percent deviation in prediction of the density as obtained for the developed approaches with different

membership function distributions are shown in Fig. 9 and Fig. 10. It has been observed that for the response density, the percentage deviation values for both the approaches using triangular shape membership function distribution are found to lie in the range of (−0.771, +1.051)% for approach 1 and (−0.263, +0.999)% for approach 2 respectively. Similarly for gaussian membership function distributions percent deviation is found to lie in the range of (−0.886, +1.0135)% for approach 1 and (−0.638, +0.571)% for approach 2 and for bell shape (−0.963, +1.088)% for approach 1 and (−2.402, +0.609)% for approach 2 respectively (see Fig. 9).

4.5 Comparison of the developed approaches using average absolute percent deviation Fig. 10 compares the performances the developed approach 1 and approach 2 with different membership function distributions in terms of mean absolute percent


138


Fig. 9: Comparison of different approaches of the developed models with different membership function distribution in terms of percent deviation in prediction for the response-density: (a) Manually constructed fuzzy logic system and (b) adaptive network based fuzzy logic system

Fig. 10: Comparison of different models performances in terms of average absolute percent deviation in prediction for the responses-density



deviation in prediction of density of the squeeze casting process. It is important to note that the performance of approach 2 would be slightly better than approach 1 in predicting both of the responses. However, the results showed that the performance of approach 2 also varies with different membership function distributions, the reason might be due to the nature of error surface. In case of approach 1 the consequent part of the rule base has been developed with the help of the human expertise and may not be optimal in all cases. On the other-hand, in case of approach 2, the evolution of optimal fuzzy logic system is through the better learning capabilities of arti ficial neural networks. The reason might be due to the inherent adaptability of the automatically defined fuzzy logic system to evolve consequent part, rule and data bases utilizing artificial neural networks. It is interesting to note that, the approach 2 of bell shaped membership function distributions outperforms all other models with minimum average absolute percentage deviation as shown in Fig. 10.

5 Concluding remarks An attempt has been made to carry out forward mapping of squeeze casting process to predict density utilizing the fuzzy logic based approaches. Two different approaches, namely manually constructed Mamdani based fuzzy logic and automatically designed Takagi and Sugeno’s (ANFIS) approaches, have been utilized for this purpose. Batch mode of training has been employed, with huge (500) amount of training data. The training data is generated artificially through response equation obtained through regression analysis. Two different approaches with three different membership function distribution are developed and their performances are compared with the help of ten test cases. It is to be noted that the test case data is collected by conducting experiments and are not used during the learning phase of ANFIS. It is interesting to note that the approach 2 performed better compared to approach 1. It is important to note that the triangular membership function distributions of approach 1 and bell shape membership function distributions of approach 2 made better predictions in the present case. The improved performance of approach 2 relies majorly on the membership function distribution and the nature of the error surface. In addition it also depends on the behaviour (linear or non-linear) of the response with variation of the process parameters. Moreover the developed approaches are capable of making better predictions with the experimental test cases with different membership function dis-

139

tributions. However, the prediction of the approach 1 can be further enhanced by increasing the number of linguistic terms. The fuzzy logic models developed are found to be useful to make accurate prediction of casting density in squeeze casting for the different combination of process parameters. The present work is useful to foundry-men, since, it provides an insight about selection of process parameters for good quality casting in squeeze casting process.

Nomenclature FLC Fuzzy logic controller L Low M Medium H High A Time delay B Pressure duration C Squeeze pressure D Pouring temperature E Die temperature ρ Density μ Membership function a1, . . . , a6 Half base widths pi, qi, ri and ui Coefficient of consequent part GA Genetic algorithms ANNs Artificial neural networks GA-NN Genetic algorithm neural network BPNN Back propagation neural network FL Fuzzy logic ANFIS Adaptive network based fuzzy interface system RMSE Root mean square error MAPE Mean absolute percent error 2 R Co-efficient of correlation determination

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Hindawi Publishing Corporation Applied Computational Intelligence and So Computing Volume 2014, Article ID 293976, 12 pages http://dx.doi.org/10.1155/2014/293976

Research Article Forward and Reverse Process Models for the Squeeze Casting Process Using Neural Network Based Approaches Manjunath Patel Gowdru Chandrashekarappa,1 Prasad Krishna,1 and Mahesh B. Parappagoudar2 1 2

Department of Mechanical Engineering, National Institute of Technology Karnataka, Surathkal 575025, India Department of Mechanical Engineering, Chhatrapati Shivaji Institute of Technology, Durg, Chhattisgarh 491001, India

Correspondence should be addressed to Mahesh B. Parappagoudar; [email protected] Received 17 May 2014; Accepted 30 September 2014; Published 27 October 2014 Academic Editor: R. Saravanan Copyright © 2014 Manjunath Patel Gowdru Chandrashekarappa et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The present research work is focussed to develop an intelligent system to establish the input-output relationship utilizing forward and reverse mappings of artificial neural networks. Forward mapping aims at predicting the density and secondary dendrite arm spacing (SDAS) from the known set of squeeze cast process parameters such as time delay, pressure duration, squeezes pressure, pouring temperature, and die temperature. An attempt is also made to meet the industrial requirements of developing the reverse model to predict the recommended squeeze cast parameters for the desired density and SDAS. Two different neural network based approaches have been proposed to carry out the said task, namely, back propagation neural network (BPNN) and genetic algorithm neural network (GA-NN). The batch mode of training is employed for both supervised learning networks and requires huge training data. The requirement of huge training data is generated artificially at random using regression equation derived through real experiments carried out earlier by the same authors. The performances of BPNN and GA-NN models are compared among themselves with those of regression for ten test cases. The results show that both models are capable of making better predictions and the models can be effectively used in shop floor in selection of most influential parameters for the desired outputs.

1. Introduction The mechanical properties in castings majorly depend on the density and secondary dendrite arm spacing. The density and secondary dendrite structure are significantly influenced by the operating conditions of the squeeze cast process variables. In majority of the foundries, industrialists are trying to establish the input-output relationship through the use of process simulation software like procast and magmasoft. The significant effect of process parameters on the temperature difference in the squeeze casting process was studied using artificial neural networks and procast simulation software [1]. Later on, authors extended their research efforts to study the solidification time (which has direct influence on the formation of secondary dendrites) with various squeeze casting conditions by using the combinations of artificial neural network and procast simulation software [2]. However, simulation software considered being often inefficient, where large

number of process variables need to be examined and large number of repetitive analysis are required in the selection of most influential process variables. This will considerably increase the execution time and computational complexity [3]. In addition, simulation software also requires knowledge of human expertise to interpret the obtained results. These limitations made investigators/researchers draw much attention towards development of an alternate method for establishing the input-output relationships. From the past two decades, much of the work has been reported on the improvement in mechanical and microstructure properties of the cast product. However, most of the work was carried out using conventional engineering experimental and theoretical approach in establishing input-output relationships and selection of optimum process parameters. The effects of squeeze cast process variables on the casting density were studied experimentally by various investigators using

2 conventional engineering (varying one process parameter at a time and keeping the rest at the midvalues) approach [4, 5]. The analytical methods such as gracia’s virtual and steady state heat flow model had been utilized by solving the governing equations to study the effects of solidification time on the density and other mechanical properties of aluminium (Al) and zinc (Zn) based alloys [6]. The effects of gap distance on the cooling rate and secondary dendrite arm spacing were studied by using the numerical and experimental approaches [7]. The effects of pouring temperatures and squeeze pressures on the cast structure and tensile strengths of wrought aluminium alloy were investigated [8]. Squeeze pressure effect on secondary dendritic structure was studied for Al based alloys [9, 10]. The effects of squeeze pressure, die, and melt temperature were studied on secondary dendrite arm spacing of LM13 alloy [11]. The following key observations are made from the above literature. (1) Authors studied the effects of squeeze cast process variables using classical engineering experimental approach, wherein a large number of experiments are required for effective analysis. (2) The practical guidelines suggested by the authors may not help the shop floor workers in the selection of the most influential process parameters, unless the input-output relationship is expressed in mathematical form. (3) The classical engineering experimental approach provides the best process parameter levels (local optimum solution) and are completely different from those of optimal process parameter setting (global optimum solution). Limited research work is carried out to address the classical engineering experimental approach to study the effects of various process parameters by modelling, analyzing, and establishing the input-output relationship. Statistical Taguchi technique has been successfully implemented to study the effects of process variables on mechanical properties of squeeze cast AC2A alloy [12–14]. It is to be noted that the authors developed mathematical expression representing the properties as a function of squeeze cast process variables. Moreover, the effect of most significant time delay parameter was left out in their analysis. Squeeze pressure, pressure duration, and die temperature were considered to study the effects on mechanical properties using statistical Taguchi technique [15]. Moreover, the authors developed multivariable linear response equation by neglecting the effect of pouring temperature and time delay parameters. More recently, authors employed statistical Taguchi tool to study the influencing parameters such as squeeze pressure, filling velocity, die, and pouring temperature on strength and ductility of AlSi9Cu3 alloy [16]. It is to be noted that the authors did not consider the pouring temperature and time delay before pressurization. Further, the mathematical expression representing the input-output relationship of the squeeze casting system was left out in their analysis. The following key observations have been made from the authors attempted statistical Taguchi tool to optimize the squeeze cast process parameters. (1) Authors measured two or more responses for the same casting conditions, analysed, and developed response equation separately. It is of paramount importance to note that since different responses were measured for the same casting conditions, the probability of

Applied Computational Intelligence and Soft Computing the dependency among the outputs was more. Hence, there is a need to develop an integral multi-input-output system that could simultaneously estimate the outputs for the same inputs. (2) The developed response equations were not used to check the prediction accuracy of the test cases. It is of paramount importance to check the prediction accuracy. The most practical requirement in foundries is to know the process parameter setting that could produce the desired output that is, backward prediction. The backward prediction might be difficult through conventional statistical tools because the transformation matrix becomes singular and might not be invertible always [17]. The problem with reverse prediction and development of an integrated system that simultaneously estimates the two or more responses can be made possible through the use of soft computational tools like neural network (NN), genetic algorithms, fuzzy logic, and their different combinations [18]. Artificial neural networks were successfully applied to carry out the forward mapping (to predict the output for the known set of inputs) of various manufacturing processes like pressure die casting [3, 19], cement-bonded moulding sand system [20] and permanent mold casting [21], and end milling processes [22]. It is interesting to note that artificial neural network was successfully applied as forward and reverse modelling tool in green sand mould system [17], cement-bonded mould system [23], sodium silicate and CO2 gas hardened mould system [24], and pressure die casting system [25]. To the authors’ best knowledge, no much work has been reported to carry out the forward and reverse mappings in the squeeze casting process using neural network based approaches. The limitations of the classical engineering, casting simulation, and statistical Taguchi techniques are addressed through the use of artificial neural networks and the present work aim for the following two objectives: (1) forward mapping: forward mapping deals with predicting the responses/outputs for the known set of input conditions. In the present work, density and secondary dendrite arm spacing are considered as the outputs, whereas squeeze casting process variables such as time delay, squeeze pressure, pressure duration, pouring temperature, and die temperature were considered as inputs; (2) reverse mapping: reverse mapping deals with the prediction of the input parameters for the desired output. Here, density and secondary dendrite arm spacing were considered as the input and squeeze cast process variables are considered as the output of the system. It is to be noted that, to carry out the forward and reverse mappings, an artificial neural networks trained with back propagation and genetic algorithm has been employed.

2. Modelling Using Artificial Neural Networks The method of identifying, analysing, and establishing the input-output relationship of the physical system is termedas

Applied Computational Intelligence and Soft Computing

3

Table 1: Squeeze casting process parameters and their respective levels. Process parameters Squeeze pressure, (𝑆𝑝 ) Pressure duration, (𝐷𝑝 ) Time delay, (𝑇𝑑 ) Pouring temperature, (𝑃𝑡 ) Die temperature, (𝐷𝑡 )

Time delay Pressure duration Squeeze pressure Pouring temperature Die temperature

Units MPa S S ∘ C ∘ C

Level 1 0.1 10 03 630 100

Squeeze casting

Casting density

process model

Secondary dendrite arm spacing

Forward mapping

Level 2 50 20 05 660 150

Level 3 100 30 07 690 200

Level 4 150 40 09 720 250

Level 5 200 50 11 750 300

training (input-output) data have been artificially generated using response equations: density = 1.21121 − 0.0120733𝑇𝑑 + 8.80233𝑒 − 05𝐷𝑝 + 0.000270477𝑆𝑝 + 0.00354289𝑃𝑡 + 0.001781𝐷𝑡

Reverse mapping

Figure 1: Forward and reverse squeeze casting process model.

+ 6.77354𝑒 − 05𝑇𝑑2 + 4.03295𝑒 − 06𝐷𝑝2 − 1.32509𝑒 − 07𝑆𝑝2 − 2.47673𝑒 − 06𝑃𝑡2 − 3.89751𝑒 − 06𝐷𝑡2 ,

modelling. The present work is focused on both forward modelling and reverse modelling of the squeeze casting process as shown in Figure 1. Squeeze casting process variables such as time delay, pressure duration, squeeze pressure, pouring temperature, and die temperature are treated as the inputs, whereas, density and SDAS are treated as the outputs in case of forward mapping. In reverse modelling, process variables are expressed as function of casting density and SDAS. The process parameters and their respective levels used for the present study are presented in Table 1. 2.1. Data Collection. The supervised learning capability of artificial neural networks requires huge training data. In actual practice, huge data collection through real experiments finds impractical for researchers/investigators. However, the requirements of huge training data have been fulfilled by generating artificially (selecting the process parameters covering entire range) at random using the response equations derived though real experiments carried out earlier by the same authors [26, 27]. 2.2. Training Data. Huge data requirements for training the artificial neural networks have been generated artificially, using the response equations by selecting the process variables lying within the respective range. It should be noted that the generated training data covers the entire range with different squeeze casting conditions. Casting density and SDAS are expressed as a function of squeeze cast process variables, namely, time delay, pressure duration, squeeze pressure, and pouring and die temperature in separate response equations. The response equations casting density and SDAS are shown in (1) and (2), respectively. It should be noted that 1000 sets of

(1)

SDAS = 313.45 + 3.71889𝑇𝑑 − 0.318161𝐷𝑝 − 0.120364𝑆𝑝 − 0.632729𝑃𝑡 − 0.22336𝐷𝑡 − 0.144949𝑇𝑑2 + 0.00238712𝐷𝑝2 + 0.0001987998𝑆𝑝2 + 0.000402338𝑃𝑡2 + 0.000513454𝐷𝑡2 .

(2)

2.3. Testing Data. The success of neural network depends on the prediction accuracy of the test cases. Hence, the network prediction accuracy has been tested for randomly generated test cases (which is used during the training process). The experiments have been performed for ten randomly generated test cases and the measured values for casting density secondary dendrite arm spacing (SDAS) are recorded. Two replicates have been used for density measurements. Whereas, average value of the SDAS in each casting sample is determined at three different locations by taking a minimum of 15 different primary dendrites. It is to be noted that, the measurements have been carried out for the primary dendrites containing more than five secondary dendrite arms. The secondary dendrite arm spacing measurements have been performed using (3). It should be noted that ten different test cases are used to check the prediction accuracy of the network under forward as well as reverse mapping as shown in (Table 5), where “𝑖” denote index term of measured dendrite, 𝑛 is the number of measurement, 𝑋𝑖 is the dendritic length of 𝑖th term, and 𝑚𝑖 is the number of dendrite arms average SDAS =

1 𝑛 𝑋𝑖 ∑ . 𝑛 𝑖=1 𝑀𝑖

(3)

4

Applied Computational Intelligence and Soft Computing Bias [Vij ]

[Wjk ]

Bias Bias Time delay Density

Pressure duration Squeeze pressure Pouring temperature

SDAS

Die temperature Input layer

Hidden layer

Output layer

Figure 2: Artificial neural network architecture used for forward mapping.

2.4. Forward Mapping. In the present work, three-layer feed forward neural network architecture consisting of input, output, and hidden layer neurons (Figure 2) is used. Five and two neurons are used for the input and output layer, respectively. However, the selection of neurons lying in the hidden layer is determined through the parametric study. Linear transfer function has been employed for input layer, whereas nonlinear log-sigmoid transfer function has been utilized for output layer neurons, respectively (see (4)–(6)). It is to be noted that the effect of the response SDAS and density was studied under statistical analysis and it was seen that the behaviour of the density and SDAS with same inputs is the opposite for the same casting conditions. So, for the response SDAS, the modified log-sigmoid activation function was used (5). However, the same sigmoid transfer function has been adopted for all the neurons lying in the hidden layer (7). The term “𝑚” indicates the constant and the value is determined after performing large number of trials, “𝑥” is the input neuron, and “𝑎” and “𝑏” transfer function constants of output layers, respectively, linear transfer function (𝑦) = 𝑚𝑥, log-sigmoid transfer function (𝑦) =

1 , (1 + exp (𝑎𝑥))

(4)

of training is adopted to optimize the structure of NN. The output of the NN is compared with the target values to determine the error. The BPNN is adaptively trained to reduce the mean square error and is calculated using (8). It should be noted that, to avoid numerical fluctuations and to speed up the training process, the training input-output data has been normalized between zero and one as follows: Minimize Error =

1 . (7) log-sigmoid transfer function (𝑦) = (1 + exp (−𝑐𝑥)) 2.5. Back Propagation Neural Network (BPNN). The supervised learning capability of back propagation algorithm is that it learns with training. One thousand sets of input-output data have been generated artificially by using regression models and passed through the NN. That is, batch mode

(8)

The term “𝑅” indicates the number of responses, “𝑁” represents the number of training data, “𝑇𝑖𝑗 ” depicts the target values, and “𝑂𝑖𝑗 ” indicates the network output. It should be noted that the error back propagation algorithm work is based on the principle of gradient descent method to reduce the mean square error. Hence, the network weights need to be updated with learning rate (𝜂) and momentum parameters (𝛼) as shown in (9). The learning rate parameter is used to avoid overfitting and the error vibration, whereas to speed up the training process when the network stucks with local optima region, the term momentum constant will be used

(5)

1 log-sigmoid transfer function (𝑦) = , (6) (1 + exp (−𝑏𝑥))

2 1 𝑅 𝑁 ∑ ∑(𝑇𝑖𝑗 − 𝑂𝑖𝑗 ) . 𝑅 × 𝑁 𝑖=1𝑗=1

Δ𝑊𝑗𝑘 (𝑡) = −𝜂

𝜕𝐸 (𝑡) + 𝛼Δ𝑊𝑗𝑘 (𝑡 − 1) . 𝜕𝑊𝑗𝑘

(9)

The term 𝑡 indicates the iteration number and 𝜕𝐸/𝜕𝑊𝑗𝑘 can be determined using the chain rule of differential equation as shown in the following equation: 𝜕𝐸 𝜕𝑌𝑘 𝜕𝑈𝑘 𝜕𝐸 = . 𝜕𝑊𝑗𝑘 𝜕𝑌𝑘 𝜕𝑈𝑘 𝜕𝑊𝑗𝑘

(10)

The terms 𝑈𝑘 and 𝑌𝑘 represent input and output of the 𝐾th neuron lying on the output layer, respectively.


5

Table 2: BPNN parametric study results of both forward and reverse mappings. NN parameters Hidden neurons Learning rate-hidden layer, 𝜂 Learning rate-output layer, 𝜂 Momentum constant, 𝛼 Activation constant-hidden layer Activation constant 1-output layer Activation constant 2-output layer Bias

Forward mapping 11 0.01 0.5885 0.455 2.8 5.5 8.65 0.0000455

Error 0.017321 0.008271 0.003099 0.003099 0.002525 0.002525 0.001984 0.001458

Reverse mapping 18 0.5885 0.2325 0.455 5.5 5.5 5.5 0.0000505

Error 0.034095 0.033450 0.033410 0.033410 0.033410 0.033410 0.033410 0.033410

Table 3: GA-NN parametric study results of both forward and reverse mappings. GA-NN parameters Mutation probability Population size Generations number

Forward mapping 0.0001447 218 10000

Error 0.001652 0.001534 0.001337

2.6. Genetic Algorithm Based Neural Network. Genetic algorithm (GA) is used from the past few decades in many of the manufacturing applications to obtain the global optimum solution. It is to be noted that the back propagation algorithm has the probability to get trapped in the local optimal region as compared to the GA (since it searches the solution in huge space). The genetic tuned NN (GA-NN) system works exactly on the same principle of auxiliary hybrid systems. The synaptic weights, activation function constants, and the bias values are supplied by GA-string and the network computes the expected output. In GA-NN, the hidden number of neurons is kept same as that of the BPNN obtained under parametric study. The mean square error is calculated and used as the fitness value of the GA-string. The GA fitness value is computed by using (11). Tournament selection, uniform cross-over, and bit-wise mutations are chosen as the GA operators to find the best possible solutions as follows: fitness (𝑓) =

2 1 𝑅 𝑁 ∑∑ (𝑇 − 𝑂𝑖𝑗 ) . 𝑅 × 𝑁 𝑖=1𝑗=1 𝑖𝑗

(11)

2.7. Reverse Mapping. Reverse mapping has been carried out to predict the recommended input parameters for the desired output. Both BPNN and GA-NN have been used to perform the said task. It is to be noted that two responses and five process variables are considered as the inputs and the outputs of the system, respectively.

3. Results and Discussions Forward mapping has been carried out using both BPNN and GA-NN to predict the density and secondary dendrite arm spacing for the known set of process variables of the squeeze casting process. The performances of the developed models have been evaluated with the help of ten randomly generated test cases (Table 5).

Reverse mapping 0.0001379 260 10000

Error 0.03219 0.02916 0.02514

3.1. Back Propagation Neural Network (BPNN). It is to be noted that, 1000 sets of input-output training data is used to train the network using batch mode. The parametric study was carried out to optimize the neural network parameters during training (see Figure 3). The parametric study is carried out by varying the neural network parameters (such as hidden neurons number, learning rate, momentum constant, activation function constants, and the bias value) one at a time and keeping the rest at their respective midvalues. It is to be noted that the results of the parametric study are shown in Table 2. The minimum mean square error at the end of the training was found to be equal to 0.001458 (Table 2). Once the training has been completed, the neural network is used for predicting ten test cases, which are not used for the NN training. The neural network predictions are compared with the actual experimental values and the average absolute percent deviation in prediction is found to be equal to 2.55%. 3.2. Genetic Algorithm Neural Network (GA-NN). As explained in the previous sections, the back propagation algorithm has been replaced by population based search algorithm to search the optimal solutions in huge space. In the present work, GA is used to optimize the neural network parameters. In GA-NN system, the performance in the prediction largely depends on genetic parameters such as mutation probability, population size, and generation number. The GA-parametric study has been carried out to determine the global solutions (Figure 4). The selection criteria for the optimum GA parameters are decided based on the minimum mean squared error obtained when varied between their respective parameter ranges. It is to be noted that uniform cross-over is used for the cross-over operation. The optimal mean square error obtained for different parameters is shown in Table 3. The optimum parameters obtained at the end of the training, with minimum value of mean squared error equal to 0.001337. Once, the Neural Network parameters are optimised using

Applied Computational Intelligence and Soft Computing 0.18 0.16 0.14 0.12 0.10 0.08 0.06 0.04 0.02 0.00

0.020

Mean square error

Mean square error

6

0.018 0.016 0.014 0.012 0.010 0.008

3

5

7

9 11 13 15 17 19 21 23 25 Number of hidden neurons

0.010

0.188 0.366 0.544 0.722 Learning rate-hidden layer (b)

0.14 0.12 0.10 0.08 0.06 0.04 0.02 0.00

Mean square error

Mean square error

(a)

0.010

0.188 0.366 0.544 0.722 Learning rate-output layer

0.900

0.16 0.14 0.12 0.10 0.08 0.06 0.04 0.02 0.00

0.010

0.188 0.366 0.544 0.722 Momentum constant

(c) 0.14 0.12 0.10 0.08 0.06 0.04 0.02 0.00 1.0 1.9 2.8 3.7 4.6 5.5 6.4 7.3 8.2 9.1 10.0

0.14 0.12 0.10 0.08 0.06 0.04 0.02 0.00 1.0 1.9 2.8 3.7 4.6 5.5 6.4 7.3 8.2 9.1 10.0 Activation function constant 1-output layer

Activation function constant-hidden layer

(f) Mean square error

Mean square error

(e) 0.14 0.12 0.10 0.08 0.06 0.04 0.02 0.00

1.0 1.9 2.8 3.7 4.6 5.5 6.4 7.3 8.2 9.1 10.0 Activation function constant 2-output layer (g)

0.900

(d)

Mean square error

Mean square error

0.900

0.14 0.12 0.10 0.08 0.06 0.04 0.02 0.00 10

208

406

604

Bias value

802

1000 ×10−7

(h)

Figure 3: Results of parametric study to determine the optimal neural network parameters: (a) error versus number of neurons in the hidden layer, (b) error versus learning rate-hidden layer, (c) error versus learning rate-output layer, (d) error versus momentum constant, (e) error versus activation function constant-hidden layer, (f) error versus activation function constant 1-output layer, (g) error versus activation function constant 2-output layer, and (h) error versus bias value.

GA, the performance of GA-NN in forwarding mapping is tested by utilizing the same test cases (i.e., the test cases used for BPNN). The average absolute percentage deviation in prediction of the responses is found to be equal to 2.234%.

3.3. Comparison of BPNN, GA-NN, and Statistical Models Performances. It is to be noted that the performances of the developed NN based approaches are compared among themselves and with statistical regression model for ten randomly generated test cases.

1.0

0.8 0.6 0.4 0.2 0.00015830

0.00013785

0.00011740

0.00009695

0.00007650

0.00005605

0.00003560

0.00001515

0.0

0.0037 0.0035 0.0033 0.0030 0.0027 0.0025 0.0023 0.0020 0.0018 0.0015 0.0013

50 78 106 134 162 190 218 246 274 302 330

7

Mean square error

Mean square error


Population size

Mutation probability (b)

Mean square error

(a) 0.0037 0.0035 0.0033 0.0030 0.0027 0.0025 0.0023 0.0020 0.0018 0.0015 0.0013

0 50 150 250 350 450 550 650 750 850 9501050 Generation number

(c)

Figure 4: GA-NN parametric study. (a) Mutation probability, (b) population size, and (c) generation number.

Table 4: Average absolute percent deviation in prediction of the responses (forward mapping). Response Density SDAS

BPNN 0.347 4.758

GA-NN 0.290 4.178

Average absolute percent deviation in prediction Regression MCFLC [28, 29] 0.377 0.503 5.157 8.888

Figure 5(a) shows the percent deviation in prediction of the ten test cases using three different models for the response density. The values of percent deviation in prediction are found to lie in the range of −0.17% to +0.85%, −0.3% to +0.86%, and −0.12% to +0.89% for the regression, BPNN, and GA-NN models, respectively. Similarly, the percent deviation in prediction of the response secondary dendrite arm spacing was found to lie in the range of −10.21% to +6.26%, −10.19% to +7.02%, and −7.27% to +6.04% for regression, BPNN, and GA-NN models, respectively (Figure 5(b)). It is to be noted that, for both responses, GA-NN model outperforms the other two models. Table 4 provides the comparison of the performances in predictions of soft computing based approaches (BPNN, GA-NN, MCFLC, and ANFIS) with that of the statistical regression model in terms of average absolute percent deviation in prediction of ten test cases for the response density and SDAS. It is to be noted that GA-NN, BPNN, and ANFIS performances are found to be almost similar and comparable, but the GA-NN outperforms all the models in prediction of the responses (Table 4). The better performance of GA-NN might

ANFIS [28, 29] 0.289 4.571

be due to the nature of error surface, where it is possible for GA to hit the global optima. 3.4. Reverse Mapping. The reverse mapping has been carried out with the aim of predicting the process parameters such as squeeze pressure, time delay, pressure duration, and pouring and die temperature for the desired density and SDAS. The NN based approaches (i.e., BPNN and GA-NN) are utilized to tackle the above-said task and the obtained results are compared among themselves. The same set of test cases is used for checking the model performances (Table 5). The results of the parametric study of both BPNN and GA-NN models are presented in Tables 2 and 3. The ten different test cases were passed through the optimized network and the average absolute percent deviation in prediction of all the responses under BPNN and GA-NN models is found to be equal to 11.66% and 7.49%, respectively. Figure 6(a) shows the deviation plots indicating the percent deviation in prediction for the response time delay. It is to be noted that the percent deviation obtained by the BPNN model is found to lie in the range of 0% to 27.27%

8

Applied Computational Intelligence and Soft Computing Table 5: Summary results of input-output results of the test cases.

Exp. no. 1 2 3 4 5 6 7 8 9 10

𝐷𝑡

11 7 6 5 5 9 9 11 4 4

30 14 37 40 10 33 48 32 21 23

263 192 236 254 142 261 174 189 213 284

101 110 63 142 71 110 96 172 196 89

671 635 674 731 723 738 637 712 646 742

Response density

0.8 0.6 0.4 0.2 0.0 −0.2

1

2

3

4

5 6 7 Test case number

8

9

10

−0.4 GA-NN

Regression BPNN (a)

Deviation in prediction (%)


1.0

𝑇𝑑

Squeeze casting process parameters 𝐷𝑝 𝑆𝑝 𝑃𝑡

8 6 4 2 0 −2 −4 −6 −8 −10 −12

Responses SDAS, 𝜇m Density, g/cm3 48.43 49.74 47.64 33.78 46.86 48.33 50.63 44.86 35.66 41.34

2.602 2.622 2.628 2.664 2.626 2.614 2.595 2.618 2.676 2.663

Response SDAS

1

2

3

4

5

6

7

8

9

10

Test case number

GA-NN

Regression BPNN (b)

Figure 5: Comparison of three models in terms of percent deviation in predictions. (a) Density and (b) secondary dendrite arm spacing.

with all points on the positive side. On the other hand, GA-NN prediction deviations are spread on either side and the corresponding maximum values are found to vary in the range of −25% to +18.18%. The average absolute percent deviation in prediction of the time delay parameter is found to be equal to 17.45% for BPNN and 11.46% for GA-NN. The performance in prediction of BPNN and GA-NN models in terms of percent deviation for the response pressure duration is shown in Figure 6(b). It is to be noted that the performances in prediction of both models result in similar pattern for the response pressure duration. GA-NN model performs slightly better, compared to BPNN, and the percent deviation values are found to lie within the range of −40% to +18.75% for BPNN and −30% to +12.5% for GANN, respectively. The average absolute percent deviation as obtained for the BPNN and GA-NN models for the ten test cases is found to be equal to 19.25% and 10.01%, respectively. Figure 7(a) compares the performance of the BPNN and GA-NN models in predicting the squeeze pressure. The percent deviation for the response squeeze pressure is found to vary in the similar pattern for both BPNN and GANN models and the corresponding percent deviation range

was found to lie in the range of −25.39% to +10.41% and −20.64% to +8.33%, respectively. It is also important to mention that except for one test case (2) GA-NN model always tries to predict the response close to the experimental values (Figure 7(a)). In addition, the computation of average absolute percent deviation in prediction of the squeeze pressure is found to be equal to 11.78% and 9.32% for BPNN and GA-NN, respectively. Figure 7(b) represents the plot of percent deviation values in prediction of pouring temperature using BPNN and GANN models. It is interesting to note that both BPNN and GA-NN follow the same path and prediction made with respect to the developed BPNN and GA-NN models is found to vary between −3.46% and +2.9% for BPNN and −3.3% and +2.1% for GA-NN, respectively. The average absolute percent deviation values for BPNN and GA-NN models are found to be equal to 2.33% for BPNN and 2.01% for GA-NN, respectively. Figure 8 shows the deviation plots of BPNN and GA-NN in predicting the response die temperature. The percent deviation in prediction is found to vary in the range between −10.34% and +11.86% for BPNN and −8.05% and +6.87% for


25 20 15 10 5 0 −5 −10 −15 −20 −25 −30

Response time delay 20

1

2

3

4


8

10

9



30

9

Response pressure duration

10 0

1

2

3

4

−10


8

9

10

−20 −30 −40 BPNN GA-NN

BPNN GA-NN (a)

(b)

Figure 6: Comparison of NN based approaches in predicting the responses. (a) Time delay and (b) pressure duration. 15

Response squeeze pressure

3

5 0 −5

1

2

3


7

8

9

10

−10 −15 −20



10

Response pouring temperature

2 1 0 1

2

−1

3

4


8

9

10

−2 −3

−25

−4

−30 BPNN GA-NN

BPNN GA-NN (a)

(b)

Figure 7: Comparison of NN based approaches in predicting the responses. (a) Squeeze pressure and (b) pouring temperature.

GA-NN. The GA-NN model performs better as compared to BPNN and it is better explained with respect to the average absolute percent deviation in prediction. The average absolute percent deviation in prediction of the response die temperature is found to be equal to 7.51% for BPNN and 4.63% under GA-NN model, respectively. The reverse mapping aim is to predict the process parameters for the desired density and SDAS. The reverse mappings meet the stringent requirements of the industry to know the recommended process parameters to achieve the desired output by eliminating the trial and error method, simulation software, and expert advice to interpret the obtained simulation results. The results show the average absolute percent deviation in prediction of the process parameters for the desired responses comparable to both BPNN and GA-NN models (Figure 9). It is also important to mention that the

grand average absolute percent deviation in prediction of all the responses using BPNN and GA-NN is found to be equal to 11.66% and 7.49%, respectively. However, through the exhaustive population based search, GA-NN results in much improved performance compared to BPNN. Better performance of GA-NN over BPNN might be due to the nature of error surface. BPNN is gradient search based approach, where the solution might be trapped in local minima.

4. Comparisons with the Earlier Work The performance of developed NN based approaches has been compared for the same test cases carried out earlier by the same authors using fuzzy logic based approaches [28, 29]. The authors worked earlier on the fuzzy logic based

10



15

5. Concluding Remarks

Response die temperature

10 5 0 2

1

3

4 5 6 7 Test case number

−5

8

9

10

−10

BPNN GA-NN


Figure 8: Comparison of two models in predicting the response die temperature.

20

18 16 14 12 10 8 6 4 2 0 Td

Dp

Sp

Pt

Dt

Responses BPNN GA-NN

Figure 9: Comparison of two models in terms of average absolute percent deviation in prediction of the test cases for process parameters.

approaches, namely, manually constructed FLC (MCFLC) and automatically evolved adaptive network based fuzzy interface system (ANFIS), using different membership functions. In the present work, an attempt is made by the authors to compare the performance of both BPNN and GA-NN models with that of the above-mentioned work carried out earlier by the same authors [28, 29]. Table 4 shows the average absolute percent deviation in prediction of all the models for predicting the responses density and SDAS via forward mapping. It is observed from Table 4 that the average absolute percent deviation in prediction of the response density is comparable for both neural network and fuzzy logic based approaches. However, the GA-NN model outperforms, for the response, SDAS in terms of prediction accuracy when it is compared with that of the fuzzy logic based approaches.

An attempt has been made to develop the forward and reverse process models for the squeeze casting process using neural network based approaches. Batch mode of training has employed the training data generated artificially at random using regression equations derived through real experiments carried out earlier by the same authors. The detailed parametric study has been carried out to optimize the network parameters in both BPNN and GA-NN approaches. The mean square error obtained during the training process is considered as the criterion for optimization. In forward mapping, the performance of BPNN and GANN models is compared among themselves and with that of the regression analysis for ten test cases. It is interesting to note that NN based models are capable of making effective predictions. However, GA-NN outperformed the BPNN model for both responses, namely, density and SDAS. The problem with the statistical regression analysis in developing the reverse process model has been effectively tackled by the NN based approaches (i.e., to predict the process variables for the desired output). The performance of the developed models, namely, BPNN and GA-NN, is compared among themselves. It is to be noted that GA-NN outperforms BPNN model for all the responses. This might be due to the nature of error surface and the problem of BPNN solutions getting trapped in local optimum. BPNN approach uses gradient based search for optimum solutions. When the error surface is multimodal, the BPNN solutions may be trapped in local minima. On the other hand, GA is a population based search, where search starts at many locations simultaneously. Hence, it is possible for GA to hit the global minima. It is important to note that the average absolute percent deviations in prediction of both neural network based approaches for reverse modelling are not found to be good enough. This might be due to the fact that complex relationship exists with the input process variables for the said responses. In addition, the number of network input parameters is less than that of the network output in case of reverse mapping. The overall performance of the developed NN based approaches has been compared for forward mapping with the results of the fuzzy logic based approaches carried out earlier by the same authors. The results are comparable for the response density; however, GA-NN shows a slightly better performance in prediction of secondary dendrite arm spacing. It is to be noted that the results of the reverse modelling are considered to be more useful for the foundry men to achieve the desired output. In addition, the developed methodology can be implemented to adjust the process parameters in on-line control of the casting quality.

Conflict of Interests The authors declare that there is no conflict of interests regarding publication of this paper.


Acknowledgment The authors greatly acknowledge the Department of Applied Mechanics and Hydraulics, National Institute of Technology Karnataka, Surathkal, for their kind help in carrying out the experiments.

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11 [14] P. Senthil and K. S. Amirthagadeswaran, “Enhancing wear resistance of squeeze cast AC2A aluminium alloy,” International Journal of Engineering, Transactions A: Basics, vol. 26, no. 4, pp. 365–374, 2013. [15] P. Vijian and V. P. Arunachalam, “Optimization of squeeze cast parameters of LM6 aluminium alloy for surface roughness using Taguchi method,” Journal of Materials Processing Technology, vol. 180, no. 1–3, pp. 161–166, 2006. [16] S.-B. Bin, S.-M. Xing, L.-M. Tian, N. Zhao, and L. Li, “Influence of technical parameters on strength and ductility of AlSi9Cu3 alloys in squeeze casting,” Transactions of Nonferrous Metals Society of China (English Edition), vol. 23, no. 4, pp. 977–982, 2013. [17] M. B. Parappagoudar, D. K. Pratihar, and G. L. Datta, “Forward and reverse mappings in green sand mould system using neural networks,” Applied Soft Computing Journal, vol. 8, no. 1, pp. 239– 260, 2008. [18] S. Benguluri, P. R. Vundavilli, R. P. Bhat, and M. B. Parappagoudar, “Forward and reverse mappings in metal casting— a step towards quality casting and automation,” AFS Transactions—American Foundry Society, vol. 119, pp. 19–34, 2011. [19] P. K. D. V. Yarlagadda and E. C. W. Chiang, “Neural network system for the prediction of process parameters in pressure die casting,” Journal of Materials Processing Technology, vol. 89, pp. 583–590, 1999. [20] A. Mandal and P. Roy, “Modeling the compressive strength of molasses-cement sand system using design of experiments and back propagation neural network,” Journal of Materials Processing Technology, vol. 180, no. 1–3, pp. 167–173, 2006. [21] E. Abhilash, M. A. Joseph, and P. Krishna, “Prediction of dendritic parameters and macro hardness variation in permanent mould casting of Al-12% Si alloys using artificial neural networks,” Fluid Dynamics & Materials Processing, vol. 2, pp. 211–220, 2006. [22] A. B. Sharkawy, “Prediction of surface roughness in end milling process using intelligent systems: a comparative study,” Applied Computational Intelligence and Soft Computing, vol. 2011, Article ID 183764, 18 pages, 2011. [23] M. B. Parappagoudar, D. K. Pratihar, and G. L. Datta, “Modelling of input-output relationships in cement bonded moulding sand system using neural networks,” International Journal of Cast Metals Research, vol. 20, no. 5, pp. 265–274, 2007. [24] M. B. Parappagoudar, D. K. Pratihar, and G. L. Datta, “Neural network-based approaches for forward and reverse mappings of sodium silicate-bonded, carbon dioxide gas hardened moulding sand system,” Materials and Manufacturing Processes, vol. 24, no. 1, pp. 59–67, 2008. [25] J. K. Kittur and M. B. Parappagoudar, “Forward and reverse mappings in die casting process by neural network-based approaches,” Journal for Manufacturing Science and Production, vol. 12, no. 1, pp. 65–80, 2012. [26] G. C. M. Patel, R. Mathew, and P. Krishna, “Effects of squeeze casting process parameters on density of LM20 alloy,” in Proceedings of the 4th International Joint Conference on Advances in Engineering and Technology (AET '13), pp. 776–785, National Capital Region, India, December 2013. [27] G. C. M. Patel, R. Mathew, P. Krishna, and M. B. Parappagoudar, “Investigation of squeeze cast process parameters effects on secondary dendrite arm spacing using statistical regression and artificial neural network models,” Procedia Technology, vol. 14, pp. 149–156, 2014.

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Manjunath Patel et al., Adv Automob Eng 2015, 4:1 http://dx.doi.org/10.4172/2167-7670.1000111

Review Article

Open Access

Modelling in Squeeze Casting Process-Present State and Future Perspectives Manjunath Patel GC1*, Krishna P1 and Parappagoudar MB2 1 2

Department of Mechanical Engineering, National Institute of Technology Karnataka, Surathkal, India Department of Mechanical Engineering, Chhatrapati Shivaji Institute of Technology, Durg, Chhattisgarh, India

Abstract The growing demand in today’s competitive manufacturing environment has encouraged the researchers to develop and apply modelling tools. The development and application of modelling tools help the casting industries to considerably increase productivity and casting quality. Till date there is no universal standard available to model and optimize any of the manufacturing processes. However the present work discusses the advantages and limitations of some conventional and non-conventional modelling tools applied for various casting processes. In addition the research effort made by various authors till date in modelling and optimization of the squeeze casting process has been reported. Furthermore the necessary steps for prediction and optimization are high lightened by identifying the trends in the literature. Ultimately this research paper explores the scope for future research in online control of the process by automatically adjusting the squeeze cast process parameters through reverse prediction by utilizing the soft computing tools namely, Neural Network, Genetic Algorithms, Fuzzy-logic Controllers and their different combinations. The present work also proposed a detailed methodology, starting from the selection of process variables till the best process variable combinations for extreme values of the outputs responsible for better product quality using experimental, prediction and optimization methodology.

Keywords: Forward and reverse modelling and optimization; Soft computing; Squeeze casting process; Statistical tools Abbreviations: ABC: Ant Bee Colony; ANFIS: Adaptive Network Fuzzy Interface System; BHN: Brinell Hardness number; BBD: Box Behnken Design; BPNN: Back Propagation Neural Network; CCD: Central Composite Design; DM: Die Material; DOE: Design Of Experiments; DP: Pressure Duration; DT: Die Temperature; FDM: Finite Difference Method; FEM: Finite Element Method; FFD: Full Factorial Design; FL: Fuzzy Logic; FVM: Finite volume Method; FV: Filling Velocity; GA: Genetic Algorithm; GA-FL: Genetic Algorithm Fuzzy Logic; GA-NN: Genetic Algorithm Neural Network; HTC: Heat Transfer Coefficient; HV: Vickers Hardness; MM: Morphological Matrix; NN: Neural Network; PSO: Particle Swarm Optimization; PT: Pouring Temperature; SA: Simulated Algorithm; SP: Squeeze Pressure; SR: Surface Roughness; TD: Time Delay; TLBO: Teacher Learning Base Algorithm; UTS: Ultimate Tensile Strength; YS: Yield strength Introduction In today’s competitive world industries are searching for light weight materials possess high strength to weight ratio with less defective processing methods. This drawn much attention towards the research to search for alternative processing method to limit the weakness of one technology with the strength of the other. Casting process considered being one among the most economical route to manufacture the automobile and aerospace components. The most common problem with the conventional casting method is the probable occurrence of defects like shrinkage and the porosity. To overcome these limitations, researchers tried to integrate the immense features of economy and design flexibility of conventional casting process (pressure die casting and gravity) and strength and integrity of forging process. This integrated casting method is termed as squeeze casting which works based on the concept of pressurized solidification. The investigations were carried out in castings with simple geometries by using either gap measurement method or heat conduction methods on heat transfer coefficients (HTC). However, it was observed that interfacial [1-15], processing methods [16-19], casting geometry and Adv Automob Engg ISSN:2167-7670 AAE, an open access journal

size [20,21], physical and chemical conditions [22], mold and casting material properties [23], process variables [24-28] and so on directly affect the HTC. The combined effect of these factors influences the HTC, thereby making it difficult to separate and study the main effects of the factors. It is to be noted that the HTC greatly influences the mechanical and micro-structure properties. Although past few decades researchers\investigators tried to improve the mechanical and microstructure properties, but it is under intensive study since the existence of the probable squeeze casting defects such as oxide inclusion, porosity, extrusion segregations, centre line segregations, sticking, cold laps, extrusion debonding, blistering, under fill, shrinkages, hot tearing and case deboning [29,30]. The major parameters that affect the quality of the squeeze cast components such as squeeze pressure, pressure duration, time delay in pressurizing the metal, pouring temperature, die temperature, inoculants, filling velocity, lubrication type, film thickness and its adherence, melt quality and quantity etc. It is understood that proper control of these parameters may eliminate the possible squeeze casting defects. There is no universal standards available to control the above said process variables to achieve the desired squeeze cast components. Hence in the present work discusses the steps followed by various researchers till date to optimize the squeeze casting process are discussed, the scope for future directions in squeeze casting process for achieving the desired results are to identified through the trends in available literature and their main differences with squeeze casting process.

*Corresponding author: Manjunath Patel GC, Department of Mechanical Engineering, National Institute of Technology Karnataka, Surathkal-575025, Karnataka, India, E-mail: [email protected] Received December 11, 2014; Accepted January 07, 2015; Published January 16, 2015 Citation: Manjunath Patel GC, Krishna P, Parappagoudar MB (2015) Modelling in Squeeze Casting Process-Present State and Future Perspectives. Adv Automob Eng 4: 111. doi:10.4172/2167-7670.1000111 Copyright: © 2015 Manjunath Patel GC, et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

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Citation: Manjunath Patel GC, Krishna P, Parappagoudar MB (2015) Modelling in Squeeze Casting Process-Present State and Future Perspectives. Adv Automob Eng 4: 111. doi:10.4172/2167-7670.1000111

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Modelling Approaches Modelling refers to the method of identifying, establishing and analyzing the input-output relationships of the physical system. Generally the modelling tools are classified into two types namely 1. Conventional modelling tools (Finite element method, Response surface methodology, Design of experiments etc.,) 2. Unconventional modelling tools (Soft computing tools like particle swarm optimization, genetic algorithm, neural networks, fuzzy logic and their different combinations) In recent years the modelling tools are used in various manufacturing systems to statistically analyze the inputs and outputs and establish the input-output relationships. Further to meet the stringent requirements of the industries modelling tools are used in two ways.

Forward modeling Forward modelling aims to predict the response for the known set of input parameters. Reverse modelling: Reverse modelling aims at determining the appropriate set of the inputs for the desired output. Furthermore reverse modelling helps in online control of the process by adjusting the input parameters responsible for the desired output. In recent years, lot of research work carried out to improve the mechanical and micro-structure properties. However most of the research happened during those periods aimed for enhancing the properties though mathematical modelling approach, classical engineering experimental approach, numerical and analytical studies, statistical experimental approaches, soft and hybrid computing approaches.

Mathematical modelling approach Finite elemental analysis method (FEM) [31-35], finite volume method (FVM) [36], finite difference methods (FDM) [37], and enthalpy method are the mathematical tools which were employed to simulate squeeze casting processes. On observing from the literatures, all the models which are capable of making effective simulations were noted. However, in terms of computational complexity and programming use of finite based on element and difference methods for complex geometries gave better results in compensation with time consumption. Using continuity and momentum equations [38], the major shrinkage problem in castings and the pressure drops in the mushy zone were calculated. The physics involved in the processes namely, radiation, conduction, convection, pressure transfer, feeding flow, phase and mass transfers, solidification and successive stages and stress/strain behaviour were considered by these models. It is quite difficult to implement mathematical formulation in numerical simulations [39], assumptions made during solidification stage, computational complexity, time consuming. Furthermore, simulation results are highly reliant on how best the software code could capture the information of physics of the process, material characteristics and boundary conditions namely heat transfer coefficients between metal-mould interfaces [40]. For numerical simulations, design of experiments (DOE) was recently used by some authors, because the replication of experiments was not required, there were no uncontrollable parameters affecting the responses, and the significant factors influencing responses and optimization were quickly identified.

Casting simulation software approach Simulation software often used in most of the foundries Adv Automob Engg ISSN:2167-7670 AAE, an open access journal

applications for decision making, where human process knowledge is not sufficient or the process calibration takes higher time than the manufacturing process can afford [41], to find the solution to bring the process to an optimal condition with less possible defects. To address the problems related to mold filling, solidification stages, filling velocity and temperature profile estimations, any casting, Procast and magma soft were utilized by the authors [42-44] to simulate the squeeze casting process. The initialization of accurate boundary conditions was the most difficult part in casting simulation software packages. Assumptions were made in boundary conditions that temperature of air around the mould was ambient and also suitable for the heat transfer coefficients [45]. Simulation software’s often used for new products, where large number of products needs to be manufactured under repetitive order. However, simulation software often considered to be inefficient due to high capital initial investment, lots of assumptions to be made in regards with material transport phenomenon and boundary conditions and practical castings are difficult to achieve the desired results in actual shop floor, not suitable for continuous simulation for cyclic analysis while searching for optimal process conditions, high computational costs and need for experts advice to interpret the obtained results. These reasons made lots of researchers to search for alternate method to optimize the process. In recent years, some authors [46,47] used procast simulation software to predict temperature difference and the solidification time of the squeeze cast components. Since optimizing the process requires huge number of input-output data and is considered to be impractical either through experimental or simulation software alone. So authors adopted statistical design of experiment (DOE) to limit the simulation trial runs and to find the optimal squeeze casting condition.

Classical engineering experimental approach The classical engineering experimental studies deals with varying one parameter at once and maintaining the rest of the mid-values within their corresponding levels. The experiments performed by various researchers using classical engineering approach to study the effects of squeeze pressure, casting temperature, die temperatures, time delay, inoculants and pressure duration on solidification time, density, secondary dendrite arm spacing, grain size, hardness, tensile and impact strengths of different aluminium based alloys [48-60]. The following advantages and limitations have been identified from the above discussed literatures, Advantages: 1) Classical engineering approach helps in knowing the behaviour of the process parameters from one level to the other for the response measured 2) It helps in identifying the range of the process parameters showing significant contribution, thus helps in determining the optimal process parameter range to fulfill the preliminary requirements for studying the complete insight information of the process through statistical design of experiments. Limitations: 1) In most literatures the authors attempted the conventional engineering approach to perform the experiments and analysis wherein, increase in process variable number and levels, increases the need of real experiments to be conducted. 2) In squeeze casting process there is large number of interconnected process variables and the results obtained from the said approach may

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Page 3 of 9 not reveal the combined influence of the input parameters on the measured outputs. 3) It is to be noted that the classical engineering experimental approach can only suggest the optimal process parameter levels and are completely different from those of global optimal process parameter setting. 4) The practical guidelines suggested by the authors to optimize the process may not help the foundry men unless the input-output relationships are expressed in mathematical form. 5) The use of conventional engineering approach uses varying one parameter at once after keeping the rest parameters at its mid-values. However it is important to mention that several process variables need to be simultaneously varied to know the complete insight information of individual and the combined (interaction) effect of the factors on the response of interest under investigation.

Statistical Design of Experiments (DOE) Statistical DOE, proved to be the cost effective modelling tool compared to the conventional engineering approach from the past few decades. The major advantages of statistical design of experiments are reduces number of experiments, several process variables can be simultaneously studied, estimate the percent contribution of each individual and the combined (interaction) effect parameters on the response (output) under investigation, graphically represents the behaviour of the process parameter on the response when the variable shifts from one level to the other and establishes the inputoutput relationship allows the user to know the quantitative change in the output values corresponding to the input variables from one set of values to another sets, thus helps to provides complete insight information of the process. There has been lot of research work carried out by various researchers to tackle the problems related to squeeze casting using statistical taguchi method. It is to be note that the taguchi method employed to optimize the squeeze cast process variables to maximize or minimize the response for different materials under investigation (Table 1). It is noted that the following key observations made from the above literatures of using statistical taguchi method to optimize the squeeze casting process are,

1) The taguchi method suggests the best process parameter levels (local optimum) and is completely different from those of optimum process parameter setting (Global minimum). 2) The use of taguchi method cannot reveal the information of behaviour of the response with respect to the input variables varied from one set of values to the other. This information is of paramount importance for a foundry-man to control the process accurately and this can be identified with the help of response surface plots obtained using response surface methodology of design of experiments. 3) The developed models to optimize the squeeze casting process are not used to check the prediction precision for a few experimental cases. It is of paramount importance for any foundry men in selection of the most influencing process parameter setting without performing the real experiments. 4) A separate model for each output expressed as a function of squeeze cast process parameters was observed. 5) The recommended design matrix of taguchi method limits to test all important factor combinations under experimental investigations.

Linear and non-linear regression models The authors [61] used two level full-factorial design of experiment (FFD) to investigate the effects of applied pressure, percentage of modifier and die temperature on percent elongation and tensile strengths of the squeeze cast components. The use of two-level FFD, considered as linear regression model helps to reduce the number of experiments and provides complete insight information of main (linear) and interaction (combined) effects of process variables on outputs under investigation. Nevertheless, the major drawback of the two-level full factorial design is the non-linear effect (if any) in the output function cannot be recognized. To identify the curvature effect the independent variables should have at least three levels. It is important to note that the numbers of experiment need to be conducted through full factorial design increases with number of levels (ref Eq. [1]). Number of experiments=(Levels) Factors

(1)

It is to be note that the curvature effect can be obtained through the use of non-linear regression models namely box-behnken design

Ref.

Material

Process variables

Response

[61]

LM24

SP, DT and DP

BHN and UTS

Optimizing PT and die lubricant can significantly improve the casting quality

[62]

LM24

SP, DT and DP

BHN and UTS

GA successfully searched the process parameters that can yield maximum possible UTS and BHN of cast components

[63]

AC2A

SP, DT, PT, DP and DM

BHN and UTS

SP, DT and DP are observed as the most significant parameters contributing towards the responses

[64]

AZ80

SP, DT and DP

HV, % elongation and UTS

[65]

2017A

SP, DT and PT,

HV and UTS

AC2A


YS

GA finds the best optimum process parameter setting using the response equation derived through taguchi method

[66]

Remarks

The heuristic MM approach has been utilized to find the optimized process parameters for highest possible properties. SP and PT showed significant contribution towards HV and UTS of cast components

[67]

LM6

SP, DT and DM

SR

Higher surface finish can be achieved with varying PT, DT and SP

[68]

LM6

SP, DT and DM

SR

SP and DT are the critically parameters responsible for enhanced squeeze casting surface finish

[69]

AlSi9Cu3

PT, SP, FV and DT

[70]

AC2A


Wear resistance

GA shown slight improvement in the wear resistance property as compared to taguchi and XL solver methods

[71]

LM20

SP, DT and PT

Density and SR

The application of grey relational analysis finds the single optimal casting condition for both the responses.

% elongation, HBS SP, FV, DT and PT are listed in ascending order based on significant importance towards the responses and UTS

Table 1: Statistical taguchi method applications in squeeze casting process.

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Page 4 of 9 (BBD) and central composite design (CCD) of experiments. Not much work has been reported yet with the use of non linear regression models for the applications in squeeze casting process. However linear and non-linear regression models are successfully implemented to develop the input-output relationship of various casting processes namely cement bonded moulding [62,63], green sand moulding [64,65], resin bonded sand mould system [66], sodium silicate-bonded moulding system [67], die casting [68-70] and evaporative casting process [71]. The following key observations drawn from the linear and non-linear regression models such as, 1) Majority of the authors studied the input-output relationships of the process using main effect and the surface plots. This study helps for a foundry man to accurately control the process. 2) The authors tested for the prediction accuracy of the developed linear and non-linear regression models for few random test cases. Comparison of the developed model performance can help the foundry men for selection of the optimum process parameter setting without conduction of experiments. 3) In statistical design of experiments, only one response can be determined at a time as a function of input parameters. It is to be note that generally in any casting process different outputs are measured for the same input casting (parameter) conditions. Hence an integrated system development is mandatory to estimate all the outputs simultaneously because the probabilities of inter-dependency among the outputs were more. 4) Reverse modelling through response equation derived through statistical tools might be difficult to perform because the models are developed independently, interdependency among the output responses might be lost and the transformation matrix might not be invertible always [72].

Modelling using soft computing approach The limitations of conventional modelling tools such as only one response can be determined at a time and the practical requirement is to obtain the input variable combinations that will produce the desired output through reverse prediction might be difficult using statistical tools. These problems can be effectively tackled through soft computing tools like GA, NN, FL, PSO and their different combinations. NN considered being excellent modelling tool to map the complex non-linear relationships among the input and output. It is to be note that neural networks learns with learning examples and need to be trained with huge input-output data base [73]. In recent years neural networks has been applied for the squeeze casting process to forecast the solidification time, temperature difference and secondary dendrite arm spacing [74] of the squeeze cast components. To avoid the rule of thumb, expert advice, try-error method used in shop floor practice, neural networks has been successfully implemented to predict filling time, solidification time and casting defects ,surface defects [75,76], solidification time [77,78], filling time and porosity , injection time [79,80], of pressure die casting process. To predict interfacial heat transfer coefficients at metal-mould interface [81], compressive strength, secondary dendrite arm spacing [82], mechanical properties [83], permeability [84] of different casting processes the soft computing based neural networks were used. To accurately control the quality of the moulding sands [85] and to predict the presence/absence of the casting defects [86] such as hot crack, misrun, scab blow hole and air lock in the sand mould system, NN is used. It is to be note from the above literatures authors successfully implemented to predict the Adv Automob Engg ISSN:2167-7670 AAE, an open access journal

outputs (responses) from the known set of inputs (process parameters) via forward modelling. Although neural networks are capable of making effective predictions but it have some limitations such as probability of getting trap with local optimum solution is high and requires huge input-output data base for training. However prediction accuracy of the neural network majorly relies on quality and the quantity of the training data. Collection of huge data base through real experiments is impractical for the researchers\investigators. It is to be note that some authors used linear (FFD) and non-linear regression (CCD and BBD) models to perform the experiments and establish the process inputoutput relationship. The statistical adequacy of the developed models is tested using co-efficient of co-relation (R2) and with few practical castings of few randomly generated test cases. The input-output data has been artificially generated using regression equation derived through real experiments, by selecting the process variables within their corresponding parameter range corresponding to the model which gives higher R2 value.

Modelling using neural-network based approaches The most practical requirement in industry is to predict the combination of process variables capable to produce the desired output through reverse prediction [83]. Till date, No much work reported yet to carry out the reverse mapping for the squeeze casting process. However some authors utilized successfully the better learning capabilities of neural networks and population based search method of genetic algorithms to tackle the problems related to green sand moulding system, cement bonded moulding system [87], sodium silicate-bonded, carbon dioxide gas hardened moulding sand system [88] and pressure die casting [89]. It is important to note that in their work the thousand sets of input-output data have been generated artificially though the response equation obtained via statistical models. Batch learning mode adopted for both neural network trained with error back propagation (BPNN) and genetic algorithms (GA-NN). In a typical neural network system the synaptic weights are generated initially at random, performs forward computation through the use of transfer functions (linear, sigmoid), predicts the network outputs, compares the network output with the target values to determine the error and those are updated to minimize the error in prediction. BPNN uses steepest descent approach (problem with getting trap at local minima region is more) and in GA-NN, GA (GA search the optimal solution in wide space and the probability of getting trapped with local solution is less) performs the task to minimize the error. However it is also important to mention that both models are capable of making effective prediction for forward and reverse prediction of the randomly generated test cases.

Modelling using fuzzy logic based approaches In recent years the application of fuzzy logic models has been increasing rapidly due to the following reasons like easy to understand, implement, ability to handle uncertainty and imprecise data and exact mathematical formulation is not required [90]. The fuzzy logic model works based on the concepts of thinking and reasoning capabilities of our human brain and this concept has been successfully implemented to develop the input-output relationship of a system to solve complex real world problems [91]. It is to be note that there are generally two types of fuzzy modelling system namely linguistic type (Mamdani approach) and precise type (Takagi-Sugeno) fuzzy modelling system. The manually constructed mamdani based fuzzy logic approach and adaptive network based Takagi and Sugeno approach has been successfully implemented to predict the secondary dendrite arm

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Page 5 of 9 spacing and density of the squeeze casting components [92,93]. The authors successfully established the input-output relationship using Mamdani based fuzzy system for various casting applications namely cement-bonded sand mould, resin-bonded sand mould [94] and green sand mould [95,96] system. However it is noteworthy that in approach 1, the manually constructed fuzzy system was used by the authors, wherein the knowledge of human expertise decides the rule and data base of the fuzzy logic controller. Furthermore, since the developed, manually-constructed rule-base relies majorly on the knowledge of human expertise about the process, it is not considered to be optimal always. Therefore, the rule and data base were optimized in the second approach. Additionally, by using the evolutional genetic algorithm in the approach 3, the authors also tried to automatically evolve the rule and the data base. Nevertheless, the procedure adopted to get the training data is the same as that adopted for the genetic neural system. For a few test cases, the performance of all the fuzzy logic based approaches has been compared midst themselves and with that of the neural network based approaches. The results shown both neural network approaches and the fuzzy logic approaches are capable of making forward and reverse predictions effectively.

Optimization FFD, CCD, BBD and taguchi method are the traditional optimization methods and the solutions obtained from these methods are not the global solutions. The global optimization method is the one deal with identifying the best combination of the process variables for extreme values of the response. Genetic algorithm (GA), simulated annealing (SA), particle swarm optimization (PSO), teaching-learning based (TLBO) algorithm and so on are considered to be the unconventional optimization tools used to determine the best parameter setting for the desired performance in any manufacturing processes. Generally these algorithms can be effectively used to find the best process parameter setting for the single and the multi-response depending on interest of the researcher/investigator. Noteworthy that, traditional methods are essential which provides the response equations derived through well planned statistical experiments. The response equations can be used as an objective functions to find the best process parameter setting, which are usually the global highest/lowest depending on the optimization problem. Noted that few limited work reported to optimize the squeeze casting process via GA. It is important to note that they used response equation derived through taguchi method for optimization and authors neglected some of the important main and interactions effects in the derived response equation. It is to be note that the response equation must have the main, square and interaction parameter effects to gain the complete insight of the process. More recently evolutionary algorithms (GA and PSO) are used for multi-response optimization of the green sand mould system. The optimized parameter setting suggested by the PSO and GA are compared with the experimental cases and the results shown PSO outperforms GA in terms of for extreme values prediction of all the responses and computational efficiency [97].

Proposed Methodology Till date the authors followed to model the squeeze casting process using classical engineering experimental approach, analytical, theoretical approaches, and taguchi method. Each method has some advantages and limitations. To address the major limitations identified in the above methods (Figure 1), the detailed experimental, prediction and optimization methodologies are proposed. In manufacturing processes, two or more process variables critically influences the outputs. Identifying the process variables and their corresponding


range can be effectively determined using the classical engineering experimental approach. However, classical engineering experiments estimate only the main effects of the process variables. Estimation of interaction effects via classical engineering experiments require more experiments to be conducted compared to statistical design of experiments. Therefore, the influencing process variables and corresponding levels via classical experimental approach are used to model the process using statistical design of experiments and response surface methodology. Modelling the process help the investigator to study the influence of independent variables, establish input-output relationship, identify the significant and insignificant process variables and further for prediction of the outputs for the known combination of inputs. This helps the foundry personnel to select the most influential input variables, without the requirement of prior background knowledge about the process mechanics and materials. Furthermore, these models help the manufacturing industries to predict the outputs without conduction of experiments, thus avoids material waste, energy consumption, existing expert reliant try-error-method, high cost involved in virtual casting simulation runs and need of expertise to interpret the obtained simulated results. However, statistical design of experiments fail to capture the interdependency among the outputs, thus restricts the model to use for online control of the process in the manufacturing industry. Online process control requires the models to predict multiple outputs and inputs simultaneously, thus helps to adjust automatically the process variables for the desired output. Statistical design of experiments might fail to estimate simultaneously more than one output simultaneously, because experimental data is collected and analysis are carried out based on response wise. Furthermore, the stringent requirement for the manufacturing industry is to predict the input parameters for the desired output (reverse prediction). Reverse prediction using statistical models requires the transformation matrix must be invertible always and are difficult with the interaction parameters in the regression equations. Further, statistical modelling tools fail to capture the interdependency among the outputs present, in any. Therefore, for online process control and capture output interdependencies an alternative tool need to be developed, that could estimates both inputs and outputs simultaneously. Soft computation tools namely GA, PSO, ABC, NN, FL, TLBO and corresponding diverse combinations proved as excellent tools to conduct forward and reverse predictions, particularly in manufacturing applications. The soft computing tools require huge (say 1000) input-output data for training and conducting actual experiments are infeasible for a foundry man to fulfill the requirements. Thus, the response equations derived through statistical models were used to generate artificially by selecting process variables between their corresponding ranges. The soft computing models are adaptively trained to update weights for the minimum error. The trained models are used to predict the random test cases to confirm the prediction precision of the models developed. The best model can be used for online monitoring, to automatically adjust the process variables for the desired outputs. It is noteworthy that, prediction helps the investigator to determine the outputs as well as inputs, but fail to estimate the global extreme values of the output, responsible for the best product quality (minimum defects). To determine the extreme values for the conflicting outputs (minimum is better for one response and maximum is better for other and vice versa) pose difficulties. For single output there is only one set of input variable combinations, whereas there are many combinations of optimum conditions for multiple outputs. Thus the multi-objective problems can be addressed effectively using evolutionary algorithms.

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Experiment methodology Start

Examine experimental need(s)

Define objective(s)

Start statistical design of experiments and select experimental design matrix for the identified process variable range

Identify control and noise factors Determine control factor ranges using Classical engineering approach

Conduct experiments as per selected design of different process variable combinations and collect appropriate set of data set with two or more replicate to improve measurement precision Establish linear or non-linear input-output relationship utilizing available software Statistical analysis of the collected data to estimate factor effects and evaluate model performances Estimate individual and combined factor effects, Significance and analysis of variance test Conduct experiments for random test cases

Generate huge inputoutput training data

Prediction methodology Forward mapping Compare the conventional modelling tools prediction with real experiments

Forward and Reverse mapping Compare unconventional modelling tools prediction with actual experiments

The major conventional modelling tools namely CCD, BBD, FFD, Taguchi etc.,

Soft computational tools namely PSO, GA, FL, ANN, SA, ABC and their different combinations

Compare the developed model performances in terms of mean absolute percent deviation in prediction of test cases and select best model for the process

Optimization methodology Conventional optimization techniques

Unconventional optimization techniques

Experimental techniques (RSM and Taguchi), Iterative search techniques namely programming (goal, linear, non-linear, dynamic and geometric) methods and sequential unconstrained minimization

Differential evolution, Artificial immune algorithm, Ant colony optimization, Tabu search, ABC, GA, PSO, TLBO, SA and their different combinations

Test prediction performances with actual experiments and select the best optimization tool for a process End Figure 1: Proposed Methodology for Modelling, Prediction and Optimization.

Concluding Remarks The present work describes the current state of art and the future scope for improving the squeeze cast component quality through the applications of conventional and unconventional modelling tools. The meaningful conclusions are drawn for the current work, 1) Conventional engineering approach of varying one parameter at once after maintaining the rest at the middle helps in deciding the process variable range for statistical design of experiments. However, the data from the literature survey and opinion of expert persons from the industry along with pilot experiments will help to identify all process variables and their operating range.


2) Casting simulation software is capable of making effective prediction, but it is not suitable for large simulation trials for cyclic analysis in bringing the solution to an optimal conditions. Further, simulation software lacks in considering the local conditions in formulating the problem. 3) Statistical design of experiments can be successfully implemented in foundry applications to analyze, identify the percent contribution of main (individual) and the interaction (combined) effect of process variables on the response under investigation. In other-words, it helps to understand the sensitivity of process variables. Further, the regression equations developed from the models can be used to make prediction of the response for the known set process variables.

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Page 7 of 9 4) The statistical modelling tools are capable of making prediction only one response at a time. In multi input-output casting system all the response are measured for the single process parameter conditions, hence development of integrated system to predict the responses simultaneously is mandatory. 5) Soft computing tools can predict multi response at a time and meets the practical requirement of the foundry men to know the recommended process parameter setting for the desired output through reverse prediction. 6) The single optimal process parameter setting for all the response can be obtained through the use of optimization algorithms such as ABC, PSO, TLBO, SA, and GA and so on. Although much research efforts reported in the available literatures, still the process industries and researchers are not using powerful modelling tools to improve the squeeze cast components. The use of statistical tools establishes the input-output relationship and provides the complete insight of the process, but fails to meet specific industry requirements. The soft computing based approaches can be efficiently used for predicting the input variables required to achieve the desired response (reverse mapping). It is noteworthy that reverse mapping can be used in online control of the process. The incremental mode of training data in soft computing approach will up-date process variables required to obtain the desired response values. Hence, the on-line control of the process can be made by adjusting the process variables quickly. The proposed methodology help the industry personnel to select and adjust the most influential process parameter any manufacturing process to achieve the desired quality with reduced time and resource consumption.

Transfer Coefficient at Metal/Mold Interface during Casting. AFS Trans 102: 877-883. 13. Kumar TP ,Prabhu KN (1991), Heat flux transients at the casting/chill interface during solidification of aluminium base alloys. Metallurgical Transactions B 22: 717-727. 14. Sully LJD (1976) The thermal interface between castings and chill molds. AFS Trans 84: 735-744. 15. Sun Z, Hu H, Niu X (2011) Determination of heat transfer coefficients by extrapolation and numerical inverse methods in squeeze casting of magnesium alloy AM60. Journal of Materials Processing Technology 211: 1432-1440. 16. Narayan Prabhu K, Ravishankar BN (2003) Effect of modification melt treatment on casting/chill interfacial heat transfer and electrical conductivity of Al–13% Si alloy. Materials Science and Engineering: A 360: 293-298. 17. Lynch RS, Olley RS, Gallaher PCJ (1975) Squeeze casting of aluminium. AFS Trans 122: 569-576. 18. Williams G, Fisher KM (1981) Squeeze forming of aluminium-alloy components. Metals Technology 8: 263-267. 19. Davies VL (1980) Heat transfer in gravity die castings. British Foundryman 73: 331-334. 20. Sun Z, Zhang X, Hu H, Niu X (2012) Section thickness-dependant interfacial heat transfer in squeeze casting of aluminum alloy A443. In IOP Conference Series: Materials Science and Engineering 27: 12073. 21. Kim TG, Lee ZH (1997) Time-varying heat transfer coefficients between tubeshaped casting and metal mold. International journal of heat and mass transfer 40: 3513-3525. 22. Krishna P (2001) A study on interfacial heat transfer and process parameters in squeeze casting and low pressure permanent mold casting. Ph.D. Thesis, University of Michigan.

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4. Zhang L, Li L (2013) Determination of heat transfer coefficients at metal/chill interface in the casting solidification process. Heat and Mass Transfer 49: 1071-1080. 5. Ho K, Pehlke RD (1984) Mechanisms of heat transfer at a metal-mold interface. AFS Trans 92: 587-598. 6. Ho K, Pehlke RD (1983) Transient methods for determination of metal-mold interfacial heat transfer.AFS Trans 91: 689-698. 7. Hou TX, Pehlke RD (1998) Determination of Mold-Metal Interfacial Heat Transfer and Simulation of Solidification of An Al-% 13 Si Casting. AFS Transactions 96: 129-136.

27. FardiIlkhchy A, Jabbari M, Davami P (2012) Effect of pressure on heat transfer coefficient at the metal/mold interface of A356 aluminum alloy. International Communications in Heat and Mass Transfer 39: 705-712. 28. Gunasegaram DR, Nguyen TT (1997) Comparison of heat transfer parameters in two permanent molds. AFS Trans 105: 551-556. 29. Britnell DJ, Neailey K (2003) Macro segregation in thin walled castings produced via the direct squeeze casting process. Journal of materials processing technology 138: 306-310. 30. Rajagopal S, Altergott WH (1985) Quality control in squeeze casting of aluminium. AFS Transactions 93: 145-154.

8. Tillman ES, Berry JT (1972) Influence of Thermal Contact Resistance on the Solidification Rate of Long Freezing Range Alloys. AFS Cast Metals Research Journal 8: 1-6.

31. Lin CJ, Jin Y, Tang HQ (2012) Finite element analyses and model of squeeze casting process for producing magnesium wheels. Advanced Materials Research 557: 2299-2302.

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11. Durham DR, Berry JT (1974) Role of the mold-metal interface during solidification of a pure metal against a chill. Trans American Foundrymen’s Society 8: 101-110. 12. Hwang JC, Chuang HT, Jong SU, Hwang WS (1994) Measurement of Heat


34. Lewis RW, Postek EW, Han Z, Gethin DT (2006) A finite element model of the squeeze casting process. International Journal of Numerical Methods for Heat and Fluid Flow 16: 539-572. 35. Quadrini F, Santo L, Tagliaferri V, Olimpi A (2010) Numerical simulation of pin squeeze casting process for cycle time and cast property prediction.

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Page 8 of 9 International Journal of Computational Materials Science and Surface Engineering 3: 164-174. 36. Sun Z, Zhang X, Niu X, Yu A, Hu H (2011) Numerical simulation of heat transfer in pressurized solidification of Magnesium alloy AM50. Heat and mass transfer 47: 1241-1249. 37. Sun ZZ, Yu A, Hu H, Han LH (2010) Mathematical modeling of squeeze casting of magnesium alloy AM50. In Defect and Diffusion Forum 297: 105-110. 38. Zhi-Jiang H, Wen Y, Bai-Cheng L (2011) Modeling and simulation on microporosity formed during squeeze casting of aluminum alloy. ActaMetall Sin, 47: 7-16.

57. Hong CP, Lee SM, Shen HF (2000) Prevention of macro defects in squeeze casting of an Al-7 wtpct Si alloy. Metallurgical and Materials Transactions B 31: 297-305. 58. Raji A, Khan RH (2006) Effects of pouring temperature and squeeze pressure on Al-8٪ Si alloy squeeze cast parts. AU JT 9: 229-237. 59. Zyska A, Konopka Z, Łągiewka M, Nadolski M (2011) The influence of modification and squeeze casting on properties of AlSi11 alloy castings. Archives of Foundry Engineering 11: 153-156. 60. Zyska A, Konopka Z, Lągiewka M (2007) The solidification of squeeze cast AlCu4Ti alloy. Archives of Foundry Engineering 7: 193-196.

39. Kajatani T, Drezet JM, Rappaz M (2001) Numerical simulation of deformationinduced segregation in continuous casting of steel. Metallurgical and Materials Transactions A 32: 1479-1491.

61. Zyska A, Konopka Z, Łągiewka M, Nadolski M (2013) Optimization of squeeze parameters and modification of AlSi7Mg alloy. Archives of Foundry Engineering 13: 113-116.

40. Gunasegaram DR, Farnsworth DJ, Nguyen TT (2009) Identification of critical factors affecting shrinkage porosity in permanent mold casting using numerical simulations based on design of experiments. Journal of Materials Processing Technology 209: 1209-1219.

62. Parappagoudar MB, Pratihar DK, Datta GL (2008) Linear and non-linear modeling of cement-bonded moulding sand system using conventional statistical regression analysis. Journal of Materials Engineering and Performance 17: 472-481.

41. Krimpenis A, Benardos PG, Vosniakos GC, Koukouvitaki A (2006) Simulationbased selection of optimum pressure die-casting process parameters using neural nets and genetic algorithms. The International Journal of Advanced Manufacturing Technology 27: 509-517.

63. Mandal A, Roy P (2006) Modeling the compressive strength of molasses– cement sand system using design of experiments and back propagation neural network. Journal of Materials Processing Technology 180: 167-173.

42. Zhihong G, Hua H, Yuhong Z, Shuwei Q (2010) Numerical Simulation of Squeeze Casting of AZ91D Magnesium Alloy. In Digital Manufacturing and Automation (ICDMA), International Conference on IEEE 2: 30-33. 43. Xu HP, Li LY (2012) Research and simulation of the temperature on multisqueeze casting. Advanced Materials Research 497: 339-343. 44. Xu CL, Ying FQ (2011) Research on numerical simulation of filling velocity of indirect squeeze casting in shaping the thin walled work piece. Applied Mechanics and Materials 48: 964-970. 45. Jolly M (2002) Casting simulation: How well do reality and virtual casting match? State of the art review. International Journal of Cast Metals Research 14: 303-314. 46. Wang RJ, Tan WF, Zhou DW (2013) Effects of squeeze casting parameters on solidification time based on neural network. International Journal of Materials and Product Technology 46: 124-140. 47. Wang RJ, Zeng J, Zhou DW (2012) Determination of temperature difference in squeeze casting hot work tool steel. International journal of material forming 5: 317-324. 48. Hosseini VA, Shabestari SG, Gholizadeh R (2013) Study on the effect of cooling rate on the solidification parameters, microstructure, and mechanical properties of LM13 alloy using cooling curve thermal analysis technique. Materials and Design 50: 7-14. 49. Maleki A, Shafyei A, Niroumand B (2009) Effects of squeeze casting parameters on the microstructure of LM13alloy. Journal of Materials Processing Technology 209: 3790-3797. 50. Yue TM (1997) Squeeze casting of high-strength aluminium wrought alloy AA7010. Journal of materials processing technology 66: 179-185. 51. Yang LJ (2003) The effect of casting temperature on the properties of squeeze cast aluminium and zinc alloys. Journal of Materials Processing Technology 140: 391-396. 52. Yang LJ (2007) The effect of solidification time in squeeze casting of aluminium and zinc alloys. Journal of materials processing technology 192: 114-120.

64. Parappagoudar MB, Pratihar DK, Datta GL (2007) Non-linear modelling using central composite design to predict green sand mould properties, Proceedings of the Institution of Mechanical Engineers. Part B: Journal of Engineering Manufacture 221: 881-895. 65. Parappagoudar MB, Pratihar DK, Datta GL (2007) Linear and non-linear statistical modelling of green sand mould system. International Journal of cast metals research 20: 1-13. 66. Surekha B, Rao DH, Rao G, Vundavilli PR, Parappagoudar MB (2012) Modeling and analysis of resin bonded sand mould system using design of experiments and central composite design. J Manuf Sci Prod 12: 31-50. 67. Parappagoudar MB, Pratihar DK, Datta GL (2011) Modeling and analysis of sodium silicate-bonded moulding sand system using design of experiments and response surface methodology. Journal for Manufacturing Science & Production 11:1-14. 68. Verran GO, Mendes RPK, Rossi MA (2006) Influence of injection parameters on defects formation in die casting Al12Si1, 3Cu alloy: Experimental results and numeric simulation. Journal of materials processing technology 179: 190-195. 69. Verran GO, Mendes RPK, DallaValentina LVO (2008) DOE applied to optimization of aluminum alloy die castings. Journal of materials processing technology 200: 120-125. 70. Chiang KT, Liu NM, Tsai TC (2009) Modeling and analysis of the effects of processing parameters on the performance characteristics in the high pressure die casting process of Al–SI alloys. The International Journal of Advanced Manufacturing Technology 41: 1076-1084. 71. Kumar S, Kumar P, Shan HS (2007) Effect of evaporative pattern casting process parameters on the surface roughness of Al–7% Si alloy castings. Journal of materials processing technology 182: 615-623. 72. Parappagoudar MB, Pratihar DK, Datta GL (2008) Forward and reverse mappings in green and mould system using neural networks. Applied Soft Computing 8: 239-260. 73. Sha W, Edwards KL (2007) The use of artificial neural networks in materials science based research, Materials & design 28: 1747-1752.

53. Maleki A, Niroumand B, Shafyei A (2006) Effects of squeeze casting parameters on density, macrostructure and hardness of LM13 alloy. Materials Science and Engineering 428: 135-140.

74. Patel GCM, Mathew R, Krishna P, Parappagoudar MB (2014) Investigation of squeeze cast process parameters effects on secondary dendrite arm spacing using statistical regression and artificial neural network models. Procedia Technology 14: 149-156.

54. Skolianos SM, Kiourtsidis G, Xatzifotiou T (1997) Effect of applied pressure on the microstructure and mechanical properties of squeeze-cast aluminum AA6061 alloy. Materials Science and Engineering 231: 17-24.

75. Zheng J, Wang Q, Zhao P, Wu C (2009) Optimization of high-pressure diecasting process parameters using artificial neural network. The International Journal of Advanced Manufacturing Technology 44: 667-674.

55. Fan CH, Chen ZH, He WQ, Chen JHD (2010) Effects of the casting temperature on microstructure and mechanical properties of the squeeze-cast Al–Zn–Mg– Cu alloy. Journal of Alloys and Compounds 504: L42-L45.

76. Swillo SJ, Perzyk M (2013) Surface casting defects inspection using vision system and neural network techniques. Archives of Foundry Engineering 13: 103-106.

56. Hajjari E, Divandari M (2008) An investigation on the microstructure and tensile properties of direct squeeze cast and gravity die cast 2024 wrought Al alloy. Materials and Design 29: 1685-1689.

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Page 9 of 9 78. Zhang X, Tong S, Xu L, Yan S (2007) Optimization of low-pressure die casting process with soft computing. In Mechatronics and Automation, International Conference on IEEE. 79. Yarlagadda PK (2000) Prediction of die casting process parameters by using an artificial neural network model for zinc alloys. International Journal of Production Research 38: 119-139. 80. Yarlagadda PK, Cheng Wei Chiang E (1999)A neural network system for the prediction of process parameters in pressure die casting. Journal of Materials Processing Technology 89: 583-590. 81. Zhang L, Luoxing L, Hui JU, Zhu B (2010) Inverse identification of interfacial heat transfer coefficient between the casting and metal mold using neural network. Energy conversion and management 51: 1898-1904. 82. Jiang LH, Wang AG, Tian NY, Zhang WC, Fan QL (2011) BP neural network of continuous casting technological parameters and secondary dendrite arm spacing of spring steel. Journal of Iron and Steel Research, International 18: 25-29. 83. Perzyk M, Kochański AW (2001) Prediction of ductile cast iron quality by artificial neural networks, Journal of Materials Processing Technology 109: 305-307. 84. Nagurbabu N, Ohdar RK, Pushp PT (2007) Application of intelligent techniques for controlling the green sand properties.Indian Foundry Journal 53: 27. 85. Jakubski J, Dobosz SM, Major-Gabryś K (2013) Influence of the training set value on the quality of the neural network to identify selected moulding sand properties. Archives of Foundry Engineering 13: 49-52. 86. Karunakar DB, Datta GL (2008) Prevention of defects in castings using back propagation neural networks.The International Journal of Advanced Manufacturing Technology 39: 1111-1124. 87. Parappagoudar MB, Pratihar DK, Datta GL (2007) Modelling of input–output relationships in cement bonded moulding sand system using neural network. International Journal of Cast Metals Research 20: 265-274.

88. Parappagoudar MB, Pratihar DK, Datta GL (2008) Neural network-based approaches for forward and reverse mappings of sodium silicate-bonded, carbon dioxide gas hardened moulding sand system. Materials and Manufacturing Processes 24: 59-67. 89. Kittur JK, Parappagoudar MB (2012) Forward and reverse mappings in die casting process by neural network-based approaches. J Manuf Sci Prod 12: 65-80. 90. Pratihar DK (2008) Soft computing, Narosa publishing house pvt. Ltd India. 91. Surekha B, Vundavilli PR, Parappagoudar MB (2012) Forward and reverse mappings of the cement-bonded sand mould system using fuzzy logic. The International Journal of Advanced Manufacturing Technology 61: 843-854. 92. Patel GCM, Prasad Krishna, Mahesh B. Parappagoudar (2015) Prediction of squeeze cast density using fuzzy logic based approaches. Archives of Foundry Engineering 15: 51-68. 93. Patel GCM, Prasad Krishna, Mahesh B. Parappagoudar (2014) Prediction of squeeze cast density using fuzzy logic based approaches. Journal for Manufacturing Science and Production 14: 125-140. 94. Surekha B, Rao DH, Rao GM, Vundavilli PR, Parappagoudar MB (2013) Prediction of resin bonded sand core properties using fuzzy logic. Journal of Intelligent and Fuzzy Systems 25: 595-604. 95. Surekha B, Vundavilli PR, Parappagoudar MB (2012) Reverse modeling of green sand mould system using fuzzy logic-based approaches. J Manuf Sci Prod 12: 1-16. 96. Surekha B, Vundavilli PR, Parappagoudar MB, Srinath A (2011) Design of genetic fuzzy system for forward and reverse mapping of green sand mould system. International Journal of Cast Metals Research 24: 53-64. 97. Surekha B, Kaushik LK, Panduy AK, Vundavilli PR, Parappagoudar MB (2012) Multi-objective optimization of green sand mould system using evolutionary algorithms. The International Journal of Advanced Manufacturing Technology 58: 9-17.

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Advanced Materials Research Vols. 463-464 (2012) pp 674-678 Online available since 2012/Feb/10 at www.scientific.net © (2012) Trans Tech Publications, Switzerland doi:10.4028/www.scientific.net/AMR.463-464.674

Prediction and Optimization of Dimensional Shrinkage Variations in Injection Molded Parts using Forward and Reverse Mapping of Artificial Neural Networks Manjunath Patel G C1, a and Prasad Krishna2, b 1

Research Scholar, Department of Mechanical Engineering, NITK, Surathkal, INDIA 2

Professor, Department of Mechanical Engineering, NITK, Surathkal, INDIA [email protected], b [email protected]

Keywords: plastic injection molding (PIM); artificial neural networks (ANN); forward and reverse mapping; back propagation neural network (BPNN); optimization

Abstract. The most significant process parameters affecting dimensional shrinkage in transverse and longitudinal directions of molded parts in Plastic Injection Molding (PIM) process are injection velocity, mold temperature, melt temperature and packing pressure. In the present work, ANN model was developed for forward and reverse mapping prediction. In forward mapping PIM process parameters are expressed as the input parameters to predict dimensional shrinkage, whereas in reverse mapping, attempts were made to predict an appropriate set of process parameters required for arriving at the required dimensional shrinkage. The trained network with one thousand inputoutput data randomly generated from regression equations reported by earlier researchers resulted in minimum mean squared error. The performance of developed model was compared with experimental values for ten different test cases. The results show that ANN model with both forward and reverse mapping is capable of prediction with an error level of less than ten percent. Introduction Injection molding process is one of the widely used manufacturing processes for mass production of near-net-shape plastic products. In this process, hot melt plastic is forced into a mold cavity and allowed to solidify. The solidified part is ejected upon the mold opening. The quality of the injection molded parts is influenced by several process parameters. The most influencing parameters that affect the dimensional shrinkage of the molded parts namely injection velocity, mold temperature, melt temperature and packing pressure were studied and analyzed by Chen et.al using Response Surface Methodology (RSM) [1]. Yarlagadda and Khong considered melt temperature, molding temperature, inverse of minimum part thickness and the difference between mold and melt temperatures as inputs for the prediction of injection time in the first neural network and the output of the first neural network namely injection time, flow length and inverse of minimum part thickness were used to predict the injection pressure in the second network and achieved optimum values [2]. Chen et al. worked on the optimization of the Plastic Injection Molding (PIM) process parameters namely injection velocity, injection pressure, switch position, packing pressure, packing time and melt temperature and discussed their effects using Taguchi’s parameter design method, Back Propagation Neural Network (BPNN) and Genetic algorithms [3]. Mathivanan and Parthasarathy achieved sink mark minimization using process parameters like ribto-wall ratio, packing pressure, packing time and melt temperature and analyzed using RSM & Genetic algorithms [4]. Sadeghi used back propagation neural network for the prediction of part quality, filling time and injection pressure for the PIM process [5]. Yin et al. demonstrated an optimization method for injection molded process parameters using BPNN and minimized the warpage of plastic products [6]. All the above literature reviews confirm that ANN is an effective tool to map relationship between input-output parameters of a PIM process.

All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of TTP, www.ttp.net. (ID: 117.211.83.5-25/03/12,18:49:57)

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Modeling of plastic injection molding (PIM) process The forecasting ability of an ANN model strongly depends on the appropriate selection of inputoutput parameters. In the proposed model, the most influencing process parameters that affect dimensional shrinkage of the molded parts are injection velocity, mold temperature, melt temperature and packing pressure. BPNN model was developed for PIM process. In order to evaluate the effect of process parameters on the dimensional shrinkage, RSM with face centre composite design was used to plan and conduct the experiments. The BPNN is used to train and test the data obtained using the regression equations reported from the literature [1]. Process parameters and their levels used in this study are listed in Table 1. The values of Vi and Ppk are presented as percentage of maximum machine velocity (Vmax= 2000 mm/s) and machine injection velocity (Pmax=328 MPa) respectively. The summary of ANN model used for the forward and reverse mapping is illustrated in Table 4. Table1. Process Parameters -Symbols and Their Levels Process Parameters

Units

Symbols

Injection velocity, Vi Packing pressure, Ppk Mold temperature, Md Melt temperature, Mt

% % ºC ºC

X1 X2 X3 X4

High (+1) 30 40 70 240

Levels Medium (0) 20 30 55 230

Low (-1) 10 20 40 220

Forward Mapping. In the present study, ANN architecture consists of three layers namely, input layer, hidden layer and output layer. The input layer receives external information, such as varying process parameters. The output layer generates the data corresponding to PIM component quality namely dimensional shrinkage. The hidden layer, do not interact with the outside world, but helps in performing the non-linear feature extraction on the data provided by the input–output layers. The weights contains information about the input and output signal [7]. Forward mapping is used to predict the dimensional shrinkage (in Transverse and Longitudinal directions) from the known set of input parameters namely injection velocity, mold temperature, melt temperature and packing pressure. The detailed parametric study is carried out to obtain the optimum network parameters (for details refer Table 4). Fig. 1 shows the neural network used in modeling (forward mapping) of PIM system.

Fig.1. Artificial Neural Network in Forward mapping. Reverse Mapping. Reverse mapping aims to determine the set of input process parameters, corresponding to a set of desired output parameters. The statistical method might fail to carry out the said reverse mapping because the transformation matrix may not be invertible at all. This problem could be handled effectively by using an ANN, as it works like a black-box data processing unit [7]. The procedure remains same as in forward mapping except that the dimensional shrinkage is the input and process parameters are the output. The detailed parametric study is carried out to obtain the optimum network parameters (for details refer Table 4).

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Collection of data In the present work, regression equations obtained from the published literature [1] for different responses were used to generate input–output data required for the training of neural network. One thousand training data were generated by selecting the values of the input variables lying within their respective ranges and determining the response by using the Eq. 1 and Eq. 2. The regression equations for dimensional shrinkage in the transverse direction (dx) (refer Eq. 1) and longitudinal direction (dy) (refer Eq.2) expressed in coded form are: dx = 0.27 + 0.026 X 1 - 0.051 X 2 + 0.049 X 3 + 0.073 X 4 + 0.057 X 12 + 0.035 X 22 - 0.016 X 1 X 2 (1) dy = 0.44 - 0.032 X 1 - 0.05 X 2 + 0.027 X 3 + 0.027 X 4 - 0.0087 X 2 X 3 + 0.0088 X 2 X 4

(2)

Results and discussions Result of forward mapping. Ten different test cases were taken in order to validate the network performance with the experimentally measured values, BPNN and DOE Predicted values as shown in Table 2. The % deviation in prediction of dimensional shrinkage (Transverse and Longitudinal direction), were found to lie in the ranges of -6.191% to +10.034% in transverse direction and 10.32% to +0.8528 in case of longitudinal direction for BPNN and for DOE, the % deviation in prediction were found to lie in the range of -7.162% to +13.84% in transverse direction and -7.32% to +2.004 % in the case of longitudinal direction. The MAPE is found to be 4.24% for BPNN prediction and being less than 10%, the prediction of ANN is considered to be accurate [8]. The summary of forward mapping is listed in Table 4. Table 2.Results of Test Cases for Response-Dimensional Shrinkage DOE & Back Propagation Neural Network (BPNN) Prediction Process parameters Test cases Vi

Ppk

Md

Mt

Dimensional Shrinkage (Transverse direction), mm Abs. Abs. EXP DOE BPNN % % value value value Dev Dev

1 20 30 55 230 0.272 2 10 20 70 220 0.240 3 30 40 70 240 0.307 4 30 30 55 230 0.257 5 10 30 55 230 0.217 6 30 40 40 240 0.249 7 20 30 70 230 0.305 8 20 30 40 230 0.220 9 10 40 40 240 0.210 10 20 30 55 240 0.329 Mean Absolute Percentage Error (MAPE)

0.270 0.233 0.329 0.239 0.187 0.231 0.319 0.221 0.211 0.343

0.735 2.917 7.166 7.004 13.83 7.229 4.591 0.455 0.477 4.255

4.865

0.260 0.248 0.304 0.243 0.219 0.238 0.283 0.228 0.223 0.296

4.117 3.333 0.977 5.447 0.922 4.417 7.213 3.636 6.190 10.03

4.657

Dimensional Shrinkage (Longitudinal direction), mm Abs. Abs. EXP DOE BPNN % % value value value Dev Dev 0.449 0.504 0.407 0.388 0.469 0.376 0.454 0.414 0.440 0.462

0.440 0.541 0.413 0.409 0.472 0.375 0.468 0.412 0.439 0.468

2.223

2.004 7.342 1.474 5.412 0.640 0.266 3.084 0.483 0.227 1.298

0.451 0.506 0.449 0.427 0.465 0.413 0.455 0.432 0.437 0.467

0.445 0.397 10.32 10.05 0.853 9.840 0.220 4.347 0.681 1.082

3.823

Result of reverse mapping. Ten different test cases were taken in order to validate the network performance with the experimentally measured values and the BPNN predicted values. The results are shown in Table 3. The results show that the experimentally measured values and the BPNN predicted values are comparable in relationship with each other. The % deviation in prediction is less than ±10% except one or two values for all the responses. The MAPE is found to be 5.98% for BPNN prediction and the prediction of ANN is considered to be accurate [8]. The summary of reverse mapping is listed in Table 4.

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Table 3.Result of Test Cases- Injection velocity, Packing pressure, Mold and Melt temperature Test cases 1 2 3 4 5 6* 7 8 9 10

Experimental Measured Dimensional Shrinkage (mm) Transverse Longitudinal direction Direction 0.272 0.449 0.316 0.489 0.272 0.449 0.344 0.394 0.257 0.388 0.075 0.282 0.305 0.454 0.220 0.414 0.329 0.462 0.188 0.414 MAPE

Back Propagation Neural Network (BPNN) Prediction Injection velocity Input BPNN value Value 20 19.296 20 18.972 20 19.296 20 20.096 30 20.554 30 27.004 20 19.262 20 20.042 20 19.215 20 20.174

Packing pressure Input BPNN value value 30 29.879 20 29.321 30 29.879 40 30.304 30 31.236 40 38.228 30 29.668 30 31.025 30 29.519 30 31.458

Mold temperature Input value 55 55 55 55 55 40 70 40 55 55

6.2823

BPNN value 55.286 56.213 55.286 54.181 52.835 42.335 55.555 53.467 55.769 52.928

Melt temperature Input BPNN value Value 230 229.564 230 230.039 230 229.564 230 229.537 230 228.717 220 223.267 230 229.791 230 228.687 240 229.945 220 228.191

7.3977 9.1188

1.1214

Table 4.Summary of ANN Model for Forward and Reverse Mapping. Type

Forward ANN Model

Reverse ANN Model

Objective Input Neurons Output Neurons Network Type Transfer Function Input Layer output Layer Hidden Layer Learning scheme Learning Rule Input & Output Neurons Training Samples Parametric Study No of Hidden Layers No of Hidden neurons Learning rate hidden layer Learning rate output layer Momentum constant Activation constant Hidden & Output layer Bias value MSE at the end of training Mean Absolute Percent Error

Dimensional shrinkage X 1, X 2, X 3, X 4 Dimensional shrinkage – dx, dy. back propagation neural network

X 1, X 2, X 3, X 4 Dimensional shrinkage – dx, dy. X 1, X 2, X 3, X 4 back propagation neural network

Linear transfer Function Log sigmoid Transfer function Log sigmoid Transfer function Supervised Learning Gradient descent rule Four & Two 1000-Training and 10- testing

Linear transfer Function Log sigmoid Transfer function Log sigmoid Transfer function Supervised Learning Gradient descent rule Two & Four 1000-Training and 10- testing

One 9 0.7220 0.3660 0.455

One 7 0.01 0.4995 0.2325

5.05 & 5.95 0.0000505 0.011923 4.24%

2.35 & 6.40 0.00005545 0.034759 5.98%

Optimization of process parameters Optimization of process parameters is routinely performed in the manufacturing industry because it affects the productivity, quality and cost. Final optimal process parameter setting is identified as one of the most important steps in plastic injection molding for improving the quality of molded parts. In the present work, the main goal is to minimize the dimensional shrinkage in thin shell plastic products by setting the optimum process parameters. ANN model was used to predict the optimum process parameters for minimum dimensional shrinkage in both longitudinal and transverse directions. Minimum dimensional shrinkage as in test case 6* shown in Table 3 can be easily

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obtained with the BPNN with percentage deviation from experimental values varying from -5.834 to 9.987. Thus, the ANN model predicts the optimum process parameters leading to better quality products with reduced cost. Summary ANN model has been successfully developed for the prediction of dimensional shrinkage variations and process parameters in the PIM process, through forward and reverse mapping respectively. Batch mode of training with supervised learning ability was adopted for training the ANN. The collection of feasible input-output data for training the network was generated at random using regression equations reported from an earlier research work. A detailed parametric study was carried out to optimize the ANN parameters. The trained network reduces the mean squared error to a very small value in both cases of forward as well as reverse mapping. Optimization of the process parameters for minimum dimensional shrinkage was achieved with the help of reverse ANN. The developed network gives satisfactory results when compared with experimentally measured values. The MAPE in prediction was found to be 4.24% for forward mapping and 5.98% for reverse mapping. The ANN can thus give satisfactory results rather than expert dependent trial and error method of establishing the process parameters, thus reducing cost and time. References [1]. Chih-Cherng Chen, Pao-Lin Su & Yan-Cherng Lin, Analysis and modeling of effective parameters for dimension shrinkage variation of injection molded part with thin shell feature using response surface methodology, International Journal of Advanced Manufacturing Technology, 2009, Springer-Verlag London Limited. P. 1087-1095. [2]. Prasad K.D.V. Yaralagadda and Cobby Ang Teck Khong, Development of a hybrid neural network system for prediction of process parameters in injection moulding, Journal of Materials Processing Technology, 2001, p. 110-116. [3]. Wen-Chin Chen, Gong-Loung Fu, Pei-Hao Tai and Wei-Jaw Deng, Process parameter optimization for MIMO plastic injection molding via soft computing, Expert Systems with Applications (2007). [4]. D. Mathivanan and N.S. Parthasarathy, Sink-mark minimization in injection molding through response surface regression modeling and genetic algorithm, International Journal of Advanced Manufacturing Technology, 2009, Springer-Verlag London Ltd. P. 1087-1095. [5]. B.H.M. Sadeghi, A BP-neural network predictor model for plastic injection molding process, Journal of Materials Processing Technology, 2000, p. 411-416. [6]. Fie Yin, Huajie Mao, Lin Hua, Wei Guo and Maosheng Shu, Back Propagation neural network modeling for warpage prediction and optimization of plastic products during injection molding, Materials and Design, 2011, p. 1844-1850. [7]. Mahesh B. Parappagoudar, D.K. Pratihar and G.L. Datta, Forward and Reverse mappings in green sand mold system using neural networks, 2008, Applied soft computing, p. 239-260. [8]. Qi Wang, Haihu Ma, and Xiaodan Wang, Prediction and Assessment of Agricultural Modernization Level Based on Topsis and Artificial Neural Network, Proceedings of the 2010 ICCASM 2010, V2- p.229-232, China.

Advanced Materials Research II 10.4028/www.scientific.net/AMR.463-464

Prediction and Optimization of Dimensional Shrinkage Variations in Injection Molded Parts Using Forward and Reverse Mapping of Artificial Neural Networks 10.4028/www.scientific.net/AMR.463-464.674

International Journal of Advances in Engineering Sciences Vol.3, Issue 1, January, 2013

A Review on Application of Artificial Neural Networks for Injection Moulding and Casting processes Manjunath Patel G C Research Scholar, Department of Mechanical Engineering, NITK, Surathkal, INDIA Email: [email protected]; Abstract: Artificial Neural networks (ANNs) have potential challenges in the eve of prediction, optimization, control, monitor, identification, classification, modelling and so on particularly in the field of manufacturing. This paper presents a selective review on use of ANNs in the application of casting and injection moulding processes. We discuss number of key issues which must be addressed when applying neural networks to practical problems and steps followed for the development of such models are also outlined. These includes data collection, division of data collected and pre-processing of available data, selection of appropriate model inputs, outputs, network architectures, network parameters, training algorithms, learning scheme, training modes, network topology defined, training termination, choice of performance criteria for training and model validations. The suitable options available for network developers were discussed and recommended suggestions to be considered are highlighted. Keywords: Metal casting processes, Injection moulding processes, Casting Materials/Alloys, Artificial Neural Networks

INTRODUCTION Neural network is one among the simplified models of our biological nervous systems. Our biological nervous system consists of massively parallel distributed large number of interconnected processing elements known as neurons [22]. For example [24], in human brain the most basic element is neuron. The beauty of human brain is its ability to think, remember and apply past experiences to our future actions. Our human brain comprises about 100billion neurons, each neuron connects up to 200000 neurons and approximately 1000-10000 interconnections are available. The neurons were arranged to form a layer and the connection pattern formed within and between the respective layers through weights referred as network architecture. There are mainly five basic neuron connection exists namely [24], 1. Single-layer feed forward network 2. Multi-layer feed forward network 3. Single node with its own feedback 4. Single layer recurrent network 5. Multi-layer recurrent network From the above five network connections currently more than fifty different network architectures were developed under supervised and unsupervised learning. A. Introduction to Metal castings Casting is one among the widely used near net shape manufacturing process started production during 4000-3000 B.C., Find major applications in both ferrous and I.

Print-ISSN: 2231-2013 e-ISSN: 2231-0347 © RG Education Society (INDIA)

Prasad Krishna Professor, Department of Mechanical Engineering, NITK, Surathkal, INDIA Email: [email protected] non ferrous casting materials such as casting engines blocks, valves, pumps, machine tools, power transmission equipments, aerospace, home appliances and so on. Because of its wide applications, functional advantage, economical benefits, near net shape manufacturing capability more than 90% of the manufacturing goods produced through casting processes [91]. Moulding, melting followed by pouring, fettling, inspection and elimination/dispatch were the major steps followed in casting process. Control during each stage in casting process plays a vital role else it may lead to casting defects like rat-tails, scabs, cracks, blow holes, oxide films, misrun, shrinkage, porosity, cold shut, scar, blister, hot tears, segregations, cracks and so on. In past few decades neural networks were used to tackle production related problems, controlling the process by reducing casting defects, lead times, scrap rate, production cost and to avoid trial and error method, expert dependent advices in optimizing the process. B. Cast alloys and composite materials introduction Cast aluminium alloys widely used in various engineering applications due to its light weight characteristics, good heat, cast-ability and electrical conductivity, low density, melting point, coefficient of thermal expansion, and casting shrinkage respectively [86]. The mechanical properties of cast alloys mainly depend on weight fractions of alloying elements, applied heat treatments, microstructures, and morphologies of the various phases [79]. The use of composite materials in recent years is due to ever increasing fuel prices, need of weight reduction in aerospace and automotive sectors. Stir casting, diffusion bonding, squeeze casting, ultrasonic method, powder metallurgy, compo casting, thixo-forging and were the major techniques to fabricate composites. C. Introduction to Injection moulding process The complete injection moulding (IM) cycle follows three stages namely filling, post-filling and mouldopening for processing plastics. Plastic materials have following properties such as light weight, corrosion resistance, transparency, ability to make complex shapes, allow to integrate with other materials, functions, excellent thermal and electrical insulation properties. Quality related problems observed from the reviewed publications during injection moulding process were sink mark, flash, jetting, flow marks, weld lines, volumetric shrinkage, warpage, dimensional shrinkage variations and others. In recent years there is a rapid growth in ANNs to address and tackle the


problems that might occur in casting as well as IM processes either to enhance mechanical, micro-structure or surface characteristics as shown based on years of publications in table 1(a). Neural networks proved to be an excellent tool from the reviewed publications starting from preparation of mould to final inspection stage refer table 1(b). 48 out of 145 network architectures (NA) reviewed used for optimum process parameter prediction, 13 NA applied during moulding, 4 NA used to study the flow behaviour or metal fill during process cycle [28], [51] & [1]. 7 NA [15], [36] & [87] used during solidification stage to enhance properties by reducing defects, 2 NA [73] & [58] used to predict the micro-structure characteristics, 1 NA [31] applied during design stage for minimum porosity, 12 NA [8], [12], [13] & [53] used during inspection stage to predict the presence/absence of defect, 3 NA [66] utilized for heat treatment stage to enhance the mechanical properties, 15 NA [25] used for process planning, other 40 NA utilised for various purpose such as 4 NA [6] & [52] cost estimation before manufacturing the component, 33 NA used for mechanical properties prediction at different stages during the process, remaining 3 NA applied for data extraction [4], state of molten metal level [46] and metal temperature [21]. Neural networks have good learning and generalization capability; they learn from examples during training and generate outputs for new inputs which were not used during the training period. The above feature of ANNs helps to use as an alternative tool to simulate complex and ill-defined problems. As shown in table 1(c). 1 NA applied for identification of heat transfer co-efficient between metal mould interfaces [36], 9 NA were used to control the process [14], [37], [48-50] & [61], 9 NA [8], [12-13], [61] & [86] utilized for classification of defects, 95 NA utilized for prediction, 11 NA [9], [11], [18], [23], [26], [35], [59] & [66] adopted to optimize the process, 2 NA [28] & [51] used for to monitor the fluid flow and metal fill towards cavity and remaining 18 NA [2], [10], [38], [47], [55], [81] & [82] were used to map the relationship between input-outputs via modelling. ANNs applied by various researchers to achieve various objectives for different cast alloys, injection moulding and casting processes. 31 NA utilized for injection moulding (IM) processes to enhance product quality, 23 NA [1], [3], [21], [32], [57], [72-73], [78-79] & [87] used to improve mechanical, micro-structure and surface characteristics of cast material/alloys (CM/A), 20 NA [8-9], [12-13], [20], [30], [38], [40], [64-65] & [71] utilized for pressure die casting (PDC) processes namely low and high pressure die casting processes, 15 NA [25] adopted for investment casting (IC) process, 15 NA [48-49], [53-54], [58], [66], [68-69] & [76] used for continuous casting process, 14 NA [16], [17], [27], [33], [44], [47] & [60] presented for stir casting process (STIRC), 6 NA [41], [55], [74] & [83] used for sand casting (SC) process, 4 NA [81] & [89] used for centrifugal casting (CFC) process, 3 NA [61], [85] & [86] make used for cossworth (CP) process, 2 NA utilized for graphite sand mold casting (GSMC) [42], semisolid metal casting (SSMC) [70], lost foam casting (LFC) [28] & [51], squeeze casting (SQC) [2] & [81] and phosphate graphite mould casting (PGMC) [43] process

respectively and remaining 4 NA adopted for each process such as green sand casting (GSC) [63], permanent mould casting (PMC) [77], strip casting (STRIPC) [46] and gravity die casting (GDC) [36] processes. II.

CLASSIFICATION OF REVIEWED WORKS

The search for papers was done utilizing available scientific and technology resource data bases namely journals, conferences, symposium and others. Total 145 NA found from 83 publications were chosen for review if they meet the following requirements, Focused on the casting processes, cast alloys and injection moulding processes, Neural network tools used as a modelling technique. From the reviewed publications following key issues were focused in applying ANNs to practical problems, 1. Generation of training samples for ANN 2. Selection of neural network type 3. Selection of input and output for network 4. Design of suitable network architecture 5. Selection of suitable learning algorithms for training 6. Selection of hidden layers, hidden neurons, activation functions, bias and other network parameters 7. Selection for evaluation of training performance, network termination, model validation 8. Applications of ANN model in casting and injection moulding processes III. PROBLEM DEFINITION Statistical design of experiments proven to be an cost effective tool for mapping the complex relationship between numbers of independent and dependent variables and optimize throughput in various manufacturing process with minimum experiments. Full factorial design (FFD), central composite design (CCD), box-behnken design (BBD) and taguchi parametric design were some of the tools available for experiment conduction and optimizing the process. Statistical tools help the designer in identifying the best set of parameter combination level to yield quality results for discrete values [4] & [18], however for continuous variables to conduct experiments at predetermined levels within the narrow range finds difficulties in some fields like foundry, welding, metal forming [55] and so on and may not help engineers to optimize the process. Modification of statistical models by incorporating new random data is not feasible. ANNs addressed these limitations effectively and refines the model by incorporating new random data at any stage during training. Form the reviewed literatures statistical methods were used to reduce the experiments/simulation runs and to fulfil the need of enough training data for ANNs. ANNs yield best prediction when compared to other statistical models in most of the case studies was observed. A. Data collection ANNs prediction accuracy depend upon the quality and quantity of the data used for training observed from the reviewed publications, various means of data collected for

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TABLE 1. REVIEW OF LITERATURES IN CASTING AND INJECTION MOLDING APPLICATIONS VIA ARTIFICIAL NEURAL NETWORKS SL. No

Number of network architectures among reviewed publications

a

Year of publications

b

Process applications

c

ANN applications

Identification-1

Control-9

Classification-9

Prediction-95

Optimizaton-11

d

Model validation

CRC-10

Max. PE-7

RMSE-7

PE-25

Graph-35

MAE-5

SDQ-5

SDE-2

e

Network training

CRC-13

MPE-20

RMSE-26

MSE-44

NRMSE-1

MAE-9

SDQ-3

MAPE-2

f

Training termination

TE/TT-2

g

Hidden layers

h

Input neurons

One-3

Two-10

i

Output neurons

One-94

Two-12

j

Topology definition

k

Training mode

l

Learning scheme

Supervised-135

Unsupervised-4

NR-6

m

Validation set

Used-21

Not used-87

NR-37

n

Simulation software

o

Data collection

p

Process and cast alloys

q

ANN Simulation software \ Network architecture

Mat.NNTB-40

LVQ-2

RBF-11

MLP-algorithms

BP-58

LM-40

r s

1997-1

1999-2

2000-3

Molding-13

2001-4

Design-1

2003-1

Process parameter-48

EL-10 One-82 Three-30 Three-13

NEB-20

2002-3

2005-6

2006-11

Heat treatmet-3

NR-73

Two-29

Three-1 Five-23

Four-8

Five-4

OBT-25

Six-6 Six-2

2008-8

Process planning-15

EL/TE-37

Four-29

2007-10

DOE-6 IM-31

REPL-4 IC-15

C-Mold-3

Meltflow-6

DOE-T/SS-11

2011-7

Inspection-12

Monitor-2 Mean.PE-21 PQI-2

2012-5

Others-46

Modelling-18 RE-1

MAPE-19

None-22

NR-4

NR-29

NMSE-1

SSE-15

TQ-6

NTEP-18

EL/TT-5 NR-9

Between seven to nine-15

Between ten to thirty-24

NR-5

Above ten-4

Nr-5

Between seven to nine-3

OAT-4

2010-13

Solidification-7

OMO-29

PPN-23

On-line mode-17

FEA/FEM-9

2009-13

T&E-44 Off-line-128

Moldflow-4

Procast-22

Virtual casting-1

ENRDOE/SS-38

TB/HB/HD-6

ENRDOE-65

GSMC-2

STIRC-14

CC-15

SC-6

Matlab-21

Qnet-2

DPL-3

VC/C++/JPL-6

SLP-4

MLP-120

SCG-5

PDC-20

CG-2

3

CFC-4

SSMC-2

NPV4.5-2

SOM-2

V-shrink-1 DOE-T-12

CM/A-23

CP-3

NNPII/Plus-3

PNN-1 MAL-2

Others-5 DOE-SS-1

SQC-2

LFC-2

Others-6

SNNS-14

NR-50

Others-4

NR-4 NR-6

Others-2

Other-1 Others-7


SS has the following advantages observed from the literatures [65], SS replace the real experiments need to be conducted. It helps in decision making-where human experts are not available and process calibration procedure takes longer than the manufacturing lead time, Where large number of process variables need to be examined with a minimum number of process range values, when die preparation cost and time were high. SS have some limitations such as simulation model are not suitable for large number of repetitive analysis required for optimization process because of high computational cost [11]. Simulation programs require need of human experts to interpret the output data [20]. Large number of simulation trials, coupled with lengthy execution or computation time/run might make investigator impractical [65]. The analyses and interpretations of simulation results were still empirical and enough computation time cannot meet the requirements of online control [71]. So to eliminate the trial and error method, reducing computational cost, repetitive analysis, need for experts and implementation of online control, advance methods are in high demand to model and optimize the process. Artificial intelligence (AI) based ANN model addresses these limitations and predict large number of outputs within few seconds once the training has completed. C. Training data quantity Collection of adequate quantity of training data is essential to enhance neural network performance. During the training process network architecture and there network parameters such as connected weights, learning rate, activation functions, constants, bias etc., need to be optimized for the desired problem under experimentation. When neural network is trained (weights are fixed) it then becomes possible to generate satisfactory results when presented with any new input data it has never experienced before. Total number of weights (TW) can be calculated for the given network [34] using TW = (Number of input neurons (IN) * Number of hidden neurons (HN)) + (Number of hidden neurons (HN) * Number of output neurons (ON))). HN increases network connections and weights, this number cannot be increased without any limit because one may reach the situation that, number of the connections to be fitted is larger than the number of the data patterns available for training. Though the neural network can still be trained, but it is not possible to mathematically determine more fitting parameters than the available data patterns for training [80]. Table 2. Represents various researchers used extremely limited data patterns wherein network connections and weights to be fitted were more than the data patterns used for training. To study and compare the effectiveness of neural network training techniques and learning algorithms must be done with large data patterns to improve generalization and avoid over-fitting but not with small data points [80]. Approximately 1000 set of data used for training yielded better results by various researchers [6], [20], [23], [29], [30] and [42]. It was observed from the literatures collected data base was divided into 3 stages namely training set, validation set and test sets. The main purpose of training was to decide the weight and bias of the

training is as shown in table 1(o). 6 NA [3], [50], [57] & [75] used data collected from design of experiments (DOE) like response surface methodologies (RSM) namely CCD & BBD, 12 NA [4], [18], [43], [45], [56], [59], [63], [70] & [84] used DOE utilizing taguchi parametric design (DOET), 65 NA utilized either trial & error method of experiment conduction, experts advice/ experience from industry refers to experiments not resembling DOE (ENRDOE), 11 NA [11], [26], [35], [40], [65], [67], [73] & [82] adopted combination of DOE-T and simulation software (SS), SS was used to avoid the need of real experiments to be conducted because it adds material, processing, labour, inspection costs and so on and the purpose of DOE-T is to reduce the number of simulation trials because of high computational time for each trial may lead to costly simulation. 1 NA [19] used integration of DOE and SS (DOE-SS), 38 NA utilized combination of ENRDOE and SS (ENRDOE/SS), 4 NA [23] & [42] used regression equations from the design of experiments in published literatures (REFPL) to satisfy need of huge data for training, Text books (TB), hand books (HB) [79], historical data (HD) [52], [68] & [76] were the other means of collected database. Some of the limitations observed from the reviewed literatures such as, DOE-T reduce the experiments need to be conducted but fails to provide enough training data for ANN simulation in reference to example 13 shown in table 2. SS fulfils need of huge training data for ANNs, however simulation model is not suitable for large number of repetitive analysis required to optimize the process leads to high computational cost [11] and need of experts to interpret the results. ENRDOE follows large number of experiments to yield best results leads to high manufacturing cost and may not provide required quantity training data. So alternative method to overcome this problem is use of DOE for experiment conduction, develop regression equation from the real experiments through analysis of variance, statistically rearranging the input variables between their respective ranges and can predict the output through regression equation obtained from DOE which satisfy the need of huge training data. B. Simulation software In recent years, numerical simulation software’s were rapidly developed and applied successfully in many casting and injection moulding industry to enhance product quality, improve properties and reduce manufacturing costs. The list of commonly used and commercially available SS for IM process observed form the reviewed literatures shown in table 1(n) namely 3 NA [5] used c-mold, 4 NA [11], [19], [26] & [35] utilized mold flow, 1 NA [67] adopted Timon-3DTM and 1 NA [29] used Partadviser CAE. Similarly in casting applications, 22 NA [25], [36], 22 NA [25], [36], [64], [65], [71] & [82] used Procast software, V-shrink [1], Virtual casting [73], Any cast [21], Maxwell [28] and finite element methods (FEM) [33], finite element analysis (FEA) [51], fluent, calcosoft, magmasoft were the advanced commercial codes were available for simulation.

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network, validation set verifies whether the estimated outputs from the network were accurate and testing determines whether network was over-trained or not. It is quite interesting to note that only 21 NA used validation sets, 37 NA not used and 87 NA not reported information about validation sets as shown in table 1(m).

Qnet for windows version 2.0, NeuralLab, havBPNet++, IBM Neural network utility, NeuroGenetic Optimise (NGO) version 2.0, Aree 3.0 Adaptive logic network development system for windows, TDL version 1.1 Neuroon-line, NeuFrame and OWL Neural network library. From the reviewed publications as shown in table 1 (q), following ANN simulation software has adopted by various researchers namely, 21 and 40 NA adopted MATLAB and MATLAB neural network tool box (Mat. NNTB), 14 NA employed using statistica neural network software (SNNS) [8], [13], [81], [78] & [85-86], 2 NA [14] & [37] uses Qnet, Neuro-planner version 4.5 (NPV) [32], 6 NA used either visual basic c (VC)/c++/ java programming language (JPL), 3 NA [16], [44] & [88] employed delphiprogramming language (DPL), 3 NA [66] professional II/plus (NNPII/plus), 1 NA [15] utilized Neuro solutions (NS)], PC neuron (PCN) [75], Neuro-computer (NC) [52], Fast artificial neural network library (FANNL) [63] and remaining networks not reported (NR) the kind of ANN simulation software adopted. From the literature survey, it has been observed that selection of ANN simulation software based on the type of neural architecture used for prediction. Because all ANN simulation software cannot predict all type of network architectures. E. Network type and architectures Currently more than 50 different neural network architectures were available from the available literatures. In casting and IM applications five different type of NA were observed from the reviewed literatures as shown in table 1(r). 120 NA make use of multi-layer perceptron network (MLP) because of its good generalization capability, 11 NA utilized radial basis function network because of its training speed and easy to construct, 2 NA [65] & [71] used learning vector quantization (LVQ) network, 2 NA [4] & [15] used self organize mapping (SOM) as an un-supervised learning network, 4 NA [13], [74] & [78] adopted single layered perceptron (SLP) network, 1 NA [13] employed probabilistic neural network (PNN), 1 NA [4] adopted the combination of SOM and MLP network, 4 NA [3], [28], [63] & [84] NR the kind of network architecture they employed for their application. MLP with different training algorithms adopted by various researchers as shown in table 1(s), namely 58 NA used back-propagation (BP), 40 NA adopted levenberg-marquardt (LM), 2 NA employed conjugate gradient (CG), 2 NA momentum adaptive learning (MAL), 5 NA employed scaled conjugate gradient (SCG), newton method, Bayesian regularization (BR), rprop [87], variable metric chaos to improve BP algorithm [69], combination of LM and BP [78] and LM and BR [57] were the other few algorithms used to tackle and improve the prediction accuracy. F. Learning (or) Training The process of modifying the neural network parameters by making proper adjustments lead to result in production of desired response. During training the network parameters were optimized, as a result of which it undergoes internal process of fitting. Table 1(l), clearly shows 135 NA

TABLE 2. LIMITED DATA SET USED FOR TRAINING

1

Network architecture IN-HN-ON 4-7-4

Total weights (TW) 56

9

[2]

2

1-12-8

108

10

[16]

3

5-10-3

80

13

[79]

4

5-8-1

48

19

[82]

5

1-8-2

26

10

[88]

6

5-15-1

90

80

[50]

Examples

Ref.

7

3-4-1

16

8

[9]

8

11-23-5 4-4-1 4-10-1 1-8-3

368 20 50 32

65 10 10 12

[41]

11

3-7-1

28

20

[71]

12

3-15-1

60

6

[58]

13

5-6-6

66

18

[59]

14

2-10-3

50

46

[27]

9 10

D.

Training Data used

[65] [44]

ANN simulation software

Simulation uses a model to develop conclusions providing insight on the behaviour of real-world problems being studied. Computer simulation is used to reduce the risk associated with creating new systems or upgrading the existing systems. Over the past few decades, computer simulation software together with statistical analysis techniques was used as decision making tool for the given task and is growing more technical, precision by reducing the error percentage in the field of business, industry and so on [62]. Computer simulation is very important because it helps in prediction of future events and occurrence. For example, simulation gives for the particular operating conditions; it predicts outputs or responses based on the past data without conducting any experiments. There are various freeware and shareware software available for ANN simulation for measurement fields [90] namely Rochester connectionist simulator, NeurDS, PlaNet 5.7, GENESIS 2.0, SNNS 4.1, Aspirin/MIGRAINES 6.0, Atree 3.0 educational kit for windows, PDP++, Uts, Multi-module neural computing environment, NevProp, PYGMALION, Matrix Back Propagation (MBP), Win NN, BIOSIM, AINET, DenoGNG, nn/xvv, NNDT 1.4, Trajan 2.1, Neural network at your finger tips etc., and some of the commercial software packages for measurement field [90] are also available for ANN simulation like BrainMaker, SAS, MATLAB Neural Network Tool, Propagator, Neuroforecaster and visual data, NESTOR, Neuroshell2, NeuroWindows, NeuFuz4, PARTEK, NeuroSolutions v2.0,

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used supervised learning scheme, 4 NA makes use of unsupervised learning and 6 NA not reported the kind of learning procedure adopted. Generally there are three kinds of learning process namely supervised learning, unsupervised learning & reinforcement learning. Supervised learning: Learning with the help of a teacher refers to supervised learning. Here input-output data were available for training. Error determination is possible by comparing neural network prediction and target output data. This error is feedback to the network for updating the weights until predicted network results close to desired target values [24]. Un-Supervised Learning: Learning without the help of a teacher referred as un-supervised learning. In un-supervised learning the target output data were not available; hence error prediction is not possible. Because no feed-back information available from the environment to inform what the output should be or whether the predicted output is right or wrong. In such case neural network must discover, patterns, regularities, features (or) categories from input data patterns and relates the input data over output, such kind of process is called as self-organizing process [24]. Reinforcement Learning: Reinforcement learning process is similar to supervised learning. Here in supervised learning correct target output values are known for each input data. But in some cases, very less information might be available. For example the network output might tell that its actual output is only 50% correct. Thus only the critic information is available not the exact information. The reinforcement signal acts as feedback information to the network during learning process [24]. G. Training modes The process of modifying the neural network parameters by updating connection weights, bias and other network related parameters if any refers to training [22]. There are normally two types of training, Incremental mode of training (on-line training)- refers to an approach in which training sample/scenarios are collected on-line and pass to the network to be trained one after the other in sequence. Batch mode of training (off-line training)- The necessary data is collected before the commencement of the training and entire training data (say more than one) is passed to the network at a time and average error in predictions is determined and is back propagated to the network to update weights and bias values to enhance prediction accuracy. From reviewed publications shown in table 1(k), off-line approach has been adopted in 128 NA, 17 NA make use of on-line prediction applications namely, to monitor the metal fill in LFC [28], prediction of aluminium silicon modification level in AlSiCu alloys [57], to monitor product quality through strip casting process [46], to predict optimal flow behaviour of molten metal inside die cavity [64], to predict crack in continuous casting process [48-49], The authors [68] analyzed characteristics of existing mould breakout prediction systems, influence factors on breakout, feasibility that mould friction is used to forecast breakout and investigated mould friction through online training

method for mould breakout prediction, researchers [75] developed in-process mixed-material caused flash monitoring system for IM process. Incremental mode of training has the following advantages, easier to implement, computationally faster than batch mode of training [22], occurrence of defects/problems can be tackled at any stage during the process leads to increase in productivity, decreasing human labour, reduces manufacturing lead time and costs [41] H. Network Topology During development stage of network, understanding of the following factors are more important such as initialization of weights, selection of activation function, learning rate, bias value, momentum constant, activation constants, hidden layers/neurons and so on. These factors not only affect network convergence but also affect prediction accuracy. Table 1(j), shows the way researchers adopted to define their network topology. Not even the best topology (NEB) used in 20 NA [38], authors dint mentioned either how many hidden layers/neurons, transfer function, training termination, learning algorithms, bias, learning rate, momentum constant, model validation, network performance criteria they adopted. 25 NA presents only best topology (OBT) which includes network parameters, hidden layer/neurons with no justification regarding selection, One at a time strategy (OAT) adopted by 4 NA [23] & [42], where in topology selection done through network parametric study, 29 NA only mentioned optimization, but actual optimization procedures followed were not reported, 23 NA [4], [6], [25], [52] & [89] proposed new methodology to define their network, authors [25] presented optimum topology selection by brute-force exhaustive enumeration of alternatives. When relatively few alternatives and/or network training time is low, in such situations genetic algorithm tool may find best possible solution to optimize networks. 44 NA adopted the most common method trial and error method (T&E). Though some new method proposed in selection of hidden layer/neurons and network topology, but they were not popular because they might fail for other applications. So till date there is no perfect methodology for defining network topology and still it is under intensive study. I. Neural network architecture parameters Normalization and De-normalization: Scaling of inputoutput values plays crucial role because improper scaled values cause incompatibility, leads to inaccurate results [5]. Normalization process helps in speed up the training process, avoids numerical overflows due to very large or small values [21]. Statistical techniques such as zero score, median, sigmoid, mini-max and statistical column normalization were available for data normalization, developed under different rules namely max rule, sum rule, product rule and so on [39]. Data normalization range selection is based on intended transfer function adopted, which helps in modifying summing weights into an output. Normalization range between (0, 1) for logistic sigmoid transfer function and (-1, +1) for hyperbolic tangent transfer

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function [66]. The purpose of de-normalization is to convert predicted scaled values into actual output. J. Initialization of weights In neural NA neurons of one layer connected to other neighbouring layer by means of connection weights. Weights contain information about input signals to solve complex problems [24]. From the review literatures it has been observed that network performance relies partly on initialization of weights. Smaller weights tend to increase the training time for network convergence, whereas larger weight matrix may cause instability in the network performance. Network weights have to initialize at small random values because if all weights start with equal weights and if the solution requires an unequal weights to be developed the network won’t converge and may fail to learn from training examples with error stabilizing or even increasing as learning continues during training period[19] & [30]. K. Transfer or Activation functions Activation function is used to convert the weighted sum of input values of a neuron to a value that represents the output of the neuron. The output of a neuron is largely depends on the intended transfer function used. Different types of transfer function are used in MLP networks are hard-limit-it generates output either 1.0 or 0.0 depending on the input, log-sigmoid- output lies in the range between 0 and 1, linear-output of transfer function is made equal to its input and ranges varies between -1.0 to 1.0 and tan-sigmoid transfer function-generates output lies in the range between -1.0 to 1.0 [22]. Radial basis function is the most commonly used transfer function in RBF networks. The RBF network trains faster than multilayer networks, but requires many neurons for high-dimensional input spaces [57]. The nature of the sigmoid transfer function used in BP algorithm does not reaches its extreme values of 0 and 1 without infinitely large weights, therefore input-output patterns are to be normalized between the ranges from 0.1 to 0.9 [71], [36]. From the literature review linear, log and tan sigmoid transfer function finds in maximum applications. Linear transfer function is used in almost many NA in input and output layers. Log and tan sigmoid transfer function used in MLP network and radial basis function in case of RBF networks finds maximum applications in case of hidden layers. Linear transfer function in RBF networks and MLP networks was normally used which helps to speed up the training process. However in case of output layer log or tan sigmoid transfer functions also used by many researchers [59], [23], [42], [67], [58], [74] to improve predictions while sacrificing the higher computational cost. Authors [42] and [23] used activation constants in the transfer function which helps in reducing the mean squared error to small values, selection of constants based on network parametric study. L. Learning rate (η) and Momentum (α) constant The purpose of using network parameter-learning rate (η) is to prevent over-learning and error vibration. The learning rate parameter range varies between 0-1. Lower value of η ensures a true gradient descent but increases total

number of learning steps to obtain the optimal solution. Higher value of η indicates rapid convergence but results in local minima by over-shoot and may never converge to minimum [30]. The momentum (α) constant parameter helps in weight updating in order to speed up the search in local minima region leads to faster convergence, increases prediction accuracy and shortening the computational time. To prevent over learning rate, error vibration and to avoid local optimum value α + η = 1.0 is adopted by authors [6]. Hence to conclude optimal vale of η and α depends on the problem to be solved and chosen experimentally via trial and error method, network parametric study by varying one at a time between the range 0-1 [42]. M. Bias Bias neuron does not receive any input and emits constant output across the weighted connections to neurons in the next layers [21], [29], and [33] The main function of using bias neuron is to prevent the weight matrix from stagnation, controlling activation function during learning process and finally helps neurons to be flexible and adaptable [77]. The range of bias value is varies between (00.15) [36]. N. Number of Input and Output neurons Table 1(h) & (i) represent the number of inputs and outputs used among reviewed publications. A single input neuron used in 3 NA [44], [76] & [88], two neurons in 10 NA, three neurons in 30 NA, four neurons in 29 NA, five neurons in 23 NA, six neurons in 6NA, seven to nine neurons employed in 15 NA, ten to thirty neurons in 24 NA [12], [54], [78] & [86] and 5 NA not reported the number of input & output neurons used. For one input variable conventional, simple regression, moving average and smoothed line function in micro-soft excel perform better than neural network. ANNs were best suited to model complicated interactions between several numbers of input variables [80]. A single output neuron used in 94 NA, two neurons in 12 NA, three neurons in 13 NA, four neurons in 8 NA, five neurons in 4 NA, six in 2 NA, seven to nine neurons employed in 3 NA, ten to hundred neurons is used in 2 NA [8] & [15], 108 output neurons used in 2 NA [85] & [86]. It is more effective to develop separate models for individual output, because training time/computational time increases dramatically when the number of outputs increases [80]. Neural networks proved to simulate with high accuracy for higher input-output neurons only when we have huge training data and ready to sacrifice computational time. O. Selection of Hidden neurons and Hidden layers Hidden layer(s) & hidden neurons play significant role in terms of convergence rate during training, learning time and prediction accuracy of the network [3]. The possible means of size choice observed from the reviewed literatures such as selection based on experience and experimentation with the problem or application in hand [3], neural network prediction accuracy can further be improved by increasing hidden layers and neurons [11] & [19], alkaikes information criterion, network information

7


criterion, neural network information criterion methods [4] available based on statistical probability and an error energy function. 82 NA employed for general problems with single hidden layer, 29 NA adopted for complicated using 2 hidden layers, 1 NA adopted three hidden layers [64], 9 NA not reported the kind of network architecture adopted as shown in table 1(g). Too many hidden neurons may have risk of over fitting in training data leads to poor generalization and increases training time [30]. Too few neurons (say one) are not sufficient to capture non-linear mapping from the collected data base. Mathematically proved by Hyken, single hidden layer with enough neurons yields successful results for feed forward neural network [17]. Kolmogorov theorem [40] & [89] H = 2p+1 (H is hidden neurons, p is input neurons) adopted to fix hidden neurons, l=Sqrt(n+m) + a, (n= input neurons, m= output neurons, a= constant (1, 10) and l is hidden neurons) employed for size choice [58], network purning technique [68], H= (input neurons + output neurons)/2 used by authors [6] & [79], network parametric study using one at a time [23] & [42] strategy was employed to fix hidden neurons. There are some few examples [13], [19], [51], [61] and [78] observed, where neural networks predict best results even when hidden neuron numbers are more than 50. According to authors [34], when the number of hidden neurons is equal to the number of training data used, the learning could be fastest but loses its generalization capability; hence for good generalization the ratio 10:1 must be used means for every 10 training patterns 1 hidden neurons yields better results. The exact size choice is still under intensive study with no conclusive solutions available because of network mapping complexity and nondeterministic nature of many successfully completed training procedures; however choice was done based on network prediction accuracy [30].

P.

NA adopted mean square error (MSE), 15 NA used sum of squared error (SSE), 9 NA employed mean absolute error (MAE), 6 NA used training quality (TQ), 20 NA adopted mean percent error (MPE), 3 NA used standard deviation quotient (SDQ), 2 NA utilized mean absolute percentage error (MAPE), 1 NA used normalized mean squared error (NMSE), 26 NA make use of root mean squared error (RMSE), 2 NA used performance quality index (PQI), 1 NA used normalized root mean squared error (NRMSE), 13 NA used correlation coefficient (CRC) and remaining . 29 NA not reported. Some literatures adopted more than one statistical index for evaluation of network training performance few examples in [6], [10], [78] and [61]. The goal of any training algorithm is to reduce the error between the predicted and the actual value. A lower error & higher CRC indicates the estimated value of network is closer to the true value [6]. Among various statistical quality indexes MSE followed by RMSE, MPE and SSE were widely used. R. Model validation The ultimate goal at the end of training is to evaluate the network prediction accuracy (Model validation) with new set of data which are not used in training; the predicted model has to provide accurate and reliable forecasts. There are various approaches used by researchers as shown in Table 1(d), [4] to evaluate the ANN model namely CRC [7], RMSE, Maximum percent error (Max. PE), Percent error (PE) [83], MAE, SDQ, Standard deviation error (SDE), Mean percent error (Mean PE), Relative error (RE), MAPE, authors [4], [27], [43], [67], [78], [79], [81] and [89] used more than one approach for model validation and attempt made by the authors [3], [4], [8], [20], [21], [27], [30-32], [36], [45], [50], [57], [66-67], [70], [72], [76], [77], [87] and [88] Expressed their prediction accuracy through graph by comparing with experimental and predicted neural network results. S. Sensitivity analysis & reverse process model Sensitivity analysis (SA) is of paramount importance to identify the most significant process parameters during manufacturing process. SA can be applied during pre-processing stage to predict which factors contributing more and less, less contributed will be discarded and more will be considered and the difference in prediction with and without can also be checked. SA on post-processing stage determines the most critical factors from the selected process parameters. 1 NA [72] presented study made on the effects of different alloying elements, chemical composition, grain refiner, modifier and cooling rate on porosity formation in Al-Si casting alloys via SA. Development of reverse process model is always in great demand because industrialist are more interested to know the optimal setting process parameters for achieving desired castings quality. Reverse process model configures the response as the inputs and the process parameters as the output during training and learns the correlation between the responses and process parameters. The statistical methods [42] such as DOE might fail to carry out reverse mapping because the transformation matrix might not be invertible at all. This problem limitation could be handled effectively by

Neural network training termination

Table 1(f) represents researchers adopted various criteria to terminate the network training will fall among the following categories such as when the error (MSE, RMSE, etc.,) between neural network predicted value and the target value is reduced or meets the pre-set value (Error goal), when the preset training epochs completed and when crossvalidation takes place between training and test data. In most of the reviewed neural network architectures the first two approaches were used. 73 NA not reported, 37 NA adopted (EL/TE) during training if the preset error limit (EL) reaches, network terminates else it continues until the preset number of training epochs (TE). 18 NA employed fixed number of training epochs (NTEP) alone, 10 NA used only EL, 5 NA utilized (EL/TT) – if EL reaches within the preset timing network terminates training else it continues until the preset TT to reach. 2 NA used (TT/TE) – if preset number of training epochs reaches within preset time network stops training else continues until the TT should reach.

Q.

Neural network training performances

To check performance of network training ability on estimated results, various statistical evaluation indexes observed in review of 145 NA is reported in table 1(e). 44

8


using neural networks, as it works like a black-box data processing unit.

V. CONCLUSIONS Following are the major observations drawn from the literatures; 1. ANNs can be employed for casting and IM processes starting from moulding to final inspection stage. 2. Multiple regression equation obtained from DOE fulfils the need of huge training data for ANN 3. ANNs addresses the limitations of simulation software by reducing repetitive analysis, computational cost and time, replaces need of experts for results interpretation and helps in implementation for online process control. 4. An open field for studies aiming at on-line approach to address future problem or defects and correcting using adaptive and real time manner adopting ANNs 5. Supervised learning, MLP networks, one or two hidden layer(s), BP & LM algorithm, off-line training mode and Matlab simulations were more common in casting and IM process. 6. Very few authors attempted on use of activation constants in transfer function and bias values for MLP networks, even though it reduces the MSE to small values and improves the prediction accuracy. 7. ANN is best used to model complex interaction among several number of input & output parameter and predicts with good accuracy only limitation is need of enough training data and ready to sacrifice for computational time and cost. 8. Although author’s attempted and proposed some empirical equations for optimum hidden layer/neurons selection, however it is not generalized one and fails in other applications while using those methods. Hence optimum selection for hidden layer (s)/hidden neurons is still under intensive study. 9. Single hidden layer finds maximum applications in MLP networks from reviewed publications, reason might be increase the hidden layers increases the computation time or mathematically proven by Simon Hyken, single hidden layer with enough neurons yields better prediction accuracy. Only few NA used validation data set and recommended that use of validation sets prevents over-fitting. 10. Extremely limited amount data sets was used by few authors for training, where the network connections to be fitted are larger than the data available for training. Hence recommendation made by some author’s neural network has to be trained using large data base to avoid over-fitting and improve generalization. 11. It is important to note that very few authors reported the criteria adopted when to stop the neural network training, because prediction accuracy relies on neural network training termination. 12. In regards to model validation based on test sets or experimental results with network predicted

IV. HYBRID MODELS Soft computing is a collection of computational techniques in computer science, artificial intelligence, machine learning and some engineering disciplines, which attempts to study, model and analyze complex relationship, which are difficult from conventional methods (hard computing) to yield better results at low cost, analytic and complete solutions [24]. Neural networks (NN), fuzzy logic (FL) and genetic algorithms (GA) are few examples of soft computing. If more than one soft computing technique employed to solve problems refers to hybrid computing or systems. Hybrid systems classification based on the following three types [34], 1. Sequential hybrids, 2. Auxiliary hybrids and 3. Embedded hybrids. Examples [34], GA obtains the optimal process parameters first and hands over pre-processed data to the NN for further processing in Sequential hybrids, Neuro-genetic system for Auxiliary hybrids, in which an NN employs GA to optimize the network architecture parameters. NN-FL is an example for embedded hybrid system, in which NN receives fuzzy inputs to process it and extract fuzzy outputs. Observations made from the reviewed publications that PSO-BPNN [6] for product and mold cost estimation of PIM process, Neural-Fuzzy model [14] to dimensionally control the molded parts in IM process, Neural-fuzzy model composed of NN for learning relationship between inputoutput data and FL for reasoning to generate more reliable suggestion for modifying induced output values from the trained neural network. Neuro-Fuzzy Model [15] developed to compare the results of modified and un-modified Al-Si alloys under vibration & non-vibration conditions which influences on mechanical properties. ANN & GA models [31] have been implemented to optimize the effective process parameters on porosity formation in Al-Si casting alloys. A hybrid of back propagation neural network and genetic algorithm for optimization of injection moulding process parameters [35], GA-NN based model is used to tackle problems related to quality of castings in green sand mould system under both forward as well as reverse mappings [42]. To determine the optimum process conditions for improving the IM plastic part quality through combination of ANN/GA model [45], To predict the optimal process conditions using NN by avoiding what if scenarios raised in casting simulation software, time consuming and GA is used to yield best output parameter values [65]. To optimize the thin walled component manufactured through the use of LPDC process for aluminium alloys by combination of NN and GA [71]. From these applications on hybrid models in casting and injection moulding processes, neural networks found to be an effective estimation and optimization tool.

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13.

14. 15.

16.

[12] Paliniswamy S, C.R. Nagarajah, K. Graves and P. Loventti, A Hybrid Signal Pre-Processing approach in Processing Ultrasonic Signals with noise, Int J Adv Manuf Technol (2009) 42:766–771 [13] Dobrzanski L.A, Krupinski M and Sokolowski J. H, Computer aided classification of flaws occurred during casting of aluminum, Journal of Materials Processing Technology 167 (2005) 456–462. [14] Lau H.C.U, Wong T.T and Pun K.F, Neural-Fuzzy modeling of plastic injection molding machine for intelligent control, Expert Systems with Applications 17 (1999) 33–43 [15] Srinivasulu Reddy K. and Ranga Janardhana G, Developing a neuro fuzzy model to predict the properties of alsi2 alloy, ARPN Journal of Engineering and Applied Sciences, VOL. 4, NO. 10, 2009, 63-73 [16] Necat altinkok, Use of artificial neural network for prediction of physical properties and tensile strengths in particle reinforced aluminum matrix composites tensile strengths in particle reinforced aluminum matrix composites, Journal of materials science 40 (2005) 1767 – 1770 [17] Muhammad hayat jokhio, Muhammad ibrahim panhwar and Mukthiaraliunar, Modeling mechanical properties of composite produced using stir casting method, Mehran university research journal of engineering & technology, vol.30, no.1, (2011), 75-88. [18] Wen-chin Chen, Gong-Loung Fu, Pei-Hao Tai and Wei-Jaw Deng, Process parameter optimization for MIMO plastic injection molding via soft computing, Expert Systems with Applications 36 (2009) 1114–1122. [19] Hasan Kurtaran, Babur Ozcelik and Tuncay Erzurumlu, Warpage optimization of a bus ceiling lamp base using neural network model and genetic algorithm, Journal of Materials Processing Technology 169 (2005) 314–319 [20] Prasad K. D. V. Yarlagadda, Prediction of die casting process parameters by using an artificial neural network model for zinc alloys, int. j. prod. res., 2000, vol. 38, no. 1, 119-139. [21] Farahany S, Erfani M, Karamoozian A, Ourdjini A and Hasbullah Idris M, Artificial neural networks to predict of liquidus temperature in hypo-eutectic Al-Si cast alloys, Journal of applied sciences 10(24): 3243-3249, 201 [22] Pratihar D. K, Soft computing. Narosa publishing house pvt. Ltd, India, 2008. [23] Manjunath Patel G C, and Prasad Krishna, Prediction and Optimization of Dimensional Shrinkage Variations in Injection Molded Parts using Forward and Reverse Mapping of Artificial Neural Networks, Advanced Materials Research Vols. 463-464 (2012) pp 674-678. [24] Sivanandam S.N. and Deepa S.N., Principles of Soft Computing, 2nd Edition, Wiley India Pvt. Ltd, New Dehli, 2011. [25] Vosniakos G.C, Galiotou V, Pantelis D, Benardos P and Pavloua P, The scope of artificial neural network metamodels for precision casting process planning, Robotics and Computer-Integrated Manufacturing 25 (2009) 909–916. [26] Fei Yin, Huajie Maoa, Lin Hua, Wei Guo and Maosheng Shu, Back Propagation neural network modeling for warpage prediction and optimization of plastic products during injection molding, Materials and Design 32 (2011) 1844–1850. [27] Adel Mahamood Hassan, Abdalla Alrashdan, Mohammed T. Hayajneh and Ahmad Turki Mayyas, Prediction of density, porosity and hardness in aluminum–copper-based composite materials using artificial neural network, journal of materials processing technology 209 (2009) 894–899. [28] Mohamed Abdelrahman, Jeanison Pradeep Arulanantham, Ralph Dinwiddie, Graham Walford and Fred Vondraa, Monitoring metalfill in a lost foam casting process, Volume 45, Number 4, October 2006, pages 459–475. [29] Sadeghi B.H.M, A BP-neural network predictor model for plastic injection molding process, Journal of Materials Processing Technology 103 (2000) 411-416. [30] Prasad K.D.V. Yarlagadda and Eric Cheng Wei Chiang, A neural network system for the prediction of process parameters in pressure die casting, Journal of Materials Processing Technology 89–90 (1999) 583–590. [31] Mousavi Anijdan S.H, Bahrami A, Madaah Hosseini H.R. and Shafyei A, Using genetic algorithm and artificial neural network analyses to design an Al–Si casting alloy of minimum porosity, Materials and Design 27 (2006) 605–609.

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Materials Engineering and Performance, 2011, DOI: 10.1007/s11665011-9933-0. Shafyei A, Mousavi Anijdan S.H and Bahrami A, Prediction of porosity percent in Al–Si casting alloys using ANN, Materials Science and Engineering A 431 (2006) 206–210. Hanumantha Rao D, Tagore G. R. N. and Janardhana G. Ranga, Evolution of artificial neural network (ANN) model for predicting secondary dendrite arm spacing in aluminium alloy casting, J. of the Braz. Soc. of Mech. Sci. & Eng., Vol. XXXII, No. 3, July-September 2010, 276-281. Calcaterra S, Campana G and Tomesani L, Prediction of mechanical properties in spheroidal cast iron by neural networks, Journal of Materials Processing Technology 104 (2000) 74-80. Joseph Chen, Mandara Savage and Jie James Zhu, Development of artificial neural network-based in-process mixed-material-caused flash monitoring (ANN-IPMFM) system in injection molding, Int J Adv Manuf Technol (2008) 36:43–52. Jouni Ikaheimonen, Kauko Leiviska, Jari Ruuska and Jarkko Matkala, Nozzle clogging prediction in continuous casting of steel, 2002, 15th Triennial World Congress, Barcelona, Spain. Abhilash E, Joseph M. A and Prasad Krishna, Prediction of dendritic parameters and macro hardness variation in permanent mould casting of al-12%si alloys using artificial neural networks, (2006) FDMP, vol.2, no.3, pp.211-220. L.A. Dobrzanski, Kowalski M and Madejski J, Methodology of the mechanical properties prediction for the metallurgical products from the engineering steels using the Artificial Intelligence methods, Journal of Materials Processing Technology 164–165 (2005) 1500– 1509. Mehmet Sirac Ozerdem and Sedat Kolukisa, Artificial neural network approach to predict the mechanical properties of Cu–Sn–Pb–Zn–Ni cast alloys, Materials and Design 30 (2009) 764–769. Sha W. and Edwards K.L., The use of artificial neural networks in materials science based research, Materials and Design 28 (2007) 1747–1752. Dobrzanski L. A, Maniara R, Sokolowski J, Kasprzak W, Krupinski M and Brytan Z, Applications of the artificial intelligence methods for modeling of the ACAlSi7Cu alloy crystallization process, Journal of Materials Processing Technology 192–193 (2007) 582–587.

[82] Rong Ji Wang, Junliang Zeng and Dian-wu zhou, Determination of temperature difference in squeeze casting hot work tool steel, Int J Mater Form, 2011, DOI 10.1007/s12289-011-1061-8. [83] HamiD Pourasiabi, Hamed Pourasiabi, Zhila amirzadeh and Mohammad babazadeh, Development a multi-layer perceptron artificial neural network model to estimate the Vickers hardness of Mn–Ni–Cu–Mo austempered ductile iron, Materials and Design 35 (2012) 782–789. [84] An-hui cai , Hua chen, Wei-ke An, Xiao-song li and Yong zhou, Optimization of composition and technology for phosphate graphite mold, Materials and Design 29 (2008) 1835–1839 [85] L.A. Dobrzanski*, M. Krupinski, R. Maniara & J.H. Sokolowski, Quality analysis of the Al-Si-Cu alloy castings, Archieves of foundry engineering, 2007, Vol. 7, Issue 2, 91-94. [86] L.A. Dobrzanski, Krupinski M and Sokolowski J.H., Methodology of automatic quality control of aluminium castings, JAMME, 2007, vol. 20, Issues 1-2, 69-78. [87] Mohsen ostad shabani and Ali mazahery, Microstructural prediction of cast A356 Alloy as a function of cooling rate, JOM, vol. 63, No. 8, 2011, 132-136. [88] Necat Altinkok and Rasit Koker, Modelling of the prediction of tensile and density properties in particle reinforced metal matrix composites by using neural networks, Materials and Design 27 (2006) 625–631. [89] Yu Jingyuan, Li Qiang 1, Tang Ji and Sun Xudong, Predicting model on ultimate compressive strength of Al2O3-ZrO2 ceramic foam filter based on BP neural network, China foundry, vol. 8, No. 3, 2011, 286289. [90] Daponte P and Grimaldi D, Artificial neural networks in measurements, Measurements, 23, (1998), Pages 93-115. [91] ASM Metals HandBook, Casting, 9th Edition, vol. 15, 1998.

Appendix:

Figure: Ishikawa diagram for artificial neural networks

12

ARCHIVES of

ISSN (1897-3310) Volume 15 Issue 1/2015

FOUNDRY ENGINEERING Published quarterly as the organ of the Foundry Commission of the Polish Academy of Sciences

51 – 68

11/1

Prediction of Secondary Dendrite Arm Spacing in Squeeze Casting Using Fuzzy Logic Based Approaches M.G.C. Patela, P. Krishnaa, M.B. Parappagoudarb*

a

b

Department of Mechanical Engineering, National Institute of Technology Karnataka-Surathkal-575025, India Department of Mechanical Engineering, Chhatrapati Shivaji Institute of Technology, Durg (C.G) 491001, India * Corresponding author.: E-mail address: [email protected]

Abstract The quality of the squeeze castings is significantly affected by secondary dendrite arm spacing, which is influenced by squeeze cast input parameters. The relationships of secondary dendrite arm spacing with the input parameters, namely time delay, pressure duration, squeeze pressure, pouring and die temperatures are complex in nature. The present research work focuses on the development of input-output relationships using fuzzy logic approach. In fuzzy logic approach, squeeze cast process variables are expressed as a function of input parameters and secondary dendrite arm spacing is expressed as an output parameter. It is important to note that two fuzzy logic based approaches have been developed for the said problem. The first approach deals with the manually constructed mamdani based fuzzy system and the second approach deals with automatic evolution of the Takagi and Sugeno’s fuzzy system. It is important to note that the performance of the developed models is tested for both linear and non-linear type membership functions. In addition the developed models were compared with the ten test cases which are different from those of training data. The developed fuzzy systems eliminates the need of a number of trials in selection of most influential squeeze cast process parameters. This will reduce time and cost of trial experimentations. The results showed that, all the developed models can be effectively used for making prediction. Further, the present research work will help foundrymen to select parameters in squeeze casting to obtain the desired quality casting without much of time and resource consuming. Keywords: Squeeze casting process, Secondary dendrite arm spacing, Fuzzy logic, Adaptive network based fuzzy interface system (ANFIS) Nomenclature FLC L M H A B C D E

Fuzzy logic controller Low Medium High Time delay Pressure duration Squeeze pressure Pouring temperature Die temperature

a1,........a6 pi, qi, ri & ui SDAS GA-NN BPNN MAPE R2 ANFIS Mctrimf

Half base widths Coefficient of consequent part Secondary dendrite arm spacing Genetic algorithm neural network Back propagation neural network Mean absolute percent error Co-efficient of correlation determination Adaptive network based fuzzy interface system Manually constructed triangular membership function

ARCHIVES of FOUNDRY ENGINEERING Volume 15, Issue 1/2015, 51 -68

51

µ ANNs GA

Membership function Artificial neural networks Genetic algorithms

Mcbellmf Mcgaussmf Angaussmf

Manually constructed bell shape membership function Manually constructed gaussian membership function Adaptive network gaussian membership function

FL

Fuzzy logic

Antrimf

Adaptive network triangular membership function

RMSE

Root mean square error

Anbellmf

Adaptive network bell shape membership function

1. Introduction The second lightest material next to magnesium is aluminium and it is also the third largest material abundantly available in the earth crust. Aluminium alloys, widely used as a casting material from the past few decades due to its inherent properties such as light weight, recycling potential, reduce fuel consumptions to save energy and provides better environmental protection for the future generation [1]. Silicon (Si) found to be the better alloying element in aluminium alloys, since it improves fluidity, abrasion resistance, reduces melting temperature, lowers density, cost effective and easily available [2]. Addition of Copper (Cu) and Magnesium (Mg) are necessary to enhance the strength of Al-Si alloys [2]. It is interesting to note that Al-Si-Cu-Mg alloys have shown better casting characteristics with improved cooling rate, minimum porosity, reliability, good dimensional accuracy, modified eutectic silicon particles, better mechanical, micro and macro-structure properties.[3]. However it is important to note that the LM20 alloy used for the present study constitutes these alloy elements. . The squeeze casting process is based on the principle of pressurized solidification concept, suggested by D.K. Chernov in the early 1878. Porosity, shrinkage, segregations are the major limitations and have drawn much attention of the researchers in squeeze casting process development. Squeeze casting process combines the desirable features of gravity, pressure die casting and forging processes. It is important to note that mechanical and micro-structure properties are largely influenced by its cooling rate of cast alloys. Higher cooling rate reduces grain size, grain boundary, shrinkage porosity, segregation between dendrites, modifies eutectic silicon particles and decreases secondary dendrite arm spacing [4]. Higher solidification rate can be achieved with proper control of squeeze cast process parameters like time delay, pressure duration, squeeze pressure, die temperature and pouring temperature. Improper choice and levels of the aforementioned parameters may lead to possible casting defects such as oxide inclusions, over/under filling, extrusion, die sticking, segregations, cold laps, poor surface quality, dimensional inaccuracy and case debonding [5]. It is important to note that these defects finally affect the microstructure characteristics like secondary dendrite arm spacing (SDAS), which can be minimized by proper control of squeeze cast process variables. Hence it is of paramount importance to develop the squeeze cast process model and analyze the input (squeeze cast process variables) and output (secondary dendrite arm spacing) relationships of the process. The potential applications of squeeze cast components are found in aerospace and automobile sectors. This made researchers/investigators to carry out a great deal of research work on micro-structural characteristics during 1990’s and 2000’s

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throughout the world. It is important to note that majority of the research work happened during those periods was based on theoretical and experimental work. Lee et al., (1998) made an attempt to investigate the effects of gap distance on cooling rate and secondary dendrite arm spacing of gravity and squeeze cast wrought aluminium alloy using numerical and experimental approach [6]. It is important to note that the applied squeeze pressure reduces the air gap between the melt and the die interface leads to higher heat transfer rate (cooling rate) results in lower secondary dendrite arm spacing. Yang (2007) studied the effect of solidification time on the mechanical properties of LM6 and ZA3 alloys utilizing two analytical models namely steady state heat flow model and gracia’s virtual model [7]. In addition, performance of the developed models was compared with the practical castings and the average percent deviations were found to be equal to 27 for LM6 and 20 for ZA3 alloys respectively. The effect of pouring temperatures and squeeze pressures on cast structure and tensile properties of wrought aluminium 7010 alloy had been investigated by Yue (1997) [8]. It is important to note that experiments performed by keeping the die temperature and pressure duration as constant. Moreover in their work, it was observed that the time delay parameter acts as a crucial role wherein fine grain structure and better tensile properties were achieved when the alloy was pressurized between its liquidus and solidus temperature. Ming et al., (2007) investigated the effects of different squeeze pressures on secondary dendrite arm spacing, tensile strength and percentage elongation of squeeze cast Al-Cu based alloys [9]. It is also important to mention that experiments were performed by keeping pressure duration, die and pouring temperature at fixed values. In addition the results showed that, the applied pressure eliminates porosity and the alloy grain structure was clearly characterized by reduced secondary dendrite arm spacing (SDAS) with increase in applied pressure. Hajari and Divandari (2008) investigated the influence of different squeeze pressure on secondary dendrite arm spacing and the mechanical properties of 2024 wrought aluminium alloy [10]. However, it is important to note that pouring temperature, die temperature and pressure duration was kept at fixed values while performing experiments. Hong et al., (2000) [11], made an investigation to analyse the effects of pouring temperature, applied pressure, time delay, die temperature, degassing and inoculation treatments on formation of macro-defects in Al7%Si alloy. It is important to note that, the experiments were performed utilizing the classical engineering approach (that is, varying one parameter at a time and keeping the rest at the fixed values). Maleki et al., (2009) [12] used a classical engineering approach for performing experiments and analyse the effects of squeeze pressure, melt and die temperatures on secondary dendrite arm spacing and aspect ratio of LM13 alloy. It is to be noted that the effect of pressure duration and time delay parameters was left out in their analysis.


Following observations have been made from the above discussed literature.  Most of the author’s attempted conventional engineering approach for conducting and analysis, wherein large number of experiments are to be conducted with an increase in number of process variables and their levels.  The results obtained from the said approach will not reveal the complete information about the impact of the interaction (combined) effect of the process variables on the response.  The practical guidelines suggested by the authors to optimize squeeze casting process may not help the foundry men for selection of process parameters unless input-output relationships are expressed in mathematical form. In recent years limited research efforts made by the authors to develop input-output relationship using statistical and taguchi parametric design. Vijian and Arunachalam (2006) [13] utilized taguchi method for experimentation and developed multi variable linear regression equation which includes output (hardness and tensile strength) as a function of input (squeeze pressure, pressure duration and die temperature) parameters. . However, the developed regression equation includes only linear terms and neglected the effects of square and interaction terms, moreover, pouring temperature variations was left out in their analysis. Bin SB et al., (2013) investigated the strength and ductility of squeeze cast AlSi9Cu3 alloys via taguchi tools [14]. The authors failed to develop the model, which could predict the response, in addition pressure duration contributions was left out in their analysis. The research efforts was made by Senthil and Amrithagadeswaran to study the effects of squeeze cast process variable on hardness, ultimate tensile strength and yield strengths of LM24 alloy [15 & 16]. In addition, the developed regression equations are not used for the prediction, percent contribution of square and interaction terms were not estimated and moreover the influence of time delay process parameter was left out in their analysis. In recent years, many researchers applied soft computing tools, such as artificial neural networks (ANNs), fuzzy logic (FL) and genetic algorithm (GA) approaches and their different combinations to model and analyse the manufacturing processes [17]. GA has been adopted to solve multi-objective optimization of various responses of squeeze casting process, Vijian and Arunachalam (2006) [13]. It is important to note that the objective function includes only main effect parameters and the paramount importance of square and interaction parameters in identifying the non-linear effects are neglected in their research work. Wang RJ et al., (2012) [18] used artificial neural networks to predict the temperature difference of the squeeze cast part. It was observed that, ANNs finds better prediction and reduces the need of costly simulation software, and need of experts to interpret the results.


Research efforts were made by some authors to develop an auxiliary hybrid system (combining desirable features of GA and ANNs) to tackle the problems related to different moulding sand and pressure die casting process [19-22]. It is also important to make a note that some authors made efforts to model and analyze the important manufacturing processes with the help of embedded type hybrid systems (combining desirable features of GA and FL, ANNs and FL) [23-27]. It is interesting to note that many authors have successfully implemented embedded type hybrid systems for various manufacturing processes and proved it as a cost effective tool to model and analyze the complex manufacturing processes. To the best of author’s knowledge, no much of the work has been reported in literature to carry out the forward mapping of squeeze casting process utilizing fuzzy logic based approaches. In the present work an attempt has been made to predict the secondary dendrite arm spacing (SDAS) utilizing Mamdani and Takagi and Sugeno based fuzzy logic approaches. Approach 1 deals with development of mamdani based fuzzy logic system where in consequent, rule base and antecedent parts are constructed with the help of human expertise. Approach 2 follows development of adaptive network based fuzzy interface system popularly known as Takagi and Sugeno’s model. This model deals with the automatic evolution of consequent and antecedent parts. It is to be noted that linear and non-linear membership function distributions are used for both of the approaches.Finally, the performance all models are compared in making the prediction of SDAS in squeeze casting.

2. Experimental details The casting quality depends mainly on the composition of the alloy, processing method and machine related parameters. In squeeze casting process the solidification occurs with applied pressures and is considered as one of the near net shape manufacturing process. It is important to note that, the microstructure of the squeeze castings depends on machine related process parameters. Figure 1, shows the schematic diagram of input (Time delay, pressure duration, squeeze pressure, pouring temperature and die temperature) and output (secondary dendrite arm spacing) of the squeeze casting process. The range of input squeeze cast process parameters considered in the present study is shown in Table 1. The process parameters and their levels have been finalized based on available literature and consulting experts

Squeeze casting process

Secondary dendrite arm spacing (SDAS)

Fig. 1. Input and Output model of the squeeze casting process


53

Table 1. Squeeze cast process parameters and their ranges

Process parameters Time delay, (Td) Pressure duration, (Dp) Squeeze pressure, (Sp) Pouring temperature, (Pt) Die temperature, (Dt)

Notation A B C D E

Units S S MPa ˚C ˚C

Level-1 03 10 0.1 630 100

Secondary dendrite arm spacing (SDAS) Micro-structure examination is carried out on the prepared squeeze cast specimen. The sectioned surface was initially grounded using belt grinder, followed by series of silicon carbide papers with increasing fineness. Continuous circulation of water was maintained during grinding. Disc polisher is used with 400 mesh Al2O3 powder, 1000 mesh SiC powder with water and diamond paste with hyfin liquid to get scratch free surface of test specimen. The prepared samples are cleaned with soap solution followed by alcohol and dried. The samples are etched with kellers reagent (2.5% HNO3 + 1.5% HCl + 1%HF + 95%H2O) solution to reveal the micro-structure. The prepared samples have been examined using optical microscope and images of microstructure is recorded. Biovis image analysis software is used to determine the SDAS values. The linear intercept method has been adopted to measure the secondary dendrite arm spacing. The quantification of secondary dendrite arm spacing is done by drawing the lines measuring the distance between the adjacent sides on the longitudinal part of a primary dendrite as a function of the distance from the dendrite tip (Zeren (2005) [38]). The SDAS is measured by using the dendrites which possess more than 5 dendrite arms. The average value of the SDAS in each casting sample is determined at three different locations by taking at least to a minimum of 15 different primary dendrites containing more than 5 secondary dendrite arms. SDAS is measured by using Eq. i and Eq. ii, ̅̅̅̅̅̅̅̅̅

(a)

Level-2 05 20 50 660 150

Level-3 07 30 100 690 200

Level-4 09 40 150 720 250

Level-5 11 50 200 750 300

∑ Where Xi is the length of the ith dendrite, n is the number of measurements, mi is the number of dendrite arms and ‘i’ is the index term of the measured dendrites. Table 2. Summary results of input-outputs of the test cases Squeeze casting Exp. process parameters No Td DP Sp Pt Dt 1 11 30 101 671 263 2 7 14 110 635 192 3 6 37 63 674 236 4 5 40 142 731 254 5 5 10 71 723 142 6 9 33 110 738 261 7 9 48 96 637 174 8 11 32 172 712 189 9 4 21 196 646 213 10 4 23 89 742 284

Response SDAS, µm 48.43 49.74 47.64 33.78 46.86 48.33 50.63 44.86 35.66 41.34

The micro-structures obtained for few test samples are shown in the Fig. 2. It is interesting note that the micro-structure of the squeeze cast samples shown in Fig. 2 (c) (Test case 9) yields lower secondary dendrite arm spacing compared to the Fig. 2 (b) (Test case 10) and Fig. 2. (a) (Test case 7) (refer table 2).

(b)

(c)

Fig 2 Micro-structure of squeeze cast samples of different test cases shown in table 6, (a) Test case 7, (b) Test case 10 and (c) Test case 9 This is because the dendrites are broken into small pieces due to the better squeeze casting conditions. This might be due to low

54

time delay value (that is, molten metal with high fluidity) and the higher applied pressure. The liquid metal with high fluidity and


pressure will result in eliminating gas entrapment, improved heat transfer co-efficient and higher solidification rate. These results will yield micro-structure with smaller dendrite arm spacing values.

possible combinations of the input variable ranges. The collection of such data through real experiments is tedious and not feasible, since, it leads to large amount of material waste, labour waste and time consuming. It is to be noted that huge amount of training data has been generated at random using the response equation. This response equation (input-output relation) is obtained earlier by same authors [Refer 28]. Further, the data used to test the models has been collected through experiments and not used in training the FLC. The non linear regression equation for secondary dendrite arm spacing (SDAS) expressed in terms of squeeze cast technical parameters is shown in Eq. [1].

2.1. Data collection The performance of the developed model predictions in artificial intelligence techniques depends on the quality and quantity of the training data used. In soft computing applications training has to be done with huge (say 500) data base and should cover all

variables. Takagi & Sugeno’s and Mamdani approach of FLC have been developed and used to predict the SDAS. The performance of the developed models is tested for both linear (Triangular) and non-linear (Generalized bell shape and Gaussian) membership function distributions with the help of 10 test cases. The input-output model of the squeeze casting process using fuzzy logic is shown in Fig.3.

2.2. Fuzzy Modelling The method of identifying, analysing and establishing the inputoutput relationship of the physical system is referred as modelling. The fuzzy concept is adopted to develop the relationship between squeeze cast process variables and the secondary dendrite arm spacing (SDAS). In the present work, fuzzy modelling aims at predicting the output for the known set of inputs. SDAS is expressed as a function of squeeze cast process

Knowledge base

Inputs

Rule base


Fuzzification

Data base

Inference engine

Defuzzification

Output SDAS

Fuzzy logic controller (FLC)

Fig. 3. Model representation of squeeze casting process using fuzzy interface system

3. Fuzzy logic controller Due to rapid development in the application of fuzzy logic to solve complex real world problems, researcher/investigators are more interested to develop the fuzzy input-output relationships. Fuzzy concept works based on the thinking and reasoning capabilities of our human behaviour and the same is used to establish the input-output relationships of the system. Easy to understand and implement, capable to handle uncertainty and exact mathematical formulation is not required are the potential advantages of the fuzzy logic systems (Pratihar DK (2008)) [29]. Takagi Sugeno and Mamdani based models of fuzzy logic system (refer table 3) have been developed in the present study to model the squeeze casting process.

In general fuzzy logic model performances depend on the knowledge base, which consists of data base and rule base. In data base, the membership function is decided, based on the distributed data of variability in the process. Triangular and trapezoidal membership functions are used for the linear type data distribution. Whereas, generalized bell shape, sigmoid, gaussian membership functions can be used if the data distributions are assumed to be non-linear. In fuzzy logic systems the variables need to be expressed in the form of linguistic terms such as low, medium, high, small, medium etc., and the input-output relationships are expressed as a function of linguistic terms in the form of rules. It is important to note that the number of rules vary with linguistic terms and process variables.


55

Table 3 Fuzzy logic system modelling approaches (Azar and Taher (2010)) [30]. Type Linguistic fuzzy modelling Approach Mamdani approach Advantage Better interpretability Limitation Low accuracy Number of parameters Few parameters Number of rules Few rules

Precise fuzzy modelling Takagi sugeno’s approach High accuracy Low interpretability More parameters More rules

3.1. Approach 1: Development of manually constructed Mamdani based FLC In this approach, Mamdani based fuzzy logic controller (FLC) has been developed to carry out forward mapping of squeeze casting process. Squeeze cast process variables such as time delay, pressure duration, squeeze pressure, pouring temperature and die temperature are considered as the inputs and secondary dendrite arm spacing (SDAS) is treated as an output. In fuzzy systems the input and output parameters need to expressed in linguistic terms. In the present case, three linguistic terms such as low (L), medium (M) and high (H) were used to represent the input-output variables of the present system. For M

L

1

H

μ 3

a1

7 Time delay

11

M

H

L

1

M

L

1 0

simplicity, triangular membership function distributions representing the input-output variables of the squeeze casting process with fuzzy logic system is shown in Fig. 3. It is important to mention that squeeze casting process is complex in nature, since it consists of large number of parameters and the output may behaves linear or non-linear with respect to change in the output. Hence, the fuzzy logic models were developed with both linear and non-linear type membership function distributions. The ‘a’ values shown in Fig. 4 indicates the half base widths of isosceles triangles and the base widths of the right angled triangles.

H

μ 1 a4

690

750

μ

Pouring temperature

μ 1

0 30

a2

1

M

L

0

H

28

a7

50

M

46

64

SDAS

Pressure duration L

H

0 630

10

M

L

μ H 0 100

μ

200

a5

300

Die temperature 0 50

a3

125

200

L = Low

M= Medium

H= High

Squeeze pressure

Inputs

Outputs

Fig. 4. Manually constructed membership function distribution for input-output variables The base width of the right angle triangular membership function distributions namely a1, a2, a3, a4, a5 and a6 values are kept equal to 4, 20, 75, 60, 100 and 18 respectively. As there are five input

56

variables and each input variable is expressed using three linguistic terms, the number of rules to be defined for the present system is found to be equal to 243 (3 × 3 × 3 × 3 × 3). The


manually constructed rule base of the fuzzy logic system is shown in Table 3. The typical rule base of the fuzzy logic system will looks as shown below, IF A is M AND B is H AND C is L AND D is H AND E is M THEN SDAS is M It is important to mention that the knowledge base of the fuzzy system consists of rule base as well as data base. The manually constructed rule base depends completely on the human expertise in their relative field and is not considered to be optimal always. Hence attempts required to automatically emulate the rule and

data base utilizing better learning capabilities of artificial neural networks (ANNs).

3.2. Approach 2: Development of adaptive network based fuzzy interface system to automatically retrieve the data and derive the rule base

Squeeze cast Process model Use of experimental data to develop response equation representing squeeze cast process variables and the secondary dendrite arm spacing (SDAS) Generate huge input-output data through response equation Development of ANFIS model that correlates the squeeze cast process variables and response   

Set initial input parameters, membership function and ANFIS structure Select learning scheme (hybrid learning scheme) Preset training cycles and error goal Load data and start ANFIS training (say 500)

No

Training finished Yes

ANFIS is ready for prediction once training completed successfully with either error goal/training epoch reached Load ANFIS testing data (say 10)

No

Testing finished Yes

View fuzzy interface structure, response surface of fuzzy interface system and modified membership function distributions Validate experimental data with ANFIS prediction

Fig. 5. Flow chart representing methodology followed for predicting density and SDAS using ANFIS


57

Artificial neural networks are excellent, cost effective modelling tool to map complex manufacturing processes, Parappagoudar and Vundavilli (2012) [17]. The reason might be due to better learning capabilities and generalize (forecast reasonable output for the inputs which are not used during the learning phase) (Hykin S. (2006)) [31]. Some of the ANNs limitations are precision of output is limited, problem with solutions getting trapped in local optimum , huge data that cover entire process variable range is required to train the network and large number of training epochs, Rajasekaran and Pai (2003) [32]. The fuzzy concepts are successfully implemented to address the problems related to the production and operation management field, Wong and Lai (2011) [33]. Greater flexibility in formulating system and capability to handle imprecise input-output data are the major advantages of fuzzy logic approach. It is important to note that, no systematic procedure available to define the membership function distributions is the major limitation of the fuzzy logic system, Yurdusev and Firat (2009) [34]. In recent years research efforts were made to develop hybrid systems to solve complex real world problems by combining the desirable features of artificial neural networks and fuzzy logic tools. The embedded type hybrid system developed to limit the weakness of one of the soft computing tool with the strengths of the other. Adaptive neuro-fuzzy interface system (ANFIS) is one such hybrid system found to have some attractive features such as easy to implement, better generalization capabilities, fast and precise learning, excellent descriptions via fuzzy rules, easy to include both numerical and linguistic knowledge for solving complex problems (Azar and Taher (2010)) [30]. It is important to note that some of the authors successfully implemented ANFIS model and proved it as the cost-effective modelling tool [35-37]. In ANFIS, an artificial neural network with the fuzzy system is used to automatically evolve the rule base. It is interesting to note that the ANFIS works with the use of hybrid learning algorithm (Gradient descent and least square estimator) to map the inputoutput relationships. The fuzzy rule is composed of both antecedent (includes membership function parameters and its shape) parameter and consequent (functional parameter of input signals which describes network output) parameters. The training of hybrid learning algorithm includes both forward and backward pass calculations. In forward computation the antecedent parameters are fixed initially and consequent parameters were identified by means of least square principle. The summation of outputs of consequent layer determines the network output. It is to be noted that the major objective of any training algorithm is to reduce the error (between the actual and network predicted), so the network parameters needs to updated and this can be accomplished with backward pass calculation. Later in backward pass calculation the consequent parameters are fixed and the premise parameters were updated by means of gradient descent method, Yurdusev and Firat (2009) [34]. The steps followed for the ANFIS model in the present work is shown in Fig. 5. The structure of the adaptive neuro-fuzzy interface systems for the squeeze casting process looks is shown in the Fig. 6. The rectangle and circle symbols used in the network architecture indicate adaptive and fixed nodes respectively. Similar to artificial neural network architecture the network includes input, output and hidden layers. Squeeze cast process variables are expressed as a function of input nodes in the input layer, whereas secondary

58

dendrite arm spacing function as an output node. The nodes functioning in the hidden layer includes membership function and the rules. In the present work there exists five inputs and one output parameter. Each input parameter is expressed in the form of three linguistic terms and the 243 possible combinations of rules exist. For the first-order Takagi and Sugeno’s model a typical output with three fuzzy rules can be expressed as shown in Eq. [3], [4] and [5]. Rule 1: if (Td is A1) and (Dp is B1) and (Sp is C1) and (Pt is D1) and (Dt is E1) then

Rule 2: if (Td is A2) and (Dp is B2) and (Sp is C2) and (Pt is D2) and (Dt is E2) then

Rule 3: (Td is Ai) and (Dp is Bi) and (Sp is Ci) and (Pt is Di) and (Dt is Ei) then

Where, i = 1, 2, 3, ..........243, p i, qi, ri, si, ti and ui are the consequent parameters, f is the output parameter, Ai, Bi, Ci, Di and Ei are the linguistic labels used to define the membership function. The adaptive network based fuzzy interface system architecture consists of six layers namely input layer, fuzzification layer, product layer, normalization layer, de-fuzzification layer and output layer. The systematic procedure in developing the inputoutput relationship and the proper functioning of each layer is described as follows, Layer 1: In layer 1, squeeze cast process variables are expressed as a function of input nodes of the input layer. The layer 1 transmits the same input values to the next corresponding layer using linear transformation function. Layer 2: The layer 2 is the fuzzification layer, in which membership function values are determined corresponding to the assigned linguistic labels shown in Eq. [6], Eq. [7], Eq. [8], Eq. [9] and Eq. [10]. Td, Dp, Sp, Pt and Dt are the input nodes expressed as membership functions in terms of Ai, Bi, Ci, Di and Ei of layer 2. Where O2,i is the output of ith node of layer 2.

(

)

( )


Triangular, generalized bell shape and gaussian are the most commonly used membership functions and the values always lies between zero and one corresponding to the input conditions. Layer 3: The layer 3 referred as product layer, which determines the number of all possible rules (35=243), 243 nodes present in the layer 3 and is usually labelled using the term Π. A maximum of

(

)

32 nodes will be activated for the particular set of input conditions and each node represents the possible combination of input variables. The information from layer 2 is received and generates the output by multiplying all the input signals as shown in Eq. [11].

( ) 1 Π

N

µA1

Td

µA2 µA3

W

W

W1f1

µB1

Dp

µB2 µB3 µC1

Sp

122 µC2

Π

N

Π

N

Σ

SDAS

µC3 µD1

Pt

µD 2 µD3 µE1

Dt

µE2 µE3 243

Input layer

Fuzzy layer

Product layer

Symbol indicates adaptive node

Normalize layer

De-fuzzy layer

Output layer

Fixed node

Fig. 6. ANFIS network architecture for predicting the response-SDAS


59

Layer 4: The layer 4 is also referred as normalization layer and nodes presented in that layer is usually labelled as N. The major function of this layer is to normalize the weight functions using Eq. [12]. The output calculation of ith node is the ratio of ith rule firing strength to the sum of all the fired rules.

4. Results and discussion The performance of the developed models to predict secondary dendrite arm spacing in squeeze casting has been tested with the help of 10 test cases generated at random. The following section presents the information about the results obtained and comparison of developed model performances with experimental values.

⁄

̅

Layer 5: The fifth layer is termed as the de-fuzzification (centre of area method) layer and each node is calculated using the product of all the normalized firing strengths and the output of the corresponding fired rule is calculated using Eq. [13]. The layer 5 consists of 243 nodes and maximum of 32 nodes will be activated for the particular input variables combination. ̅

̅ (

4.1. Approach 1 The approach 1 deals with the manual construction of the rule and data base of the fuzzy logic system with the help of human expertise. For simplicity, linear type triangular shape membership function distribution is used for the present system and shown in Fig. 3. The base width of ‘a’ values shown in the triangular shape membership function distributions is same as explained in the earlier section. The performance of both approaches has been compared. Further, for each of the approach comparison of performance has been made for three different membership function distribution. The performance comparison results are summarized and presented in Table 5. The prediction accuracy of the developed models relies majorly on accurate construction of the rule base defined with the knowledge of human expertise. The developed manually constructed rule base to predict the secondary dendrite arm spacing is presented in Table 4.

)

Layer 6: The last layer is the output layer, since only one output variable is used for the present study only single node is present. The output calculation is performed using the summation of all the received input signals from the 5th layer shown in Eq. [14]. ∑ ∑

∑̅

Table 4 Manually constructed rule base of the fuzzy logic system Rule No.

A

B

C

D

E

SDAS, µm

Rule No.

A

B

C

D

E

SDAS, µm

Rule No.

A

B

C

D

E

SDAS, µm

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

L L L L L L L L L L L L L L L L L L L L L L L L L


L L L L L L L L L M M M M M M M M M H H H H H H H

L L L M M M H H H L L L M M M H H H L L L M M M H


H M M M M M M M M M M M M M M M M M M M M L M M L

82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106

M M M M M M M M M M M M M M M M M M M M M M M M M





H H H H M M M M M H M M M M M M M M M M M M M M M

163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187






H H H H H H H M H H H H H M M M M M H M M M M M M

60


26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81

L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L

L L M M M M M M M M M M M M M M M M M M M M M M M M M M M H H H H H H H H H H H H H H H H H H H H H H H H H H H

H H L L L L L L L L L M M M M M M M M M H H H H H H H H H L L L L L L L L L M M M M M M M M M H H H H H H H H H

H H L L L M M M H H H L L L M M M H H H L L L M M M H H H L L L M M M H H H L L L M M M H H H L L L M M M H H H


L M M M M M M M M M M M M M M L M M L L M M M M L L L L L M M M M M M M L M M M M M L L L L L M L L L L L L L L

107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162

M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M M





M M H M H M M M M M M M M M M M M M M M M M M M M M M L M H M M M M M M M M M M M M M M M M M M M M M M M M L L

188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243

H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H






M M H H H H M H H M M H M H M M M M M M M M M M M M M M M H H H H M M M M M M M M M M M M M M M M M M M M M M M

61

using ANFIS model and is shown schematically in Fig. 5. As explained in the previous sections both linear (triangular) and non-linear (generalized bell shape and gaussian) type membership function distributions have been used and the prediction performance of the developed models are compared with ten different test cases. The test results are summarized in Table 5. The input-output values of ten different squeeze casting conditions (that is test cases, collected through experiments) are presented in Table 6.

4.2 Approach 2 The steps followed to predict the secondary dendrite arm spacing (SDAS) using ANFIS model is shown in the Fig. 4. It is to be noted that huge amount of training data (say 500) is generated artificially at random by utilizingthe response equation, obtained earlier by the same authors. Five input parameter (time delay, squeeze pressure, pressure duration, pouring temperature and die temperature) and single output (SDAS) parameter have been considered to develop input-output relationship in squeeze casting

(a)

(b)

(c) Fig. 7. Convergence of ANFIS training (RMSE v/s Number of training epoch) for response-SDAS; (a) Triangular membership function, (b) Generalized bell shape membership function and (c) Gaussian membership function distribution It is of paramount importance to note that the prediction accuracy of the developed models rely on the closeness of the predicted and the actual values during training and is usually measured using root mean squared error (RMSE). The root mean squared error obtained at the end of the training for different membership function distributions for the response secondary dendrite arm spacing is shown in Fig. 7.

4.3 Comparison of the developed models The performance of developed models (that is Approach1 and Approach 2 with different membership distribution functions) has been compared with the help of test cases. The results are summarized in Table 5.

62

4.3.1 Approach 1 It is interesting to note that the prediction of triangular membership function distribution shown in Fig. 8 (a) are close to the ideal line as compared with Fig. 8 (b) of generalized bell shape and Fig. 8 (c) of gaussian membership function distributions respectively. The summary results of the test cases in predicting the SDAS is presented in Table. 2. However, the accuracy and prediction capability of the developed model performances are evaluated based on mean absolute percentage error (Refer Eq. [15]). 8.911, 8.888 and 9.408 are the values of mean absolute percentage deviation obtained in predicting the SDAS for triangular, generalized bell shape and gaussian membership function distribution respectively and the same is presented in Table 5.


(a)

(b)

(c)

Fig 8 Comparison of predicted and actual SDAS via approach 1, (a) Triangular membership function distributions, (b) Bell shape membership function distributions and (c) Gaussian membership function distributions The mean absolute percent error is obtained by using the following equation:

∑|

|

Where P is the predicted, n is the number of data sets and O is the observed values.

4.32 Approach 2 In approach 2, ANNs receives fuzzy inputs, processes it and extracts fuzzy outputs. The function of artificial neural networks in this approach is to automatically define the structure, tune the

fuzzy parameters, rule base, data base and membership function distributions. The performance of the developed models can be further enhanced by utilizing different membership function distributions [26 and 27]. It is also important to note that performance of the developed models also rely on the quantity and quality of the training data, degree of closeness with actual and network predicted values and is usually determined using the root mean squared error at the end of the training. Five hundred set of input-output data is used for training and the network training was terminated with the error reaching steady state. The RMSE values obtained at the end of the training for triangular, generalized bell shape and gaussian membership function distributions are found to be equal to 0.1328,0.2512 and 0.2734 respectively (Refer Fig. 6). The adjusted ‘a’ values of six variables for different membership function distributions are presented in Table 5

Table 5 The optimized or adjusted ‘a’ values of fuzzy parameters

Membership function distributions Triangular Generalized bell Gaussian

a1 3.7786 3.4442 3.8413

a2 19.3613 19.6671 19.4823

Half base width of right angled triangle a3 a4 a5 74.8241 59.3171 98.9814 74.8939 60.0567 100.1465 74.8434 59.8642 99.1276


a6 18.2993 18.2993 18.2993

63

The developed models performance is compared with the help of few experimental test cases and shown in Fig. 8. The best fit line is used to compare the model predicted and the actual values of SDAS. It is interesting to note that the best fit line of all the models looks similar. However, the triangular membership function shown in Fig. 9 (a) performs slightly better in comparison with Fig. 9 (b) of generalized bell shape and Fig. 9(c) of gaussian membership function distributions. It is also important to observe that majority of the data points of triangular shape

membership function of the fuzzy logic system falls close to the ideal line compared to rest. The summary result of the test cases for secondary dendrite arm spacing prediction is presented in the Table 6. Moreover the developed model performances are evaluated by means of MAPE values for 10 different test cases. The mean absolute percent error values for triangular, generalized and Gaussian membership function distribution are found to be equal to 4.571, 5.298 and 5.422 respectively (Refer Table 5).

Table 6 Summary results of test cases of fuzzy models for the response SDAS Approach 1 Test case no 1 2 3 4 5 6 7 8 9 10

Actual SDAS, µm

48.43 49.74 47.64 33.78 46.86 48.33 50.63 44.86 35.66 41.34 MAPE

Triangular Predict ed 46.96 46.38 46.37 43.77 47.91 46.48 47.50 46.00 45.24 43.58

Abs.% deviatio n 3.035 6.755 2.666 29.574 2.241 3.836 6.182 2.541 26.865 5.418 8.911

G bell shape Predi cted 46.08 46.00 46.02 43.05 47.44 46.00 46.37 46.00 45.64 41.07

Abs.% deviatio n 4.852 7.519 3.401 27.442 1.238 4.829 8.414 2.541 27.987 0.653 8.888

Approach 2 Gaussian Abs. deviati on 4.605 7.499 3.463 29.34 1.472 4.808 8.039 2.541 28.660 3.653 9.408

Predic ted 46.20 46.01 45.99 43.69 47.55 46.01 46.56 46.00 45.88 42.85

Triangular Predi cted 53.11 53.53 47.85 33.89 49.44 45.79 52.62 42.75 38.32 41.01

G bell shape

Abs.% deviati on 9.663 7.620 0.441 0.326 5.506 5.263 3.930 4.704 7.459 0.798 4.571

(a)

Predi cted 52.64 54.07 47.74 35.69 49.24 45.76 52.58 43.55 39.59 40.71

Abs. % deviatio n 8.693 8.705 0.210 5.654 5.079 5.325 3.851 2.920 11.021 1.524 5.298

Gaussian Predi cted 52.71 53.36 47.62 32.43 49.42 45.56 52.51 42.02 39.49 40.48

Abs. % deviatio n 8.837 7.278 0.042 3.996 5.463 5.739 3.713 6.331 10.740 2.080 5.422

(b)

(c)

Fig. 9 Comparison of predicted and actual SDAS values using approach 2; (a) Triangular membership function, (b) Bell shape membership function and (c) Gaussian membership function distribution

64


generalized bell shape and gaussian membership function distribution the percent deviation in prediction values are found to vary in the range of (-27.987%, +8.414%), (-29.337%, +8.0387%) for approach 1 and (-11.208%, +5.325%), (-10.740%, +5.739%) for approach 2 (Refer Figs. 10). It is interesting to note that the percent deviation pattern is found to be similar for all three models (that is, approach 1 with different membership function distributions, Refer Fig. 10 (a)).

4.4 Comparison of the developed approaches using percent deviations The variation in predicting the SDAS for approach 1 and approach 2 is shown in Fig. 10 (a) and Fig. 10 (b) respectively. The percent deviation in predicting SDAS values for both the approaches using triangular membership function distribution is found to lie in the range of (-29.574%, +6.755%) for approach 1 and (-9.664%, +5.263%) for approach 2. Similarly, for

Triangular membership function Bell shape membership function Gaussian membership function

Percent deviation in prediction

15 10 5 0 -5

1

2

3

4

5

6

7

8

9

10

-10 -15 -20

Test case number

-25 -30 -35

(a) Triangular membership function Bell shape membership function Gaussian membership function

Percent deviation in prediction

8 6 4 2 0 -2

1

2

3

4

5

6

7

8

9

10

-4 -6 -8

Test case number

-10 -12

(b)

Fig 10 Comparison of different approaches of the developed models with different membership function distribution in terms of percent deviation in prediction for the response-SDAS, (a) Manually constructed fuzzy logic system and (b) Adaptive network based fuzzy logic system

4.5 Comparison of the developed approaches using average absolute percent deviation The prediction ability of the developed approaches, with three different membership function distributions have been evaluated using mean absolute percent error and shown in Fig. 11. It is also important to note that prediction of approach 2 would show slightly better performance as compared with approach 1.

However, it is has been observed that the performance of the approach 2 also varies with linear and non-linear type membership function distributions, the reason might be due to the nature of error surface during training. The improved performance of approach 2 might be due to the automatic evolution of antecedent and consequent parts of fuzzy logic system utilizing huge training data through better learning capabilities of artificial neural networks. On the other hand, the antecedent and the consequent parts of the fuzzy logic system developed in approach


65

1 is with the help of human expertise and are not considered to be optimal always. It is important to note that the generalized bell shape of approach 1 and triangular shape membership function of approach 2 perform better compared to other membership

Secondary dendrite arm spacing

10

Mean absolute percent error

function distributions. Moreover, the triangular shape membership function distributions of approach 2 outperforms all other models in terms of mean absolute percent error as shown in Fig. 11

9 8 7 6 5 4 3 2 1 0 Mctrimf

Mcbellmf

Mcgaussmf

Antrimf

Anbellmf

Angaussmf

Models Fig 11 Comparison of different model performances in terms of average absolute percent deviation in prediction for the responsesSecondary dendrite arm spacing

5. Concluding remarks An attempt has been made to carry out the forward mapping to predict the secondary dendrite arm spacing using Mamdani model and Takagi Sugeno model (ANFIS) of the fuzzy logic based approaches. It is to be noted that antecedent and the consequent parts of the fuzzy logic system is designed based on the human expertise for Mamdani model, whereas, for Takagi and Sugenos model the antecedent and consequent parts are automatically evolved by utilizing huge training data with the better learning capabilities of artificial neural networks. Batch mode of training has been employed, with huge training data (say 500) base for better training and accurate prediction. Huge data base collection through real experiments is impractical to achieve and are generated artificially at random using response equation obtained through real experiments. Ten different test cases generated at random were used to compare the performance of the developed approaches with both linear and non-linear type membership function distributions. It is also important to note that the test data collected through real experiments are not used during the learning phase of the ANFIS system. It is interesting to note that generalized bell shape membership function of approach 1 and triangular membership of approach 2 made better predictions. Moreover the approach 2 prediction performed better compared to approach 1 in the present case. The improved prediction performance of approach 2 depends mainly on the quality and quantity of the data used for training, membership function distributions and the nature of the error surface. In addition the prediction performance of also depends on the linear or non-linear behaviour of the response. It is interesting to note that all models with different membership function distributions of the fuzzy logic based approaches are capable of making prediction for

66

SDAS values in squeeze casting. It is also important to mention that the approach 1 predictions can be further enhanced with increasing the number of linguistic terms, which will increase the number of rules and computational complexity. The developed fuzzy logic models can be effectively used for making predictions of secondary dendrite arm spacing at different squeeze casting conditions and eliminate the need of extensive experimental work. The present work is of paramount importance for the foundry men for the selection of most influential parameters to achieve the desired casting quality in squeeze casting process.

Acknowledgement The authors greatly acknowledge Dept. of Applied Mechanics and Hydraulics of NIT Karnataka, India, for their kind co-operation in carrying out the real experiments.

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Available online at www.sciencedirect.com

ScienceDirect Procedia Technology 14 (2014) 149 – 156

2nd International Conference on Innovations in Automation and Mechatronics Engineering, ICIAME 2014

Investigation of squeeze cast process parameters effects on secondary dendrite arm spacing using statistical regression and artificial neural network models Manjunath Patel G C1*, Robins Mathew1, Prasad Krishna1, Mahesh B. Parappagoudar2 1

Department of Mechanical Engineering, National Institute of Technology Karnataka, Surathkal-575025, India 2 Department of Mechanical Engineering, Chhatrapati Shivaji Institute of Technology, Durg (C.G) 491001, India

Abstract The near net shape manufacturing capability of squeeze casting process have the potential to produce high dense components with refined micro-structure. However, squeeze cast micro-structure is influenced by large number of process variables such as squeeze pressure, time delay, pressure duration, die temperature and pouring temperature. In the present work, an attempt is made to develop the model by considering aforementioned process variables. Further, significant contribution of each process parameter on the secondary dendrite arm spacing is studied by using statistical regression tool. The mathematical relationship has been developed for secondary dendrite arm spacing was used to generate the training data artificially at random and tested with the help of few test cases. It is to be noted that the test cases chosen were different from training data. Scaled conjugate gradient, Levenberg-Marquardt algorithm and regression model predictions were compared. It is interesting to note that, all models were capable to make good prediction with an average of 5 percentage deviation. Levenberg-Marquardt algorithm outperforms in terms of prediction compared to other models in the present work. The reason might be due to the nature of error surface. © 2014The TheAuthors. Authors. Published by Elsevier Ltd.is an open access article under the CC BY-NC-ND license © 2014 Published by Elsevier Ltd. This Selection and/or peer-review under responsibility of the Organizing Committee of ICIAME 2014. (http://creativecommons.org/licenses/by-nc-nd/3.0/). Peer-review under responsibility of the Organizing Committee of ICIAME 2014. Keywords:Squeeze casting process, LM20 alloy, Response surface plots, Secondary dendrite arm spacing and Artificial neural networks

1. Introduction Aluminium silicon alloys widely used as casting material due to its inherent properties such as excellent fluidity,

* Corresponding author. Tel.: +91-9844859032; fax: +91 824 2474033 E-mail address: [email protected]

2212-0173 © 2014 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/). Peer-review under responsibility of the Organizing Committee of ICIAME 2014. doi:10.1016/j.protcy.2014.08.020

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G.C. Manjunath Patel et al. / Procedia Technology 14 (2014) 149 – 156

wettability, formability, high specific strength, good castability, shrinkage reduction, corrosion resistance, low thermal expansion co-efficient, wear resistance, excellent mechanical properties [1-2]. The silicon widely used in aluminium alloys might be due to the salient features such as low density, improves fluidity, reduce melting temperature, abrasion resistance, low cost and easily available. Addition of copper and magnesium are mandatory to improve the strength of the alloy [2]. In order to meet the stringent limitations of conventional casting process such as gas and shrinkage porosities, the research focussed on use of advanced squeeze casting processes which combines the features of both casting and forging processes. LM20 alloy belongs to the combination of Al-Si-Cu-Mg-Ni family. These combination alloys have salient features yields better casting characteristics [3], modifies silicon morphology [4], micro and macro structure [5] properties, refines dendritic structure [6] when processed using squeeze casting process. Skolianos et al., (1997) made an attempt to study the effect of squeeze pressure on mechanical and microstructure properties of squeeze cast AA6061aluminium alloy [6]. Fan et al., (2010) explored the effects of casting temperatures on ultimate tensile strengths and micro-structure properties such as grain size and secondary dendrite arm spacing (SDAS) of squeeze cast Al-Zn-Mg-Cu alloy [7]. Yue (1997) analyzed the effect of pouring temperatures and squeeze pressures at different squeeze casting conditions on the grain size structure of squeeze cast AA7010 wrought alloy [8]. Hajjari and Divandari (2008) investigated the effects of squeeze pressures on mechanical and micro-structure properties of squeeze cast wrought AA2024 alloy [9]. Senthil and Amirthagadeswaran, (2013) made an efforts to investigate the influencing squeeze casting process variables on mechanical, micro and macrostructure properties of squeeze cast AC2A alloy [10]. Maleki et al., (2009) considered the most influencing process parameters such as squeeze pressure, melt and die temperature to explore the effects on grain size, SDAS and aspect ratio of eutectic silicon particles [11]. Krishna (2001) reported high quality squeeze cast products are influenced by squeeze casting process variables and till date there is no universal standard available to obtain optimal process parameters to yield high quality squeeze cast parts [12]. ANNs proved as the cost effective tool in prediction, optimization, control, monitor, identification, modeling, classification and so on particularly in the field of casting and injection moulding processes [13]. Wang et al, (2011) made an attempt to predict the temperature difference of the squeeze cast part at different casting conditions utilizing with back propagation algorithm of ANNs [14]. Wang et al., (2013) utilized artificial neural networks to study the effects of squeeze cast process parameters on the solidification time of the squeeze cast hot die steel using procast simulation software [15]. From the above literatures it is confirmed that squeeze casting process parameters also decides the final cast structure, the quantitative information regarding the SDAS as a function casting variables are necessary for an industrialist to reduce the defects and ANNs can effectively map the complex non-linear relationship between the interplay of input-output parameters in various casting applications. The present work focused to explore the effects under both experimentally and simulation studies. An attempt made to experimentally investigate the final solidified structure using mechanical modification process parameters such as squeeze pressure (Sp), pressure duration (Pd), time delay in applying pressure (Td), pouring (Pt) and die (Dt) temperatures and develop the mathematical model using regression analysis technique. To avoid costly manufacturing in analyzing the effects, artificial neural network simulation model using levenberg-marquardt (LM) and scaled conjugate gradient (SCG) algorithms was developed and the performance in predictions was compared with experimentally measured SDAS values. 1.1. Materials and Methods In the present work LM20 aluminium alloy was used as a casting material due to its interesting features such as free from hot tear, excellent fluidity, pressure tightness, wear and corrosion resistance properties. These distinguished features of this alloy made LM20 alloy have wide applications in marine castings, meter cases, street lightings, casting subjected to atmospheric conditions, automobile office and domestic equipments. H13 hot die steel was used as the die material to withstand high pressure applied during solidification and normally in squeeze casting process dies were exposed to several number of thermo-mechanical cycles. Hence the dies were heat treated to an hardness of 45-48 Rc to withstand thermal fatigue, cracking, corrosion, erosion and indentation [16]. The quantitative chemical examination performed using optical emission spectrometer (OES) for the casting and the die material to know the exact chemical composition used in the present experimental study. The result of chemical analysis of LM20 alloy as per references standard ASTM E1251-07 the obtained chemical composition of LM20 alloy is Si-

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10.41%, Fe-0.287%, Cu-0.177%, Mn-0.526%, Mg-0.175%, Cr-0.017%, Ni-0.016%, Zn-0.347%, Ti-0.175%, and Al-87.84% by weight. The obtained chemical composition of H13 hot die steel such as C-0.39%, Mn-0.38%, Si-1%, Cr-4.9%, P-0.019%, Mo-1.17%, V-0.79%, Fe-90.91% by weight. 2. Experimental details & plan H13 hot die steel was used to prepare the punch and the cylindrical die cavity. The punch is fitted at the middle of the cross head and the die was placed on the base plate of 40 tonne universal testing machine. Mica strip electrical heater was used to pre-heat both die and punch. J-type thermocouple connected to digital indicators was used to accurately control the die temperatures. Electrical resistance crucible furnace was used to prepare the melt. K-type thermocouple connected to digital indicator was used to measure the temperature of the melt before pouring. Cover flux was used to clean the melt and hexachloroethane tablet was used as degasser to remove absorbed or dissolved gases in the melt. The measured quantity of the prepared melt is poured into the pre-heated cylindrical die cavity and punch was then brought to come in contact with the melt to apply pressure. Pressure is applied for predetermined time, the punch was withdrawn and casting was ejected from the die surface. The choice of process parameters considered in the present study is based on some pilot experiments conducted in the lab and from the available literatures. The experiments conducted by varying one parameter at a time and keeping the rest at their respective middle level. The process parameters and the respective levels used in the current study are shown in table 1. Table 1. Process parameters and their respective levels Process parameters Squeeze pressure, (Sp) Pressure duration, (Dp) Time delay, (Td) Pouring temperature, (Pt) Die temperature, (Dt)

Units MPa S S Û& Û&

Level-1 0.1 10 03 630 100

Level-2 50 20 05 660 150

Level-3 100 30 07 690 200

Level-4 150 40 09 720 250

Level-5 200 50 11 750 300

3. Microstructure specimen preparation and examination Micro-structure examination performed on the squeeze cast specimens of 15 mm sample size thickness. The sectioned surface is initially grounded using belt grinder, followed by series of silicon carbide papers with increasing fineness. Continuous circulation of water was maintained during grinding. Disc polisher using 400 mesh Al2O3 powder, 1000 mesh SiC powder with water, finally with diamond paste and hyfin liquid until scratch free surface was observed. The prepared samples were cleaned with soap solution followed by alcohol and dried. The samples were etched with kellers reagent (2.5% HNO3+ 1.5% HCl + 1%HF + 95%H2O) solution to reveal the micro-structure. The prepared samples were viewed using optical microscope and the obtained images were used to measure the secondary dendrite arm spacing (SDAS). 4. Regression Analysis Regression analysis is a statistical tool helps the researcher/investigator to explore the effects, analyze the behaviour and to obtain the optimum process parameter setting for the corresponding process variables [17]. In the present work regression analysis is adopted to develop the relationship between the squeeze cast process variables and the measured secondary dendrite arm spacing. The data used to develop the regression equation is shown in table 3 and the obtained regression equation is shown in equation (1). Response surface plots obtained from the minitab software was used to analyse the effects of squeeze cast process variables on the measured SDAS. Significant test was conducted to know the effects, contributions and the significance of squeeze cast process variables towards the improvement for SDAS values. The terms used in table 2: is as follows [18], Coef refers to coefficients used in equation (1) for representing the relation between the squeeze cast process variables and the measured SDAS. SE Coef stands standard error for the estimated coefficients; smaller the value more precise will be the co-efficient. The ratio of coefficient and the corresponding standard error results in T-value. T-value for the independent variable can be used to test, whether the predictor significantly affects the measured response. The p-value is the minimum value for a pre-set level of significance, at which the hypothesis of equal means for a given factor can be rejected. The obtained results of significance test were evaluated at 95% confidence level and all the squeeze cast process variables were significant for the measured SDAS shown in Table 2. All the individual process variables shown less

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than 0.05 p-values indicate all parameters are significant impact on SDAS. From the ANOVA table it can be seen that all the square, linear and regression terms were less than 0.05 p-values, this indicates all terms are significant. Table 2. Significance tests and ANOVA test results for Secondary dendrite arm spacing (SDAS) Significance test of squeeze cast process parameters Term Coef SE Coef T P Constant 313.45 93.344253 3.358 0.008 Td 3.71889 0.6136782 6.06 0 Dp -0.318161 0.1060537 -3 0.015 Sp -0.120364 0.0358013 -3.362 0.008 Pt -0.632729 0.2628704 -2.407 0.039 Dt -0.22336 0.027906 -8.004 0 Td*Td -0.144949 0.0428463 -3.383 0.008 Pd*Pd 0.0023871 0.0017137 1.393 0.197 Sp*Sp 0.0001988 0.0001354 1.468 0.176 Pt*Pt 0.0004023 0.0001904 2.113 0.064 Dt*Dt 0.0005135 6.855E-05 7.49 0

SDAS

ANOVA for Secondary dendrite arm spacing Source

DF

Seq. SS

Adj. SS

Adj. MS

F

P

Regression Linear Square Residual Error Total

10 5 5 9 19

347.458 282.981 64.477 6.048 353.506

347.458 273.589 64.477 6.048

34.7458 54.7178 12.8954 0.6721

51.7 81.42 19.19

0 0 0

313.45 3.71889Td 0.318161D p 0.120364 S p 0.632729 Pt 0.22336 Dt 0.144949Td2 0.00238712 D p2 0.0001987998 S p2 0.000402338 Pt 2 0.000513454 Dt2

(1)

4.1 Secondary dendrite arm spacing measurement SDAS measurement is of paramount importance in deciding the mechanical properties and is influenced by the major parameters namely liquid metal treatment, solidification time, temperature gradient between the metal-mould interfaces and alloy chemical composition. Linear intercept method was used for the measurement of SDAS via image analysis software. The quantification of SDAS is done by drawing the lines measuring the distance between the adjacent sides on the longitudinal part of a primary dendrite as a function of the distance from the dendrite tip [19]. The total 21 samples were prepared for micro-structure observations and three optical micro-graph images were taken on each sample at different locations and at least five measurement values were taken in each location and the obtained average values is presented in table 3. Table 3. Experimental observations of measured SDAS Exp. No 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

Squeeze cast process parameters Td Dp Sp Pt Dt 3 30 100 690 200 5 30 100 690 200 7 30 100 690 200 9 30 100 690 200 11 30 100 690 200 7 10 100 690 200 7 20 100 690 200 7 40 100 690 200 7 50 100 690 200 7 30 50 690 200 7 30 150 690 200 7 30 200 690 200 7 30 100 630 200 7 30 100 660 200 7 30 100 720 200 7 30 100 750 200 7 30 100 690 100 7 30 100 690 150 7 30 100 690 250 7 30 100 690 300 ---0.1 690 200

Secondary dendrite arm spacing (μm) SDAS1 SDAS2 SDAS3 38.797 36.514 35.889 38.77 42.873 41.314 47.477 46.130 44.461 49.833 49.050 48.346 49.505 50.106 50.141 51.574 49.093 49.734 48.841 48.610 46.389 44.844 44.173 43.269 43.656 42.511 43.771 52.353 48.402 49.558 42.178 41.793 40.997 39.743 40.192 39.743 52.588 50.923 52.094 48.402 48.610 47.241 44.091 41.796 42.140 43.359 43.755 41.728 52.953 52.497 51.540 50.787 48.559 48.440 47.214 46.869 47.195 49.559 49.053 48.148 58.589 59.978 59.793

Mean SDAS (μm) SDAS 37.067 40.986 46.023 49.076 49.917 50.134 47.947 44.095 43.313 50.104 41.656 39.893 51.868 48.084 42.676 42.947 52.330 49.262 47.097 48.920 59.453

4.2 Response surface plots Response surface plots obtained from the Minitab software was used to visualize graphically the relationship


between the squeeze cast process variables and the SDAS. The surface plots obtained for the response-SDAS by varying two parameters and keeping the rest at the middle levels was shown in Figure 1. The following observations made from the surface plots are, 1. Fig. 1(a) and (b) depicts the response surface plots of the effects of two process variables namely time delay in pressurization with respect to the duration of pressure application and squeeze pressure respectively. The surface plots seen to be almost flat indicates a strong linear relationship exist between the process variables and the SDAS values. At low time delay in pressure application and high squeeze pressure and pressure duration yields lower SDAS values because, at low time delay the metal have enough fluidity and the applied squeeze pressure for longer duration forces the molten metal close enough to the die cavity by eliminating all possible gasses results in increase the heat transfer coefficient yields fine dendrite arm spacing values. 2. Fig. 1 (c) shows SDAS values has adverse effects with time delay and die temperature and lower SDAS values obtained at low time delay and middle level of die temperature. Low time delay and low die temperature the premature solidification takes place before the pressure is applied due to existence of large temperature difference between the die and the metal temperature and low time delay and high die temperature keeps the fluidity of the metal for longer duration results in shrinkage in the casting, possibility of the miss runs and in addition cycle time also increases leads to higher SDAS values. 3. Time delay in pressurization and pouring temperatures has shown slight curvature with respect to SDAS values as shown in Fig. 1 (d). Fine dendrite spacing obtained at time delay of 3 seconds and pouring temperature of about 660 to 720Û&+RZHYHUWKHHIIHFWRISRXULQJWHPSHUDWXUHVLVQHJOLJLEO\VPDOOFompared to the die temperature shown in Fig. 1 (c). 4. The effect of pressure duration with respect to the squeeze pressure and the pouring temperature shown linear relation with the SDAS values shown in Fig. 1 (e) and (f). High applied pressure increases the melting point of the alloy and pushes the molten metal close to the die surface and not allowing the metal to pull out from the die surface at longer pressure duration keeps the metal close to die cavity until the complete solidification takes place results in finer dendrite arm spacing values, however negligible improvement after 40 seconds of pressure duration was observed. 5. Pouring temperature with respect to the squeeze pressure shown linear relation with SDAS values as shown in Fig. 1 (g). Squeeze pressure contribution to yield low SDAS is more compared to the pouring temperature was observed. Increase/decreasing the pouring temperature shown small undesirable effect with respect to squeeze pressure on SDAS. 6. Die temperature shown quadratic effect with respect to increase in pressure duration, squeeze pressure, and pouring temperature on SDAS values shown in Fig. 1 (h), (i) and Fig. (j) respectively. In all figures minimum secondary dendrite arm spacing obtained at the approximately 200Û&GLHWHmperature. Increase in squeeze pressure and pressure duration results in improved SDAS values Fig. (h) and Fig. (i). However with respect to pouring temperature small increase in SDAS values after 720Û&PLJKWEHGXHWRWKHLQFUHDVHLQVROLGLILFDWLRQWLPH. Confirmation experiment: From the experimental study the optimum combination of squeeze cast process parameter levels were determined. The confirmation experiment was conducted corresponding to optimal process parameter setting and yielded the fine secondary dendrite arm spacing values for squeeze cast LM20 alloy shown in table 4 (Exp. No 22). The applied pressure of 200 MPa breaks the dendrite arms in to small particle size due to higher heat transfer rate shown in Fig. 2 (b). Fig. 2 (c) depicts dendrites with large arm spacing along with micro-shrinkage porosity in the gravity cast samples were clearly visualized. Fig. 2 (a) depicts the time delay of 3 seconds yields better results with smaller dendrite arm spacing values.

153

154


(a)

(d)

(g)

(b)

(c)

(e)

(f)

(h)

(i)

(j) Figs1. Surface plots of secondary dendrite arm spacing with (a) time delay and pressure duration, (b) time delay and squeeze pressure, (c) time delay and die temperature, (d) time delay and pouring temperature, (e) pressure duration and squeeze pressure, (f) pressure duration and pouring temperature, (g) squeeze pressure and pouring temperature, (h) pressure duration and die temperature, (i) squeeze pressure and die temperature, and (j) pouring temperature and die temperature Table 4.Comparison of measured SDAS with regression and ANN models prediction Exp. No.

Squeeze Cast Process Parameters Td Dp Sp Pt Dt

Mean SDAS (mm) 1 3 30 100 690 200 37.067 2 5 30 100 690 200 40.986 3 7 30 100 690 200 46.023 5 11 30 100 690 200 49.917 6 7 10 100 690 200 50.134 7 7 20 100 690 200 47.947 9 7 50 100 690 200 43.313 10 7 30 50 690 200 50.104 11 7 30 150 690 200 41.656 12 7 30 200 690 200 39.893 13 7 30 100 630 200 51.868 15 7 30 100 720 200 42.676 16 7 30 100 750 200 42.947 17 7 30 100 690 100 52.33 18 7 30 100 690 150 49.262 20 7 30 100 690 300 48.92 Training- Mean absolute percent error (MAPE) 4 9 30 100 690 200 49.076 8 7 40 100 690 200 44.095 14 7 30 100 660 200 48.084 19 7 30 100 690 250 47.097 22 3 50 200 720 200 30.133 Testing-Mean absolute percent error (MAPE)

Levenberg-Marquardt Absolute Prediction % Error 36.694 1.0063 41.812 2.0153 45.771 0.5476 50.210 0.5870 50.225 0.1815 47.759 0.3921 43.227 0.1986 50.298 0.3872 42.238 1.3972 39.698 0.4888 51.869 0.0019 43.808 2.6525 42.569 0.8802 52.704 0.7147 47.954 2.6552 49.108 0.3843 0.906 48.865 0.4299 44.328 0.5284 48.671 1.2208 46.885 0.4501 31.502 4.5432 1.4535

Scaled Conjugate Gradient Absolute Prediction % Error 37.059 0.0216 40.880 0.2586 46.171 0.3216 50.235 0.6371 50.535 0.7999 48.250 0.6319 42.891 0.9743 50.259 0.3094 42.656 2.4006 39.758 0.3384 51.403 0.8965 42.957 0.6584 42.042 2.1072 53.193 1.6491 48.522 1.5022 49.799 1.7968 0.956 48.486 1.2022 44.405 0.7030 48.629 1.1334 46.110 2.0957 32.947 9.3386 2.8946

Regression Equation Absolute Prediction % Error 36.798 0.7257 41.919 2.2764 45.729 0.6388 50.425 1.0177 50.098 0.0718 47.598 0.7278 42.418 2.0633 49.687 0.8322 42.489 1.9971 39.794 0.2482 51.256 1.1799 43.626 2.2261 42.812 0.3143 52.972 1.2268 48.111 2.3365 49.191 0.5539 1.153 48.571 1.0290 44.261 0.3765 48.458 0.7778 46.156 1.9980 26.114 13.337 3.5038

Artificial Neural Network models: Artificial neural network models are proven to be the cost effective tool from the

155


past few decades to map the complex non-linear relationship exists between the input-output variables. The model works based on the principle of our biological nervous system. In our biological nerve system there are large numbers of interconnected processing units referred as neurons. The neurons of one layer connected to the neighbouring layer through connection strength called as weights. The weights contain information about the input signal. The connection pattern thus formed within and between the adjacent layers is referred as network architecture. The squeeze cast process parameters and SDAS expressed as a function of input-output neurons in the input and output layer respectively. The choice of hidden neurons in the hidden layer is determined under experimentation based on the minimum mean squared value between the targeted and the neural network predicted value. Pure linear function is used in the input and output layer and tan-sigmoid activation function is used in the hidden layer. The batch mode of training was employed for both LM and SCG algorithm.16 patterns of the experimental data chosen randomly along with artificially generated 234 data patterns from the regression analysis was used to train the neural network and the network prediction accuracy was checked for the remaining 4 data points which was never experienced during the training process shown in table 4. Co-efficient of determination (R2) and Mean absolute percentage error (MAPE) was used to check the model prediction accuracy for the test cases. The range of R2 value always lies between zero and one. Higher R2 value indicates strong co-relation exists between the actual and predicted values. If R2 value is zero indicates there is no co-relation at all. The MAPE and R2 was also calculated to ensure the prediction accuracy between the actual and the model predicted values shown in table 5. Table 5. Summary results of the developed models Algorithm

Response

SCG SDAS LM SDAS Regression

Optimum Network Architecture (Ni-Nh-No) 5-23-1 5-9-1

MSE training set 0.009159 0.000125

Co-efficient of correlation determination (R2)-Test cases 0.9913 0.9978 0.9937

Mean Absolute Percentage Error (MAPE) 2.8946 1.4535 3.5038

(a) (b) (c) Fig. 2 Micro-structure at different casting conditions (a) Exp.No. 1 (Table 4), (b) Exp.No. 22 (Table 4) and (c) Exp.No. 21 (Table 3)

5. Conclusions It is evident from the experimental work the cast micro-structure depends on the squeeze cast process variables during solidification and the following observations conclusions can be drawn from the current study, 1.

2.

3.

Experiments performed by varying one process parameter individually and keeping the rest of the parameters at middle level. Increase in time delay before pressurization of the liquid metal shown increase in SDAS values due to reduced heat transfer co-efficient and non elimination of the gas completely between the metal mould interfaces. Pressure duration and squeeze pressure shown strong linear relationship with SDAS values. Increase in squeeze pressure and pressure duration decreases the SDAS values because of improved contact area between the metal-die interfaces and the applied pressure for longer duration not allowed the metal to pull away from the die surface. Die temperature is found to have non-linear relation with SDAS. It is interesting to know that, the combination of minimum die temperature and pouring temperature will result in maximum value of SDAS. Increase in die temperature will initially reduce SDAS value and found increasing after crossing mid value

156


4.

5.

of die temperature. However, increase in pouring temperature will reduce SDAS value. Further, pouring temperature is found to have more or less linear relation with SDAS. Confirmation test was conducted for the optimal process parameter levels observed from the response surface plots namely, squeeze pressure at 200 MPa, pressure duration of 50 s, time delay of 3 s, pouring temperature at 720Û& DQG GLH WHPSHUDWXUH DW Û& \LHOG lower SDAS values. The mean SDAS value corresponding to optimal parameters is found to be equal to 30.133 μm. Artificial neural network models were developed for the squeeze casting process. The developed models were trained with data collected from the experimental work and artificially generated data through regression equation. The trained neural network reduces the mean squared error (MSE) to a minimum value. The MSE value set for the training of NN was equal to 0.000125. It is to be noted that, lower value of MSE might require more number of iterations. However this will result in better training of NN. The accuracy of the developed network was tested for few test cases which are never experienced during the training process. LM algorithm outperforms the developed regression model and the SCG algorithm in the present work. Hence the developed ANNs can be used to predict and select the optimal process parameter setting by any novice user without having prior background knowledge about the squeeze casting process.

Acknowledgements The authors wish to thank Department of Applied Mechanics and Hydraulics, National Institute of Technology Karnataka, Surathkal for providing research facilities References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19]

Hosseini VA, Shabestari SG and Gholizadeh R, Study on the effect of cooling rate on the solidification parameters, microstructure, and mechanical properties of LM13 alloy using cooling curve thermal analysis technique, Materials & Design,vol.50, pp. 7–14, 2013 Hegde S and Prabhu KN, Modification of eutectic silicon in Al–Si alloys, Journal of materials science, vol. 43.9, pp. 3009-3027, 2008 Maleki A, Shafyei A, and Niroumand B, Effects of squeeze casting parameters on the microstructure of LM13 alloy, Journal of Materials Processing Technology,vol. 209, no. 8, pp. 3790-3797, 2009 Ye H, An overview of the development of Al-Si-alloy based material for engine applications, Journal of Materials Engineering and Performance, vol. 12.3, pp. 288-297, 2002 Maleki A, Niroumand B, and Shafyei A, Effects of squeeze casting parameters on density, macrostructure and hardness of LM13 alloy,Materials Science and Engineering: A, vol. 428.1, pp. 135-140, 2006 Skolianos SM, Kiourtsidis G and Xatzifotiou T, Effect of applied pressure on the microstructure and mechanical properties of squeeze-cast aluminum AA6061 alloy, Materials Science and Engineering: A, vol. 231, no. 1, pp. 17-24, 1997 Fan CH, Chen ZH, He WQ, Chen JH and Chen D, Effects of the casting temperature on microstructure and mechanical properties of the squeeze-cast Al–Zn–Mg–Cu alloy, Journal of Alloys and Compounds, vol. 504, no. 2, pp. L42-L45, 2010 Yue TM, Squeeze casting of high-strength aluminium wrought alloy AA7010, Journal of materials processing technology, vol. 66, no. 1, pp. 179-185, 1997 Hajjari E and Divandari M, An investigation on the microstructure and tensile properties of direct squeeze cast and gravity die cast 2024 wrought Al alloy, Materials & Design, vol. 29, no. 9, pp. 1685-1689, 2008 Senthil P and Amirthagadeswaran KS, Experimental study and squeeze casting process optimization for high quality AC2A aluminium alloy castings, Arabian Journal for Science and Engineering, pp. 1-11, 2013 Maleki A, Shafyei A and Niroumand B, Effects of squeeze casting parameters on the microstructure of LM13 alloy, Journal of Materials Processing Technology, vol. 209, no. 8, pp. 3790-3797, 2009 Krishna P, A study on interfacial heat transfer and process parameters in squeeze casting and low pressure permanent mold casting, Ph.D. Thesis, University of Michigan, 2001 Patel M and Krishna P, A review on application of artificial neural networks for injection moulding and casting processes, International Journal of Advances in Engineering Sciences, vol. 3.1, pp. 1-12, 2013 Wang RJ, Zeng J and Zhou D, Determination of temperature difference in squeeze casting hot work tool steel, International journal of material forming, vol. 5.4, pp. 317-324, 2012 Wang RJ, Tan WF and Zhou DW, Effects of squeeze casting parameters on solidification time based on neural network, International Journal of Materials and Product Technology, vol. 46, no. 2, pp. 124-140, 2013 Ghomashchi MR and Vikhrov A, Squeeze casting: an overview, Journal of Materials Processing Technology, vol. 101, no. 1, pp. 1-9, 2009 Sykes A, An introduction to regression analysis, Law School, University of Chicago, pp. 1-5, 1993 Parappagoudar MB, Pratihar DK and Datta GL, Linear and non-linear modeling of cement-bonded moulding sand system using conventional statistical regression analysis, Journal of Materials Engineering and Performance, vol. 17.4, pp. 472-481, 2008 Zeren M, Effect of copper and silicon content on mechanical properties in Al–Cu–Si–Mg alloys, Journal of Materials Processing Technology, vol. 169, no. 2, pp. 292-298, 2005.

Available online at www.sciencedirect.com

ScienceDirect Procedia Technology 14 (2014) 157 – 164

2nd International Conference on Innovations in Automation and Mechatronics Engineering, ICIAME 2014

Optimization of squeeze cast process parameters using taguchi and grey relational analysis Manjunath Patel G C1*, Prasad Krishna1 and Mahesh B. Parappagoudar2 1 2

Department of Mechanical Engineering, National Institute of Technology Karnataka, Surathkal-575025, India Department of Mechanical Engineering, Chhatrapati Shivaji Institute of Technology, Durg (C.G) 491001, India

Abstract The near-net shape manufacturing capabilities of squeeze casting process have greater potential to achieve smooth uniform surface and internal soundness in the cast components. In squeeze casting process, casting density and surface finish is influenced majorly by process variables. Proper control of the process variables is essential to achieve better results. Hence in the present work an attempt made using taguchi method to analyze the squeeze cast process variables such as squeeze pressure, die and pouring temperature considering at three different levels using L9 orthogonal array. Pareto analysis of variance performed on each response to find out optimum process parameter levels and significant contribution of each individual process parameter towards surface roughness and density of LM20 alloy. Grey relation analysis used as a multi-response optimization technique to obtain the single optimal process parameter setting for both the responses surface roughness and casting density. © 2014 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license © 2014 The Authors. Published by Elsevier Ltd. (http://creativecommons.org/licenses/by-nc-nd/3.0/). Selection and/or peer-review under responsibility of the Organizing Committee of ICIAME 2014. Peer-review under responsibility of the Organizing Committee of ICIAME 2014. Keywords: LM20 alloy, Grey based Taguchi method, Squeeze casting and Process parameters

1. Introduction In today’s competitive manufacturing environment industries are trying to search for light weight materials with high strength, recycling potential materials, near net shape casting process, reduce vehicles weight, fuel and energy consumption for better environmental protection for future generations. Aluminium considered being second lightest material next to magnesium widely used in aircraft application [1]. Silicon (Si) used as the major alloying element in * Corresponding author. Tel.: +91-9844859032; fax: +91 824 2474033 E-mail address: [email protected]

2212-0173 © 2014 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/). Peer-review under responsibility of the Organizing Committee of ICIAME 2014. doi:10.1016/j.protcy.2014.08.021

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aluminium alloy because of its excellent fluidity, low density, abrasion resistance, cost effective, easily available and reduces the melting temperature [2]. Copper (Cu) and magnesium (Mg) alloying elements were mandatory to improve strengths of Al-Si alloys [3]. Manganese (Mn) enhances the internal soundness of the casting, Titanium acts as grain refiner to refine micro-structures, Iron (Fe) improves the strength and reduces die sticking. Nickle (Ni) reduces the co-efficient of thermal expansion and when combines with copper it enhance the strength at elevated temperature [4]. Al-Si-Cu-Mg-Ni combination alloy possess better casting characteristics and rate of solidification, minimum porosity, good structural integrity, modifies eutectic silicon particles, excellent mechanical properties and refined micro as well as macro-structure properties, when the casting made of these combination alloys [5]. Squeeze casting is one among the modern casting process developed to address the limitations of conventional casting processes such as shrinkage or gas porosity, use of runners and gates leads to material wastage, difficult to cast wrought aluminium alloys and to make die constructions simpler. The near net shape manufacturing capability of the squeeze casting process need to produce the component that can be immediately used in services and would not add costly secondary processes such as machining, polishing, shot blasting, plating and ball burnishing. However the most common defects that might occur during squeeze casting process such as hot tearing, minimum porosity, oxide inclusion, under filling/overfilling, cold laps, case debonding and segregations [6]. These defects need to be reduced because it influence majorly on casting density and surface finish of the processed alloy. Superior surface finish is of primary importance to enhance the tribological, fatigue, corrosion properties and finally aesthetic appearance of the casted product. Casting density need to be considered as one of the quality characteristics because it directly relates to the internal casting defects such as porosity, shrinkages and micro-voids. The amount of porosity content present in the casted samples decreases the available load area, provoke stress concentration and crack initialization resulting in poor tensile strength and ductility of the alloy [7]. The physical and mechanical properties of aluminium alloy majorly depends on chemical composition, casting process, solidification, cooling rate during and after solidification, heat treatment and post solidification disinfection [4]. However for heat treatment and post disinfection adds additional cost and must be balanced with the properties gained. Hence in the present work for the particular casting material (LM20 alloy) using advanced squeeze casting process an attempt being made to investigate the effects of squeeze cast process variables on casting density influenced by cooling rate during solidification and surface finish after solidification. In recent years use of statistical methodology to analyze the effect of squeeze cast process parameters were increasing because to obtain the optimal process parameter setting with minimum number of experiment conduction, reduce expert dependent trial and error method leads to material wastage, to avoid costly simulation software both in terms of computation time, high capital investment in purchase of simulation software and need of experts to interpret the simulation results. Shi-bo Bin et al., (2013) analyzed the effects of pouring temperature, die temperature, filling velocity and forming pressure on tensile strength, percentage elongation and hardness of squeeze cast AlSi9Cu3 alloys using taguchi method [8]. An attempt made by Vijian and Arunachalam (2007) to investigate the effects of influencing process variables such as applied pressure, die temperature and pressure duration on hardness and ultimate tensile strength of squeeze cast LM24 alloy utilizing taguchi technique [9]. Senthil and Amrithagadeswaran (2012), focussed to improve the ultimate tensile strength and hardness of AC2A alloy by controlling the influencing process variables namely die temperature, die insert material (Copper, brass, stainless steel and hot die steel), pouring temperature, squeeze pressure and pressure duration by employing the taguchi parametric design tool [10]. Vijian and Arunachalam (2007) obtained the optimal process parametric setting for hardness and ultimate tensile strength of squeeze cast LM24 alloy by considering the process variables such as squeeze pressure, die temperature and pressure duration using taguchi and genetic algorithm tools [11]. Senthil and Amrithagadeswaran (2013), made an attempt to improve yield strength of squeeze cast AC2A alloy by considering the process variables such as die temperature, die insert material (Copper, brass, stainless steel and spheroidal graphite iron), pouring temperature, squeeze pressure and pressure duration by utilizing the taguchi and genetic algorithm tools [12]. Syrcos (2003) [13], investigated the influence of die cast process parameters on casting density of the AlSi9Cu13 alloy. Abou and El-khair (2004) [14], studied the influence of squeeze pressure on macro and micro-structure properties of AlSi6Mg0.3 alloys. The influence of squeeze pressures on density, hardness, ductility and tensile strengths of solid and hollow components of the gun metal was studied by Vjian and Arunachalam

159


(2005) [15]. The density, mechanical and microstructure properties of squeeze cast Al-8%Si alloy was studied with effects of pouring temperature as an influencing parameter by Raji and R. H. Khan (2006) [16]. Hajjari and Divandari (2008) [17] used squeeze casting process for processing of wrought 2024 aluminium alloy to reduce the shrinkage porosities, which occurs normally in conventional casting processes. Verran et al., (2008) [18] investigated the effects of die cast process parameters on density of Al12Si1.3Cu alloy for compressor engines. Vijian and Arunachalam (2006) considered surface roughness as an important quality characteristic to analyze the influencing process variables such as die temperature, die insert material (copper, cast iron and stainless steel) and squeeze pressure using taguchi technique for LM6 alloy [19]. Sutiyoko (2012), indentified pouring temperature is one of the important parameter influencing surface roughness during lost foam casting process [20]. Boschetto et al., (2007) stated surface roughness is strongly dependent on applied pressure not only in terms of average value but also of dispersion, since applied squeeze pressure improves metal-mold interfaces [21]. Bates et al., (1968), identified defects appeared on the casting surface affects the machinability during secondary process; furthermore rough surface reduces fatigue life of steel castings [22]. Vijian et al., (2007) considered die temperature, squeeze pressure and die material (die steel, mild steel and cast iron) to study the influence on surface roughness for squeeze cast LM6 alloys using taguchi method and reported die temperature and squeeze pressure are the significant parameters which improves surface finish [23]. Form the above literatures it is anticipated that surface finish and casting density is influenced by the process variables. Accurate control of these process variables is essential to achieve higher casting density and lower surface roughness. So the present work aims for the following two objectives, 1. To analyze the effects and to obtain the optimal process parameter settings for surface roughness and casting density of LM20 alloy using Taguchi technique. 2. Grey relational analysis is used to obtain single optimal process parameter setting for both surface roughness and casting density. 2. Materials and Methods The quantitative chemical analysis performed using optical emission spectroscopy (OES) to know the exact chemical composition used in the present study as per ASTM E1251-07 standard. The obtained chemical composition of LM20 alloy is Si-10.41%, Fe-0.287%, Cu-0.177%, Mn-0.526%, Mg-0.175%, Cr-0.017%, Ni0.016%, Zn-0.347%, Ti-0.175%, and Al-87.84% by weight. 3. Experimental Methodology The major parameters influencing the casting density and surface roughness are applied pressure, pressure duration, die and pouring temperature. Increase in squeeze pressure and pressure duration improves surface finish and casting density but it affects die life and problem with punch retractions are more. Low pressure and pressure duration may not be sufficient to eliminate all possible gasses and reduces the metal-mould interface affects both casting density and surface finish. Low die and pouring temperature results in pre-mature solidification before the pressure is applied and reduces the metal-mould interface, where as high die and pouring temperatures increases the cycle time, amount of flash and affects the die life. High density and superior surface finish can be obtained mainly by controlling the process variables. Hence in the present work an attempt made using Taguchi parametric design to bring the process to an optimal condition by conducting minimum number of experiments. The selection of process parameters and levels were chosen after conducting some pilot experiments in the lab and from the available literatures. The process parameters and their levels used in the current experimental study are shown in table 1. Table1. Process parameters and their respective levels Process parameters

Notation

Units

Level-1

Level-2

Level-3

Squeeze pressure, (Sp)

A

MPa

40

80

120

Pouring temperature, (Pt)

B

Û&

630

675

720

Die temperature, (Dt)

C

Û&

150

225

300

160


4. Experimental procedure The 40 tonne universal testing machine is used to apply the pressure on to the liquid metal poured into the cylindrical die cavity by means of punch fitted at the middle of the cross head. The die and the punch are made of the H13 hot die steel material and heat treated to a hardness of 45 Rc to withstand high applied pressure. Melt was prepared using electrical resistance crucible furnace of 5 kg melting capacity up to maximum of 900Û&'LHSUH-heat done through mica strip electric heater of 450Û&PD[LPXPFDSDFLW\--type thermocouple was inserted inside the die of about 5 mm from the die cavity. K-type thermocouple along with digital indicator was used to measure the melt temperature. Cover flux (45%NaCl+45%KCl+10%NaF) was used to clean the metal and hexachloroethane (C2Cl6) tablet was used as a degasser. Experiments were conducted using L9 orthogonal array of Taguchi parametric design. A measured quantity of the molten metal is poured into the pre-heated cylindrical die cavity, applying pressure up to 60 seconds for each casting conditions and the solidified castings were ejected from the die cavity. Two replicates were taken and measure the surface finish at three different locations as shown in Fig. 1on each casted sample as per reference JIS 2001 standard and using Archimedes principle, the casting density measurement was performed on each of the casting samples. The result of both casting density and the surface roughness is presented in table 2. 5. Taguchi Method Taguchi method involves reducing the variation in the process through robust design of experiments and to achieve high quality product at low cost [24]. In the present work taguchi method has been used to fulfil the following objectives: 1. To find the optimal process parameter setting for each response, 2. To estimate the percent contribution of each individual factor and 3. To achieve high quality product at low cost Squeeze pressure, die and pouring temperature were considered in the present study to analyze surface roughness and density. Total degrees of freedom for the three parameters each at three levels is 6. The notation E used in 5th column of table 2 is assigned as an error term. Hence L9 (34) orthogonal array with 9 experimental runs were selected (Degrees of freedom=9-1=8). Signal to noise (S/N) ratio is a quality indicator term used in taguchi parametric design helps the experimenters and designers to evaluate the effect of change in design parameter on the outcome of the product or process [25]. Surface roughness (Ra DQGGHQVLW\ȡ ZHUHFRQVLGHUHGDVWKHperformance quality characteristics with the concept of smaller the better and larger the better respectively. S/N ratio of each experimental run is calculated for surface roughness and density using equations 1 & 2 respectively. The calculated S/N ratios of both the responses were presented in table 2. Where Yi is the response value for a trial condition repeated n times.

S / N Surface roughness

S / N D e n s ity

§1 n 2· 10 Log10 ¨¨ ¦ Yi ¸¸ ©n i 1 ¹

§1 1 0 L o g 1 0 ¨¨ ©n

n

¦

i 1

1 Yi 2

(1)

· ¸¸ ¹

(2)

Surface roughness t l ti

Fig. 1 Surface roughness measurement location

161

G.C. Manjunath Patel et al. / Procedia Technology 14 (2014) 157 – 164 Table 2. Experimental observation and S/N ratio for surface roughness and density Exp.

A

B C

E

No

Surface roughness, Ra (μm)

'HQVLW\ȡJFP3)

S/N

S/N 5DWLRIRUȡ

Ra1

Ra2

Ra3

ȡ1

ȡ2

Ratio for Ra

1

1

1

1

1

1.41

1.38

1.32

2.640

2.644

-2.73765

8.438649

2

1

2

2

2

1.28

1.19

1.16

2.648

2.652

-1.66341

8.464910

3

1

3

3

3

1.12

1.16

1.17

2.615

2.621

-1.21549

8.359376

4

2

1

2

3

0.75

0.76

0.71

2.659

2.662

2.611666

8.499261

5

2

2

3

1

0.66

0.67

0.72

2.658

2.655

3.300945

8.486192

6

2

3

1

2

0.81

0.76

0.78

2.656

2.654

2.118081

8.481289

7

3

1

3

2

0.38

0.44

0.40

2.663

2.668

7.798919

8.515562

8

3

2

1

3

0.51

0.46

0.48

2.674

2.676

6.307223

8.546474

9

3

3

2

1

0.34

0.37

0.39

2.670

2.672

8.700954

8.533476

Table 3. Pareto ANOVA for three level factors Factors

A 1

Sum of factor levels

2 3

Sum of squares of differences Degrees of freedom Percentage contribution ratio

ȈA1 ȈA2 ȈA3

SA 2 SA/ST

B

C

E

Total

Ȉ%1 ȈB2 ȈB3

ȈC1 ȈC2 ȈC3

Ȉ(1 ȈE2 ȈE3

T

SB 2 SB/ST

SC 2 SC/ST

SE 2 SE/ST

ST 8 1

T = ȈA1 + ȈA2 + ȈA3 SA = (ȈA1- ȈA2)2 + (ȈA1- ȈA3)2 + (ȈA3- ȈA2)2 SB = (ȈB1- ȈB2)2 + (ȈB1- ȈB3)2 + (ȈB3- ȈB2)2 SC = (ȈC1- ȈC2)2 + (ȈC1- ȈC3)2 + (ȈC3- ȈC2)2 ST = SA + SB + SC + SE Table 4. Pareto ANOVA for Surface Roughness Factors Sum at factor levels

1 2 3

Sum of squares of differences Degrees of freedom Percentage contribution ratio Cumulative contribution ratio Optimum levels

A -5.61655 8.030692 22.80710 1212.493 2 96.52317 96.52317 A3

B 7.672936 7.944755 9.603545 6.552724 2 0.521644 97.04482 B3

C 5.687654 9.649207 9.884375 33.36168 2 2.65583 99.70065 C3

E 9.264250 8.253587 7.703400 3.760397 2 0.299355 100

A 25.26293 25.46674 25.59551 0.168727 2 73.69576 73.69576 A3

B 25.45347 25.49758 25.37414 0.023475 2 10.25335 83.94911 B2

C 25.46641 25.49765 25.36113 0.030697 2 13.40752 97.35664 C2

E 25.45832 25.46176 25.40511 0.006052 2 2.643368 100

Total 25.2214

1256.168 8

Table 5. Pareto ANOVA for Density Factors Sum at factor levels

Sum of squares of differences Degrees of freedom Percentage contribution ratio Cumulative contribution ratio Optimum levels

1 2 3

Total 76.32519

0.228951 8

162


The procedure used for the computation of Pareto analysis of variance (ANOVA) is presented in table 3. The Pareto ANOVA is performed to find out the percentage contribution of each factor towards the responses surface roughness and density. The obtained results were presented in table 4 and 5 respectively. Higher percentage contribution of squeeze pressure found for both responses because squeeze pressure forces molten metal close enough to the die cavity by eliminating all possible gasses between the metal-mould interface, results in closed replica of the die surface finish and improves heat transfer rate results in high casting density values. For the response surface roughness, percentage contribution of pouring temperature is negligible and for the response density a significant contribution of die and pouring temperature to improve the casting density values was observed. Furthermore, Pareto ANOVA suggests the optimal levels A3B3C3 and A3B2C2 for surface roughness and density respectively. It must be interesting to note that the obtained optimum levels were not among the combination of 9 different casting conditions tested. This was expected because of the multi-factor nature of 9 experiments conducted from 33 = 27 combinations [9]. For studying the parametric significance ANOVA was performed for both surface roughness and density shown in table 6. Table 7 shows the response variation of each factor when the factor shifts from level 1 to level 3. Table 6. ANOVA for Surface Roughness and Density Responses Sources of variation A B C E Total

Sum of squares of differences 1212.493 6.552724 33.36168 3.760397

Surface Roughness Mean Degrees of freedom square 2 606.2465 2 3.276362 2 16.68084 2 1.880199 8

Variance 322.4375 1.742562 8.87185

Sum of squares of differences 0.168727 0.023475 0.030697 0.006052

Density Degrees of freedom 2 2 2 2 8

Mean square 0.084364 0.011738 0.015349 0.003026

Variance 27.87954 3.878883 5.072208

From table 7 higher S/N ratio obtained for all factors at level 3 for the surface roughness indicate that superior surface finish can be obtained using the combination of A3B3C3 parameters. Similarly higher S/N ratio obtained at level 3 for squeeze pressure, level 2 for pouring and die temperature indicate that high dense components can be obtained using combination of A3B 2C2 parameters. Table 7. Average effect of responses using S/N ratio

Levels 1 2 3 Max-Min Rank

Surface Roughness A B -1.872 2.556 2.676 2.648 7.602 3.201 9.474 0.645 1 3

C 1.896 3.216 3.295 1.399 2

E 3.088 2.751 2.567 0.521

A 8.4231 8.4889 8.5318 0.1087 1

Density B C 8.4845 8.4888 8.4991 8.4992 8.4580 8.4537 0.0411 0.0453 3 2

E 8.4861 8.4873 8.4684 0.0189

5. Grey Relational Analysis The purpose of grey relational analysis used in the present study is to obtain the single optimum process parameter setting for both the responses surface roughness and density of LM20 alloy. The system in which the information is completely known is referred as white system, while the information is completely unknown is known as black system. Any system which lies between these two limits is called as grey system [26]. Grey relational analysis is the normalization evaluation technique in which the S/N ratio of each response is normalized between zeros to one. The next step is to calculate the deviation sequence using an ideal value 1 for the normalized responses. The grey relational co-efficient can be calculated using equation 3. Finally the grey relation grade is calculated by taking an average grey relation co-efficient of surface roughness and density. Higher grey relation grade need to be chosen as an optimal process parameter setting for both the response and obtained at experimental number nine casting condition as shown in table 8.

163


Grey relation coefficient

' min €.' max ' oi €.' max

(3)

:KHUH ǻmin LV ]HUR ǻmax is one, € is distinguishing coefficient is 0.5 and ǻoi is the deviation sequence of the experimental trials. Table 8. Multi response optimization using grey relational analysis Exp. No 1 2 3 4 5 6 7 8 9*

S/N Ratio Ra ȡ -2.73765 -1.66341 -1.21549 2.611666 3.300945 2.118081 7.798919 6.307223 8.700954

Data pre-processing Ra ȡ

8.43865 8.46491 8.35937 8.49926 8.48619 8.48129 8.51556 8.54647 8.53348

0.00000 0.09391 0.13307 0.46765 0.52791 0.42450 0.92114 0.79073 1.00000

0.42369 0.56406 0.00000 0.74766 0.67781 0.65160 0.83478 1.00000 0.93053

Deviation sequence ǻo1 ǻo2

Grey relation coefficient Ra ȡ

1.00000 0.90609 0.86693 0.53234 0.47209 0.57550 0.07886 0.20927 0.00000

0.33333 0.35556 0.36578 0.48433 0.51436 0.46490 0.86377 0.70495 1.00000

0.57630 0.43594 1.00000 0.25234 0.32219 0.34840 0.16522 0.00000 0.06947

Grey relation grade

0.46455 0.53422 0.33333 0.66459 0.60813 0.58934 0.75163 1.00000 0.87801

0.39894 0.44491 0.34956 0.57446 0.56124 0.52712 0.80770 0.85248 0.93900

6. Confirmation experiments The confirmation experiments conducted for the suggested optimal process parameter setting and the measured surface roughness and density values were presented in table 9. Superior surface finish and density values were achieved compared to the L9 experiments performed earlier. However the drawback of taguchi analysis was overcome using grey relational analysis and yields better surface finish and density values. Table 9. Confirmation experiments for Taguchi and Grey relational analysis Methodology

Responses

Optimum levels

Average experimental values

Taguchi analysis

Surface Roughness

A3B3C3

0.316 μm and 2.661 g/cm3

Grey relational analysis

Density Surface Roughness and Density

A3B2C2 A3B3C2

2.678 g/cm3 and 0.43 μm 0.367 μm and 2.671 g/cm3

7. Conclusion Following conclusions were drawn from the current experimental study, 1.

2.

3.

Taguchi parametric design is adopted for the squeeze cast technology to yield high dense components and superior surface finish by conducting minimum number of experiments. L9 orthogonal array was adopted to perform the experiments, quality indicator term S/N ratio, Pareto ANOVA was performed to find out the optimum levels and significant contribution of each individual factor towards the responses. Confirmation experiments conducted at optimum levels as suggested by the taguchi method. Taguchi off-line quality control tool found to be an effective tool for optimization of squeeze cast process parameters to achieve high surface finish of about 0.316 μm and yields high dense components of about 2.678 g/cm3. The squeeze pressure acts as a major contributing parameter for both surface finish and density because the applied pressure push the molten metal to accommodate close to the die surface results in closed replica of the die surface finish and improves the heat transfer rate between metal-mould interfaces yields higher casting density approximately equal to theoretical density (2.68 g/cm3) of LM20 alloy. Grey relational analysis performed to obtain the single optimal process parameter setting for both the responses. Grey relational analysis suggested an optimal process parameter setting namely squeeze pressure at 120 MPa, die temperature at 225Û&DQGSRXULQJWHmperature at 720Û&UHVSHFWLYHO\WRDFKLHYH smooth uniform surface finish of about 0.367 μm and high dense cast components 2.671 g/cm3.

164


Acknowledgements The authors express sincere thanks to Department of Applied Mechanics and Hydraulics, National Institute of Technology Karnataka, Surathkal for providing research facilities References [1] Grard C, Aluminum and its alloys: their properties, thermal treatment and industrial application. New York: D. Van Nostrand Company, pp. 1-268, 1922 [2] Hegde S, Prabhu KN, Modification of eutectic silicon in Al–Si alloys, Journal of materials science, vol. 43.9, pp. 3009-3027, 2008 [3] Hosseini VA, Shabestari SG and Gholizadeh R, Study on the effect of cooling rate on the solidification parameters, microstructure, and mechanical properties of LM13 alloy using cooling curve thermal analysis technique, Materials & Design, vol. 50, pp. 7–14, 2013 [4] Kaufman JJG and Elwin L Rooy, Aluminum alloy castings: properties, processes and applications, ASM International, 2004 [5] Maleki A, Shafyei A and Niroumand B, Effects of squeeze casting parameters on the microstructure of LM13 alloy, Journal of Materials Processing Technology, vol. 209.8, pp. 3790-3797, 2009 [6] Britnell DJ and Neailey K, Macrosegregation in thin walled castings produced via the direct squeeze casting process, Journal of materials processing technology, vol. 138.1, pp. 306-310, 2003 [7] Zhao HD, Wang F, Li YY and Xia W, Experimental and numerical analysis of gas entrapment defects in plate ADC12 die castings, Journal of materials processing technology, vol. 209.9, pp. 4537-4542, 2009 [8] Shi-bo Bin, Shu-ming Xing, Long-mei Tian, Ning Zhao and Lan L.I, Influence of technical parameters on strength and ductility of AlSi9Cu3 alloys in squeeze casting, Transaction of Nonferrous Met. Soc. China, 23, pp. 977-982, 2013 [9] Vijian P and Arunachalam VP, Optimization of squeeze casting process parameters using Taguchi analysis, Int J Adv Manuf Technol, 33, pp. 1122-1127, 2007 [10] Senthil P and Amrithagadeswaran K.S, Optimization of squeeze casting parameters for non symmetrical AC2A aluminium alloy castings through Taguchi method”, Journal of Mechanical Science and Technology, 26 (4), pp.1141-1147, 2012 [11] Vijian P and Arunachalam V.P, Modelling and multi objective optimization of LM24 aluminium alloy squeeze cast process parameters using genetic algorithm, Journal of Materials Processing Technology, 186, pp. 82–86, 2007 [12] Senthil P and Amrithagadeswaran K.S, Experimental study and squeeze casting process optimization for high quality AC2A aluminium alloy castings, Arabian Journal of Science & Engineering, DOI 10.1007/s13369-013-0752-5, 2013 [13] Syrcos GP, Die casting process optimization using Taguchi methods, Journal of materials processing technology, 135.1, pp. 68-74, 2003 [14] Abou and El-khair MT, Microstructure characterization and tensile properties of squeeze-cast AlSiMg alloys, Materials Letters 59.8, pp. 894-900, 2005 [15] Vijian P and Arunachalam VP, Experimental study of squeeze casting of gunmetal, Journal of materials processing technology, 170.1, pp. 32-36, 2005. [16] Raji A and Khan R H, Effects of pouring temperature and squeeze pressure on Al-8̃ Si alloy squeeze cast parts, AU JT 9.4, pp. 229-237, 2006 [17] Hajjari E and Divandari M, An investigation on the microstructure and tensile properties of direct squeeze cast and gravity die cast 2024 wrought Al alloy, Materials & Design 29.9, pp. 1685-1689, 2008 [18] Verran GO, Mendes RPK, and Dalla Valentina LVO, DOE applied to optimization of aluminum alloy die castings, Journal of materials processing technology 200.1, pp. 120-125, 2008 [19] Vijian P and Arunachalam VP, Optimization of squeeze cast parameters of LM6 aluminium alloy for surface roughness using Taguchi method. Journal of Materials Processing Technology, 180, pp. 161–166, 2006 [20] Suyitno and Sutiyoko, Effect of Pouring Temperature and Casting Thickness on Fluidity, Porosity and Surface Roughness in Lost Foam Casting of Gray Cast Iron, Procedia Engineering, 50: 88 – 94, 2012 [21] Boschetto A, Costanza G, Quadrini F and Tata ME, Cooling rate inference in aluminum alloy squeeze casting, Materials letters, 61(14), pp. 2969-2972, 2007 [22] Bates, Charles E, Rodney L. Naro and John F Wallace, Effect of Mold-Steel Interface Reactions of Casting Surface and Properties, Case western reserve univ cleveland oh dept of metallurgy, 1968 [23] Vijian P, Arunachalam VP, and Charles S, Study of surface roughness in squeeze casting LM6 aluminium alloy using Taguchi method, Indian journal of engineering & materials sciences, 14, pp. 7-11, 2007 [24] Roy RK, A primer on the Taguchi method, competitive manufacturing series, New York, pp. 7-80, 1990 [25] Ozcelik B and Erzurumlu T, Comparison of the warpage optimization in the plastic injection molding using ANOVA, neural network model and genetic algorithm, Journal of materials processing technology, 171.3, pp. 437-445, 2006 [26] Balasubramanian S and Ganapathy S, Grey relational analysis to determine optimum process parameters for wire electro discharge machining (WEDM), Int. J. of Engineering Science and Technology 3.1, pp. 95-101, 2011

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