Multi-objective parametric optimization on machining with wire electric discharge machining

ORIGINAL ARTICLE

Multi-objective parametric optimization on machiningwith wire electric discharge machining

Kapil Kumar & Sanjay Agarwal

Received: 27 December 2010 /Accepted: 29 November 2011 /Published online: 21 December 2011# Springer-Verlag London Limited 2011

Abstract The selection of optimum machining conditions,during wire electric discharge machining process, is of greatconcern in manufacturing industries these days. The increasingquality demands, at higher productivity levels, require the wireelectric discharge machining process to be executed moreefficiently. Specifically, the material removal rate needs to bemaximized while controlling the surface quality. Despite ex-tensive research on wire electric discharge machining process,determining the desirable operating conditions in industrialsetting still relies on the skill of the operators and trial-and-error methods. In the present work, an attempt has beenmade to optimize the machining conditions for maximummaterial removal rate and maximum surface finish based onmulti-objective genetic algorithm. Experiments, based onTaguchi’s parameter design, were carried out to study the effectof various parameters, viz. pulse peak current, pulse-on time,pulse-off time, wire feed, wire tension and flushing pressure,on the material removal rate and surface finish. It has beenobserved that a combination of factors for optimization of eachperformance measure is different. So, mathematical modelswere developed between machining parameters and responseslike metal removal rate and surface finish by using nonlinearregression analysis. These mathematical models were thenoptimized by using multi-objective optimisation techniquebased on Non-dominated Sorting Genetic Algorithm-II toobtain a Pareto-optimal solution set.

Keywords WEDM . Taguchi technique .Multi-objectivegenetic algorithm

1 Introduction

Machining processes play a significant role in manufacturingindustry where cost and quality are the main driving forces.Among various manufacturing processes existing today, wireelectrical discharge machining (WEDM) is one of the widelyused processes [1] because of its capability of machiningintricate shapes and profiles irrespective of hardness of thematerial. This process finds widespread applications inmould-making tool and die industries, aerospace, automobileand electronics industries.

The principle of WEDM is shown in Fig. 1. In thisprocess, a small-diameter wire is used as the electrode tocut a narrow width of cut in the workpiece. The workpiece isfed continuously and steadfastly past the wire in order toachieve the desired cutting path. Numerical control is usedfor precise control of the motions during cutting. As it cuts,the wire is continuously advanced between a supply reel anda take-up reel to present a fresh electrode of constant diam-eter to the work. This helps maintain a constant width of cutduring cutting. The dielectric fluid is continuously injectedto flush away minute amounts of the removed material.

One of the most investigated areas of machining isprocess modeling and optimization as these result in bothreduced production cost and improved product quality.However, experimental optimization of any machiningprocess is costly and time consuming due to the com-plex, coupled and non-linear nature of the input–outputvariables of machining processes [2]. This means that,

K. Kumar : S. Agarwal (*)Department of Mechanical Engineering,Bundelkhand Institute of Engineering and Technology,Jhansi 284 128, Indiae-mail: [email protected]

Int J Adv Manuf Technol (2012) 62:617–633DOI 10.1007/s00170-011-3833-1

due to the highly complicated interactions between pro-cess parameters, current analytical models and analysescannot provide accurate process prediction for betterquality control and higher throughput. Therefore, an effi-cient method is needed to determine the optimal machin-ing parameters.

In case of WEDM, the most significant performanceindicators are metal removal rate and surface finish. Metalremoval rate (MRR) is an indicator for productivity whilesurface roughness (Ra) is a measure of work quality.WEDM, being a complex stochastic process, is very diffi-cult to determine optimal machining parameters for bestmachining performance. Moreover, the performance meas-ures, viz. MRR and Ra, are conflicting in nature as it isdesirable to have higher MRR with a lower value of surfaceroughness (or high surface finish).

The overall objective of this research is to apply a modelingand optimization methodology for the highly non-linear andcomplex manufacturing process of WEDM. In this direction,prediction models to estimate MRR and surface finish (SF)were developed from the experimental data. Subsequently, thedeveloped models were used for optimization of the processparameters. As the chosen objectives MRR and SF are

conflicting in nature, the problem was formulated as a multi-objective optimization problem and then a popular evolutionaryalgorithm, Non-dominated Sorting Genetic Algorithm (NSGA-II) was used to retrieve the optimal set of input variables.

2 Literature review

WEDM is a necessary operation in several manufacturingprocesses in some industries, which gives importance to vari-ety, precision and accuracy. Several researchers have attemp-ted to improve the performance characteristics, namely, thesurface roughness, cutting speed, dimensional accuracy andmaterial removal rate, etc., but the full potential utilization ofthis process is not completely solved because of its complexand stochastic nature and higher number of variables involvedin this operation. In order to improve the process performance,experiments were conducted with different steel materials forinvestigating the effects of cutting parameters on surfaceroughness in the WEDM process and practical results can beused in industry in order to select the best suitable parametercombination to get the required surface roughness values forthe products [3]. A semi-empirical model of surface finish of

Pulse Power +

-

Machine controllers such as CNC, Servo, Axis motors, gap etc

Worktable

Upper Wire Guide

WEDM cut

Spool of Wire

Workpiece

Lower Wire Guide

Deionized Water

Nozzle forDielectric supply

Electrode wire

Width of cut

Take up reel

Fig. 1 Schematic diagramof WEDM

618 Int J Adv Manuf Technol (2012) 62:617–633

workpiece in EDM has been established by employing dimen-sional analysis based on pertinent process parameters such aspeak current, pulse duration, electric polarity and properties ofthe work material and then verified by using standard Taguchimethod [4]. After that, a new approach came for the optimi-zation of EDM process with various machining parameters tooptimize the multiple performance characteristics, viz. mate-rial removal rate, surface roughness and electrode wear ratio,and results were found good [5]. Further, the use of the greyrelational analysis (GRA) based on an orthogonal array andfuzzy-based Taguchi method was to be done for optimizingthe multi-response, viz. electrode wear ratio, material removalrate and surface roughness, on EDM process and found thatthe grey relational analysis is more straightforward than thefuzzy-based Taguchi method for optimizing the EDM processwith multiple process responses [6].

The optimization of multiple response characteristic is morecomplex compared to the optimization of single performancecharacteristics [7]. In addition, the optimization of the WEDMprocess of Al2O3 particle-reinforced material (6061 alloy) withmultiple performance characteristics such as surface removalrate and surface roughness, based on grey relational analysis,was to be reported by Chiang and Chang [8]. For furtherimprovement, the optimization of multiple performance char-acteristic indices in the high speed EDM process has beenachieved through proper system model simulation by the ap-plication of a fuzzy logic analysis coupled with Taguchi dy-namic experimental approach [9]. To improve the machiningprecision and accuracy and enhance the speed and stability ofEDMprocess, large discharge current is applied and aluminiumpowder added into the working fluid throughout the experi-ment conducted by using Taguchi dynamic approach coupledwith a proposed ideal function model. The designed tool elec-trode with two basic geometries of square and circle as thedistinct characteristics of workpiece was employed to helpdevelop a versatile process for wider industrial application [10].

In order to predict the surface finish and material removalrate while machining D2 tool steel, Scott et al. [11] devel-oped the empirical models. It was observed that there wasno single combination of levels of the different factors thatcould be optimal under all situations. To locate the optimalmachining parameters, the non-dominated point approachwas applied, using explicit enumeration of all possiblecombinations and the dynamic programming method. Afeed forward neural network methodology [12] was usedto determine the optimal cutting parameters for improvingthe cutting performance measures of machining speed andsurface finish. Response surface methodology and artificialneural networks was used for modeling of WEDM process,which involves modeling of the responses of cutting speed,surface roughness and surface waviness for AISI 420 [13].

An experimental investigation was carried out by Huang et al.[14] to study the effect of machining parameters on gap width,surface roughness and depth of white layer. Ramakrishnan etal. [15] developed a mathematical model with the responsesurface methodology in order to predict the performancecharacteristics of the WEDM process. Hewidy et al. [16]developed mathematical models correlating the variousWEDM machining parameters with metal removal rate, wearratio and surface roughness based on the response surfacemethodology also. Sarkar et al. [17] used a feed forwardback-propagation neural network to model the machiningprocess. Fuzhu Han et al. [18] experimentally investigatedthe influence of machining parameters on surface roughnesstaking brass as the electrode and Cr12 alloy as the workpiece.Ko-Ta Chiang [19] used the response surface methodology toinvestigate the influence of machining parameters on materialremoval rate, electrode wear ratio and surface roughness ofAl2O3+TiC mixed ceramic material.

In order to achieve an accurate estimation for non-linearelectrical discharging and thermal erosion process, Jin-Yuanet al. [20] used the multiple Gaussian process regression tooptimize the high-speed wire EDM process due to its sim-plicity and flexibility identity. To predict and select the bestcutting parameters for the performance characteristics,namely, material removal rate and surface roughness, artifi-cial neural network models were developed using back-propagation algorithms. These performance characteristicswere optimized concurrently using multi-response signal-to-noise ratio in addition to Taguchi’s parametric design ap-proach [21]. The trim cutting operation of WEDM of γ-titanium aluminide has been optimized for a given machiningcondition by desirability function approach and Pareto optimi-zation algorithm. It was observed that the performance of thedeveloped Pareto optimization is superior compared to thedesirability function approach [22].

Literature survey reveals that particular efforts were con-centrated to determine the most accurate models for surfaceroughness and material removal rate. These empirical mod-els were utilized as objective functions and were optimizedto obtain the machining conditions for the required materialremoval rate and the surface roughness. Also, the literaturereview suggests that the most dominant modeling and opti-mization tools used to date were Taguchi-based regressionanalysis, response surface methodology and artificial neuralnetworks. However, the accuracy and possibility of deter-mining the global optimum solution depends on the type ofmodeling technique used to express the objective functionand constraints as functions of the decision variables [23].Therefore effective, efficient and economic utilization ofWEDM process necessitates an accurate modeling and op-timization procedure.

Int J Adv Manuf Technol (2012) 62:617–633 619

In most conventional deterministic approaches such asmultiple regression and response surface methodology, a pre-diction model has to be determined in advance and a set ofcoefficients has to be found. Because of the pre-specified sizeand shape of the models, these are not adequate enough tocapture a complex relation between the influencing variablesand output parameters. Like the said approaches, althoughartificial neural networks have also been used extensively inthe literature for modeling, they have the drawback of notbeing able to explicitly quantify the relationships betweeninputs and outputs.

In this work, the optimization problem of WEDM wasexplicitly formulated as a multi-objective optimization prob-lem as the determination of the optimal machining conditionsinvolves a conflict between maximizing metal removal rateand minimizing the surface roughness (or maximizing thesurface finish). It can be noted that the classical optimizationmethods (weighted sum methods, goal programming, min–max methods, etc.) are not efficient for handling the multi-objective optimization problems because they do not findmultiple solutions in a single run, thereby requiring them tobe applied as many times as the number of desired Pareto-optimal solutions [24]. The above-mentioned difficulty ofclassical optimization methods is eliminated in evolutionaryalgorithms as they can find the multiple solutions in a singlerun. Because of the above, a most commonly used evolution-ary approach, NSGA-II, was used in this paper for multi-objective optimization of WEDM. Genetic algorithm (GA)-based multi-objective optimization methodologies have beenwidely used in the literature to find the Pareto-optimal solu-tions [25–28]. Especially, NSGA-II has proven its effective-ness and efficiency in finding the well-distributed and well-converged sets of near-Pareto-optimal solutions [29]. Themulti-objective optimization methodology adopted in thiswork is depicted in Fig. 2.

The literature review above indicates that most of thestudies have been concentrated on other types of steels. Inrecent years, along with other types of steels, high-speed steel(M2, SKH9) has also emerged as an important material forindustrial applications. Despite extensive research on WEDMprocess, determining the desirable operating conditions duringWEDM of high-speed steel (M2, SKH9), in industrial setting,still relies on the skill of the operators and trial-and-errormethods. So, the determination of the parametric settings thatcan simultaneously optimize multiple responses of wire elec-tric discharge machining of this material is an important issueto the engineers. Therefore, it is imperative to develop a suit-able technology guideline for optimum machining conditionsforWEDMof high-speed steel (M2, SKH9). In addition to this,researchers have usually preferred to apply GRA-basedapproaches for optimizing the multiple responses of WEDMprocess although there exist some other easily comprehendibleand computationally simple approaches for multi-response op-timization. The relative optimization performances of thesemethods are unknown, and therefore there are chances thatthe past researchers on WEDM processes have achieved sub-optimal or near-optimal solutions. So, the aim of the presentwork is to obtain the optimum machining conditions forWEDM of high-speed steel (M2, SKH9) for maximum mate-rial removal rate and maximum surface finish based on multi-objective genetic algorithm. Experiments, based on Taguchi’sparameter design, were carried out to study the effect of variousparameters, viz. pulse peak current, pulse-on time, pulse-offtime, wire feed, wire tension and flushing pressure, on materialremoval rate and surface finish. From the experimental data,multiple regression models for the MRR and surface finish areobtained in the present work. A non-dominated sorted geneticalgorithm has been used to obtain an optimal combination ofparameters and a non-dominated set obtained is reported in thispaper.

Optimization

Identification of input and output

process parameters

Conducting experiments and

recording responses

Model building module

Prediction models of MRR & SF

Multiobjective formulationMaximize MRR

Maximize SF (SF=1/Ra) Subject to feasible bound

of input variables

NSGA-II module

MR

R

SF

Pareto optimal solution set

Model building Fig. 2 Multi-objective optimi-zation methodology


3 Experimentation

3.1 Materials, machine tool and measurement

Wire EDM is a very complicated process consisting ofcomplex interactions between a large numbers of variablessuch as machine tools, workpiece materials and operatingparameters. However, to facilitate experimental data collec-tion, only six dominant factors were considered in the plan-ning of experimentation. A sprint-cut high-precision four-axis CNC wire EDM was used to machine the high-speedsteel (M2, SKH9) pieces of size 230×25×10 mm, havingcut in length with 12-mm depth along the longer length. Thecomposition of high-speed steel (M2, SKH9) workpiecematerial used for experimentation in this work is as givenin Table 1. The parameters, selected for experimentation,were as shown in Table 2, along with their limits, units andnotations. The photographic view of the machine and ma-chining zone has been shown in Fig. 3a, b, respectively. Theother details of experimentation have been shown in Table 3.A 0.25-mm-diameter stratified wire (zinc-coated copperwire) with vertical configuration was used and discardedonce used. High metal removal rate in WEDM without wirebreakage can be attained by the use of a zinc-coated copperwire because the evaporation of zinc causes cooling at theinterface of the workpiece and wire and a coating of zincoxide on the surface of the wire helps prevent short circuits[30]. The two most important performance measures inWEDM are metal removal rate and workpiece surfaceroughness. The material removal rate (g/min) was calculatedby weight difference of the specimen before and after ma-chining using high-precision balance. The surface rough-ness was measured with Talysurf-6 at three differentlocations (at 0.8 μm cutoff value) on the workpiece aftermachining and the average value has been taken in thepresent study.

The resolution of surface roughness measuring instru-ment is 0.8 . This means that the 0.8 is the minimum valueof surface roughness that can be measured by the surfaceroughness measuring instrument. However, the differencesin the readings of surface roughness are much higher thanthe resolution of the surface roughness measuring instru-ment. So, the instrument will be able to distinguish between

the values clearly, and hence measurements made by thisinstrument could be considered as accurate enough for thepresent study. Apart from this, there are sources of error inany measuring system. The term ‘precision’ is often used inthis connection. Perfect precision means that the measure-ments will be made with no random variability in the mea-sured values or the standard deviation of the measuringsystem is zero. So, in order to measure the reproducibilityof the measurements, standard deviations were calculatedfor each set of measurements of the surface roughness. It wasfound that some values of surface roughness are inside onestandard deviation from the experimental mean value whilesome other values need two standard deviations to fit the data.This means that the measured values of surface roughness (asshown in Table 5) have good degree of precision.

3.2 Design of experiment based on Taguchi method

In order to evaluate the effect of cutting parameters of wireEDM process in terms of cutting performance such as surfaceroughness of the machined workpiece and the amount ofmaterial removed, a Taguchi method is used here to modelthe wire EDM process. The Taguchi method has become apowerful tool for the systematic application of design andanalysis of experiments for the purpose of designing andimproving the product quality [31].

Based on literature and experiments, it was revealed that thepulse peak current imposed in conjunction with the pulseduration (A×B), the pulse peak current imposed in conjunctionwith the pulse-off time (A×C) and the pulse peak currentimposed in conjunction with flushing pressure (A×F) affectthe MRR and SF in the WEDM process. Therefore, the inter-action effect of these parameters was considered for examina-tion of the MRR and SF.

According to Taguchi-based methodology, the characteristicthat a larger value represents better machining performance,such as MRR, is called the-larger-the-better type of problem.On the other hand, the characteristic that a smaller value

Table 1 Chemical composition of high-speed steel (M2, SKH9) usedin experimentation

Material C Si Mn Cr W V Mo Fe

(M2,SKH9)

0.80% 0.40% 0.40% 4.30% 6.5% 2.0% 5.0% Balance

Table 2 Setting of levels for control factors

Control factors Symbols Unit Levels

I II III

Pulse peak current A A 10 20 30

Pulse duration B μs 21 29 37

Pulse-off time C μs 50 56 62

Wire feed D m/min 7 8 9

Wire tension E g 1,020 1,140 1,260

Flushing pressure F kg/cm2 2.1 2.5 2.9


indicates better machining performance, such as surface rough-ness, is addressed as the-smaller-the-better type of problem.The S/N ratio, i.e. η, can be calculated as shown below:(a) Forthe-larger-the-better type of problems:

S N= ratio ¼ η ¼ �10 log1

n

Xni¼1

1

y2MRR

!ð1Þ

(2) For the-smaller-the-better type of problems:

S N= ratio ¼ η ¼ �10 log1

n

Xni¼1

y2SR

!ð2Þ

where yMRR and ySR denote the response for metal removal rateand surface roughness, respectively, and n denotes the numberof trials in each experiment.

The standard linear graph is modified using the lineseparation method, as shown in Fig. 4, to assign the factorsand interactions to various columns of the orthogonal array[31]. The array chosen was L27, which have 27 rowscorresponding to the number of experiments, with 13 col-umns at three levels as shown in Table 4. The factors andtheir interaction are assigned to the columns by modifyingthe standard linear graph. The unassigned, truly empty col-umn in orthogonal array represents an estimate of errorvariation. The experiments were conducted for each combi-nation of rows (factors) as per selected L27 orthogonal arrayand the results were presented in Table 5. Figure 5 showssome of the typical scanning electron microscope (SEM)observations of the wire EDM machined surface underdifferent machining conditions.

Surface morphology plays an important part in under-standing the characteristics of machined surfaces. During

DISPLAY SCREEN

POWER ON/OFF

KEY BOARD

WIRE FEED SPOOL

WORK HEAD

WORK TANK

LOWER NOZZLE

UPPER NOZZLE

WORKPIECE

a

b

Fig. 3 a Photographic view ofthe machine. b Photograph ofmachining zone


WEDM process, the discharged energy produces very hightemperatures at the point of the spark, causing a minute partof the specimen to melt and vaporize. With each discharge, acrater is formed on the machined surface. The surface mor-phology is a function of many parameters such as pulsedcurrent, pulse-on time, etc. SEM was conducted in order toevaluate the effect of machining parameters on the surfacetextures of the high-speed steel (M2, SKH9). Figure 5shows the two-dimensional SEM image of the machinedsurface obtained from the WEDM specimens. The darkercontrast corresponds to the lower areas of surface and thebrighter corresponds to the higher. It is clear that the mor-phology of the WEDM surface was dependent on the settingof the machining parameters such as applied pulsed peakcurrent, pulse-on duration, etc. Moreover, the WEDM sur-faces abound with the craters and ridged surfaces. Thecraters and ridge-rich surfaces were formed by melted ma-terial, which was blasted out of the surface by the dischargepressure, and subsequently quickly reached solidification tem-perature through being cooled by the surrounding workingfluid.

In the present investigation, the SEM photographs aretaken for those machined workpieces which give better resultsin terms of material removal rate and surface roughness. Thenumbers a, c and e in the SEM photographs corresponding toexperiment numbers 1, 15 and 23 (Table 5) show the desiredsurface roughness. Similarly, the numbers b, d and f in theSEM photographs corresponding to experiment numbers 13,16, 25 (Table 5) show the desired MRR. Looking at Table 5,the ascending order of SR is obtained from experiment numb-ers 23, 15 and 1, respectively, and the descending order ofMRR is obtained from experiment numbers 25, 13 and 16,respectively. SEM micrographs indicate that a foamy andporous layer is formed after machining. The foamy structureis caused by the generation of many gas bubbles duringmachining; the generations of bubbles are clearly visible.These effects are related to the oxidation and/or decomposi-tion of HSS induced by the thermal energy (temperature10,000–12,000°C during sparking) of the WEDM process.The oxidation and decomposition of HSS generate a largeamount of gas responsible for the porous structure of themachined surface. Further, the oxidation and/or decomposi-tion reactions may increase the material removal rate of HSSby WEDM process in de-ionized water.

Many spark-induced craters and melt formation dropletsexist in these micrographs. The WEDMed surface at lowlevel of pulse-off time is shown in the micrograph of exper-iment no. 1 (Fig. 5a). This revealed that, at lower pulse-offtime, more number of discharges in a given time duringmachining led to an increase in cutting rate, resulting tolarge craters and micro-damage on the surface. The forma-tion of the craters in the WEDMed surface is also due tosparks that form at the conductive phase, generating meltingor possible evaporation. It is obvious that large crater sizesresult in a rough surface. The moderate level of pulse-offtime and higher level of pulse peak current was used inexperiment no. 23 (Fig. 5e), which shows appropriatenessfor producing higher surface finish. The observations sug-gest that WEDM processing at a lower level of pulse-offtime and a lower level of pulse peak current, in the sameexperiment, can damage the surface integrity, resulting inlarge craters and micro-cracks.

The WEDMed surface at high level of pulse-on time isshown in the micrograph of experiment no. 25 (Fig. 5f).This revealed that, at higher pulse-on time, more dischargeenergy, which subsequently causes a more powerful explo-sion and results in deep craters on the surface of the work-piece. Deep craters indicate high rates of metal removal andpoor surface finish. On the contrary, experiment no. 13(Fig. 5b) shows decrease in MRR with the increase inpulse-on time. This happens as the discharge currentdecreases and a smaller amount of material is removed. Itis desirable to use higher values of pulse-on time to obtainhigher rates of metal removal. The moderate level of pulse-

1(A)

2(B)

5(C)

3, 4

6, 7

9, 10

• • • 11(D) 12(E) 13

8(F)

Fig. 4 Modified liner graph for L27

Table 3 Fixed parameters

Wire Zinc-coated copper wireof diameter 0.25 mm

Shape and size of workpiece Rectangular piece of230×25×12 mm3

Location of workpiece on working table At the centre of the table

Angle of cut Vertical

Pulse peak voltage 12 V

Spark gap voltage 20 V

Servo Feed 2,150 (mm/min)

Cutting Speed (%) 100

Dielectric fluid Deionized water

Temperature of dielectric 28°C

Conductivity of dielectric fluid 20 mho


on time and lower level of pulse peak current used inexperiment no. 13 (Fig. 5b) provide less energy to thesurface during machining, resulting in moderate surfaceroughness and hence lower MRR.

4 Results and discussion

The first step in data analysis of the present study is tosummarize the test results for each experiment performedby the use of Taguchi’s L27 orthogonal array. The S/N ratiosare then computed in each of the 27 trial conditions, and thevalues, the average of each parameter at different levels, areshown in Table 5. The response graphs are shown for S/Nratio for MRR and SF in Fig. 6. The S/N ratio analysis(Fig. 6) suggests that the factors at levels A3, B2, C1, D3,E1 and F3 are the best levels that give the maximum MRR.Similarly, the factors at levels A2, B1, C1, D1, E2 and F1

are the best levels that give maximum SF. It must be notedthat the above combination of factorial levels for both per-formance characteristics was not one of the 27 combinationstested for the experimentation. This was expected becauseof the multi-factorial nature of the experimental designemployed.

Figures 7 and 8 show the interaction effect of parametersfor MRR and SF, respectively. It could be seen from Fig. 7that high MRR can be achieved by considering the interac-tion between level A3 and levels F1, A3 and B3 and levelA3 and level C1. From Fig. 7, maximum SF can be achievedby considering the interaction between level A1 and levelF3, level A1 and level B1 and level A1 and level C3. It isinteresting to note that the optimal settings of parameters forMRR and SF are quite different and pose difficulty inachieving the goals of all objectives.

It could be seen from Fig. 6 and the S/N ratio response thatthe priority levels of significant factors, for performance

Table 4 Orthogonal array for L27 Taguchi design

L27 1, A 2, B 3 (A×B)1 4 (A×B)2 5 C 6 (A×C)1 7 (A×C)2 8, F 9 (A×F)1 10 (A×F)2 11, D 12, E 13

1 1 1 1 1 1 1 1 1 1 1 1 1 1

2 1 1 1 1 2 2 2 2 2 2 2 2 2

3 1 1 1 1 3 3 3 3 3 3 3 3 3

4 1 2 2 2 1 1 1 2 2 2 3 3 3

5 1 2 2 2 2 2 2 3 3 3 1 1 1

6 1 2 2 2 3 3 3 1 1 1 2 2 2

7 1 3 3 3 1 1 1 3 3 3 2 2 2

8 1 3 3 3 2 2 2 1 1 1 3 3 3

9 1 3 3 3 3 3 3 2 2 2 1 1 1

10 2 1 2 3 1 2 3 1 2 3 1 2 3

11 2 1 2 3 2 3 1 2 3 1 2 3 1

12 2 1 2 3 3 1 2 3 1 2 3 1 2

13 2 2 3 1 1 2 3 2 3 1 3 1 2

14 2 2 3 1 2 3 1 3 1 2 1 2 3

15 2 2 3 1 3 1 2 1 2 3 2 3 1

16 2 3 1 2 1 2 3 3 1 2 2 3 1

17 2 3 1 2 2 3 1 1 2 3 3 1 2

18 2 3 1 2 3 1 2 2 3 1 1 2 3

19 3 1 3 2 1 3 2 1 3 2 1 3 2

20 3 1 3 2 2 1 3 2 1 3 2 1 3

21 3 1 3 2 3 2 1 3 2 1 3 2 1

22 3 2 1 3 1 3 2 2 1 3 3 2 1

23 3 2 1 3 2 1 3 3 2 1 1 3 2

24 3 2 1 3 3 2 1 1 3 2 2 1 3

25 3 3 2 1 1 3 2 3 2 1 2 1 3

26 3 3 2 1 2 1 3 1 3 2 3 2 1

27 3 3 2 1 3 2 1 2 1 3 1 3 2


characteristic MRR, are as follows: A, C, B, A×B, A×C, E,A×F, D and F. Similarly, the priority levels of significantfactors, for performance characteristic SF (Fig. 6) and the S/Nratio response, are as follows: A, C, B, A×C, A×B, D, E, A×Fand F. It could also be seen from Figs. 6 and 7 that factors A, Cand B are the most significant factors for both performancecharacteristics, MRR and SF, whereas factor F is a less signif-icant factor but its interaction with factor A gives considerableeffect on the objective performance characteristic.

In order to study parameter significance, ANOVAwas per-formed as shown in Tables 6, 7, 8 and 9. However, the F-valueshave been estimated in Tables 7 and 9, considering the poolederror and the corresponding pooled sum of squares. FromTables 6 and 7, it could be seen that the pulse current (A),pulse-on time (B), pulse-off time (C) and interaction effect offactor ‘A’ and factor ‘F’ significantly affects the variability in

MRR of 50.08%, 16.31%, 17.98% and 9.70%, respectively.Similarly, from Tables 8 and 9, it could be seen that the pulsecurrent (A), pulse-on time (B), pulse-off time (C), wire feed (D)and interaction effect of factor ‘A’ and factor ‘F’ are factorssignificantly affecting the variability in SF of 29.85%, 27.05%,29.11%, 4.08% and 7.04%, respectively.

5 Confirmation experiments

Conducting a confirmation experiment is a crucial, final andindispensable part of the Taguchi method. Its aim, afterselecting the optimal parameters, is to predict and verifythe improvement of the performance characteristics with theselected optimal machining parameters, i.e. to verify theoptimum condition suggested by the matrix experiment

Table 5 Experimental design using L27 orthogonal array

Experimentnumber

A B C D E F MRR (g/min) S/N ratio(dB)

Ra (μm) S/N ratio(dB)

Trial 1 Trial 2 Trial 3 Averagevalue

Trial1

Trial2

Trial3

Averagevalue

1 1 1 1 1 1 1 0.1862 0.2001 0.2098 0.1987 −14.036 1.42 1.73 1.59 1.58 96.036

2 1 1 2 2 2 2 0.1785 0.1958 0.1927 0.1890 −14.470 1.61 1.58 1.46 1.55 96.193

3 1 1 3 3 3 3 0.1811 0.1760 0.1937 0.1836 −15.200 1.41 1.58 1.54 1.51 96.420

4 1 2 1 3 3 2 0.2163 0.2033 0.2101 0.2099 −14.722 1.59 1.69 1.64 1.64 95.703

5 1 2 2 1 1 3 0.1869 0.2089 0.2012 0.1990 −13.5597 1.53 1.70 1.63 1.62 95.8096

6 1 2 3 2 2 1 0.2012 0.1644 0.1801 0.1819 −13.9837 1.51 1.73 1.53 1.59 95.9720

7 1 3 1 2 2 3 0.2288 0.1973 0.2330 0.2197 −14.8033 1.60 1.77 1.58 1.65 95.6503

8 1 3 2 3 3 1 0.1998 0.2122 0.2087 0.2069 −13.56803 1.59 1.83 1.50 1.64 95.703

9 1 3 3 1 1 2 0.1912 0.2129 0.1917 0.1986 −14.0404 1.60 1.71 1.55 1.62 95.896

10 2 1 1 1 3 1 0.3631 0.3223 0.3463 0.3439 −9.27135 2.66 1.42 1.66 2.58 91.7626

11 2 1 2 2 1 2 0.3498 0.3412 0.3008 0.3306 −9.61394 2.39 2.66 2.66 2.57 92.2321

12 2 1 3 3 2 3 0.229 0.3479 0.3480 0.3396 −9.380646 2.63 2.71 2.46 2.60 91.700

13 2 2 1 3 2 2 0.3592 0.3418 0.3682 0.3564 −9.322017 2.93 2.64 2.71 2.76 91.1818

14 2 2 2 1 3 3 0.3512 0.3401 0.3548 0.3487 −9.15096 2.81 2.69 2.72 2.74 91.2449

15 2 2 3 2 1 1 0.3393 0.3462 0.3402 0.3419 −9.3220 2.84 2.59 2.85 2.76 91.1818

16 2 3 1 2 1 3 0.3441 0.3596 0.3562 0.3533 −9.0371 2.92 2.77 2.83 2.84 90.9336

17 2 3 2 3 2 1 0.3622 0.3536 0.3603 0.3587 −8.90537 2.72 2.80 2.91 2.81 91.0258

18 2 3 3 1 3 2 0.3312 0.3633 0.3354 0.3433 −9.28652 2.70 2.70 2.82 2.74 91.2449

19 3 1 1 1 2 1 0.5402 0.5022 0.4996 0.5140 −5.7807 3.66 3.86 3.85 3.79 88.1780

20 3 1 2 2 3 2 0.5329 0.5146 0.5185 0.5220 −5.64658 3.88 3.71 3.84 3.81 88.4043

21 3 1 3 3 1 3 0.5055 0.5293 0.5036 0.5128 −5.81039 3.81 3.90 3.78 3.83 88.3360

22 3 2 1 3 1 2 0.5961 0.5669 0.5884 0.5838 −4.67471 3.84 3.99 3.87 3.90 88.1787

23 3 2 2 1 2 3 0.5683 0.5885 0.5748 0.5772 −4.77347 3.94 3.78 3.80 3.84 88.31337

24 3 2 3 2 3 1 0.5921 0.5633 0.5588 0.5714 −4.86119 3.69 3.99 3.81 3.83 88.3360

25 3 3 1 2 3 3 0.6012 0.5986 0.6250 0.6066 −4.34195 3.87 4.21 3.89 3.99 87.9805

26 3 3 2 3 1 1 0.5812 0.6123 0.5678 0.5871 −4.62575 4.12 3.99 3.56 3.89 88.2010

27 3 3 3 1 2 2 0.5633 0.5853 0.5977 0.5721 −4.85056 3.93 3.77 3.79 3.83 88.33602


estimating how close the respective predictions are with thereal ones. The predicted S/N ratio for metal removal rate and

surface finish can be calculated with the help of the follow-ing prediction equations:

bη1 ¼ M þ A3 �M� �þ B3 �M

� �þ A3B3 �M� �� A3 �M

� �� B3 �M� �� þ C1 �M

� �þ A3C1 �M� �� A3 �M

� �� C1 �M� �� þ D1 �M

� �þ E1 �M� �þ F3 �M

� �þ A3F1 �M� �� A3 �M

� �� F3 �M� �� ð3Þ

bη2 ¼ M þ A1 �M� �þ B1 �M

� �þ A1B1 �M� �� A1 �M

� �� B1 �M� �� þ C3 �M

� �þ A1C3 �M� �

� A1 �M� �� C3 �M

� �h iþ D3 �M� �þ E3 �M

� �þ F3 �Mð Þ

þ A1F3 �M� �� A1 �M

� �� F3 �M� �� ð4Þ

where bη1and bη2 are the predicted average of MRR and SFrespectively, M is the overall experimental average,A3;B3;C1;D1;E1;F3 and A1;B1;C3;D3;E3;F3 are themean response of factors for MRR and SF, respectively.

After solving the above equations, new combinations offactor levels A3 B3 C1 D1 E1 F3 and A1 B1 C3 D3 E3 F3were obtained that can be used to predict MRR and SFthrough prediction equations.

a

e

b

c d

f

10 m

10 m 10 m

3 m 10 m

3 m

Fig. 5 Typical SEM micrographsshowing the wire EDM cut surfa-ces observed under different ma-chining conditions. a A: 10 A, B:21 μs, C: 50 μs, D: 7 m/min, E:1,020 g, F: 2.1 kg/cm2; bA: 20 A,B: 29 μs, C: 50 μs, D: 9 m/min, E:1,140 g, F: 2.5 kg/cm2, c A: 20 A,B: 29 μs, C: 62 μs, D: 8 m/min, E:1,020 g, F: 2.1 kg/cm2; dA: 20 A,B: 37 μs, C: 50 μs, D: 8 m/min, E:1,020 g, F: 2.9 kg/cm2, e A: 30 A,B: 29 μs, C: 56 μs, D: 7 m/min, E:1,040 g, F: 2.9 kg/cm2; f A: 30 A,B: 37 μs, C: 50 μs, D: 8 m/min, E:1,260 g, F: 2.9 kg/cm2


Experiments were performed three times with each com-bination of different factors for both performance character-istics and average values were compared with the resultobtained from the predicted equations as shown in Table 10.Figure 9 shows the SEM results of the confirmation experi-ments. It can be interpreted from Table 6 that the obtainedMRR and SF have reasonable accuracy for the resultingmodel because an error of 3.42% for S/N ratio of MRRand 3.96% for S/N ratio of SF were measured. However,the obtained errors can be further alleviated if the number ofmeasurements for each experiment is increased. This vali-dates the development of a mathematical model for predict-ing the measures of performance based on knowledge ofinput parameters.

6 Multi-objective optimization of machining parameters

In any machining process, a mathematical model has tobe developed, relating the machining output to the ma-chined parameters and used for prediction, process con-trol or optimization [15]. In order to evaluate the effectof cutting parameters of WEDM process in terms ofcutting performance such as surface finish of the ma-chined workpiece and the amount of material removed,Taguchi method was applied to model the WEDM pro-cess. Based on the analysis, the optimal parameters andtheir interaction effects are selected and the mathemati-cal equations are conformed for each performance char-acteristic to suitable coefficients. These coefficients are

96

94

92

90

88

A1 A2 A3 B1 B2 B3 C1 C2 C3 D1 D2 D3 E1 E2 E3 F1 F2 F3

Mea

n of

S/N

rat

ios

(d

B)

for

SF

A1 A2 A3 B1 B2 B3 C1 C2 C3 D1 D2 D3 E1 E2 E3 F1 F2 F3

-5

-7.5

-10

-12.5

-15

Mea

n of

S/N

rat

ios

(d

B)

for

MR

R

Fig. 6 Graphical representation of wire EDM factor effects

C1C2C3

c

-15

B1B2B3

b

S/N

rat

io (

dB)

-15

-12.5

-10

-7.5

F1F2F3

a

A1 A2 A3 A1 A2 A3 A1 A2 A3

Fig. 7 Interaction effects of a pulse current (A) and flushing pressure (F), b pulse current (A) and pulse-on time (B) and c pulse current (A) andpulse-off time (C) on MRR


called the model constants. The development of mathe-matical models followed by optimization is essential todetermine the machine settings that will satisfy multipleobjectives of maximization of metal removal rate andsurface finish.

The mathematical model can be written here in the fol-lowing form.

Y ¼ K0 þ K1 � Aþ K2 � Bþ K3 � C þ K4 � D

þ K5 � E þ K6 � F þ K7 � A� Bþ K8 � A

� C þ K9 � A� F ð5Þ

Here, Y0performance output term (MRR, SF)K0Ki (i 00, 1, 2………9) are the model constants.The values of these constants can be calculated by using

non-liner regression analysis method with the help of

MINITAB software. The calculated coefficients are substi-tuted in Eq. (5) and the following relations are obtained:

MRR ¼ �1:2� 102 � 2:94� 10�2Aþ 1:64� 10�2B

� 1:78� 10�3C � 5:5� 10�3Dþ 9:56

� 10�2E � 3:29� 10�1F þ 5� 10�4AB

� 6:96� 10�4AC þ 2:83� 10�2AF ð6Þ

SF ¼ 0:442� 10�2 þ 0:16� 10�2A� 0:136

� 10�1Bþ 0:958� 10�2C þ 0:143� 10�1D

� 0:350� 10�1E þ 0:120F þ 0:413� 10�3AB

þ 0:152� 10�3AC � 0:144� 10�1AF ð7ÞThe correlation coefficients (r2), calculated for both

Eqs. 6 and 7, are found to be 0.984 and 0.982, respectively.The higher correlation coefficient (r2) confirms the suitabil-ity of the developed model and the correctness of the calcu-lated constants [31].

The developed mathematical models are optimized byusing NSGA-II. It is an elitist NSGA-II which has the

C1C2C3

B1B2B3

88

90

92

94

96

F1F2F3

A1 A2 A3 A1 A2 A3 A1 A2 A3

S/N

rat

io (

dB)

a b c

Fig. 8 Interaction effects of a pulse current (A) and flushing pressure (F), b pulse current (A) and pulse-on time (B) and c pulse current (A) andpulse-off time (C) on SF

Table 6 ANOVA for S/N ratios for MRR

Factor DOF SS V F-ratio

A 2 234.762 117.381 45.514a

B 2 77.683 38.841 15.06a

C 2 85.400 42.700 16.556a

D 2 1.884 0.942 0.17

E 2 5.021 2.510 0.97

F 2 2.299 1.149 0.45

A×B 4 24.170 6.043 2.343

A×C 4 11.050 2.7625 0.10

A×F 4 48.690 12.173 4.719

Residual error 2 5.158 2.579

Total 26 496.117

aF0.10; 2; 209.0, F0.10; 4; 204.32

Table 7 S/N ratio of MRR pooled ANOVA

Factor DOF SS V F-ratio P×100%

A 2 234.762 117.381 136.25a 50.08

B 2 77.683 38.841 45.08a 16.31

C 2 85.400 42.700 49.58a 17.98

A×F 4 48.690 12.173 14.13a 9.70

Residual error 22 18.955 0.8615 – 5.92

Total 26 465.49 – – 100

aF0.10; 2; 22 02.56, F0.10; 4; 22 02.22


features required for a good multi-objective genetic algo-rithm. The reason for using NSGA-II for WEDM is that,being a complex machining process, it is very difficult todetermine optimal parameters for improving machining per-formance. In addition to this, there is no single optimalcombination of machining parameters as the influences ofthe parameters on the metal removal rate and the surfacefinish is quite the opposite. In single-objective optimization,one attempt to obtain the best decision is usually the globalminimum or maximum, depending on the optimizationproblem. In case of multiple objectives, there may not existone solution, which is the best with respect to all objectives.In WEDM process, it is difficult to find a single optimalcombination of parameters for both metal removal rate andsurface finish as the parameters influence them differently.Hence, there is a need for a multi-objective optimizationmethod to arrive at the solutions to this problem. Variousclassical methods of obtaining the solutions to multi-objective problems are available. Some examples are min–max, weighted sum and distance function methods. Thesemethods change the multi-objective problem into a single

objective with the corresponding weights based on theirrelative importance. These methods suffer from a drawbackthat the decision-maker must have a thorough knowledge ofranking of objective functions. Also, these methods failwhen the objective functions become discontinuous. GApossesses advantages in that it does not require any gradientinformation and inherent parallelism in searching the designspace, thus making it a robust adaptive optimization tech-nique [32]. For multi-objective optimization methods likeNSGA, some modification to simple GA is necessary. Thus,the primary goal here is the determination of optimumconditions that result in maximum material removal ratewithout significantly decreasing the surface quality of themachined components. The problem of optimization of thewire EDM process can be described as maximizing theMRR and SF subject to a criterion of set of constraints oninput variables. So, in order to optimize the present problemusing NSGA-II:

(a) The following parameters were specified based on thestudy to get optimal solutions with low computationaleffort:

1. Maximum number of generations01002. Total population size0503. Mutation probability00.254. Crossover probability00.8

The basis of specifying the three fundamental GA attrib-utes, namely, population size (ps), crossover probability (pc)and mutation probability (pm), was based on the results from alarge number of optimization runs, as well as the examinationof those commonly used values and the characteristics of thecurrent optimization problem. In order to determine the pop-ulation size, a large number of optimization runs was made.The results of the optimization showed that the objectivefunction value reaches its maximum value for a populationsize of 50. With further increase in the population size, noappreciable change in the value of objective function wasobserved. Hence, a population size of 50 has been taken inthis work. Crossover rate should generally be high because thecrossover probability is a control parameter. In order to deter-mine the crossover probability for this work, five differentvalues of crossover probability—0.5, 0.6, 0.7, 0.8, and 0.9—have been tried out. The results of the optimization show thatthe 0.8 crossover rates produce faster initial convergence, andhence a crossover rate of 0.8 has been chosen in this study.The mutation rate affects the optimization result in the sensethat too small a mutation rate (e.g. 0) may lead to a localoptimum, while too big a value (e.g. 1) may lead to randomsearch. Hence, mutation rate is taken as 0.25 in order to avoidstopping GA at a local optimum.

Implementation of the aforementioned three operators con-stitutes one generation. After each generation, the average

Table 8 ANOVA for S/N ratios for SF

Factor DOF SS V F-ratio

A 2 98.4149 49.2074 36.62a

B 2 90.6822 45.3411 33.74a

C 2 97.5601 48.7800 36.30a

D 2 14.3709 7.18545 5.348a

E 2 2.0597 1.02905 0.769

F 2 1.7354 0.86772 0.645

A×B 4 3.5642 0.89105 0.663

A×C 4 9.4872 2.37180 1.765

A×F 4 24.9840 6.24600 4.648a

Residual error 2 2.687 1.3435

Total 26 345.545

aF0.10; 2; 2 09.0, F0.10; 4; 2 04.32

Table 9 Pooled error variance ANOVA for SF

Factor DOF SS V F-ratio P×100%

A 2 98.4149 49.2074 124.47a 29.85

B 2 90.6822 45.3411 114.96a 27.05

C 2 97.5601 48.7800 123.68a 29.11

D 2 14.3709 7.18545 18.219a 4.08

A×F 4 24.9840 6.24600 15.837a 7.04

Residual error 16 6.3102 0.39438 – 3.32

Total 26 332.32 – – 100

aF0.10; 2; 16 02.67, F0.10; 4; 16 02.33


values of the objective function of the new population will bekept as the performance index (PI). The best solution will bekept as the elitist performer. Elitism is used to keep the bestsolution from the old population into the new population.Three criteria are used to terminate the GA. The first is im-provement criterion based on PIs of each generation. With thiscriterion, the algorithm will stop if PIs of two consecutivegenerations have no significant improvement. The secondcriterion is based on the number of new solutions identifiedwithin a generation, called ‘no new solution criterion’. If therehas been no new solution for consecutively two generations,then the search process is stopped. The third criterion is on thebasis of the number of generations called ‘generation numbercriterion’. If the above two criteria have not been satisfied, thenthe search process also terminates at a set number of gener-ations. The number of generations has been taken as 100because it has been observed that, for the formulated optimi-zation problem, a larger number of generation size, such as 100or even larger, improves the optimization results marginally.

(b) Objective functions: maximize MRR and Maximizesurface finish {SF01/surface roughness (Ra)}, subjectto the following constraints:

Amin � A � Amax;Bmin � B � Bmax;Cmin � C

� Cmax;Dmin � D � Dmax;

Emin � E � Emax and Fmin � F � Fmax

The presence of multiple objectives in a problem givesrise to a set of optimal solutions (largely known as Pareto-optimal solution) instead of a single optimal solution. TheNSGA-II is an improved version of NSGA and is describedin [33]. NSGA-II can converge to the global Pareto-optimalfront as well as maintain the diversity of population on thePareto-optimal front. The Pareto-optimal front of bothobjectives is shown in Fig. 10. Therefore, by using theNSGA-II for both objective functions, 50 optimal solutionsare obtained within the range considered as shown in Fig. 10and Table 11. For the verification of optimal solutionsobtained using NSGA-II (Table 11), confirmation test hasbeen conducted for few optimal solutions as listed in Table 11for a different factor combination. The experiments have beenrepeated three times and average values have been reported inTable 11. Now these average values have been compared withthe optimal solutions obtained using NSGA-II as shown inTable 11. It could be observed from Table 11 that the errorbetween experimental results and optimal values of MRR andSR is within an acceptable level, i.e. within ±10%. This isconsidered a good prediction of MRR and SR of machinedsurfaces where a typical scattering is present. However, theerrors can be further reduced if the number of measurements isincreased.

Further, by analysing the Pareto’s front, some decisionscould be taken, depending upon specific requirements of theprocess. For instance, at point 1, a component can be machinedwith the best surface quality but with minimum metal removalrate. On the other extreme of the front, i.e. at point 2, the

Table 10 Confirmation experiment result for MRR and SF

Level combination Optimal machining parameters Values of MRR and SR obtained experimentally

Prediction S/N ratio (db) Experiment S/N ratio (db) Test1 Test 2 Test3 Average value

MRR A3B3C1D1E1F3 −8.1586 −8.4384 0.363a 0.3611a 0.3544a 0.3595a

SF A1B1C3D3E3F3 96.686 100.514 1.59b 1.42b 1.55b 1.52b

aMaterial removal rate (g/min)b Surface roughness (μm)

b

200 m

a

50 m

Fig. 9 SEM image of wireEDM cut surface for confirma-tion experiments for a materialremoval rate and b surface finish


highest material removal rate can be achieved but it will be ofthe worst surface quality. All the other points are in-betweencases. As it can be observed from the graph, no solution in thefront is better than any other as they are non-dominated sol-utions. The choice of one of solution over the other depends onthe requirement of the manufacturing engineer. For example, ifone chooses to machine a component with a surface quality of1.25 μm, one can select the set of input variables from thefourth row of Table 11. Accordingly, one would achieve themetal removal rate of 0.153 g/min. To illustrate further theadvantage of the proposed methodology, two more examplesare explained as follows: From the experimental results ofTable 5, the parameters listed in the sixth row lead to Ra valueof 1.59 μm and MRR of 0.1819 g/min. After optimization, itcan be noted that the MRR is increased to 0.237 g/min for thesame surface finish (solution no. 8 in Table 11), with a 31%increase in MRR. In another instance, from the tenth row ofTable 5, the set of input variables leads to MRR of 0.3439 g/min and Ra value of 2.58 μm. After optimization, the Ra valuewas reduced to 1.87 μm (solution no. 5 in Table 11) withalmost the same value of MRR. A suitable combination ofvariables can be selected based on the requirement, i.e. a goodsurface quality or a higher production rate.

Thus, the solution set (Table 11) gives an adequate un-derstanding for the selection of the appropriate processparameters to meet the functional requirements of the com-ponents. The operating parameters can be selected for agiven surface quality based on the requirement of materialremoval rate. So, WEDM process can be made economicalby proper selection of operating parameters in order tomaximize material removal rate with minimum surfaceroughness, with the help of the optimization proceduredeveloped in this work.

6.1 Comparison with other researches

A comparison of the optimization results obtained in thepresent work with those reported in the literature is difficultbecause different materials, WEDM machines of differentmanufacturers and different machining parameters havebeen used by others. Scott et al. [11] used Robofil 100machine and identified 32 non-dominated combinations ofprocess parameters. However, the discharge currents andpulse durations used in the investigations are very muchlower than the values used in the present work. Work carriedout by Spedding and Wang [13] on Robofil 300 comescloser to the present work. However, machining was doneon AISI 420 steel workpiece of 31.5-mm height using abrass wire electrode and only four setting parameters werechosen. Out of the 19 optimal solution sets reported bythem, MRR of 0.241 g/min corresponding to the surfaceroughness value of 3.2 μm was taken for comparison. Thisroughness value represents the mid-value of surface rough-ness values reported. From Table 11, it can be seen thatMRR of 0.814 g/min was obtained (S. no. 50) for a surfaceroughness value of 3.23 μm, which is the closest to 3.2 μmtaken for comparison. This shows that the optimum MRRfor this case is 3.37 times higher than that reported bySpedding and Wang [13]. The difference comes from thecombined effect of material property, workpiece height andelectrode material. It is to be noted that the workpiecematerial has high thermal conductivity and the workpieceof 25-mm height was machined using a zinc-coated copperwire in the present investigation.

7 Conclusion

The present study reveals that factors like pulse peak current,pulse duration, pulse-off period, wire feed, wire tension andflushing pressure are the primary influencing factors whichhave affect not only on the productivity but also on the surfacequality of machined components. Optimal machining condi-tions are obtained for maximization of both the material re-moval rate and the surface finish based on the modelsdeveloped using the non-linear regression method. The resultsof optimization indicate that the material removal rate andsurface finish is influenced more by pulse peak current, pulseduration, pulse-off period and wire feed than by flushingpressure and wire tension. Results also indicate that the surfacequality decreases as the MRR increases and they vary almostlinearly. Out of 50 optimal solutions, the best parametric com-bination that yield the highest possible MRR, while maintain-ing the specified surface finish requirement, i.e. 3.69 μm,would be as follows: pulse peak current030 A, pulseduration037 μs, pulse-off time050 μs, wire feed07 m/min,wire tension01260 g, flushing pressure02.1 kg/cm2. Further,

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1 1.5 2 2.5 3 3.5 4

R a ( m)

MR

R (

g/m

in)

Point 2

Point 1

Fig. 10 Pareto-optimal front


Table 11 Optimal solutions using NSGA-II along with confirmation test results

Solution number A (A) B (μs) C (μs) D (m/min) E (g) F (kg/cm2) Ra (μm) MRR (g/min) Confirmation test

Ra (μm) MRR (g/min)

1 13.87 23.548 50.041 7.005 1,259.941 2.098 1.98 0.394 2.08 0.381

2 29.98 35.992 50.004 7.151 1,259.929 2.097 3.58 0.918 3.37 0.902

3 29.91 35.96 50.006 7.257 1,259.989 2.123 3.57 0.912 – –

4 10.171 20.068 67.497 7.173 1,259.969 2.097 1.25 0.153 – –

5 10.765 21.306 52.650 7.015 1,259.976 2.099 1.87 0.345 – –

6 23.595 31.438 50.137 7.062 1,259.96 2.148 2.84 0.684 – –

7 16.86 29.744 50.149 7.11 1,259.935 2.096 2.66 0.629 – –

8 10.43 20.172 55.815 7.385 1,259.921 2.095 1.59 0.237 1.52 0.256

9 20.285 29.114 50.041 8.059 1,259.869 2.096 2.49 0.565 – –

10 10.00 20.000 68.283 7.746 1,259.997 2.149 1.23 0.143 – –

11 20.0975 29.039 66.748 7.03 1,259.99 2.095 1.45 0.190 1.60 0.179

12 10.00 20.000 55.735 7.024 1,259.968 2.096 1.57 0.225 – –

13 21.86 29.744 50.148 7.095 1,259.97 2.097 2.66 0.630 – –

14 13.00 22.200 68.713 7.721 1,259.985 2.098 1.42 0.181 – –

15 11.745 20.698 68.391 7.004 1,260.00 2.091 1.35 0.170 – –

16 13.155 22.262 50.128 7.753 1,259.994 2.090 1.91 0.363 – –

17 17.055 25.822 50.137 7.062 1,259.96 2.098 2.22 0.482 – –

18 11.33 20.532 66.986 7.026 1,259.99 2.094 1.36 0.170 1.25 0.161

19 22.2175 29.887 50.006 7.22 1,260.00 2.098 2.7 0.643 – –

20 17.65 27.06 50.727 7.379 1,259.869 2.096 2.25 0.479 – –

21 14.2775 22.711 69.716 7.179 1,259.918 2.097 1.48 0.197 – –

22 24.5125 31.805 50.145 7.01 1,260.00 2.098 2.94 0.720 2.85 0.701

23 21.9125 31.765 50.093 7.272 1,259.996 2.099 2.92 0.712 – –

24 22.62 31.048 50.005 7.002 1,260.00 2.099 2.8 0.678 2.98 0.697

25 10.0375 20.015 51.604 7.286 1,259.967 2.093 1.68 0.267 – –

26 15.1375 25.055 50.043 7.015 1,259.78 2.099 2.07 0.429 – –

27 20.2725 29.109 50.000 7.003 1,259.928 2.096 2.51 0.585 – –

28 14.8975 22.959 50.000 7.011 1,259.984 2.098 2.06 0.413 – –

29 10.025 20.01 56.54 7.198 1,259.918 2.092 1.55 0.214 1.65 0.229

30 11.235 21.494 69.301 7.200 1,259.959 2.150 1.29 0.158 – –

31 10.430 20.172 51.054 8.164 1,259.934 2.106 1.71 0.275 – –

32 10.180 20.072 50.016 8.104 1,259.997 2.121 1.73 0.285 – –

33 17.880 27.152 50.037 7.175 1,259.758 2.115 2.29 0.507 – –

34 26.0825 33.433 50.00 7.000 1,259.919 2.121 3.12 0.780 – –

35 29.4375 35.775 50.001 7.048 1,260.00 2.099 3.52 0.901 3.71 0.889

36 30.00 37.00 50.005 7.039 1,260.00 2.103 3.59 0.922 – –

37 17.88 27.152 50.026 7.152 1,259.758 2.151 2.29 0.507 2.48 0.551

38 13.7175 22.487 69.729 7.032 1,259.967 2.141 1.45 0.190 – –

39 13.175 22.27 69.811 7.386 1,259.98 2.130 1.4 0.180 – –

40 24.3175 31.727 50.051 7.036 1,259.941 2.103 2.92 0.716 – –

41 11.3075 20.523 50.019 8.469 1,260.00 2.102 1.79 0.309 1.88 0.291

42 29.9225 35.969 50.004 7.271 1,260.00 2.112 3.57 0.943 – –

43 10.0025 20.001 69.658 8.341 1,259.982 2.109 1.18 0.125 – –

44 21.485 29.594 50.033 7.004 1,260.00 2.118 2.63 0.623 2.72 0.633

45 22.14 29.856 50.011 7.15 1,259.927 2.106 2.69 0.642 – –

46 14.2875 22.715 69.517 7.626 1,259.926 2.141 1.49 0.196 – –

47 29.9925 36.997 50.001 7.006 1,259.994 2.131 3.69 0.958 – –

48 11.8175 20.727 56.478 7.000 1,259.966 2.132 1.67 0.252 1.55 0.233

49 12.2965 22.077 69.036 7.198 1,259.949 2.135 1.39 0.179 – –

50 27.0525 33.821 50.00 7.004 1,259.993 2.126 3.23 0.814 3.48 0.801


the most encouraging aspect inferred by these results was thatthe set of optimal solutions enabled the manufacturing engi-neer to choose a particular optimal set of input variablesdepending upon his requirements. The selection of optimumvalues is essential for the process automation and implemen-tation of a computer-integrated manufacturing system. Thus,the solutions set obtained under optimized conditions not onlymake the WEDM a more commercially viable process forindustrial applications but also turns a spotlight on WEDMprocess as a promising field for further advancements.

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Multi-objective parametric optimization on machining with wire electric discharge machining