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Original Article

Proc IMechE Part B:J Engineering Manufacture1–9� IMechE 2014Reprints and permissions:sagepub.co.uk/journalsPermissions.navDOI: 10.1177/0954405414526382pib.sagepub.com

Multi-response optimization of wireelectrical discharge machining processparameters for Al7075/Al2O3/SiChybrid composite using Taguchi-basedgrey relational analysis

Shyam Lal1, Sudhir Kumar2, Zahid A Khan1 and Arshad N Siddiquee1

AbstractThe effect of various wire electrical discharge machining process parameters such as pulse on time, pulse off time, pulsecurrent and the wire drum speed on machined surface quality characteristics such as surface roughness and kerf widthhas been discussed. The experiments were carried out with L27 orthogonal array on hybrid metal matrix composite pre-pared by inert gas–assisted electromagnetic stir casting process using particulates 7.5% Al2O3 and 7.5% SiC each inAl7075 alloy. Taguchi-based grey relational analysis, a multi-response optimization technique, was used to find the opti-mal process parameter setting for the best quality machined characteristics. Results of analysis of variance showed thatthe order of significance was pulse on time, pulse current, pulse off time and the wire drum speed contributing 50.02%,39.50%, 4.58% and 2.75%, respectively, while machining the hybrid composite. Confirmation test was carried out atselected optimal parameter setting, which showed improvement in grey relational grade, thus confirming the robustnessof grey relational analysis.

KeywordsWire electrical discharge machining, surface roughness, kerf width, hybrid composite, Taguchi, grey relational analysis,analysis of variance

Date received: 29 May 2013; accepted: 13 January 2014

Introduction

Metal matrix composites (MMCs) are prepared using aductile metal matrix and one or more reinforcing con-stituent having high strength and hardness. The pre-pared MMCs having improved properties findimportance in various fields such as aerospace, defenceand automobile industry.1 Machining of these MMCsis difficult by conventional machines due to abrasivenature of reinforcement.2 Among non-conventionalmachining methods, wire electrical discharge machining(WEDM) is most versatile and useful technologicalprocess to machine these materials. This process hascapability to machine intricate shapes and profiles irre-spective of hardness of materials.3 The most importantperformance measures in WEDM are material removalrate (MRR), surface roughness (SR) and kerf width.The high value of MRR will result in reduced produc-tion cost, whereas low value of SR will improve theproduct quality. Good quality surfaces improve fatigue

strength, corrosion and wear resistance of the work-piece.4,5 Kerf, that is, cutting width, determines thedimensional accuracy of the finished parts.

Literature survey

Mahapatra and Patnaik6 studied on parametric optimi-zation of WEDM process on D2 tool steel using L27

orthogonal array (OA) Taguchi method. The results ofanalysis of variance (ANOVA) showed that dischargecurrent, pulse duration and discharge flow rate are the

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1Department of Mechanical Engineering, Jamia Millia Islamia, New Delhi,

India2Noida Institute of Engineering and Technology, Greater Noida, India

Corresponding author:

Sudhir Kumar, Noida Institute of Engineering and Technology, Greater

Noida, Uttar Pradesh, India.

Email: s_k_tomar02@yahoo.com

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significant factors for maximizing the MRR and surfacefinish (SF). Genetic algorithm (GA) was used to obtainthe optimum machining parameters for multi-objectiveoutputs using several combinations of the weight. Thestudy concluded that optimal machining performancewith maximization of MRR and SF occurs under equalimportance of weighting factors.

Ramakrishnan and Karunamoorthy7 studied themodelling and multi-response optimization of com-puter numerical controlled (CNC) WEDM processparameters while machining Inconel� 718. The perfor-mance characteristics were MRR and SR with processparameters such as pulse on time, delay time, wire feedspeed and ignition current. Different weighting factorswere used while calculating the multi-response signal-to-noise (MRSN) ratio. The optimal machining condi-tions were determined by the response graph usingANOVA. The confirmation tests were found a fineagreement between the predicted and actual machiningperformance. The MRR is increased to 1.11 times andSR decreased by 1.09 times.

Tzeng et al.8 optimized the turning operation withmultiple performance characteristics using L27 OATaguchi method and grey relational analysis (GRA)for SKD 11 tool steel. Results of ANOVA on the cal-culated value of grey relational grade (GRG) foundthat depth of cut contributed 38.73%, cutting speedcontributed 29.95%, cutting fluid mixture ratio con-tributed 18.27% and feed rate contributed 16.04%when the minimization of quality targets such asroughness average (Ra), roughness maximum androundness was considered simultaneously. The optimalparameter combination for turning operation was iden-tified using GRA and the results of confirmatory testswere found to be better than the experiments.

Aydin et al.9 studied on the multi-response optimiza-tion of tensile and % elongation of friction stir welding(FSW) process on AA1050-H22 Al alloy. The confir-matory test at optimal parameter setting showedimproved tensile strength with lower elongation. Thisshowed the application feasibility of GRA in combina-tion with Taguchi technique for continuous improve-ment in welding quality.

Kumar et al.10 optimized WEDM process para-meters of Incoloy� 800 superalloy with multi-performance characteristics such as MRR, cornerradius (CR) and kerf based on grey Taguchi method.The results of ANOVA showed that gap voltage is amajor influencing factor contributing 45.59% to per-formance measure followed by pulse on time 30.71%,wire feed 15.12% and pulse off time 8.58%. The confir-matory test for optimal pair setting showed animprovement of 7.74%, 8.64% and 6.34% in MPR,kerf width and SR, respectively, when compared withthe initial parameter setting to highest GRG.

Datta and Mahapatra11 studied the process beha-viour of WEDM with six process parameters on MRR,SF and kerf width for D2 tool steel using TaguchiL27 OA. GRA was also adopted to convert the

multi-objective criteria into an equivalent single-objective function. Optimal setting was verified and itshowed good agreement with practical values throughconfirmatory tests.

Jangra et al.12 optimized WEDM process parameterson MRR and SR for tungsten carbide–cobalt (WC-Co)composite using Taguchi-based GRA. Using ANOVA,two process parameters, namely, taper angle and thepulse on time, were found to be affecting the GRG sig-nificantly. The percentage errors between experimentalvalues and predicted values for MRR and SR usingGRA are 2.2 and 0.35, respectively.

Ganguly et al.13 used Taguchi method with GRA todetermine the laser micro-drilling parameters on zirco-nium oxide (ZrO2) ceramic work material with multiplequality characteristics such as hole taper angle andheat-affected zone (HAZ). The results showed that theimprovement of hole taper and HAZ width from theinitial condition to optimal condition is 16.29% and8.77%, respectively, which validates the effectiveness ofthe proposed optimization method.

Kumar and Agarwal14 studied the WEDM multi-objective parametric optimization while machininghigh-speed steel (HSS) material using L27 OA. A math-ematical model was developed between machiningparameters and responses such as MRR and SF usingnonlinear regression analysis. The model was optimizedusing multi-objective optimization technique based onnon-dominated sorting genetic algorithm-2 (NSGA-2)along with Minitab software. The confirmatory testswere conducted at the optimal solutions and it showedthat an error between experiment results and optimalvalues of MRR and SF was within an acceptable levelof 610%.

In the literature, few studies have been reportedregarding the machining of composites. The objectiveof this study is multi-response optimization of WEDMmachining parameters such as pulse on time, pulse offtime, pulse current and wire drum speed while machin-ing newly developed AA7075/SiC/Al2O3 hybrid compo-site. Taguchi-based GRA has been employed to directlyintegrate the WEDM machining quality characteristics,such as SR and kerf width. Using Minitab software(version 15), the ANOVA is performed to determinewhich parameter has significant affect on the multi-performance characteristics. Confirmation experimentsare conducted to verify the optimal process parametriccombination as predicted by Taguchi GRA.

Materials and methods

Preparation of hybrid composite

In this study, the hybrid MMC has been fabricated byinert gas–assisted electromagnetic stir casting process.The hybrid composite consists of 7.5 wt% Al2O3 and7.5 wt% SiC particulates in metal matrix Al7075 alloy.The Al alloy of 7xxx series is having great potential tobe utilized in aerospace and automotive industries

2 Proc IMechE Part B: J Engineering Manufacture

because of its high strength-to-weight ratio and goodresistance to corrosion. Al7075 is zinc base alloy, hav-ing its maximum percentage of (5.65 wt%) after thebase element aluminium. Zinc imparts good ductility,formability and wettability to the alloy. Also it offersgood resistance to corrosion. The other elements pres-ent are copper, magnesium, chromium, silicon, tita-nium and iron. The weight % composition of Al7075alloy is shown in Table 1. Reinforcements SiC andAl2O3 in particulate form are used to fabricate thehybrid composite. These reinforcements have 20–40 mm size particles.

Machining parameters and response

The four input process parameters in WEDM, namely,pulse on time, pulse off time, pulse current and the wiredrum speed, were chosen to study their effects on SRand kerf width while machining the hybrid composite.The ranges of these process parameters were selectedon the basis of the pilot experiments. The levels of vari-ous parameters and their designations are presented inTable 2.

Design of experiment using Taguchi method

Taguchi philosophy is an efficient tool for the design ofa high-quality manufacturing system. It is a methodbased on OA experiments, which provide much reducedvariance for the experiment with optimum setting ofprocess control parameters. The four control para-meters, that is, pulse on time (A), pulse off time (B),pulse current (C) and the wire drum speed (D), at threelevels were selected in this study. L27 OA was chosenand the 27 experiments were done according to Table 3.This table only represents particular level of the variousfactors of the process at which the experiments wouldbe conducted. This table does not indicate any observeddata. Column 1 presents serial order of experiments.Columns A–D indicate various levels of the parametersaccording to OA. The Minitab 15 software was used toanalyse the results.

Experimental set-up for WEDM process

WEDM is a spark erosion process. The sparks are gen-erated between the workpiece and the wire electrode.The dielectric fluid is continuously fed into the machin-ing zone. The material is getting removed by a series ofdiscrete sparks taking place at the area to be machinedthrough electro-thermal mechanism. Photographic viewof the wire electrical discharge machine is shown inFigure 1. This is a non-contact material removing pro-cess and no direct contact occurs between the wire elec-trode and the workpiece. Thus, no stress is created in

Table 1. Composition of Al7075 alloy.

Zn (wt%) Cu (wt%) Mg (wt%) Cr (wt%) Si (wt%) Ti (wt%) Fe (wt%) Al

5.65 1.78 2.51 0.27 0.36 0.19 0.48 Balance

Table 2. Process parameters and their levels.

Symbol Process parameter Level 1 Level 2 Level 3

A Pulse on time (ms) 4 10 16B Pulse off time (ms) 2 4 6C Current (A) 2 4 6D Wire drum speed (m/min) 4 6 8

Table 3. L27 orthogonal array.

Experimental run Control factors and levels

A B C D

1 1 1 1 12 1 1 2 23 1 1 3 34 1 2 1 25 1 2 2 36 1 2 3 17 1 3 1 38 1 3 2 19 1 3 3 210 2 1 1 111 2 1 2 212 2 1 3 313 2 2 1 214 2 2 2 315 2 2 3 116 2 3 1 317 2 3 2 118 2 3 3 219 3 1 1 120 3 1 2 221 3 1 3 322 3 2 1 223 3 2 2 324 3 2 3 125 3 3 1 326 3 3 2 127 3 3 3 2

Lal et al. 3

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the processed material. The continuous flow of dielec-tric fluid flushes away the removed particles from themachined region. The strength and hardness of thework materials are not affected in WEDM, but meltingpoint of the work material is an important property.This is why WEDM finds extensive uses in machiningof hard materials. The movement of wire is controllednumerically to achieve the desired cut in the workpiece.The wire is held by a pin guide at the upper and lowerparts of the workpiece. Since the wire is subjected tocomplex oscillations due to electrical discharge betweenwire and the workpiece. So it is essential to hold thewire in its designed position against the workpiece. Thewire is discarded after used once for a cut at set level ofprocess parameters. A fresh length of wire is used foreach cut in next experiment. The dimensional consis-tency of machined parts by WEDM is decided by kerfwidth produced. The details of kerf produced inWEDM are shown in Figure 2. The rectangular speci-mens of 4 mm thickness were prepared from the midportion of the cast ingot. The length and width of spe-cimen were 70 mm 3 30 mm giving sufficient run forthe machine to make various cuts of 10 mm lengthaccording to design of experiment. The top and bottomsurfaces of specimen were given smooth finish using600 grade emery papers. The wire EDM machine usedwas WEDM program and control system JiangnanSaite NC, China. Molybdenum electrode wire of0.18 mm diameter was used in this study. Deionizedwater was used as dielectric fluid at room temperature(30 �C). After machining, the specimens were cleanedwith acetone. The kerf was measured using the FocusTool Maker’s Microscope (380). The kerf values weremeasured at eight places spread over the entire lengthof cut, leaving 1 mm length at the beginning and 1 mmat the end. The kerf values used in this study are the

mathematical average of eight measurements madefrom the specimen in each cut. SR (Ra) was measuredin micrometre using Mitutoyo Surftest SV-2100. Oneach machined surface, SR was measured at threeplaces spread over the entire machined area and in thedirection of cut (perpendicular to wire travel path). Theaverage values of these measurements were used in thisstudy. The cut-off length was 0.8 mm and stylus travelspeed was 0.5 mm/s. The kerf is calculated by summingup the ‘wire diameter to 23 wire–workpiece gap dis-tance’. The wire–workpiece gap usually ranges from0.025 to 0.075 mm and is constantly maintained by acomputer-controlled positioning system.3 The observedaverage values of SR and kerf width at different levelsof the WEDM process parameters are shown inTable 4. Experiments were carried out using TaguchiL27 OA. The design of experiments consisted of 27combinations of four process parameters at three dis-crete levels, as shown in Table 4. In Taguchi methodparameter design, the basic method converts the objec-tive parameter to the signal-to-noise (S/N) ratio, whichis treated as the quality characteristic evaluation index.The S/N ratio is used to measure the sensitivity of thequality characteristic being investigated in a controlledmanner. In Taguchi method, the term ‘signal’ repre-sents the desirable effect (mean) for the output charac-teristic, and the term ‘noise’ represents the undesirableeffect (or signal disturbance) for the output characteris-tic, which influences the outcome due to external fac-tors, namely, noise factors. The least variation and theoptimal design are obtained by means of S/N ratio.The quality characteristic smaller-the-better (SB) isselected for SR and kerf width. In Taguchi method, aloss function is defined to calculate the deviationbetween experimental values and the designed values.Loss function value is further converted into S/N ratio.Minimizing quality loss is equivalent to maximizing theS/N ratio. The S/N ratio for SR and kerf width is givenby the expression

Figure 1. Photographic view of wire electrical dischargemachine.CNC: computer numerical controlled.

Figure 2. Details of kerf width in WEDM.

4 Proc IMechE Part B: J Engineering Manufacture

SN

� �SB¼ �10 log 1

n

Xni¼1

y2i

" #ð1Þ

where yi is the ith result of experiment and n is therepeated number of the ith experiment.15 S/N ratio val-ues for SR and kerf width are calculated according toequation (1) and shown in Table 5. The calculated val-ues of S/N ratios are used in further calculations of thegrey relational coefficients (GRCs). TraditionalTaguchi method can optimize a single-objective func-tion but cannot solve multi-objective optimizationproblem.16 The grey system theory proposed by Deng17

has been proven to be useful for dealing with the prob-lems with poor, insufficient and uncertain information.In recent years, GRA has become a powerful tool toanalyse the process with multiple performance charac-teristics. Based on the literature survey, we find thatGRA is a better approach for optimization of multipleresponse characteristics in different fields. Therefore,GRA is utilized for multiple optimizations of machin-ing characteristics SR and kerf width, while machiningnewly developed hybrid composite by WEDM.

GRA theory

GRA is an improved method for identifying and priori-tizing key system factors and is useful for variable inde-pendence analysis. No information–no solution and allinformation–unique solution being the extremities.

Table 4. L27 OA with surface roughness and kerf width for hybrid composite.

Experiment number Pulse ontime (ms)

Pulse offtime (ms)

Current(A)

Wire drumspeed (m/min)

Surfaceroughness (mm)

Kerf width(mm)

1 4 2 2 4 2.595 2282 4 2 4 6 3.221 2653 4 2 6 8 4.026 2814 4 4 2 6 2.216 2275 4 4 4 8 3.098 2736 4 4 6 4 3.594 2607 4 6 2 8 2.182 2308 4 6 4 4 2.806 2509 4 6 6 6 3.067 26910 10 2 2 4 3.852 24211 10 2 4 6 4.920 27912 10 2 6 8 5.316 29613 10 4 2 6 3.477 24514 10 4 4 8 4.157 28615 10 4 6 4 4.785 28016 10 6 2 8 3.431 23917 10 6 4 4 4.209 28518 10 6 6 6 4.455 29719 16 2 2 4 4.164 26720 16 2 4 6 4.736 30021 16 2 6 8 5.607 31422 16 4 2 6 3.868 28223 16 4 4 8 4.326 30324 16 4 6 4 5.018 29125 16 6 2 8 3.880 28426 16 6 4 4 4.180 27727 16 6 6 6 4.497 298

Table 5. S/N ratio values for surface roughness and kerf width.

Experimentnumber

SR (mm) SNRA1 Kerf (mm) SNRA1

1 2.595 28.28409 228 247.15872 3.221 210.1606 265 248.46493 4.026 212.0977 281 248.97414 2.216 26.91277 227 247.12055 3.098 29.82107 273 248.72336 3.594 211.1108 260 248.29957 2.182 26.77769 230 247.23468 2.806 28.96237 250 247.95889 3.067 29.73428 269 248.59510 3.852 211.7142 242 247.676311 4.92 213.8393 279 248.912112 5.316 214.5109 296 249.425813 3.477 210.825 245 247.783314 4.157 212.3752 286 249.127315 4.785 213.5973 280 248.943216 3.431 210.7074 239 247.56817 4.209 212.4832 285 249.096918 4.455 212.9773 297 249.455119 4.164 212.3905 267 248.530220 4.736 213.5082 300 249.542421 5.607 214.9738 314 249.938622 3.868 211.7486 282 249.00523 4.326 212.7209 303 249.628924 5.018 214.0111 291 249.277925 3.88 211.7772 284 249.066426 4.18 212.4235 277 248.849627 4.497 213.0589 298 249.4843

SR: surface roughness.

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Grey system with incomplete information, in betweenthem, gives a variety of feasible solutions. Instead ofattempting to find the best solution, grey analysisprovides techniques for determining a good solution,that is, an appropriate solution for real-worldproblem.18

Normalizing the data

In GRA, the dimensions of factors are usually differentand their magnitude difference is large. Therefore,experimental data are first normalized ranging from 0to 1. The process is known as grey relational generation(GRG). The GRG also expresses the deviation betweenthe experimental value and the ideal value. Accordingto the importance of quality characteristics, there arethree criteria for optimization in GRA, namely, ‘larger-the better’, ‘SB’ and ‘nominal-the-best’. In the presentanalysis, the lower value of SR and kerf width repre-sents better machining performance, and therefore,the ‘lower-the-better’ is chosen for them. In this study,smaller SR and smaller kerf width are desirable.The normalized values of SR and kerf are computed,8,19

according to equation (2), and are shown in Table 6

Xij ¼max Yij � Yij

max Yij �min Yijð2Þ

GRC. The GRC (jij) is determined to express the rela-tionship between reference and actual experimental nor-malized data. The GRC8,19 can be calculated as follows

jij ¼Dmin þ jDmax

Dij þ jDmaxð3Þ

where Dij = |Xoj 2 Xij| and Xoj are the reference dataor best data; Dmax is the maximum value of Dij, Dmin isthe minimum value of Dij and jij is the distinguishing oridentification coefficient, and its value lies between 0and 1. Usually, the distinguishing coefficient is assumedat 0.5 to fit the practical requirements. The calculatedGRC for SR and kerf width is shown in Table 6. In thistable, no unit is required by any data and it only pre-sents the calculated values of S/N ratio, normalized val-ues and the GRCs for SR and kerf width. The highestnormalized value is 1 and appearing at Experimentnumber 21, while minimum value is 0 at Experimentnumber 7.

Table 6. Normalized S/N ratios and calculated grey relational coefficients and overall grey relational grade.

Experimentnumber

GRA (SR) GRA (kerf width) GRG

SNRA1 Norm GRCsr SNRA1 Norm GRCkf

1 28.28409 0.183793 0.379879 247.1587 0.013548 0.336371 0.3581252 210.1606 0.412746 0.459874 248.4649 0.477063 0.488789 0.4743313 212.0977 0.649085 0.587603 248.9741 0.657757 0.593653 0.5906284 26.91277 0.01648 0.337036 247.1205 0 0.333333 0.3351855 29.82107 0.371318 0.442995 248.7233 0.568734 0.536904 0.4899496 211.1108 0.528681 0.514764 248.2995 0.418353 0.462258 0.4885117 26.77769 0 0.333333 247.2346 0.040467 0.342575 0.3379548 28.96237 0.26655 0.405367 247.9588 0.297466 0.415789 0.4105789 29.73428 0.360728 0.438877 248.595 0.52324 0.511896 0.47538710 211.7142 0.602294 0.556975 247.6763 0.197223 0.383796 0.47038511 213.8393 0.861576 0.783179 248.9121 0.635741 0.57853 0.68085512 214.5109 0.943515 0.898497 249.4258 0.818046 0.733188 0.81584213 210.825 0.493802 0.49692 247.7833 0.235198 0.395319 0.4461214 212.3752 0.682941 0.611951 249.1273 0.712118 0.634613 0.62328215 213.5973 0.832048 0.748557 248.9432 0.646769 0.586008 0.66728216 210.7074 0.479458 0.489936 247.568 0.158775 0.372794 0.43136517 212.4832 0.696117 0.621981 249.0969 0.701322 0.626035 0.62400818 212.9773 0.75641 0.672414 249.4551 0.828442 0.744537 0.70847519 212.3905 0.684814 0.613357 248.5302 0.500238 0.500119 0.55673820 213.5082 0.821183 0.736576 249.5424 0.859419 0.780541 0.75855921 214.9738 1 1 249.9386 1 1 122 211.7486 0.606494 0.559594 249.005 0.668706 0.601472 0.58053323 212.7209 0.725126 0.645266 249.6289 0.890088 0.819791 0.73252824 214.0111 0.882531 0.809758 249.2779 0.765538 0.68077 0.74526425 211.7772 0.609981 0.561786 249.0664 0.690489 0.617657 0.58972126 212.4235 0.68884 0.616402 248.8496 0.613567 0.564058 0.5902327 213.0589 0.766366 0.681539 249.4843 0.838802 0.756203 0.718871

Average value of overall GRG = 0.5815

GRA: grey relational analysis; SR: surface roughness; GRG: grey relational grade; GRCsr: grey relational coefficient for surface roughness; GRCkf: grey

relational coefficient for kerf width.

6 Proc IMechE Part B: J Engineering Manufacture

GRG. After calculating the GRC, the GRG is calculatedfrom equation (4) for the quality characteristics and isdirectly integrated to determine single overall GRG byutilizing a weighting method. The GRG (gi) for the ithexperiment can be calculated as follows16

gi ¼ 1m

XWjjij ð4Þ

where m is the number of quality characteristics and Wj

is the weighting factor for jth response. The overall per-formance characteristic of the multiple response pro-cess depends on the calculated GRG. The value of j

for calculating the GRG is taken to be 0.5. The resultsof GRG are calculated with equal weighting ratio forthe quality characteristics SR and kerf width. Thisapproach converts a multiple response process optimi-zation problem into a single response optimization situ-ation with the objective function as overall GRG. Theoptimal parameter setting for optimizing the overallGRG can be performed by Taguchi method. Theresults of GRG are shown in Table 6.

Results and discussion

ANOVA for responses

Relative effect of the different factors can be obtainedby ANOVA.16 The analysis was done using Minitab 15software for GRG values to find the effect of four mainprocess parameters and their second-order interactionwhile machining the hybrid composite. The results ofANOVA are shown in Table 7 based on the 95% confi-dence level (a = 0.05). Table 7 shows the parameterssuch as sum of square (SS), mean of square (MS),degree of freedom (DOF), Fisher’s ratio (F) and prob-ability value (p). All the four process parameters suchas pulse on time, pulse off time, pulse current and thewire drum speed had significant effect (p \ 0.05),whereas no interaction showed significant effect. Thepulse on time was the most significant parameter con-tributing maximum (50.02%) to SR and kerf. The con-tributions from other parameters were pulse off time4.58%, pulse current 39.50 and the wire drum speed2.75%. Response table for the means of the GRG isshown in Table 8. The mean response refers to the

average value of the GRG for each parameter combi-nation at different levels. This table indicates that themean values of GRG and the data are unitless. In col-umn 1, the three levels are shown as 1, 2 and 3 and thedelta indicates the difference between the highest valueand the lowest value. The ranks indicate the order ofimportance and as first rank for pulse on time, secondrank for discharge current, third rank for pulse off timeand the forth rank to wire drum speed. The values aredepicted graphically in Figure 3. The graph indicatesthat pulse on time, pulse current and wire drum speedhave negative effect on the GRG, that is, SR and kerfwidth increase with increase in value of these para-meters. The graph of pulse off time indicates that ithad positive effect, that is, increase in its value lowersSR and kerf width.

Effect of process parameters

The study of ANOVA shows that all the four processparameters, that is, pulse on time, pulse off time, pulsecurrent and the wire drum speed, are significant. InWEDM process, the material is being removed fromthe surface by spark erosion process. The higher pulseon time and pulse current produces longer spark dura-tion of high intensity, that is, more amount of discharge

Table 7. Analysis of variance for S/N ratios (GRG).

Source DF Sequential SS Adjusted SS Adjusted MS F p % Contribution

Pulse on time 2 75.434 75.4344 37.7172 334.4 0 50.02Pulse off time 2 6.911 6.9107 3.4554 30.64 0.001 4.58Pulse current 2 59.57 59.5696 29.7848 264.07 0 39.50Wire drum speed 2 4.151 4.1512 2.0756 18.4 0.003 2.75Pulse on 3 pulse off time 4 0.58 0.5796 0.1449 1.28 0.373 0.38Pulse on time 3 pulse current 4 2.004 2.004 0.501 4.44 0.052 1.33Pulse on time 3 wire drum speed 4 1.473 1.4729 0.3682 3.26 0.095 0.98Residual error 6 0.677 0.6767 0.1128 0.45Total 26 150.799

DF: degree of freedom; SS: sum of square; MS: mean of square.

Figure 3. Effect of process parameters on GRG (main effects)for means.

Lal et al. 7

energy per spark reaching the surface. Because of this,large amount of material melts per spark on the surface.The high discharge energy in the spark striking the sur-face produces deeper and wider size craters, therebyincreasing SR. The wire drum speed had a negativeeffect on the GRG, that is, SR and kerf width increasewith increase in wire drum speed. The higher wire drumspeed adds to effective flushing of debris material fromthe gap, thereby increasing kerf width. The higher drumspeed also contributes to particle pull out, leading tocreation of large size cavities and voids, thereby increas-ing SR. Increasing the pulse off time has positive effecton the GRG, that is, SR and kerf width decrease as thepulse off time increases. This is because with increasedpulse off time, less number of discharges occur for aspecific period of time resulting in less number of sparkinduces craters and melt formation droplets on the sur-face indicating less SR and kerf width.

Estimation of optimum performance characteristic

Optimum levels of design parameters are used for theprediction as well as confirmation that the performancemeasures improve. The optimum value of GRG is pre-dicted at the selected levels of significant parameters.The significant process parameters and their optimumlevels are chosen from the response graph (Figure 2) asA1, B3, C1 and D1, that is, pulse on time of 4 ms, pulseoff time of 6 ms, pulse current of 2 A and wire drumspeed of 4 m/min. The estimation mean of responsecharacteristic (mGRG) can be computed as15

mGRG ¼ GRGþ ðA1 �GRGÞ þ ðB3 �GRGÞþ ðC1 �GRGÞ þ ðD1 �GRGÞ

where GRG is the overall mean of GRG (0.5815);mGRG = 0.4401 + 0.5430 + 0.4562 + 0.54572 3(0.5815) = 0.2405 (Table 8).

The confidence interval (CI) for the predicted meanfor the confirmation experiment can be calculated bythe expression15

ðCIÞCE ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiFað1; feÞVe

1heff

þ 1R

� �sð5Þ

where Fa is the F value for 95% CI and fe is the DOFfor error = 6; from Table 7, the CI was calculated.Total DOF associated with the estimated mean is2 + 2 + 2 + 2 = 8, and total number of experiment

is 27. Effective number of replications (heff) is calcu-lated using the expression as

heff ¼1

1þ Total degree of freedomofmeanð6Þ

Therefore, heff = 27/(1 + 8) = 3. Sample size forconfirmation experiment R is 1. Tabulated F ratio at95% confidence level (a = 0.05); F = 5.99. So,CICE = 60.2317. The predicted mean of GRG ismMRR = 0.2405. At 95% CI, the predicted optimumvalue of GRG is

ðmGRG � CICEÞ\ mGRG \ ðmGRG þ CICEÞð0:2405� 0:2317Þ\ mMRR \ ð0:2405þ 0:2317Þ0:0088\ mGRG \ 0:4722

Confirmation test

A confirmation test was conducted to ensure therobustness of the optimal machining combination ofdesign parameters using Taguchi OA. Three confirma-tion tests were conducted at the optimum level of pro-cess parameters. The average mean value of GRG isfound and shown in Table 9. Table 9 shows the com-parison of the estimated GRG (calculated using equa-tion (4)) with the actual GRG obtained from theexperiment using the optimal process parameter combi-nation. It is found that there is a good agreementbetween the predicted value (0.2405) and experimentalvalue (0.33655). The increase in GRG from initial fac-tor setting to the optimal process parametric setting isof 0.09605. Here, it may be noted that the multiple per-formance characteristics of WEDM process such as SRand kerf width are improved together by applying thisapproach.

Conclusion

Taguchi-based GRA was used to optimize the multipleperformance characteristics while machining hybridMMC by WEDM for SR and kerf width. The follow-ing conclusions were drawn from this study:

1. The optimum parameters for multiple parameters’optimization setting were found to be the pulse ontime of 4 ms, pulse off time of 6 m, pulse current of2 A and the wire drum speed of 4 m/min for

Table 8. Response table for means (GRG).

Level Pulse on time Pulse off time Pulse current Wire drum speed

1 0.4401 0.6339 0.4562 0.54572 0.6075 0.5676 0.5983 0.57543 0.6969 0.543 0.69 0.6235Delta 0.2569 0.091 0.2338 0.0778Rank 1 3 2 4

8 Proc IMechE Part B: J Engineering Manufacture

AQ7AQ7

AQ8AQ8

AQ9AQ9

AQ10AQ10

AQ11AQ11

optimum value of SR (2.187 mm) and kerf width(229 mm).

2. The results of ANOVA showed that all the fourprocess parameters were significant for the overallGRG.

3. The results of ANOVA showed that the maximumcontribution to overall GRG was by pulse on time(50.02%) and followed in decreasing order by pulsecurrent (39.50%), pulse off time (4.58%) and wiredrum speed (2.75%).

4. The confirmatory test showed that there isimprovement in the overall GRG at optimal levelof process parameters 0.0088 \ mGRG \ 0.4722.

Declaration of conflicting interests

The authors declare that there is no conflict of interest.

Funding

This research received no specific grant from any fund-ing agency in the public, commercial or not-for-profitsectors.

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Table 9. Response at optimum levels of process parameters.

Trial number Surface roughness (mm) Kerf width (mm) Experimental value GRG CI

1 2.185 229 0.33655 0.0088 \ mGRG \ 0.47222 2.189 229 0.33676 0.0088 \ mGRG \ 0.47223 2.186 229 0.3366 0.0088 \ mGRG \ 0.4722

Average experimental value GRG = 0.33664

GRG: grey relational grade; CI: confidence interval.

Lal et al. 9