Optimization of ECM Process Parameters Using NSGA-II

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Journal of Minerals and Materials Characterization and Engineering, 2012, 11, 931-937

Published Online October 2012 (http://www.SciRP.org/journal/jmmce)

Optimization of ECM Process Parameters Using NSGA-II

Chinnamuthu Senthilkumar1*, Gowrishankar Ganesan1, Ramanujam Karthikeyan2

1Department of Manufacturing Engineering, Annamalai University, Annamalai Nagar, Tamilnadu, India

2Department of Mechanical Engineering, Birla Institute of Technology and Science, Pilani, Dubai

Email: *[email protected]

Received July 1, 2012; revised August 5, 2012; accepted August 15, 2012

ABSTRACT

Electrochemical machining (ECM) could be used as one of the best non-traditional machining technique for machining

electrically conducting, tough and difficult to machine material with appropriate machining parameters combination.

This paper attempts to establish a comprehensive mathematical model for correlating the interactive and higher-order

influences of various machining parameters on the predominant machining criteria, i.e. metal removal rate and surface

roughness through response surface methodology (RSM). The adequacy of the developed mathematical models has also

been tested by the analysis of variance (ANOVA) test. The process parameters are optimized through Nondominated

Sorting Genetic Algorithm-II (NSGA-II) approach to maximize metal removal rate and minimize surface roughness. A

non-dominated solution set has been obtained and reported.

Keywords: Electro Chemical Machining; Metal Removal Rate; Response Surface Methodology; Surface Roughness;

NSGA-II

1. Introduction

Electrochemical machining (ECM) is one of the non-

traditional machining techniques; it can achieve a wanted

shape of a surface using metal dissolution by electro-

chemical reaction and can be applied to metals such as

high-strength, heat-resistant and hardened steel. ECM

has been used in industry for cutting, deburring, drilling

and shaping [1]. In ECM electrical current passes be-

tween the cathode tool and the anode workpiece through

an electrolyte solution. The workpiece is eroded in a way

that can be described by Faraday’s law of electrolysis.

ECM is suitable for the machining of components of

complex shape and high strength alloys, as typically

found in the semiconductors industries [2]. Metal Matrix

Composites (MMC’s) are relatively new class of materi-

als characterized by lighter weight and greater wear re-

sistance than those of conventional materials. These ma-

terials have been considered for use in automobile brake

rotors and various components in internal combustion

engines. The machining of MMCs is very difficult due to

the highly abrasive nature of the reinforcement [3]. Tra-

ditional edged cutting tool machining processes are un-

economical for such materials as the attainable degree of

accuracy and surface finish are quite poor. Machining of

complex shapes in such materials by traditional processes

is still more difficult. To meet these demands, ECM pro-

cesses has now emerged [4]. The present paper, therefore,

emphasizes features of the development of comprehend-

sive mathematical models for correlating the interactive

and higher-order influences of the various machining

parameters on the most dominant machining criteria, i.e.

the metal removal rate and surface roughness phenomena,

for achieving controlled ECM. The investigation into

controlled ECM has been carried out through response

surface methodology (RSM), utilizing the relevant ex-

perimental data as obtained through experimentation.

The adequacy of thedeveloped mathematical models has

also been tested by the analysis of variance test. The

process parameters were optimized using Non-Domi-

nated Sorting Genetic Algorithm-II (NSGA-II) to maxi-

mize MRR and minimize Ra.

2. Experimental Planning

Experiments were conducted on METATECH ECM

equipment. The dimensions of the specimens were 30

mm in diameter and 6 mm in height. The tool was made

up of copper with a square cross section. Electrolyte was

axially fed to the cutting zone through a central hole of

the tool. The electrolyte used for experiment was fresh

NaCl solution, because of the fact that NaCl electrolyte

has no passivation effect on the surface of the job. The

test specimens of LM25 Al/10%SiCp composites were

produced through stir casting. The machining has been

carried out for fixed time interval. The observations were

made by varying predominant process parameters such as

*Corresponding author.

C. SENTHILKUMAR ET AL.

932

applied voltage, electrolyte concentration, electrolyte flow

rate, and tool feed rate. MRR was measured from the

weight loss. The surface roughness of the machined test

specimens was measured using a Talysurf tester with a

sampling length of 10 mm.

3. Response Surface Methodology

Response surface methodology (RSM) is the procedure

for determining the relationship various between process

parameters with the various machining criteria and ex-

ploring the effect of these process parameters on the

coupled responses [5], i.e. the material removal rate and

surface roughness phenomena. In order to study the ef-

fects of the ECM parameters on the above-mentioned

two most important machining criteria, the metal re-

moval rate (MRR) and surface roughness phenomenon

(Ra), a second-order polynomial response surface mathe-

matical model can be developed as follows to evaluate

the parametric effects on the various machining criteria

nn n

uo ii iiiijij

ii ij

Yaax axaxx





 

 



(1)

where Yu is the corresponding response, e.g. the MRR

and Ra created by the various process variables of ECM

parameters. ai represents the linear effect of xi, aii repre-

sents the quadratic effect of xi and aij reveals the lin-

ear-by-linear interaction between xi and xj. The second

term under the summation sign of the polynomial equa-

tion i.e. Equation (1) attributes to linear effects, where as

the third term of the above equation represents the higher

order effects and lastly the fourth term of the above equ-

ation includes the interactive effects of the process pa-

rameters. In the response surface methodology each vari-

able is coded in a manner so that the upper level is taken

as +2 and lower level as −2 for designing the experiment

and the test observations in an optimized way. The actual

and coded parametric values for each parameter are listed

in Table 1.

A well-designed experimental plan can substantially

reduce the number of experiments. For determining the

Table 1. Actual and corresponding coded values for each

parameter.

Levels

Parameters

−2 −1 0 1 2

Electrolyte concentration,

X1 (g/lit) 10 15 20 25 30

Electrolyte flow rate,

X2 (lit/min) 5 6 7 8 9

Applied voltage,

X3 (Volts) 12 13 14 15 16

Tool feed rate,

X4 (mm/min) 0.2 0.4 0.6 0.8 1

equation of the surface integrity, experimental designs

have been developed with an attempt to formulate the

mathematical relations using the smallest number of ex-

periments possible. Keeping in view of the present re-

search objectives, response surface methodology has

been utilized in order to develop the mathematical rela-

tionship between the response, Yu i.e. MRR and surface

roughness and the predominant machining parameters

are electrolyte flow rate, electrolyte concentration, ap-

plied voltage and tool feed rate according to the experi-

mental plan based on central composite rotatable second

order design as shown in Table 2.

Table 2. Different controlling parametric combinations and

test results.

Ex.No. X1 X

2 X

3 X

4 MRR

(g/min)

(µm)

1 −1−1 −1−1 0.124 10.274

2 1 −1 −1−1 0.098 9.952

3 −11 −1−1 0.245 8.752

4 1 1 −1−1 0.278 8.196

5 −1−1 1 −1 0.197 8.851

6 1 −1 1 −1 0.219 8.248

7 −11 1 −1 0.197 9.324

8 1 1 1 –1 0.342 7.724

9 −1−1 −11 0.194 9.247

10 1 −1 −11 0.299 9.987

11 −11 −11 0.249 7.972

12 1 1 −11 0.389 8.131

13 −1−1 1 1 0.482 6.386

14 1 −1 1 1 0.472 6.265

15 −11 1 1 0.529 6.729

16 1 1 1 1 0.656 6.583

17 −20 0 0 0.173 10.925

18 2 0 0 0 0.324 9.647

19 0 −2 0 0 0.214 8.689

20 0 2 0 0 0.299 7.854

21 0

0 −20 0.099 9.548

22 0 0 2 0 0.286 7.136

23 0 0 0 −2 0.299 9.597

24 0 0 0 2 0.721 6.845

25 0 0 0 0 0.227 6.389

26 0 0 0 0 0.287 6.253

27 0 0 0 0 0.295 6.054

28 0 0 0 0 0.245 6.921

29 0 0 0 0 0.268 6.824

30 0 0 0 0 0.226 6.354

31 0 0 0 0 0.289 6.542

C. SENTHILKUMAR ET AL. 933

4. Development of Empirical Models Based

on RSM

After knowing the values of the observed response, the

values of the different regression coefficients of second

order polynomial mathematical equation i.e. Equation (1)

have been evaluated and the mathematical models based

on the response surface methodology have been deve-

loped by utilizing test results of different responses ob-

tained through the entire set of experiments by using a

computer software, MINITAB.14.

On Equation (1), the effects of various machining

process variables on MRR and Ra has been evaluated by

computing the values of different constants of Equation

(1) utilising the relevant experimental data from Table 2.

The mathematical relationship for correlating the MRR

and Ra the considered machining process parameters is

obtained as follows:













34 1

222

234

12 1314

23 2434

MRR

1.65380.0334 X0.0417X

0.3976X 5.0188X0.00008X

0.00002X0.01602X 1.5837X

0.00442 XX0.0004 XX0.01175 XX

–0.00575 XX0.015 XX0.2493 XX,

R 95.77 %

 













(2)













341

222

244

12 1314

2324 34

Ra 150.2250.977X11.29X

12.74X 7.388X0.035X

0.367X0.384X 8.855X

0.0023X X0.031XX0.232X X

0.439X X0.268X X1.983XX

R= 96.05%

 

 









(3)

5. Optimization

To optimize cutting parameters in the machining of

Al/SiCp composites, a non-dominated sorting genetic

algorithm was used. The objectives set for the present

study were as follows:

1. Maximization of the metal removal rate (MRR)

2. Minimization of average surface roughness (Ra)

The two-objective genetic algorithm optimization me-

thod used is a fast, elitist non-dominated sorting genetic

algorithm (NSGA-II) developed by Deb [6]. This algo-

rithm uses the elite-preserving operator, which favors the

elites of a population by giving them an opportunity to be

directly carried over to the next generation [7]. The

NSGA-II is a modified version, which has a better sort-

ing algorithm, incorporates elitism and does not require

the choosing of a sharing parameter a priority. The flow

chart of the NSGA-II is shown in Figure 1.

5.1. Description of NSGA-II Algorithm

The steps involved in the solution of optimization prob-

lem using NSGA-II are as follows.

5.1.1. Population Initialization

The population is initialized based on the problem range

and constraints if any.

5.1.2. Non-Dominated Sort

The initialized population is sorted based on non-domi-

nation. The fast sort algorithm is described as below

- For each individual p in main population P

- Initialize Sp = 0. This set would contain all the indi-

viduals that is being dominated by p.

- Initialize np = 0. This would be the number of indi-

viduals that dominate p.

- For each individual q in P

- If p dominates q then. add q to the set Sp i.e.





SS q

- Else if q dominates p then increment the domination

counter for p i.e. np = np + 1

- If np = 0 i.e. no individuals dominate p then p belongs

to the first front; Set rank of individual p to one i.e

Prank = 1. Update the first front set by adding p to

front one, i.e.,





Fq

- This is carried out for all the individuals in main

population P.

- Initialize the front counter to one, i = 1

- The following is carried out while the ith front is non-

empty i.e. 0



- Q = 0. The set for storing the individuals for (i + 1)th

front.

- For each individual p in front Fi

- For each individual q in Sp (Sp is the set of individuals

dominated by p)

- If nq = nq − 1, decrement the domination count for

individual q.

- If nq = 0 then none of the individuals in the subse-

quent fronts would dominate q.

- Hence set qrank = i + 1. Update the set Q with individ-

ual q i.e. UQQq



- Increment the front counter by one.

- Now the set Q is the next front and hence Fi = Q.

This algorithm is better than the original NSGA [8]

since it utilize the information about the set that an indi-

vidual dominate (Sp) and number of individuals that

dominate the individual (np).

5.1.3. Crowding D i s tance

Once the non-dominated sort is complete the crowding

distance is assigned. Since the individuals are selected

based on rank and crowding distance all the individuals

C. SENTHILKUMAR ET AL.

934

Figure 1. Flow chart of NSGA-II program.

in the population are assigned a crowding distance value.

Crowding distance is assigned front wise and comparing

the crowding distance between two individuals in diffe-

rent front is meaningless (Raghuwanshi et al., 2004). The

crowing distance is calculated as below

- For each front Fi, n is the number of individuals.

- Initialize the distance to be zero for all the individuals

i.e. Fi(dj) = 0,where j corresponds to the jth individual

in front Fi.

- For each objective function m

- Sort the individuals in front Fi based on objective m

i.e. I = sort(Fi,m).

- Assign infinite distance to boundary values for each

individual in Fi i.e.





 and







- For k = 2 to (n – 1)

 

max min

kmIk

Id Idff



 

 

- I(k)·m is the value of the mth objective function of the

kth individual in I

- The basic idea behind the crowing distance is finding

the Euclidian distance between each individual in a

front based on their m objectives in the m dimen-

sional hyper space. The individuals in the boundary

are always selected since they have infinite distance

assignment.

5.1.4. Selection

Once the individuals are sorted based on non-domination

and with crowding distance assigned, the selection is

carried out using a crowded-comparison-operator (αn).

(1) Non-domination rank prank i.e. individuals

The comparison is carried out as below based on

in front

- rank

belong to the same front Fi then Fi(dp) >

urna-

5.1.5. Genetic Operators.

ed Binary Crossover (SBX)

lates the binary cross-

will have their rank as prank = i.

(2) Crowding distance Fi(dj)

p < nq if

prank < q

- Or if p and q

Fi(dq) i.e. the crowing distance should be more.

The individuals are selected by using a binary to

ent selection with crowed- comparison-operator.

Real-coded GA’s use Simulat

operator for crossover and polynomial mutation [8].

1) Simulated Binary Crossover.

Simulated binary crossover simu

er observed in nature and is given as below.



1,1, 2,

111

kkkkk

cpp







 





2,1, 2,

111

kkkk







 





th th

where ci,k is the i child with k component, pi,k is the

selected parent and



k (0) is a sample from a random

number generated havinghe density





if0 1

 







1,if



 



1





This distribution can be obtained from a uniformly

sampled random number u between (0,1).



c is the dis-

tribution index for crossover. That is

 







2uu





 















2) Polynomial Mutation:

is performed by The polynomial mutation





cp pp 

kk kkk

where ck is the child and pk is the parent with pu being

the upper bound on the parent component, l

p is the

lower bound and k is small variation which is calculated

from a polynomial distribution by using



δ21,if0.5

kk k









δ121,if 0.5

kkk







 



rk is an uniformly sampled random number beteen (0,1) w

and m



is mutation distribution index.

C. SENTHILKUMAR ET AL. 935

5.1.6. Recombin ation and Selection

The offspring population is combined with the current

erformed to set

est performance. The parameters are: Prob-

ariance (ANOVA) and the F-ratio test

ed to justify the goodness of fit of the

aining an optimal solution.

points in the pareto solution set. The non-

rresponding objective

generation population and selection is p

the individuals of the next generation. Since all the pre-

vious and current best individuals are added in the popu-

lation, elitism is ensured. Population is now sorted based

on non-domination. The new generation is filled by each

front subsequently until the population size exceeds the

current population size. If by adding all the individuals in

front Fj the population exceeds N then individuals in

front Fj are selected based on their crowding distance in

the descending order until the population size is N. And

hence the process repeats to generate the subsequent

generations.

The control parameters of NSGA–II must be adjusted

to give the b

ility of gross over Pc = 0.9 with distribution index ηc =

20, mutation probability Pm = 0.25 and population size Pz

= 100. It was found that the NSGA-II with those control

parameters produces better convergence and distribution

of optimal solutions located along the Pareto optimal

solutions. The 1000 generations are quite enough to find

the true optimal solutions.

6. Discussion

The analysis of v

have been perform

developed mathematical models. The results of the

analysis of variance are presented in Tabl e 3. The calcu-

lated values of F-ratio for the lack of fit are found to be

lesser than the standard percentage point of F distribution

for 99% confidence limit is 7.87 for MRR and Ra. Also,

values of R2 of regression analysis have been calculated

to test whether data is fitted in the developed model and

these values show that data for each response are fitted in

the developed models. The P-value for the model MRR

and surface roughness is lower than 0.05 (i.e. p= 0.05, or

95% confidence) indicates that the model is considered

to be statistically significant.

A single objective optimization algorithm will nor-

mally be terminated upon obt

owever, for most of the multi-objective problems, there

could be a number of optimal solutions .Suitability of

one solution depends on a number of factors including

user’s choice and problem environment, and hence find-

ing the entire set of optimal solutions may be desired.

Among the Pareto optimal solutions, none of the solu-

tions is absolutely better than any other solution and

hence this solution is called as non-dominated solution

[9]. GAs can find good solutions to linear and nonlinear

problems by simultaneously exploring multiple regions

of the solution space and exponentially exploiting prom-

ising areas through mutation, crossover and selection

operations. In general, the fittest individuals of any po-

pulation are more likely to reproduce and survive to the

next generation, therefore improving successive genera-

tions. Non dominating Sorting GA (NSGA-II) by Deb

and Goel (2002) is of the best methods for generating the

Pareto frontier and is used in this study. The NSGA-II

algorithm ranks the individuals based on dominance. The

fast non dominated sorting procedure allows us to find

the non domination frontiers where individuals of the

frontier set are not dominated by any solution. The crow-

ding distance is calculated for each individual of the new

population. Crowding factor gives the GA the ability to

distinguish individuals that have the same rank. This

forces the GA to uniformly cover the frontier rather than

bunching up at several good points by trying to keep

population diversity. The comparison operator (<n) is

used by the GA to sort the population for selection pur-

poses [10].

The procedure was repeated ten times to get greater

number of

minated solution set obtained over the entire optimiza-

tion process is shown in Figure 2.

This shows the formation of the pareto front leading to

the final set of solutions. The co

nction values and decision variables of this non-domi-

nated solution set are given in Table 4. The 31 out of 100

sets were presented since none of the solutions in the

non-dominated set is absolutely better than any other;

any one of them is an acceptable solution. The choice of

one solution over the other depends on the requirement

of the process engineer. If a better surface finish or a

higher production rate is required, a suitable combination

of variables can be selected from Table 4. From the ex-

perimental results presented in Table 2, the parameters

listed in the experiment number 25 leads to minimum Ra

of 5.021 µm and the corresponding MRR of 0.358

gm/min, where the electrolyte concentration, electrolyte

Figure 2. Optimal chart obtained through NSGA-II for com-

posite Al/10%SiCp composite using NaCl.

C. SENTHILKUMAR ET AL.

936

t results for the developed models.

p-value

Table 3. Analysis of variance tes

Sum of squares Mean sum of squares F-value

Source D.f MRR Ra MRR Ra MRR Ra MRR Ra

Linear 4 0.473 10.668 0.000000 168 25.70.0175 2.4213 15. 0.

Square 4 7. 6 4 0

0.1314 1034 0.0328 .804819.88 4.070.000 .000

teraction6 0.0505 2.4704 0.0084 1.1839 5.10 7.67 0.004 0.001

ack of fi10 0.0211 1.8967 0.0021 0.1896 2.4 1.98

Error 6 0.0052 0.5737 0.0008 0.0956

Total 30 0.6253 62.566

Tableptiminatioarameters for ECM Al/10%Si composite using NaCl.

Sl No. m)

4. Oal combns of pofCp

X1 X

2 X

3 X

4 MRR (g/min) Ra (µ

1 10 6.589 5 16 1.0 0.248

2 10 5 16 1.0 0.240 6.624

3 21 5 16 1.0 1.178 4.733

4 18 5 15 0.9 0.312 6.333

5 13 5 15 1.0 0.517 5.670

6 18 5 15 1.0 1.041 4.805

7 16 5 15 1.0 0.831 5.020

8 15 5 15 1.0 0.764 5.131

9 14 5 15 0.9 0.592 5.478

10 15 5 15 1.0 0.751 5.152

11 11 5 15 0.9 0.391 6.052

12 19 5 15 1.0 1.070 4.785

13 17 5 15 1.0 0.916 4.918

14 16 5 15 1.0 0.786 5.093

15 12 5 15 1.0 0.439 5.897

16 16 5 15 1.0 0.822 5.047

17 13 5 15 1.0 0.553 5.576

18 16 5 15 1.0 0.865 4.979

19 10 5 16 1.0 0.270 6.498

20 15 5 15 1.0 0.732 5.187

21 10 5 16 1.0 0.290 6.420

22 13 5 16 1.0 0.568 5.537

23 14 5 15 0.9 0.618 5.418

24 11 5 16 0.9 0.379 6.092

25 13 5 15 1.0 0.578 5.512

26 12 5 15 1.0 0.421 5.955

27 14 5 15 1.0 0.678 5.292

28 15 5 15 0.9 0.578 5.512

29 19 5 15 1.0 1.143 4.749

30 11 5 15 1.0 0.719 5.152

31 18 5 16 1.0 0.998 4.838

C. SENTHILKUMAR ET AL. 937

Table 5.lidation tesults for Al/1SiCp compositeNaCl.

R (gm/min) Ra (µm

Vat res0% using

MR)

yte

concentration,

gm/lit

ectrolyte

flow rate,

Lit/

plied Tool feed

rate, ed Actual %Error

Electrol El

min voltage, Volts mm/min PredictedActual %ErrorPredict

1 16 15 0.831 0.810 2 5.020 5.131 3 5 1.0

flow rate, d volt ta/li

7 lit/min, 1lts and 0minpectively. By op-

mizing using NSGA-II, the Ra value is very close to the

etween these performances. From

imized by

ted sorting genetic algorithm (NSGA

inated solution set is obtained. The

RR ha usul-

ve oation thod,ominsortinge-

netic algorithm-II. A pareto-optimal set of 100 solutions

in an Air-Lubricated Hydrodynamic Bearing,”

International Journal of Advanced Manufacturing Tech-

nology, Vol. 2726.

doi:10.1007/s0

applieage andool feed rate re 20 gmt, M

4 vo.6 mm/ res

experimental value has been selected from the Table 4,

trail no: 7. The Ra value is 5.020 µm and the corre-

sponding MRR is 0.831 gm/min and the pertinent pa-

rameters are electrolyte concentration, electrolyte flow

rate, applied voltage and tool feed rate are MRR is 0.831

gm/min and the pertinent parameters are electrolyte con-

centration, electrolyte flow rate, applied voltage and tool

feed rate are 16 gm/lit, 5 lit/min, 15 volts and 1.0

mm/min respectively. This indicates that values obtained

from the NSGA-II optimization technique are in close

agreement with the experimental values and more or less

the same parameter settings. In this study, after deter-

mining the optimum conditions and predicting the re-

sponse under these conditions, a new experiment was

designed and conducted with the optimum values of the

machining parameters. Verification of the test results at

the selected optimum conditions for MRR and Ra are

shown in Table 5.

The predicted machining performance was compared

with the actual machining performance and a good agree-

ment was obtained b

e analysis of Table 5, it can be observed that the cal-

culated error is small. The error between experimental

and predicted values for MRR and Ra lie within 2% and

3%, respectively. Obviously, this confirms excellent re-

producibility of the experimental conclusions.

7. Conclusion

The ECM process parameters have been opt

using non domina

II), and a non dom

second order polynomial models developed for MRR and

Ra have been used for optimization. The choice of one

solution over the other depends on the process the engi-

neer. If the requirement is a better Ra or higher MRR, a

suitable combination of variables can be selected. Opti-

mized value obtained through NSGA-II, is 5.020 µm and

the corresponding MRR is 0.831 gm/min and the perti-

nent parameters are electrolyte concentration, electrolyte

flow rate, applied voltage and tool feed rate are 16 gm/lit,

5 lit/min, 15 volts and 1.0 mm/min respectively. Optimi-

zation will help to increase production rate considerably

by reducing machining time. The objectives such as

is obtained.

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