Modeling and optimization of kerf taper and surface ... - Springer Link

Journal of Mechanical Science and Technology 27 (7) (2013) 2115~2124 www.springerlink.com/content/1738-494x

DOI 10.1007/s12206-013-0527-7

Modeling and optimization of kerf taper and surface roughness in laser cutting of titanium alloy sheet† Arun Kumar Pandey and Avanish Kumar Dubey* Mechanical Engineering Department, Motilal Nehru National Institute of Technology Allahabad - 211004, Uttar Pradesh, India (Manuscript Received March 21, 2012; Revised December 12, 2012; Accepted January 24, 2013) ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Abstract Laser cutting of titanium and its alloys is difficult due to it’s poor thermal conductivity and chemical reactivity at elevated temperatures. But demand of these materials in different advanced industries such as aircraft, automobile and space research, require accurate geometry with high surface quality. The present research investigates the laser cutting process behavior of titanium alloy sheet (Ti-6Al-4V) with the aim to improve geometrical accuracy and surface quality by minimizing the kerf taper and surface roughness. The data obtained from L27 orthogonal array experiments have been used for developing neural network (NN) based models of kerf taper and surface roughness. A hybrid approach of neural network and genetic algorithm has been proposed and applied for the optimization of different quality characteristics. The optimization results show considerable improvements in both the quality characteristics. The results predicted by NN models are well in agreement with the experimental data. Keywords: Genetic algorithm; Kerf taper; Neural network; Optimization; Surface roughness; Titanium alloy ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

1. Introduction Titanium and its alloys are increasingly used in many industries due to their superior properties such as high tensile strength to density ratio, high strength to weight ratio, high corrosion resistance, fatigue resistance, high crack resistance, and ability to withstand moderately high temperatures without creeping [1]. Ti-6Al-4V is an alloy of Titanium (Grade 5) which is extensively used in aerospace, medical, marine, chemical processing sectors and automobile sectors. It is significantly stronger than commercially pure titanium while having the same stiffness and thermal properties. This grade is an excellent combination of strength, corrosion resistance, light weight, good creep and fracture toughness characteristics, weld and fabricability [2]. In consequence, its uses are numerous such as turbine blades, discs, rings, airframes, fasteners, components, vessels, cases, hubs, forgings and biomedical implants. The conventional cutting methods face difficulties in cutting of titanium (Ti) and its alloys. Ti is chemically reactive at elevated temperatures, due to which the tool material either rapidly dissolves or chemically reacts during the cutting, resulting premature tool life [3]. Due to poor thermal conductivity of titanium alloys, the *

Corresponding author. Tel.: +91 532 2271535, Fax.: +91 532 2545341 E-mail address: [email protected], [email protected] † Recommended by Associate Editor Young Whan Park © KSME & Springer 2013

heat generated during the cutting is not dissipated properly which results melting of tool tip and reduces tool life. While machining the titanium alloys, the contact length between tool and chip has found very small which implies that the high cutting temperatures and high cutting stresses are concentrated near the cutting edge. Due to this the tool failure may occur rapidly. The low elastic modulus permits greater deflection of the workpiece during machining and increases complexity of the machining. Laser cutting is an advanced beam cutting process, in which the laser beam is directed and focused onto the surface of the workpiece to rapidly heat it up, resulting in melting and /or vaporization, depending on the beam intensity and workpiece material (Fig. 1). The molten metal and/or vapor are then blown away using a pressurized assist gas jet [4]. The schematic and mechanism of laser cutting is shown in Fig. 1. Nd:YAG (solid laser) and CO2 (gas laser) are most commonly used for the cutting applications due to their high power. The Nd:YAG laser which is an optically pumped solid state laser, operating at a wavelength of 1.06 µm, gives low beam power due to the poor heat conductivity of YAG crystal. When operated in pulsed mode, it gives high peak power, good focusing characteristics and narrow heat affected zone (HAZ) [5]. Due to shorter wavelength, the Nd:YAG laser is much better absorbed by the metals and highly reflective materials as compared to CO2 laser and also permits to focus the laser beam at small spot of the workpiece i.e. provides better

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Fig. 1. Schematic of Laser cutting.

energy concentration [6]. The quality of cut in laser cutting mainly depends on the appropriate selection of inputs such as laser parameters, material properties and cutting parameters. Many researchers have investigated the effect of these parameters on different quality characteristics such as kerf width, cut edge surface roughness, dross inclusions, recast layer formation and thickness of heat affected zone (HAZ) for the different category of materials. Yilbas et al. [7] have investigated the effect of oxygen in laser cutting of stainless steel and mild steel sheet. They have found that by increasing the oxygen pressure, the size of surface plasma and tendency of formation of micro cracks have increased. Shuja et al. [8] have done simulation to predict the melt pool geometry in the laser repetitive pulse heating of steel and they have shown that the simulation results are in good agreement with experimental results. Miranda and Quintino [9] have experimentally analyzed the effect of laser power, plate thickness, assist gas type and assist gas pressure on the cutting speed in the laser cutting of calcareous stones. They have found that the maximum cutting speed obtained increases with the laser power and decreases with the plate thickness. Yilbas et al. [10] have done FEM based modeling for the prediction of surface temperature and stress developed in the cutting region for the laser cutting of zirconia tiles and also shown that the cut section is free from major cracks and dross attachment occurs at the kerf exit. Yilbas et al. [11] have demonstrated that the first and second law efficiencies improve at high laser cutting speeds and low laser output power levels for the laser cutting of Kevlar laminates. Kim et al. [12] have experimentally investigated the laser assisted machining of silicon nitride ceramics and shown that as the laser power increased, the temperature of the specimen surface rose, causing structural changes in the ceramic and raising the efficiency of cutting. But on the other hand the hardness of the machined surface decreases due to oxidation. Non-contact nature of laser cutting may overcome the difficulties faced during conventional cutting of Ti alloys. But reported research works indicate that achieving the quality cuts is still a big challenge. When Titanium alloys are laser cut with oxygen assist gas, at even low pressure, the uncontrolled

burning of cutting front starts due to low thermal conductivity and high chemical reactivity of these alloys which results wider kerf with poor surface quality. During air assisted laser cutting, the reaction of Titanium with oxygen and nitrogen produces a thin layer of hard and brittle oxides and nitrides which generates thicker HAZ layers in comparison to that of nitrogen or argon [13]. Rao et al. [14] have separately used three assist gases nitrogen (N2), argon (Ar) and helium (He) for the pulsed laser cutting of 1 mm pure titanium sheet. They have shown that the laser cuts produced with Ar and N2 are straight and parallel while He assist gas gives wavy cut surface. Almeida et al. [15] have used N2 assist gas and they have analyzed cut edge surface morphology. They reported increase in hardness of cut edge surface and changed surface morphology due to precipitation of N2. The nonlinear behaviors of the laser-material interactions play a significant role in creation of the final surface profile and the resultant geometry of the laser cut features. The need to precisely control a large number of parameters often with random components makes the task of improving the process performance very difficult. Moreover, modeling all these factors using conventional, analytical and numerical methods pose a substantial challenge. In practice, the operator has to perform number of experiments to set the appropriate process control parameters related to the laser apparatus, motion control system and workpiece material [16]. This trial-and-error approach is costly and time consuming. To overcome this problem, soft computing techniques based on artificial intelligence (AI), such as artificial neural network (ANN), fuzzy logic (FL) and genetic algorithm (GA) may be efficiently used for modeling and optimization in laser cutting process [17]. Some of the researchers have applied these techniques in the laser cutting of few materials. Yousef et al. [18] have done ANN modeling for the material removal process during the pulsed Nd:YAG laser cutting of brass, copper and stainless steel. They demonstrated how a multilayered neural network can be used to model the nonlinear laser cutting process in an effort to predict the level of pulse energy needed to create a dent or crater with the desired depth and diameter. Syn et al. [19] have used fuzzy logic for the modeling of laser cutting of 1 mm thick incoloy alloy sheet and shown that the fuzzy model might be used to predict the surface roughness and dross inclusions. Jimin et al. [20] have done ANN based modeling for the non-vertical laser cutting (3-D) of 1 mm thick mild steel sheet. They found that the ANN model successfully predicted cutting results. The review of literature indicates that very few researchers have studied the laser cutting behavior of Ti alloys. The reported works show that non linear behavior of laser cutting process can better be predicted by using AI tools. Keeping this in view, a hybrid approach of NN - GA has been proposed and applied for modeling and optimization of pulsed laser cutting of Ti alloy sheet. Firstly ANN has been applied for the modeling of kerf taper (KT) and cut edge surface roughness (SR) with the help of experimental data obtained by the designed

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experimentation. Pulse width, pulse frequency, cutting speed and assist gas pressure have been selected as process parameters (control factors). The developed ANN models for KT and SR have been taken as objective functions in the GA based optimization of these quality characteristics. The developed ANN models have also been compared with the experimental data for the validation of the models. Statistical analysis has been used to check the adequacy of the developed models.

Table 1. Chemical composition of titanium alloy sheet (Grade-5). Al

Fe

Sn

V

Ti

6.22%

0.187%

0.56%

3.35%

89.60%

Table 2. Control factors and their levels used in experimentation. Symbol A

Factor

Unit

Level 1

Level 2

Level 3

Gas pressure

×10 N/mm2

5

7

9

2. Experimentation

B

Pulse width

ms

1.4

1.8

2.2

2.1 Design of experiments

C

Pulse frequency

Hz

6

10

14

Cutting speed

× (1/60) mm/s

15

20

25

A well designed experimental plan can substantially reduce the total number of experiments without affecting the accuracy during experimental study of any manufacturing process. Taguchi’s robust parameter design methodology has proved to be an effective approach in producing high quality products at a relatively low cost. The fundamental principle of Taguchi’s robust parameters design methodology is to improve the quality of the product by minimizing the effect of the cause of variations without eliminating the cause. This is achieved by optimizing the product and process designs to make the performance minimally sensitive to the various causes of variations. Taguchi has suggested properly designed experimental matrices known as orthogonal arrays (OAs) to conduct the experiments. The OAs are selected based on the number of process parameters, their levels and interaction between them, if any. The minimum three levels of the process parameters are required to explain the nonlinear (curvature) relationships [21]. As laser cutting process is complex and nonlinear process, that’s why three levels of each parameter have been selected for the experimentation. In the present work four control factors with three levels of each have been considered. Hence, experiments can be performed by using simplest L9 OA. But authors have selected L27 OA for high resolution factor [22]. 2.2 Experimental details A pulsed Nd:YAG (200 W) laser cutting system with CNC work table supplied by SIL Pune, India has been used for the L27 OA based experimentation. The assist gas used for the experimentation is nitrogen as use of oxygen gives uncontrolled burning of cutting front due to the low thermal conductivity, high chemical reactivity at elevated temperature and also exothermic nature of oxygen while inert gases are expensive. The assist gas is passed through a nozzle of 1 mm diameter, which remains constant throughout the experiment. The focal length of the lens is 50 mm and the stand-off distance is 1mm. The titanium alloy sheet (Ti-6Al-4V) thickness 1.4 mm is used as work material. The chemical compositions of the Ti-6Al-4V have been shown in the Table 1. From the theoretical point of view, three basic processes such as absorption of laser beam (heat), melting of material and expulsion of melted material from the melting pool are

D

required to cut the material in the laser cutting process. The impinging laser power on the workpiece is controlled by the pulsed parameters such as pulse width and pulse frequency while the rate of the laser power is controlled by the combination of pulse frequency and cutting speed. The expulsion of the material is controlled by the combination of cutting speed and applied assist gas pressure. That’s why these four parameters (assist gas pressure, pulse width, pulse frequency and cutting speed) are very important from quality point of view as well as to obtain complete through cutting in pulsed laser cutting process. On the other hand, proper assist gas pressure is required for the ejection as well as cooling of the cutting front. The cutting speed is very important in pulsed mode because it controls the extent of spot overlap as well as heat input in the kerf and those are directly responsible for kerf quality. The effect of laser energy or power is very important in laser cutting but it has been found that pulse parameters contribute significantly in pulsed mode laser cutting. In pulsed mode laser cutting as peak power is inversely proportional to the pulse width i.e. pulse width controls the peak power while pulse frequency controls the extent of spot over lap as well as heat input to the kerf. An exhaustive pilot experimentation has been performed in order to decide the range of each control factors for complete through cutting. The pilot experiments are performed into two stages, in first stage, the ranges of individual process parameters have been decided by varying the one parameter at a time to obtain complete through cutting while in the second stage, the ranges of all process parameters are decided by considering the simultaneous variation of all process parameters. Based on these experiments, the ranges of the different control factors (process parameters) and their levels are shown in Table 2. 2.3 Characterization of cut quality attributes The quality characteristics or responses selected for the analyses are cut edge surface roughness (SR) and kerf taper (KT). Straight cuts of 15 mm long are made for the each experimental run and kerf widths are measured at three different places along the length of cut on the top as well as

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Fig. 2. Representation of average surface roughness (Ra).

Fig. 4. Experimental values of KT and SR.

Fig. 3. Diagram of kerf quality characteristics in laser cutting process.

bottom side. Average values of which give the top kerf width and bottom kerf width, respectively. Top and bottom kerf widths are measured by using optical microscope with 10X magnification supplied by Radical instruments, India. The average values of cut edge surface roughness (Ra values) are represented in microns which are the arithmetic mean of the absolute value of the vertical heights between the actual profile and mean profile line as shown in Fig. 2. In this study Ra values have measured at three different places of the cut edge surface with the help of surface roughness tester (SJ-series) supplied by Mitutoyo, Japan and average of all three Ra values, gives the SR for an experimental run. The KT may be calculated by using the formula shown in Eq. (1).

(a)

(b)

(TopKerfwidth − BottomKerfwidth) *180 KT ( ) = 2πt 0

(1)

where, t is the thickness of the sheetmetal. The different quality characteristics such as top kerf width, bottom kerf width and surface roughness have shown graphically in Fig. 3. The experimental values of different quality characteristics used in the study such as SR and KT are shown in Fig. 4. After the measurement has been completed, in order to analyze the top as well as bottom kerf and cut edge roughness, the samples are first ground and polished with rough and fine papers. After that the samples were etched in the Kroll’s reagent (which is a mixture of HNO3+HF+H2O) for 10 seconds. The etched samples were photographed with Electron Probe Micro Analyzer (EPMA), Model JXA-8100 (Japan). The EPMA micrographs of the top and bottom kerf, and cut edge surface at initial parameter level setting are shown in Figs. 5 and 6, respectively.

Fig. 5. EPMA images of (a) Bottom kerf at A = 5 kg/cm2, B = 1.4 ms, C = 6 Hz and D = 15 mm/min; (b) Top kerf at A = 5 kg/cm2, B = 1.4 ms, C = 6 Hz and D = 15 mm/min.

Fig. 6. EPMA images of cut edge surface at A = 5 kg/cm2, B = 1.4 ms, C = 6 Hz and D = 15 mm/min.

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Fig. 7. Nonlinear model of a neuron.

3. ANN modeling An artificial neuron is an information processing unit that is fundamental to the operation of a neural network. The model of a neuron is shown in Fig. 7, which forms basis for designing of an artificial neural network. There are three basic elements of a neuronal model. (1) A set of synapses or connecting links, each of which is characterized by a weight or strength of its own. (2) An adder for summing the input signals, weighted by the respective synapses of the neuron. (3) An activation function for limiting the amplitude of the output of a neuron. The neuronal model shown also includes an externally applied bias, denoted by bk. The bias has the effect of increasing or lowering the net input of the activation function depending on whether it is positive or negative respectively. In mathematical form, a neuron k may be described by writing the following pair of equations [23], n

uk = ∑ wkj x j

(2)

yk = φ (uk + bk )

(3)

j =1

where X1, X2, X3 and X4 are the values of inputs, Wk1, Wk2, Wk3……….. Wkj are the synaptic weights of neuron k, uk is the linear combiner output due to the input signals, φ ( ) is the activation function, and Y is the output of the neuron. In this study, the artificial neural network has been used to model the complex and non linear relationship between the input and output parameters of laser cutting. An ANN can be viewed as a function that maps input vectors into output vectors. Before training a network, the architectures of the network has been decided i.e. numbers of hidden layer and numbers of neurons in the hidden layer. According to the Fausett, the back propagation network with one hidden layer is adequate for a large number of applications [24]. So in this study, the network with one hidden layer has been used. In order to decide the number of neurons in hidden layer, the mean square error (MSE) for the different number of neurons has been computed. Based on minimum MSE, the numbers of

Fig. 8. Network architectures for KT.

neurons in the hidden layer has been decided for both the quality characteristics i.e. numbers of neurons in hidden layer for the KT and SR have been decided as 6 and 5 neurons respectively. The ANN models for the KT and SR have been developed by using 4-6-1 and 4-5-1 network architectures. The network architectures for KT have been shown in the Fig. 8. Similar type of architectures (with 5 hidden neurons) has also been used for the SR. In the Fig. 8, X1, X2, X3, and X4 are showing four control factors considered in the study and b1, b2, b3, b4, b5 and b6 are the biases for the hidden layer neurons 1, 2, 3, 4, 5, and 6 respectively. The bias b has been applied to the output layer neuron and w1, w2, w3, w4, w5 and w6 are the weights between hidden layer neurons to the output layer neuron. For finding the different weights between input layer neurons & hidden layer neurons and hidden layer neurons to the output layer neuron, first the experimental output data have been normalized to avoid the variability of the data. The experimental data for KT and SR have been normalized by using Eq. (4). yij* =

yil

(4)

max y ij

where Y*ij = the normalized value of the jth quality characteristics in ith experimental runs, Yij = the actual experimental value of the jth quality characteristics in ith experimental runs and Max. Yij = the maximum value of Yij. After normalizing the data, by selecting the random weights, the output for the network Y have been computed by using the Eqs. (5) and (6). The activation function used for the hidden layer neurons is log sigmoid i. e. the output for the different neurons of hidden layer may be computed by using Eq. (5) [which is modification of the Eq. (3)],

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1 1+ e

(5)

 − ( u k + b k ) 

n1 = 0.098082 x1 −1.904 x2 + 0.55163x3 + 0.0092879 x4 − 3.570

(8) n2 = 4.1042 x1 − 6.9435 x2 + 0.89499 x3 + 0.51084 x4 − 27.702

where k = the number of neurons in the hidden layer. For the reducing complexity and computation, the activation function for the output layer has been considered as pure linear. The output of the network may be computed by using the following equation,

(9) n3 = −1.7184 x1 + 0.92694 x2 + 0.223x3 − 0.23086 x4 + 11.436

(10) n4 = 0.79944 x1 − 3.879 x2 + 1.0576 x3 + 0.16713 x4 − 14.6659

(11) n5 = −1.7596 x1 + 1.411x2 − 0.051306 x3 − 0.27225 x4 + 13.7031 .

k

y = ∑ y k wk + b .

(12)

(6)

i =1

For the normalized KT, Then MSE for the network has been computed and after that MSE for the network has been tried to minimize, i.e. by approaching MSE to zero, the different weights of the networks have been tried to compute. The manual computations of the different weights for the networks are complex and time consuming. In order to avoid these problems, the updated weights have been found by training the network with the neural network toolbox of MATLAB by fixing the MSE as zero. The networks have been trained with the normalized experimental data by using Levenberg Marquadt (LM) algorithms because the LM algorithm is fastest and least memory consuming one. The MATLAB function TRAINLM has been utilized for training the network which works on the back propagation algorithm. The TRAINLM is a network training function that updates weight and bias values according to Levenberg-Marquardt optimization. MSE for the network for KT and SR have been obtained as 4.23839*10-30 and 3.36168*10-26 respectively which are very much closer to the target (MSE) set for the training of the networks. These updated weights have been used for finding the neural network based mathematical models for the KT and SR. The neural network based mathematical models for the normalized KT (YNKT) and normalized SR (YNSR) have been obtained as, For the normalized SR,

y NKT = −0.86826 y1 + 0.35913 y2 − 1.6831y3 − 35.5541 y4 + 0.65796 y5 + 1.2506 y6 + 2.0376

(13)

where y1 = 1

1 + exp ( − n1 ) 

,

y3 = 1

1 + exp ( −n3 ) 

,

y5 = 1

1 + exp ( − n5 ) 

,

y2 = 1

,

1 + exp ( − n2 )  y4 = 1 , 1 + exp ( − n4 )  y6 = 1 1 + exp ( −n6 ) 

and n1 = 3.3858 x1 + 14.2472 x2 − 0.88487 x3 − 3.546 x4 + 34.0737

(14) n2 = 10.6344 x1 − 7.4356 x2 + 0.72567 x3 + 2.2252 x4 − 122.6116

(15) n3 = 0.79329 x1 − 2.7334 x2 + 0.21745 x3 − 0.11332 x4 + 1.4979

(16) n4 = −0.042674 x1 − 0.45604 x2 − 0.11173x3 + 0.30592 x4 − 9.3449

(17) n5 = 13.0032 x1 − 9.5039 x2 − 0.82832 x3 − 3.4257 x4 + 16.6225

(18) n6 = −9.3615 x1 − 9.5816 x2 − 0.76113 x3 + 2.0141x4 + 19.1963

(19) y NSR = 3.9737 y1 − 2.2789 y 2 + 1.2063 y 3 − 3.2547 y 4 − 3.7532 y 5 + 2.6173

(7)

where x1 , x2 , x3 , and x4 are the input process parameters. 4. Model validation

where

4.1 Theoretical validation y1 = 1  , 1 + exp (−n1 ) y3 = 1  , 1 + exp (−n3 ) y5 = 1   1 + exp (−n5 )

and

y2 = 1 , 1 + exp (−n2 ) y4 = 1 , 1 + exp (−n4 )

In order to check, the data predicted by ANN models are well fitted or not, the regression analysis of the models has been carried out. The results obtained by regression analysis for SR and KT have been shown in Figs. 9 and 10, respectively. The regression coefficients for training of SR & KT models have been found 0.99999 & 0.98781 respectively and the overall regression coefficient for the ANN models of SR & KT have been found 0.98273 & 0.96598, respectively. Hence, the data predicted by ANN models are well fitted.

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(a)

Fig. 9. Regression plots of ANN models of SR. (b) Fig. 11. Comparison results of (a) KT; (b) SR.

4.2 Experimental validation In order to check validation of the models, the data predicted by the ANN models have been compared with the experimental data for different sets of control factors. The comparison results for KT and SR have been shown in Fig. 11. From the Fig. 11, it is clear that the data predicted by ANN models are closer to the experimental data. The percentage prediction error (PPE) for each experimental run has been calculated by using Eq. (20).

PPE =

( Experimentalvalue − predictedvalue ) *100

(20)

Experimentalvalue

The maximum prediction errors of ANN models for KT & SR have been found 1.944% & 1.449% respectively and the average prediction error for the KT and SR have been found 0.569%, and 0.619% respectively, which are negligible. Hence, the developed ANN models may be used to predict the KT and SR for different sets of control factors successfully.

5. Optimization Fig. 10. Regression plots of ANN models of KT.

Genetic algorithms (GAs) are computerized search and optimization algorithms based on the mechanics of natural

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(a)

Fig. 12. Flow diagram for GA based optimization.

genetics and natural selection. The operations of GAs begin with a population of random strings representing design or decision variables. Thereafter, each string is evaluated to find the fitness value. The population is then operated by three main operators namely reproduction, crossover and mutation to create a new population of points. The new population is further evaluated and tested for termination. If the termination criterion is not met, the population is iteratively operated by the three operators and evaluated. This procedure is continued until the termination criterion is met [25]. The different steps involved in GA-based optimization [26] have been shown in Fig. 12. Eqs. (7) and (13) have been used as objective function for optimization of SR and KT, respectively. The different equations (from 7 to 12 for SR and from 13 to 19 for the KT) have been written in MATLAB and those MATLAB files are further used in the GA based optimization of the KT and SR. In this study, the population size of 80, crossover rate 0.90, mutation rate of 0.1, and number of generations 300 have been used. For crossover, double point crossover has been used. After selecting all these parameters, GA based optimization solver has been run and optimization has been terminated after 300 generations. The optimization results obtained for KT and SR have been shown in Figs. 13 and 14, respectively. Fig. 13, it is clear that the improvement in the best fitness value of KT is up to 295th generation. After 295th generation, no improvement in the best fitness value has been registered and best fitness value at this generation has been found equal to 0.097817 (normalized KT). The best values of individual control factors have been found as 5.004, 1.7005, 13.9995and 16.6782 for factors 1, 2, 3 and 4, respectively. It means the optimum value of KT at the optimum level of control factors (gas pressure-50.04 N/mm2, pulse width-1.7005 ms, pulse frequency-13.9995 Hz and cutting speed-0.278 mm/s or 16.68 mm/min) is 0.6168º (0.097817*6.30573). Similarly from Fig.

(b) Fig. 13 (a) Change in the fitness value of KT; (b) Best value of individual control factors.

(a)

(b) Fig. 14. (a) Change in the fitness value of SR; (b) Best value of individual control factors.

14, it may be concluded that the best fitness value of SR has been improved up to 275th generation, and after 275th generation, both best fitness value and mean of fitness values have same value equal to 0.12957 (normalized SR). For this

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Table 3. Comparison results. Initialvalues Optimum values Improvements Kerf taper (°)

2.8662

0.6168

78.48%

Surface roughness (µm)

8.4100

2.0537

75.58%

(a)

(b)

Fig. 17. EPMA images of cut edge surface at (a) Initial parameter level, A = 5 kg/cm2, B = 1.4 ms, C = 6 Hz and D = 15 mm/min; (b) Optimum parameter level for SR, A = 6.3708 kg/cm2, B = 1.40 ms, C = 6.2512 Hz and D = 15 mm/min. (a)

(b)

Fig. 15. EPMA images of Top kerf at (a) Initial parameter level, A = 5 kg /cm2, B = 1.4 ms, C = 6 Hz and D = 15 mm/min; (b) Optimum parameter level for KT, A = 5.005 kg/cm2, B = 1.7005 ms, C = 13.9995 Hz and D = 16.6782 mm/min.

(a)

(b)

Fig. 16. EPMA images of Bottom kerf at (a) Initial parameter level, A = 5 kg/cm2, B = 1.4 ms, C = 6 Hz and D = 15 mm/min; (b) Optimum parameter level for KT, A = 5.005 kg/cm2, B = 1.7005 ms, C = 13.9995 Hz and D = 16.6782 mm/min.

fitness value, the best individual values have been found as 6.3708, 1.40, 6.2512 and 15.00 for factors 1, 2, 3 and 4, respectively. Therefore, the optimum value of SR at optimum level of control factors (63.708 N/mm2 of gas pressure, 1.40 ms of pulse width, 6.2512 HZ of pulse frequency and 0.25 mm/s or 15 mm/min of cutting speed) is equal to 2.0537 µm (0.12957*15.85). The optimization results for KT and SR have been compared with the results at initial parameter setting. These results are shown in the Table 3. The comparison results show that KT and SR values have been reduced by 78.48% and 75.58%, respectively. These improvements can also be observed by the EPMA micrographs of top and bottom kerf, and cut edge surface at optimum parameter level settings against initial settings as shown in Figs. 15-17, respectively. 6. Conclusions The proposed NN - GA hybrid approach has been successfully applied for modeling and optimization of kerf

taper and surface roughness in laser cutting of difficult-to-cut Titanium alloy sheet. The main findings of the paper are given below, (1) The developed artificial neural network based models for kerf taper and cut edge surface roughness have been found reliable and adequate with average prediction errors of 0.569% and 0.619%, respectively. (2) The kerf taper and surface roughness values predicted by ANN based models have been found close to the experimental values. (3) The kerf taper and surface roughness values have been successfully reduced and the optimum laser cutting parameters suggested for kerf taper and surface roughness as gas pressure-50.04 N/mm2, pulse width-1.7005 ms, pulse frequency-13.9995 Hz, cutting speed-0.278 mm/min or 16.66 mm/min and 63.708- N/mm2, pulse width-1.40 ms, pulse frequency-6.2512 Hz, cutting speed-0.25 mm/s or 15 mm/min, respectively. (4) The results of optimization show that the kerf taper and surface roughness values have been considerably reduced by 78.48% and 75.58%, respectively. References [1] A. Patnaik, N. Poondla, U. Baithini and T. S. Srivastan, On the use of gas metal arc welding for manufacturing beams of commercially pure titanium and a titanium alloy, Materials and Manufacturing Processes, 26 (2) (2011) 311- 318. [2] S. K. Ghosh and S. Chatterjee, On the direct diffusion bonding of titanium alloy to stainless steel, Materials and Manufacturing processes, 25 (11) (2010) 1317-1323. [3] D. A. Dornfeld, J. S. Kim, H. Dechow, J. Hewson and L. J. Chen, Drilling burr formation in titanium alloy, Ti-6Al-4V, Annals of CIRP, 48 (1) (1999) 73-76. [4] E. K. Asibu Jr., Principles of laser materials processing, John Wiley & Sons, Inc., Hoboken, New Jersey (2009). [5] A. K. Dubey and V. Yadava, Laser beam machining—A review, International Journal of Machine Tools & Manufacture, 48 (6) (2008) 609-628. [6] A. K. Dubey and V. Yadava, Experimental study of

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Nd:YAG laser beam machining—An overview, Journal of Materials Processing Technology, 195 (1-3) (2008) 15-26. [7] B. S. Yilbas, J. Nickel and A. Coban, Effect of oxygen in laser cutting process, Materials and Manufacturing Processes, 12 (6) (1997) 1163-1175. [8] S. Z. Shuja, B. S. Yilbas and O. Momin, Laser repetitive pulse heating and melt pool formation at the surface, Journal of Mechanical Science and Technology, 25 (2) (2011) 479487. [9] R. M. Miranda and L. Quintino, CO2 laser cutting of calcareous stones, Materials and Manufacturing Processes, 19 (6) (2004) 1133-1142. [10] B. S. Yilbas, S. S. Akhtar and C. Karatas, Laser straight cutting of zirconia tiles, Journal of Mechanical Science and Technology, 26 (2) (2012) 591-599. [11] B. S. Yilbas, A. Z. Sahin, C. Chatwin and T. Ayar, Laser cutting of Kevlar laminates: First and second law analysis, Journal of Mechanical Science and Technology, 25 (4) (2011) 855-862. [12] J. D. Kim, S. J. Lee and J. Suh, Characteristics of laser assisted machining for silicon nitride ceramic according to machining parameters, Journal of Mechanical Science and Technology, 25 (4) (2011) 995-1001. [13] L. Shanjin and W. Yang, An investigation of pulsed laser cutting of titanium alloy sheet, Optics and Lasers in Engineering, 44 (10) (2006) 1067-1077. [14] B. T. Rao, R. Kaul, P. Tiwari and A. K. Nath, Inert gas cutting of titanium sheet with pulsed mode CO2 laser, Optics and Lasers in Engineering, 43 (12) (2005) 1330-1348. [15] I. A. Almeida, W. D. Rossi, M. S. F. Lima, J. R. Berretta, G. E. C. Ngueira, N. U. Wetter and N. D. Vieira Jr., Optimization of titanium cutting by factorial analysis of pulsed Nd:YAG laser parameters, Journal of Materials Processing Technology, 179 (1-3) (2006) 105-110. [16] J. Ciurana, G. Arias and T. Ozel, Neural network modeling and particle swarm optimization (PSO) of process parameters in pulsed laser micromachining of hardened AISI H13 Steel, Materials and Manufacturing Processes, 24 (3) (2009) 358-368. [17] O. B. Nakhjavani and M. Ghoreishi, Multi criteria optimization of laser percussion drilling process using artificial neural network model combined with genetic algorithm, Materials and Manufacturing Processes, 21 (1) (2006) 11-18. [18] B. F. Yousef, G. K. Knopf, E. V. Bordatchev and S. K. Nikumb, Neural network modeling and analysis of the material removal process during laser machining, International Journal of Advanced Manufacturing Technology, 22 (1-2) (2003) 41-53. [19] C. Z. Syn, M. M. Mokhtar, C. J. Feng and Y. P. Manurang, Approach to prediction of laser cutting quality by employing fuzzy expert system, Expert Systems with applications, 38 (6) (2011) 7558-7568. [20] C. Jimin, Y. Jianhua, Z. Shuai, Z. Tiechuan and G. Dixin,

Parametric optimization of non vertical laser cutting, International Journal of Advanced Manufacturing Technology, 33 (2) (2007) 469-473. [21] M. S. Phadke, Quality engineering using robust design, Prentice-Hall, Englewood Cliffs, New Jersey (USA) (1989). [22] P. J. Ross, Taguchi techniques for quality engineering, Tata McGraw-Hill Publishing Company Limited, New Delhi (India) (1996). [23] S. Haykin, Neural networks, a comprehensive foundation, Pearson Education Pte. Limited, Delhi (India) (2002). [24] S. K. Dhara, A. S. Kaur and S. Mitra, An artificial neural network approach on parametric optimization of laser micromachining of die-steel, International Journal of Advanced Manufacturing Technology, 39 (1-2) (2008) 39-46. [25] W. Paszkowicz, Genetic algorithms, a nature-inspired tool: Survey of applications in materials science and related fields, Materials and Manufacturing Processes, 24 (2) (2009) 179197. [26] K. Dev, Optimization for engineering design (Algorithms and examples), PHI Learning, New Delhi, India (2009).

Arun Kumar Pandey has received his M. Tech degree in production from M.I.T.S. Gwalior (RGTU University Bhopal) Madhya Pradesh, India and is now research scholar at M.N.N.I.T. Allahabad, (Uttar Pradesh), India. He has published many papers at reputed International journals and conferences. His area of interest is Laser Material processing, Nonconventional machining and applications of Artificial Intelligence and Design of Experiment techniques in various advanced machining processes. He is reviewer of various reputed international journals and also, life time member of ISTE. Avanish Kumar Dubey has completed B.E. (Production & Industrial Engineering), M.Tech. (CAD/ CAM) and Ph.D. (Mechanical) from MNNIT Allahabad (Uttar Pradesh), India. He has published many papers in various refereed International & National journals and conferences. He is now working as Associate Professor in Mechanical Engineering Department, MNNIT Allahabad (Uttar Pradesh), India. He is life time member of Institution of Engineers (India). His area of interest is Laser Material processing, Nonconventional machining processes, Design of experiment applications in manufacturing processes and applications of Artificial Intelligence in advanced machining processes. He is a member of editorial boards of some refereed international journals and also reviewer of many refereed international journals of repute.