taguchi and multi-objective genetic algorithm-based...

Indian Journal of Engineering & Materials Sciences Vol. 26, June-August 2019, pp. 211-219

Taguchi and multi-objective genetic algorithm-based optimization during ECDM of SiCp/glass fibers reinforced PMCs

Parvesh Antila*, Sarbjit Singhb, Sundeep Kumara, Alakesh Mannab & Nitish Katalb

aCollege of Agricultural Engineering & Technology, CCS HAU, Hisar, Haryana 125001, India bPunjab Engineering College, Chandigarh 160 012, India

Received 3 August 2018; Accepted 17 July 2019

The acceptance of electrically nonconductive fibrous materials has been increased over the past decade in industrial applications due to their better strength to weight ratio and electrically nonconductive nature. But precise machining of these types of materials has always been a challenging task for the research fraternity. The precise machining of these materials refers to reduced overcut along with significant material removal rate (MRR). In such perspective, multi-objective genetic algorithm (MOGA) evident to be suitable optimization technique for prediction and process selection in manufacturing industries. The present paper deals with multi-objective optimization of electrochemical discharge machining (ECDM) process parameters during machining of SiCp and glass fibers reinforced polymer matrix composites (PMCs) using MOGA. The experiments have been designed as per Taguchi’s design of experiments using L16 orthogonal array. Electrolyte concentration, inter-electrode gap, duty factor, and voltage have been used as process parameters whereas MRR and overcut have been observed as output quality characteristics (OQCs). The obtained experimental results have been optimized by multi-response optimization technique MOGA to attain high MRR with minimum possible overcut. The quality of machined holes has been analyzed using scanning electron microscope (SEM). The analysis reveals that result optimized through MOGA produces enhanced output quality characteristics.

Keywords - Electrochemical discharge machining, Level diagrams, Multi-objective genetic algorithm (MOGA), Pareto optimal set, Polymer matrix composites, Taguchi’s methodology

1 Introduction The demand for polymer matrix composites in

manufacturing industries is increasing rapidly due to their better mechanical properties and non-conductive nature. The extensive applications of these composites have motivated researchers to focus on the fabrication of hybrid composites with enhanced mechanical behavior1,2. The composites used in aerospace industries require precise machining operations like drilling for assembly purpose3 but hybrid composites reinforced with abrasive particles deteriorate the machining behavior of composites4. These difficulties in conventional machining of hybrid composite motivate the researchers to develop new hybrid unconventional machining process. Electrochemical discharge machining (ECDM) is unconventional machining process and particularly used for machining of electrically nonconductive materials5. The researchers6,7 explored the various domain of ECDM to enhance the output quality characteristics of

the process. For that purpose, various optimization techniques like Taguchi’s methodology8,9, response surface methodology10, artificial neural network11, grey relational analysis12 etc. have been used by researchers to optimizing single or multi-response behavior of output quality characteristics. The optimal combination of input parameters generates optimized output response. Genetic algorithm is one of the most robust and globally accepted optimization algorithms over several decades and has been applied to multifarious application in almost every domain Genetic algorithm was first used by Holland13 to find out optimal solution of any objective function. The genetic algorithm mimics the phenomenon of natural selection. Due to its ability to provide better solution for surviving, it been extensively used by researchers in various manufacturing domains. Kuwar et al.14 used genetic algorithm during EDM of carbon fibre-based epoxy composites; Yan et al.15 used genetic algorithm along with fuzzy logic controller during wire EDM machining; Rajesh et al.16 used response surface methodology and genetic algorithm optimize

–––––––– *Corresponding author (E-mail: [email protected])

mailto:[email protected])

INDIAN J ENG MATER SCI, JUNE-AUGUST 2019

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EDM process. Sharma et al. used genetic programming along with Taguchi’s methodology to explore porosity of shape memory alloys. Using conventional genetic algorithm, Deb17 introduced the hybrid multi-objective variant of genetic algorithm and termed as Multi-objective genetic algorithm (MOGA). MOGA is a global search algorithm and has ability to find solutions of various diverse problems with non-convex, multi-modal and discontinuous search spaces. Katal et al.18 used MOGA to analyze optimal QFT (quantitative feedback theory) controller and pre filter for buck convertor. Kumar et al.19 used MOGA to optimize process parameters of wire electric discharge machining during machining of high-speed steel. Yusliza et al.20 used multi-objective genetic algorithm during wire electric discharge machining of Ti-48Al intermetallic alloys. 1.1 Motivation for problem formulation

The acceptability of fiber-reinforced composites components is considerably increased in aviation and

automobile industries. However, these components require precise machining operation such as drilling for assembly purpose. The precise drilling is fundamentally required for component’s performance. Keeping this requirement in mind, the problem is formulated in the present research paper. The formulated problem is stated as “optimization of electrochemical discharge machining of PMCs for higher material removal rate and least over cut”. The effect of input process parameters on material removal rate (MRR) and overcut (OC) was optimized using multi-objective genetic algorithm (MOGA). 2 Material and Experimental Planning

The glass fiber reinforced polymer matrix composite with SiC as secondary reinforcement was used for experimentation1. The machining of glass fiber reinforced polymer matrix composite was performed on electrochemical discharge machining (ECDM) setup as shown in Fig. 1. The experiments were planned as per Taguchi’s methodology using L16 orthogonal array. The electrolyte concentration (g/L),

Fig. 1 — (a) Schematic representation of ECDM process and (b) ECDM setup.

Algorithm 1: General structure of the multi-objective genetic algorithm. Input: GA Parameters, Optimization problem Output: Pareto Optimal Set (POS) P begin

t ← _ Initialize Parents G(t) calculate objectives Ji(G), i=1, 2, …, n as per coding routine; Create Pareto P(G); Evaluate the fitness of G; while (termination criteria not satisfied) do use Crossover to create C(t) from G(t); use Mutation to create C(t) from G(t); calculate objectives Ji(C), i=1, 2, …, n as per coding routine; update Pareto frontP(G,C); Evaluate the fitness of (G,C); use Selection for generating G(t+1) from G(t)&C(t); t ←t + 1 end output Pareto optimal set P(G,C)

end

ANTIL et al.: OPTIMIZATION OF ECDM DURING MACHINING OF SiCp/GLASS FIBERS REINFORCED PMCS

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inter-electrode gap (mm), duty factor and voltage (V) used as input process parameters and their experimental range is shown in Table 1. Hardened steel needle of diameter 0.5 mm was used as tool electrode. The sodium hydroxide was used as an electrolyte for experimentation. The material removal rate (mg/min) and overcut (mm) were observed as output quality characteristics. The scanning electron microscope was used to analyze the machined hole quality. 2.1 Optimization using taguchi’s methodology

Taguchi’s methodology is an effective technique used to optimized output quality characteristics (OQCs) influenced by multiple process parameters21. It helps in obtaining a well-adjusted combination of experiments to make experimental design easy and well-organized. The quality of deviation present in OQCs is represented by signal to noise ratio and depends upon the objective function of OQCs. The selection criterion for S/N ratio of material removal rate (MRR) is taken as larger the

better and for over cut (OC), smaller the better. Each experiment was performed three times and average value of OQCs is shown in Table 2. 2.2 Analysis of variance (ANOVA)

ANOVA for material removal rate and overcut during ECDM of SiC/glass fiber reinforced PMCs is shown in Table 3. For material removal rate, P value in case of electrolyte concentration and voltage is less than 0.05 which shows that these process parameters play key role during ECDM process. Electrolyte concentration has major contribution (53.07%)

Table 1 — Process parameters and levels.

Process Parameters Symbol Level 1

Level 2

Level 3

Level 4

Electrolyte Concentration (g/l) E 80 90 100 110 Inter Electrode Gap (mm) I 110 120 130 140 Duty Factor D 0.5 0.66 0.75 0.8 Voltage (V) V 45 50 55 60

Table 2 — Experimental results for OQCs.

Experiment Number

Process Parameters Output Quality Characteristics EC IEG DF V MRR (mg/min) OC (mm)

1 80 110 0.5 45 1.1 0.139 2 80 120 0.66 50 1.286 0.146 3 80 130 0.75 55 1.438 0.149 4 80 140 0.8 60 1.514 0.151 5 90 110 0.66 55 1.528 0.152 6 90 120 0.5 60 1.572 0.165 7 90 130 0.8 45 1.557 0.142 8 90 140 0.75 50 1.611 0.157 9 100 110 0.75 60 1.653 0.159 10 100 120 0.8 55 1.643 0.139 11 100 130 0.5 50 1.586 0.153 12 100 140 0.66 45 1.472 0.147 13 110 110 0.8 50 1.489 0.129 14 110 120 0.75 45 1.474 0.133 15 110 130 0.66 60 1.655 0.158 16 110 140 0.5 55 1.643 0.149

Table 3 — ANOVA for MRR and over cut.

Process Parameters

Material Removal Rate Over Cut DOF SS MS P Value P (%) SS MS P Value P (%)

Eectrolyte Conc. 3 0.172824 0.05760 0.007 53.07 0.00029 0.00009 0.006 20.29 Inter Elecrode Gap 3 0.03865 0.01288 0.050 11.86 0.00012 0.00004 0.023 08.39

Duty Factor 3 0.01831 0.00610 0.143 5.662 0.00032 0.00011 0.006 22.37 Voltage 3 0.09123 0.03041 0.018 28.01 0.00067 0.00022 0.002 46.85

Error 3 0.00460 0.00153 01.41 0.00007 0.00002 04.89 Total 15 0.32563 0.00143

DOF- Degree of Freedom; SS- Sum of Squares; MS- Mean Squares; P(%)- Percentage Contribution


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followed by voltage (28.01%) during ECDM process. Whereas, for over cut, electrolyte concentration, voltage and duty factor lies in significant category as these parameters possess P value less than 0.05. In controlling the overcut during machining, voltage (46.85%) possesses highest contribution followed by duty factor (22.37%) and electrolyte concentration (20.29%).

The significant process parameters as per ANOVA result are found to be electrolyte concentration and a voltage whose plots are plotted along with other process parameters in Fig. 2.The plotted trends show that initially with increase in level of electrolyte concentration, MRR increases but with further increase in electrolyte concentration, there is slightly decrease in MRR. The main reason for this behavior of decrease in MRR at higher concentration is the incremental degree of dissolution efficiency. The degree of dissolution efficiency at high concentration is lesser as compared to low concentration22. As far as voltage is concerned, MRR increases with increase in level of voltage because increase in voltage increases the rate of spark generation in spark zone23. For over cut, electrolyte concentration, voltage and inter-electrode gap are found to be significant parameters. As per the Raw data graph plotted in Fig. 3, the overcut initially increases but then decreases with increase in levels of electrolyte concentration. The reason behind this trend is increase in conductivity of solution. The increased conductivity of the solution results in increased electrochemical reaction as well as circuit current. The available trends for inter-electrode gap show that overcut increases with increase in levels of inter-electrode gap. It is because increase in inter-electrode gap scatters the produced spark over machined surface which makes it difficult to concentrate on specified target. Also from lower to higher level of voltage, overcut increases because high current density is generated at high voltage24. 2.3 Optimization using multi-objective genetic algorithm

Multi-objective genetic algorithm (MOGA) methodology is used to solve a mathematical model in which output quality characteristics are affected by number of process parameters. Duri ng optimization, one objective function is prepared for maximizing MRR and minimizing over cut. Then this function is solved by different combination of mutation, cross-over operator and selection. Crossover operator is used to generating new non-

dominating solutions by exploiting the current good solutions that have not been explored in the current Pareto front. NSGA-II non-dominated sorting is used to assign Pareto rank to each individual and crowding distance assignment is used to estimate the density of the Pareto front. The obtained non-dominated set of solutions i.e. Pareto optimal set has equally optimal solutions and there is no scope of further improvement of any objective without sacrificing the other. The flow chart for MOGA methodology is shown in Fig. 4. Regression equations as shown in equation 1 and equation 2 are further solved by using multi-objective genetic programming. The lower and upper bound of the process parameters are defined in equations 3 to 6.

The basic formulation of the multi-objective problem (for minimization case) is given as:

Fig. 2 — S/N ratio for MRR.

Fig. 3 — S/N ratio for over cut.


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niiiigg

mJJJJ

,,1,,0,0 : subject to

,,2,1min

2.4 Optimal design of ECDM for optimized OQCs

The acceptability of advanced machining process depends on the ability to produce quick and precise results. As the ECDM process is primarily used for machining of nonconductive materials, the high rate of machining along with minimum possible overcut is difficult task to be achieved. In the present work, use of multi-objective genetic algorithm aims at finding Pareto optimal set of solutions that maximize the MRR and minimizes the overcut during machining process. The regression equations obtained for MRR and OC are given as: 퐽 = 푀푅푅 = −0.56575 + 0.007138 ∗ 퐸퐶 + 0.0041775 ∗퐼퐸퐺 + 0.26995 ∗ 퐷퐹 + 0.01326 ∗ 푉 … (1) 퐽 = 푂퐶 = 0.09619 − 0.00017 ∗ 퐸퐶 + 0.000235 ∗퐼퐸퐺 − 0.029 ∗ 퐷퐹 + 0.0011 ∗ 푉 … (2) where EC is electrolyte concentration, IEG is an interelectrode gap, DF is duty factor and V is voltage. The upper and lower bound of the process parameters are provided as: 80 ≤ Electrolyte Concentration ≤ 110 … (3) 110 ≤ Inter Electrode Gap ≤ 140 … (4)

0.5 ≤ Duty Factor ≤ 0.8 … (5) 45 ≤ Voltage ≤ 60 … (6)

The design aims at finding the optimal values of electrolyte concentration, IEG, DF and voltage such that maximum values of MRR are obtained while minimizing the overcut. Mathematically given as:

퐹푖푛푑퐸퐶퐼퐸퐺퐷퐹푉

,푤ℎ푖푐ℎ 푚푎푥(퐽 )

푚푖푛(퐽 )

Subject to

80 ≤ 푬푪 ≤ 110110 ≤ 푰푬푮 ≤ 140

0.5 ≤ 푫푭 ≤ 0.845 ≤ 푽 ≤ 60

The optimization has been carried out in MATLAB and MOGA parameters considered for the optimization are as follows: Population size of 60, tournament-based selection function with a tournament size of 2, crossover fraction of 0.8, constraint dependent mutation function, intermediate crossover, and distance crowding for calculating the density of Pareto front. The Pareto front and the Pareto optimal set of solutions is shown in Figs 5 and 6, respectively. The plot for average distance between individuals is shown in Fig. 7 and it is evident that the diversity in Pareto optimal solutions is maintained throughout the optimization process. The average distance amongst individuals is measured throughout

Fig. 4 — Flow chart for MOGA methodology.


216

the generations to keep a check that diversity is maintained and elitism is controlled. Fig. 8 shows the plot for average spread among the members in the

Pareto front, and act as stopping criteria when the algorithm converges to a Pareto optimal set of solutions. It gives a measure of the movement of Pareto front, when the algorithm converges towards a Pareto optimal set of solutions, the average spread decreases and the optimization process stops. 2.5 Optimal solution selection using level diagrams

After multi-objective optimization using a genetic algorithm, a Pareto optimal set (POS) of solutions have been obtained. There are total 21 solutions obtained as shown in Table 4 and all are Pareto optimal which means it is not possible to improve the MMR without sacrificing the overcut. So, in order to choose the ideal

Fig. 5 — Pareto front between MRR & OC obtained after optimization.

Fig. 6 — Plot for Pareto optimal set of solutions obtained after optimization.

Fig. 7 — Plot for the average distance between individuals.


217

solution from the POS, the use of level diagrams have been explored. Level diagrams provide a clear visualization and evaluation of the Pareto front J*

p. Design objectives Jq() used in th`e optimization process are normalized as shown in equation 7:

Jq Jq - Jq

min

Jqmax - Jq

min , q Î 1, , m … (7)

Where,

ÎÎ

ÎÎ

mJJJJ

mJJJJ

JJJ

JJJ

pmp

pmp

**1

**1

max,,max

andmin,,min

1max

1min

A p-norm J pis applied for each normalized

objective vector J to compute the distance to an ideal solution Jideal=Jmin.

Most commonly used norms are, 1-norm, 2-norm and -norm which can be obtained mathematically as equation 8:

q

m

qq

m

qq JJJJJJ ˆmaxˆ,ˆˆ,ˆˆ

1

22

11

… (8)

Level diagrams provide two-dimensional

representation for each design objective and the decision variable in ordered pairs. The design objectives Jq , J

p and decision variables

l, J p are plotted, such that the solutions have

the y-axis on all the graphs. This aids in the characterization of the inclination of the solution along the Pareto front. In this work, ||⋅||2 (2-norm) has been considered for the estimation of the best parameters that offer maximum MMR and least overcut.

Table 4 — MOGA based optimized MRR and OC.

S. No. EC IEG DF V MRR (mg/min) OC (mm) 1 105.0 135.0 0.75 55.0 1.6794 0.1488 2 107.3216 135.014946 0.799410 55.01118 1.7095 0.14700 3 105.5603 135.013631 0.799296 55.01101 1.6969 0.14730 4 105.0 135.0 0.75 55.0 1.6794 0.14881 5 105.1577 135.00079 0.755468 55.00160 1.6820 0.14863 6 105.3412 135.01366 0.796998 55.00902 1.6947 0.14740 7 108.4051 135.03323 0.7993126 55.01354 1.7174 0.14682 8 108.19108 135.02751 0.7999501 55.01055 1.7159 0.14684 9 105.22023 135.0064 0.7898399 55.00682 1.6919 0.14763 10 109.99960 135.00597 0.7999899 55.01110 1.7288 0.14652 11 106.05324 135.01119 0.7995642 55.01154 1.7005 0.14721 12 106.74132 135.01323 0.7996614 55.01140 1.7055 0.14709 13 108.45640 135.03400 0.7999930 55.01431 1.7179 0.14680 14 108.10525 135.01759 0.7982062 55.00806 1.7148 0.14690 15 105.18484 135.00121 0.7517772 55.00002 1.6812 0.14873 16 105.35084 135.00320 0.7578204 55.00239 1.6841 0.14853 17 107.03155 135.01757 0.7999591 55.00771 1.7076 0.14703 18 106.55547 135.01179 0.7990485 55.00728 1.7039 0.14713 19 106.38712 135.01262 0.7992673 55.00712 1.7028 0.14716 20 107.60949 135.01372 0.7991756 55.00887 1.7115 0.1469 21 105.858165 135.01120 0.7995513 55.00721 1.6991 0.1472

Fig. 8 — Plot for the average spread between individuals.


218

The design objectives of MMR and overcut have been visualized using the level diagram and are shown in Fig. 9. The level diagram for design parameters is shown in Fig. 10. In order to choose the ideal solution, a point has been chosen (marked as Violet Star) which offers the maximum values of MMR and also offers overcut within permissible limits. By using the level diagrams, the ideal solution from the Pareto optimal set, the best values of MRR of 1.72882 and Overcut of 0.14652 can be achieved after setting the values of process parameters EC, IEG, DF and V to 109.9997, 135.00597, 0.7999899 and 55.0111 respectively. The comparative analysis of results obtained through Taguchi’s methodology and multi-objective genetic algorithm has been depicted in Table 5. The comparative analysis shows improvement in MRR and reduction in overcutting by 4.41% and 8.21% respectively by using MOGA approach. The scanning electron microscopic images

of machined hole are shown in Fig. 11. The analysis of the machined surface shows that the hole machined by Taguchi’s methodology have highly irregular surface and contains fibrous residuals. These fibrous residuals influence the assembly function and

Fig. 10 — Visualization of the decision variables using the level diagram.

Table 5 — Comparison of obtained results.

Output Quality Characteristics

Taguchi’s Orthogonal Array Multi-Objective Genetic Algorithm % Deviation Parametric Values Output

Result Optimal Parametric Values Output

Result MRR (mg/min) EC (110); IEG (130); DF

(0.66); V(60) 1.655 EC( 109.999); IEG (135.005); DF (0.799);

V (55.011) 1.728 4.41

Over Cut (mm) 0.158 0.146 8.21

Fig. 9 — Visualization of design objectives of OQCs using the level diagram.


219

increase damage possibilities in components. The hole machined by the MOGA technique have comparatively better inside finishing and reduced irregularities as well as reduced spark affected zone. 3 Conclusions

The multi-objective genetic algorithm was used to optimize the process parameters in the machining of SiCp/glass fibers reinforced polymer matrix composite. Material removal rate and overcut were observed as output quality characteristics. The experimentation was planned as per Taguchi’s design of experiments using L16 orthogonal array. The following conclusions were drawn from the present investigation:

(i) The optimal values for process parameters during ECDM of SiCp/glass fibers reinforced polymer matrix composite was found to be electrolyte concentration( 109.999); inter-electrode gap (135.005); Duty Factor (0.799) and voltage (55.011). The comparative analysis of results shows an increase in material removal rate and reduction in overcut can be attained by using parametric values obtained by MOGA.

(ii) The electrolyte concentration and voltage are found to be significant parameters leading by electrolyte which affects the MRR whereas, in case of overcutting, electrolyte concentration, voltage and duty factor lies in significant category-leading by voltage.

(iii) The quality of the hole generated by Taguchi’s methodology shows widespread spark affected zone in comparison with hole generated by

using MOGA. Also, the matrix cracking and irregularity is comparatively higher in Taguchi methodology based machined hole.

(iv) MOGA can be proficiently used for the multi-objective optimization of electrochemical discharge machining process as improved results can be achieved using this technique.

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Fig. 11 — SEM of machined composite using (a) Taguchi’s methodology and (b) MOGA.

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