Application of particle swarm optimization and

J Braz. Soc. Mech. Sci. Eng. DOI 10.1007/s40430-016-0675-7

TECHNICAL PAPER

Application of particle swarm optimization and response surface methodology for machining parameters optimization of aluminium matrix composites in milling operation Rashmi Laxmikant Malghan1 · Karthik M. C. Rao2 · Arun Kumar Shettigar2 · Shrikantha S. Rao1 · R. J. D’Souza3 

Received: 30 August 2016 / Accepted: 4 November 2016 © The Brazilian Society of Mechanical Sciences and Engineering 2016

Abstract Face milling is extensively used machining operation to generate the various components. Usually the selection of the process parameters are incorporated by trial and error method, literature survey and the machining hand book. This kind of selection of process parameters turns out to be very tedious and time-consuming. In order to overcome this there is a need to develop a technique that could be able to find the optimal process parameters for the desired responses in machining. The present paper illustrates an application of response surface methodology (RSM) and particle swarm optimization (PSO) technique for optimizing the process parameters of milling and provides a comparison study among desirability and PSO techniques. The experimental investigations are carried out on metal matrix composite material AA6061-4.5%Cu-5%SiCp

to study the effect of process parameters such as feed rate, spindle speed and depth of cut on the cutting force, surface roughness and power consumption. The process parameters are analyzed using RSM central composite face-centered design to study the relationship between the input and output responses. The interaction between the process parameters was identified using the multiple regression technique, which showed that spindle speed has major contribution on all the responses followed by feed rate and depth of cut. It has shown good prediction for all the responses. The optimized process parameters are acquired through multiresponse optimization using the desirability approach and the PSO technique. The results obtained from PSO are closer to the values of the desirability function approach and achieved significant improvement.

Technical Editor: Márcio Bacci da Silva.

Keywords  Desirability · Optimization · Response surface methodology · Particle swarm optimization · Metal matrix composite

* Rashmi Laxmikant Malghan [email protected] Karthik M. C. Rao [email protected] Arun Kumar Shettigar [email protected] Shrikantha S. Rao [email protected] R. J. D’Souza [email protected] 1

Department of Mechanical Engineering, NITK, Surathkal 575025, India

2

Department of Mechatronics Engineering, MIT, Manipal 576104, India

3

Department of Mathematics and Computational Engineering, NITK, Surathkal 575025, India



Abbreviations AMMCs Aluminium metal matrix composites ANOVA Analysis of variance ANN Artificial Neural Network CCFCD Central composite face-centered design CNC Computer numerical control DOE Design of experiment GA Genetic algorithm MMC Metal matrix composite RSM Response surface methodology PSO Particle swarm optimization RCCD Rotatable central composite design List of symbols FX Cutting force, N

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Ra Surface roughness, µm Gbest Global best pbest Particle best R-sq Pre R-squared R-sq(adj) Adj R-squared

1 Introduction The main criterion in process planning of any machining operation is to select the appropriate machining parameters. Generally, the machining parameters are decided based on the literature or using any machining data hand book. But it is a well-known reality that the process parameters selected from these resources are far away from the optimal process parameters. The other method to choose the process parameters is by performing trials of experiments. But the trials made always may not be accurate and they may lead to some error. Hence carrying out such trials may not be ultimate solution as cost and time factors are involved. Nowadays, in manufacturing environment the computer numerical control (CNC) machines need to be utilized to the fullest to get back the valuable pay back. The economic utilization of the CNC machines is mainly dependent on the appropriate selection of the machining parameters, as well as reduction of the machining time. In the present scenario, development of new generation of reinforced materials provides considerable tailorability of mechanical properties. Among several types of MMCs, aluminium matrix composites (AMMCs) have gained greater exposure in automobile and other industries due to light weight, high strength-tostiffness ratio, alterable thermal and electrical properties, etc. Arunkumar et al. [1]. During machining of AMMs high heat is generated at machining region as observed by Suresh et al. [2]. This causes dimensional inaccuracies in the workpiece and considerably high wear in the tool. The possible tool wear can be minimized by improving the properties of tool material. Investigation of process parameters on surface integrity of machining of AMMCs using coated inserts has not been addressed. Therefore, effect of process parameters on surface integrity is analyzed using graphical representation. It is necessary to develop a technique of predicting the significant process parameters before actual machining is carried out to obtain the desired responses. Generally, the non-traditional optimization techniques are incorporated to overcome the aforesaid issues. In the present study, the PSO is carried out and compared with Desirability approach to identify the machining parameters to obtain the desired responses.

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2 Literature review Baji et al. [3] presented a study on the influence of cutting parameters on surface roughness of steel workpiece in face milling operation. The RSM based on the rotatable central composite design (RCCD) has been used together with an analysis of variance (ANOVA) and regression analysis. To obtain the minimal value of surface roughness, the surface roughness equation has been optimized by finding the partial derivatives and solving the system of equations. A comparison of results obtained by means of the Taguchi method with the regression model was carried out. The Taguchi method, based on orthogonal arrays, has been used also for determining the influence of particular cutting parameters. Hae-Sung Yoon et al. [4] used RSM technique in face milling operation and concluded that material-removal power increased with the feed rate, spindle speed and depth of cut. The material-removal power was found to consist of ~7.6% of the total power consumption. Rodolfo et al. [5] presented an intelligent supervisory system from a modelbased approach. They applied their system as a case study for predicting tool wear in machining processes. Rodolfo et al. [6] represented Fuzzy logic-based torque control system for milling process optimization. Wong et al. [7] investigated the feasibility of using a neural network to represent machinability data. In order to predict optimum machining parameters under different cutting conditions, they used the feed-forward neural network. They developed and implemented an object-oriented neural network-handling library in the milling process. The prediction of surface roughness in computer numerically controlled (CNC) face milling was studied by Benardos et al. [8]. They trained an artificial neural network (ANN) model with the Levenberg–Merquardt algorithm and determined the influence of the factors using Taguchi design of the experimental method. A model for surface roughness prediction using the RSM by combining its methodology with factorial design of experiments has been developed by Choudhury et al. [9]. In addition, the application of perception-type neural networks to tool-state classification during a metal-milling operation has been studied by Dimla et al. [10]. They investigated both single-layer networks and multi-layer networks and found that the multi-layer networks had better performance than the single-layer tool-state classification. The milling force prediction model was implemented and compared by Radhakrishnan et al. [11] using Regression and ANN models. Regression analysis is a statistical technique used for developing a relationship between dependent and independent variables. The analysis was carried out to predict the force with an accuracy of 94.2%. The back propagation neural network algorithm was used to train and predict

J Braz. Soc. Mech. Sci. Eng.

the FX to an accuracy of 95.3%, better than the regression model. Sharif et al. [12] have incorporated Genetic Algorithm (GA) to find the optimal cutting conditions for acquiring minimum surface roughness value in milling process and concluded that good surface finish can be obtained at the high speed, high rake angle and low feed rate. Benardos et al. [8] have included the ANN technique in the study to predict surface roughness value. The authors concluded that the mean error of 1.86% obtained by using ANN seemed to be consistent throughout the range of values. In their research, Ab. Rashid et al. [13] presented the development of mathematical model for surface roughness prediction before milling process to evaluate the fitness of machining parameters: spindle speed, feed rate and depth of cut. Ciurana et al. [14] performed the experiments on Nd:YAG laser system on AISI H13 hardened tool steel for making mold cavities and implemented a model for volume error, machining time and surface roughness using ANN and PSO techniques and concluded that PSO is suitable to identify the optimum process parameters. Lee et al. [15] incorporated the PSO and GA to obtain the optimum process parameters in grinding operation for grinding silicon carbide and stated that PSO is relatively better than GA and is well suited for dealing with multi objective optimization problems. A lot of research articles are available on determining the optimal machining parameters using the evolutionary techniques such as GA, Fuzzy Logic and ANN. But most of the researchers concentrated on ANN to predict surface roughness using different algorithms. But, very limited work has been carried out to predict the multi-objective responses or output comprising of cutting force, surface roughness, power consumption, material removal rate, etc. In the present work, the PSO technique has been included to overcome the issues of the performance measures based on the multi-objective optimization in face milling operation. The selected machining parameters play an imperative role in determining the product quality, reducing machining cost and increasing productivity. However, many of the techniques are not proficient in determining the global optimum solution. In order to overcome the issue of determining the global optimum solution the PSO optimization technique has been developed. Hence the PSO technique has been incorporated in the present study for optimizing the machining parameters. Thus, in this study the PSO and desirability approach are used to identify the machining parameters to obtain desired responses such as cutting force (FX), surface roughness (Ra) and power consumption. At the end of the study, the comprised model is validated with the help of the confirmatory experimental results.

3 Experimental set up and methodology In the present study, the material AA6061-4.5%Cu5%SiCp, having length of 100 mm length, 60 mm breadth and 12 mm thickness was chosen as workpiece material. The experiments were conducted with dry machining condition using CNC Vertical Milling machine (Spark DTC 250). The chemical composition properties of Aluminium alloy (AA6061) is depicted in Table 1. These metal matrices are reinforced with 5% wt. SiC particles. The cutting parameters considered were spindle speed, feed rate and depth of cut, and with their ranges as shown in Table 2. The experiments were designed and conducted based on the design and analysis of experiment. In the design of experiment (DOE), three factors of cutting parameters and three levels have been considered. In the experimental study, the structural parameters for the machine tool are constant for every experiment inasmuch as all of the experiments are conducted on the same machine tool. The viable range of the machining parameters is taken considering the machine limitations. Later, the Ra values have been measured with a Mitutoyo surface roughness tester for the machined surface. The Ra was acquired at minimum of three different locations on the milled surface. Later on, the average Ra was calculated. The current consumed by each axis is acquired through the Servoguide diagnostic software (FANUC). The cutting force on each axis was calculated by indirect approach, using the current consumed. The indirect way of calculating the force is stated in the work of Kim et al. [16]. 3.1 Methodology: the main concept The main concept in the present study was to increase the utilization of machine capacity. Even though the machine has higher capacity to perform the machining operations, due to operator’s lack of knowledge of machine, the machines are run at sub-optimal conditions. Hence, it is desired to know Table 1  Composition of AA6061 Element

Al

Si

Cu

Mg

Cr

Weight%

97.9

0.60

4.5

1.0

0.20

Table 2  The cutting parameters and their levels Levels

Spindle speed (rpm)

Feed rate (mm/min)

Depth of cut (mm)

Level-I Level-II

1000 2000

300 400

1 2

Level-III

3000

500

3

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Table 3  Machining parameters with experimental design and their results Expt. no Spindle speed (rpm)

Feed rate (mm/min)

Depth of cut (mm)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

1000 3000 1000 3000 1000 3000 1000 3000 1000 3000 2000 2000 2000 2000 2000 2000 2000 2000 2000

300 300 500 500 300 300 500 500 400 400 300 500 400 400 400 400 400 400 400

1 1 1 1 3 3 3 3 2 2 2 2 1 3 2 2 2 2 2

20

2000

400

2

the optimal machine capacity utilization based on the power consumption. For example, 10 mm depth of cut can be achieved by removing material at spindle speed of 1000 rpm, feed rate of 300 mm/min and depth of cut 1 mm. The power consumed for each 1 mm per pass is 0.059597 kW. Therefore, the number of passes required to achieve the desired depth of cut is 10. Hence, the power consumption required is 0.59597 kW. A better Ra value is achieved at 1000 spindle speed, 300 feed rate and depth of cut of 2 mm per pass with the power consumption being 0.06943 kW. The number of passes required is five passes to achieve the desired depth of cut of 10 mm. Therefore, the required power consumption is 0.34715 kW. Thus, the power consumed 0.34715 kW is lesser in contrast to 1 mm depth of cut. In the present study, power consumption response is used as maximum capacity utilization of CNC machine. The main objective of using this strategy is to minimize the machining time without affecting the quality performance of the machine to decrease the machining cost. Few researchers concentrated only on the optimal process parameters without considering the maximum capacity utilization of the CNC machine. The power consumption consists of cutting forces required to remove the material and forces required to move the component

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against the tool for each pass. The power required to move the component against the tool for each pass remains constant without the affect of depth of cut. The machining parameters are selected based on recommended range supplied by the tool manufacturer, maximum spindle speed and feed rate of machine. Several experiments had been conducted within the aforesaid range to identify the desired range of process parameters and determine the feasible machining parameters as depicted in Table 3. In the present study, RSM technique was incorporated for design and analysis of the experiments. RSM technique helps with its strategies to overcome the analysis quandaries thus leading to better results. It usually identifies the significance of the process parameters on the responses and the main purpose of RSM is to predict the response. The central composite face-centered design (CCFCD) was used to implement the response models using RSM. A total of 20 experiments which incorporated 8 cube points, 6 center points in cube, 6 axial points and with alpha value of 1 were performed. The range of the process parameters was set by taking into consideration the tool or insert specification and even by performing the trial experiments in order to achieve the desired responses. Then, the experiments were performed to use the multiple regression equation in order to identify the interaction effect between the process parameters and the responses. Later on, the desirability and PSO techniques were employed to determine the optimal process parameters. The validation step is carried out by conducting the experiments in order to verify the established model. 3.2 Parametric optimization using desirability function Desirability function approach is a multiple-response optimization method by Deringer et al. [17]. This approach was first introduced in 1980 by Suich and Deringer. The method finds operating conditions “targeted” as the most desirable response value. The general approach is to first convert each response ×1 into an individual desirability function di that varies over the range 0 ≤  di ≤ 1. The desirability functions are categorized into three sectors based on the response characteristics: 1. If the target for the response is a maximum value/“Higher is Better”.

   0�  

1

ri−ri∗ ri′ −ri∗

�a ri ≤ ri∗ ri∗ < ri < ri′ , ri ≥ ri′

J Braz. Soc. Mech. Sci. Eng.

where ri* is the minimum adequate value of ri, ri′ is the maximum adequate value of ri and a describes the shape function for desirability 2. If the target for the response is a minimum value/“Smaller is better”  ri ≤ ri′′   1� �b ∗ ri −ri ri′′ < ri < ri∗ , ∗ ′′   ri −ri 0 ri ≥ ri∗

where r‫״‬i is the minimum value of ri, ri* is the maximum adequate value of ri and b describes the shape function for desirability. 3. If the target for the response is between lower and higher value/“Nominal is better”

� � ri−ri∗  ri∗ < ri < Oi  Oi−ri∗      � �a ri−ri∗ , Oi < ri < ri∗  Oi−ri∗       0 ri > ri ∗ or ri∗ > ri

where Oi is the objective value, c and a describe the exponential parameters which verify the shape of the desirability function. 3.3 Development of optimal machining parameters The optimal process parameters are achieved by employing the PSO and desirability approach. The PSO was implemented using MATLAB and the Desirability approach was carried out using Minitab software. The projected model is represented in Table 11 and the working conditions for the PSO model are illustrated in the algorithm. Table 11 clearly indicates projected model and signifies the parameters that play a vital role in obtaining finer convergence characteristics of PSO as depicted in Fig. 1. These parameters play a significant role in obtaining good convergence characteristics of PSO as shown in Fig. 1. If the number of parameters increases, the learning rate increases. In turn, the number of iterations increases in the search space. If the convergence is attained within a less number of iteration than the outcome probability of getting global optimum solution is at higher rate. Therefore, there is a boundary on maximum velocity to be attained by the particles. The velocity enhancement step is represented as follows:

If (vir > (Xulim − yir ) and vir < (Xllim − yir )) then, vir = −0.5 × vir

(1)

Fig. 1  Convergence of PSO technique

The above criterion indicates the abandoned increase in velocity of particles, so it is necessary to make the search algorithm to be limited boundary range. The direction of the velocity gets altered in opposite direction if the velocity of the particles surpasses the specified range. This results in faster convergence towards global optimum solution. 3.4 Proposed methodology Based on the literature survey, it has been observed that the PSO technique yields good result as compared to the rest of the techniques. So the PSO technique is incorporated in this present study. PSO is stochastic optimization technique which is a population-based optimization technique; PSO technique was implemented by Dr. Eberhart et al. [18] in the year 1995. The PSO technique was implemented by taking an inspiration of flocking birds. In the PSO algorithm, the particles are estimated by the fitness function to be optimized and have velocities for the particles. The PSO has two important values which are termed as pbest and gbest. The pbest value is the best solution achieved so far among the particles, and the gbest value is the best solution obtained so far in the population. Once these two values, i.e. pbest and gbest are acquired, the particles are upgraded with their velocity and positions using the equations. PSO incorporates various parameters such as number of particles, range of particles, global vs local values, dimension of particles and learning factor. The information mechanism sharing in PSO is entirely diverse as compared to the rest of the techniques. The information sharing in PSO is a one-way sharing mechanism. In PSO, the gbest has the right to share the information with others. As the evolution glances only for the

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J Braz. Soc. Mech. Sci. Eng.

best solution, all the particles present intend to converge towards the best solution as quick as possible in most of the cases. The PSO algorithm mainly consists of three different factors as follows: (1) social, (2) cognitive and (3) inertia. All these three constraints play an important role. The social constraint concentrates mainly on accelerating the particle towards the best position. The best position is the one which is so far followed by all the neighboring swarm. This position is considered to be as the global best (gbest) position. The Cognitive constraint concentrates on accelerating the individual particle towards its best position (pbest), the position (pbest) which is accomplished by the individual particles so far. The inertia constraint plays a vital role in maintaining the stability between the gbest and pbest investigation competence among the search space. If the fitness values of gbest and pbest values are compared among each other and if the pbest value is found to be better than the gbest value, then the value of the gbest changes. The equations are incorporated with the provision to vary the position of individual particles to reach global optimum solution in search space:

vir+1 = w × vir + c1 × Q1 × (pbesti − yir ) + c2 × Q2 × (gbest − yir ),

(2)

where vir  = ‘ith’ particle momentum at ‘rth’ iteration; w  = inertia weight; c1, c2  = learning factors which vary in the range of 1–4; Q1, Q2 = random numbers between 0 and 1; pbesti = pbest location of ‘ith’ particle or pbest value is the best solution achieved so far among the particle; r , yr , yr , . . . yr gbest  = gbest location of swarm; yir  = [yi1 iN i2 i3 ] and “ith” particle current position at “rth” iteration in N-dimensional search space or gbest value is the best solution obtained so far in the population. After calculating the momentum, the next position of the rth particle is calculated as follows:

yir+1 = yir + vir+1

(3)

Inertia weight can be determined using the Eq. (4) or the Inertia weight can be chosen to be any random value. This determined inertia weight can be substituted in Eq. (2):

W = wmax −

[(Wmax − Wmin ) × itercurr ] , itertotal

(4)

where Wmax  = maximum inertia weight; Wmin  = minimum inertia weight; itercurr  = current iteration; and itertotal = total number of iteration. Algorithm 1. Initialize the population of n particles randomly. 2. For each particle, the fitness value is calculated. 3. If the obtained fitness value of the particle is better than the best fitness value (pbest) in history, then the present value is assigned as new best fitness value (new pbest). 4. Choose the particle with the best fitness value of all the particles which are considered so far as the global best (gbest). 5. The velocity and position of each particle need to be calculated. 6. Each particle velocities are secured to a maximum velocity. If the sum of the acceleration causes the velocity on that dimension to surpass the specified range set by the user, then velocity needs to be limited. 7. Terminate if minimum error condition is reached or the maximum iteration is reached; else go to step 2.

4 Results and discussion The statistical method of regression analysis was adopted and was executed using the Design Expert software. The best fit equations to combine the machining parameters and

Table 4  Regression equations SL. no

Responses

Regression equation

1

FX

2

Ra

3

−215.06991 + 0.10846 × spindle speed + 0.83246 × feed rate + 10.39903 × depth of cut − 8.19703E−005 × spindle speed × feed rate − 2.23735E−003 × spindle speed × depth of cut − 6.21407E−004 × feed rate × feed rate 2.71064 − 9.21591E−004 × spindle speed + 4.74818E−003 × feed rate + 0.40541 × depth of cut − 2.33750E−006 × spindle speed × feed rate + 2.28750E−004 × spindle speed × depth of cut − 1.18750E−003 × feed rate × depth of cut + 9.72727E−008 × spindle speed × spindle speed + 5.72727E−006 × feed rate × feed rate − 0.17773 × depth of cut × depth of cut

Power consumption −0.18139 + 3.7262467E−005 × spindle speed + 4.74091E−004 × feed rate + 9.10346E−003 × depth of cut + 1.69738E− 07 × spindle speed × feed rate

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J Braz. Soc. Mech. Sci. Eng. Table 5  ANOVA analysis for FX Source

Sum of squares

df

Mean square

F value

p value Prob > F

Model Spindle speed Feed rate Depth of cut Spindle speed × feed rate Spindle speed × depth of cut Feed rate × feed rate Residual Lack of fit Pure error

54,750.09 50,690.95 2937.52 350.98 537.53 40.05 193.07 78.08 72.44 5.63

6 1 1 1 1 1 1 13 8 5

9125.02 50,690.95 2937.52 350.98 537.53 40.05 193.07 6.01 9.06 1.13

1519.36 8440.3 489.11 58.44 89.5 6.67 32.15