R.V.a,* D.P. - APEM journalapem-journal.org/Archives/2016/APEM11-4_271-286.pdf · Rao, Rai, Ramkumar, Balic 272 Advances in Production Engineering & Management 11(4) 2016 mization

271

AdvancesinProductionEngineering&Management ISSN1854‐6250

Volume11|Number4|December2016|pp271–286 Journalhome:apem‐journal.org

http://dx.doi.org/10.14743/apem2016.4.226 Originalscientificpaper

A new multi‐objective Jaya algorithm for optimization of modern machining processes

Rao, R.V.a,*, Rai, D.P.a, Ramkumar, J.b, Balic, J.c aDepartment of Mechanical Engineering, Sardar Vallabhbhai National Institute of Technology, Surat, India bDepartment of Mechanical Engineering, Indian Institute of Technology, Kanpur, India cProduction Engineering Institute, Faculty of Mechanical Engineering, University of Maribor, Slovenia

A B S T R A C T A R T I C L E I N F O

In thiswork, themulti‐objectiveoptimizationaspectsofplasmaarcmachin‐ing (PAM), electro‐dischargemachining (EDM), andmicro electro‐dischargemachining (μ‐EDM) processes are considered. Experiments are performedand actual experimental data is used to develop regression models for theconsideredmachiningprocesses.AposterioriversionofJayaalgorithm(MO‐Jayaalgorithm)isproposedtosolvethemulti‐objectiveoptimizationmodelsinasinglesimulationrun.ThePAM,EDMandµ‐EDMprocessesareoptimizedusingMO‐JayaalgorithmandasetofPareto‐efficientsolutionsisobtainedforeachoftheconsideredmachiningprocessesandthesameisreportedinthiswork.ThisParetooptimalsetofsolutionswillprovide flexibilityto thepro‐cessplannertochoosethebestsettingofparametersdependingontheappli‐cation. The aimof thiswork is to demonstrate theperformanceofMO‐Jayaalgorithmandtoshowitseffectivenessinsolvingthemulti‐objectiveoptimi‐zationproblemsofmachiningprocesses.

©2016PEI,UniversityofMaribor.Allrightsreserved.

Keywords:PlasmaarcmachiningElectro‐dischargemachiningMicro‐electro‐dischargemachiningMulti‐objectiveoptimizationJayaalgorithmPosterioriapproachSustainability

*Correspondingauthor:[email protected](Rao,R.V.)

Articlehistory:Received10November2016Revised25November2016Accepted1December2016

1. Introduction

Inordertosurviveina fiercemarketscenariomanufacturingindustriesarerequiredtomain‐tainhighqualitystandards,produceatlowestcost,increaseproductionrate,conserveresourcesand at the same timeminimize the environmental impact of the processes they use.Machinetoolsaremajorpillarsofanymanufacturingsystemandareusedonalargescaleforprocessingofmaterials.However,machiningprocessesarecharacterizedbyhighenergyconsumption,hightoolwearrate,poorsurfacequalityandgenerationoflargescalewasteproductsintheformofusedlubricants,coolants,dielectricorelectrolytic fluids,chipsanddebrisoftoolorworkpiecematerials,etc.Thus,forsuccessofanymanufacturingsystemintermsofeconomyandtoreduceitsimpactontheecologyitiscrucialtoimprovetheefficiencyofthesemachinetools.Further‐more,inordertoimprovethesustainabilityoftheprocessitisimminentthatthemachinesareoperatedasefficientlyaspossible.

Theperformanceofanymachiningprocessextensivelydependsuponthechoiceofprocessparameters.Therefore,forbestperformancefromanymachiningprocessitisimportanttosettheprocessparametersoptimally.Inordertodeterminetheoptimalsettingofprocessparame‐tersitisimportanttomaptherelationshipbetweeninputandoutputparameters.DeWolfetal.[1]investigatedtheeffectofprocessparametersonmaterialremovalrate,electrodewearrateandsurfacefinishinEDMprocess.AichandBanerjee[2]appliedteachinglearningbasedopti‐

Rao, Rai, Ramkumar, Balic

272 Advances in Production Engineering & Management 11(4) 2016

mizationprocedureforthedevelopmentofsupportvectormachinelearnedEDMprocessanditspseudo Pareto optimization. Zhang et al. [3] enumerated and characterized 128 scenarios insustainablemachiningoperationinvolving7objectivesincludingenergy,cost,time,power,cut‐ting force, tool life and surface finish.Guptaet al. [4]presented the resultsof optimizationofmachiningparametersandcuttingfluidsduringnano‐fluidbasedminimumquantitylubricationturningoftitaniumalloybyusingparticleswarmoptimizationandbacteriaforagingoptimiza‐tiontechniques.

Researchershavealsoappliedanumberofnumericalandmetaheuristicoptimizationalgo‐rithmsforoptimalsettingofmachiningprocessparameters[5‐13].Themetaheuristicoptimiza‐tionalgorithmsaremostlyinspiredbythetheoryofevolutionorofbehaviorofaswarm.Allevo‐lutionaryalgorithmsor swarmbasedalgorithms require tuningofparameters likepopulationsize,numberofiterations,elitesize,etc.Inaddition,differentalgorithmsrequiretheirownalgo‐rithm‐specificparameters.The impropertuningofalgorithm‐specificparametersadverselyaf‐fectstheperformanceofthesealgorithms.Inaddition,thetuningofpopulationsizeandnumberofiterationsisalsorequired.

Rao[14]proposedtheJayaalgorithmwhichalgorithm‐specificparameter‐lessalgorithm.TheperformanceofJayaalgorithmhasalreadybeentestedonanumberofunconstrainedandcon‐strainedbenchmark functionsandengineeringoptimizationproblems.Formoredetails aboutthe algorithm, the readersmay refer to https://sites.google.com/site/jayaalgorithm. The Jayaalgorithm is simple in implementation as a solution is updated only in a single phase using asingleequation.However,themulti‐objectiveversionofJayaalgorithmisnotyetdeveloped.

Inthecaseofmachiningprocessesduetoco‐existenceofmultipleperformancecriteriathereis a need to formulate and solvemulti‐objective optimization problems (MOOP). A priori ap‐proachsuchasnormalizedweightedsumapproach,epsilonconstraintmethod,etc.requireas‐signingtheweightsofimportancetotheobjectivesbeforesimulationrunofthealgorithm.Fur‐ther,itisrequiredtorunthealgorithmindependentlyforeachsetofweightstoobtaindistinctsolutions.Aposterioriapproachdoesnotrequireassigningweightsofimportancetotheobjec‐tivesinadvance.ThisapproachprovidesasetofPareto‐efficientsolutionsforaMOOPinasinglerunofsimulation.TheprocessplannercanthenselectoneoutofthesetofPareto‐efficientsolu‐tionsbasedontheorderofimportanceofobjectives.

Thus, in thiswork a parameter‐less posteriorimulti‐objective version of Jaya algorithm isnamedasmulti‐objectiveJaya(MO‐Jaya)algorithmisproposedandtheMOOPsofthreemodernmachiningprocessesnamelyplasmaarcmachining(PAM),electro‐dischargemachining(EDM),andmicroelectro‐dischargemachining(µ‐EDM)aresolvedusingMO‐Jayaalgorithm.The JayaandMO‐Jayaalgorithmsaredescribedinfollowingsections.

2. The Jaya algorithm

In the JayaalgorithmP initial solutionsare randomlygeneratedobeying theupperand lowerboundsoftheprocessvariables.Thereafter,eachvariableofeverysolutionisstochasticallyup‐datedusingEq.1.Thebestsolutionistheonewithmaximumfitness(i.e.bestvalueofobjectivefunction)andtheworstsolutionistheonewithlowestfitness(i.e.worstvalueofobjectivefunc‐tion).

, , , , , , , , abs , , , , , , abs , , (1)

Herebestandworstrepresenttheindexofthebestandworstsolutionsamongthepopulation.p,q,raretheindexofiteration,variable,andcandidatesolution.Op,q,rmeanstheq‐thvariableofr‐th candidate solution inp‐th iteration.αp,q,1 andαp,q,2 are numbers generated randomly in therangeof[0,1].Therandomnumbersαp,q,1andαp,q,2actasscalingfactorsandensureexploration.The absolute value of the variable (instead of a signed value) also ensures exploration. Fig. 1givestheflowchartforJayaalgorithm.


Advances in Production Engineering & Management 11(4) 2016 273

Fig.1FlowchartofJayaalgorithm

3. The multi‐objective Jaya algorithm

TheMO‐JayaalgorithmisaposterioriversionofJayaalgorithmforsolvingMOOPs.ThesolutionsintheMO‐Jayaalgorithmareupdated inthesimilarmanneras intheJayaalgorithmbasedonEq.1. In the interestofhandlingproblems inwhichmore thanoneobjectiveco‐exist theMO‐Jayaalgorithm isembeddedwithdominancerankingapproachandcrowdingdistanceevalua‐tionapproach.

TheMO‐JayaalgorithmisaposterioriversionofJayaalgorithmforsolvingMOOPs.Thesolu‐tionsintheMO‐JayaalgorithmareupdatedinthesimilarmannerasintheJayaalgorithmbasedonEq.1.Intheinterestofhandlingproblemsinwhichmorethanoneobjectiveco‐existtheMO‐Jayaalgorithm isembeddedwithdominancerankingapproachandcrowdingdistanceevalua‐tionapproach[12].

In theMO‐Jaya algorithm, the superiority among the solutions is decided according to thenon‐dominancerankandvalueof thedensityestimationparameter i.e. crowdingdistance (ξ).Thesolutionwithhighestrank(rank=1)andlargestvalueofξischosenasthebestsolution.Ontheotherhandthesolutionwiththelowestrankandlowestvalueofξ isselectedastheworstsolution.Suchaselectionschemeisadoptedsothatsolutioninlesspopulousregionoftheobjec‐tivespacemayguidethesearchprocess.Oncethebestandworstsolutionsareselected,thesolu‐tionsareupdatedbasedontheEq.1.

Afterallthesolutionsareupdated,theupdatedsolutionsarecombinedwiththeinitialpopu‐lationtosothatasetof2Psolutions(wherePisthesizeofinitialpopulation)isformed.Thesesolutions are again ranked and the ξ value for every solution is computed.Based on thenewrankingandξvaluePgoodsolutionsarechosen.

TheflowchartofMO‐JayaalgorithmisgiveninFig.2.ForeverycandidatesolutiontheMO‐Jayaalgorithmevaluatestheobjectivefunctiononlyonceineachiteration.Therefore,thetotalno.offunctionevaluationsrequiredbyMO‐Jayaalgorithm=populationsize×no.ofiterations.However,whenthealgorithmisrunmorethanonce,thenthenumberoffunctionevaluationsistobecalculatedas:no.offunctionevaluations=no.ofruns×populationsize×numberofitera‐tions. The methodology used for ranking of solutions, computing the crowding distance andcrowdingcomparisonoperatoraredescribedinthefollowingsub‐sections.



Fig.2FlowchartofMO‐Jayaalgorithm

3.1 Ranking methodology

The approach used for ranking of solutions is based on the non‐dominance relation betweensolutionsandisdescribedasfollows.InanMobjectiveoptimizationproblem,Pisthesetofsolu‐tionstobesortedandn=|P|.

Domination:Asolutionx1issaidtodominateanothersolutionx2ifandonlyiffi(x1)≤fi(x2)forall1≤i≤Mandfi(x1)<fi(x2)foratleastonei,whereiϵ {1,...,M}(whenallobjectivesaretobeminimized).

Non‐domination:Asolutionx*inPisnon‐dominatediftheredoesnotexistanysolutionxjinP ‐whichdominatesx*.

Similarly,everysolutioninPcompeteswitheveryothersolutionandthenon‐dominatedsolu‐tionsareremovedfromPandassignedrankone.TheremainingsolutionsinPareagainsortedinthesamewayandthenon‐dominatedsolutionsareremovedandassignedranktwo.UnlessallthesolutionsinPreceivearankthisprocedureiscontinued.Agroupofsolutionswithsamerankisknownasfront(F).

3.2 Computing the crowding distance

Thecrowdingdistance(ξj)isanestimateofthedensityofthesolutionsinthevicinityofapar‐ticularsolutionj.ForaparticularfrontF,letl=|F|thenforeachmemberinF,ξiscalculatedasfollows.

Step1:Initializeξj=0Step2:SortallsolutionsinFthesetintheworstorderofobjectivefunctionvaluefm.Step3:Inthesortedlistofmthobjectiveassigninfinitecrowdingdistancetosolutionsattheex‐tremesofthesortedlist(i.e.ξ1=ξl=∞),forj=2to(l–1),calculateξjasfollows:



(2)

Wherejrepresentsasolutioninthesortedlist,fmistheobjectivefunctionvalueofm‐thobjec‐tiveof j‐thsolution,andarethehighestandthelowestvaluesofthem‐thobjectivefunctioninthecurrentpopulation.Likewise,ξiscomputedforallthesolutionsinallFs.

InthecaseofMOOPsthereexistmorethanoneoptimalsolution.Therefore,theaimistofindasetofPareto‐efficientsolutions.InMO‐Jayaalgorithminordertoavoidclusteringofsolutionsaboutasinglegood(higherrank)solution,thegoodsolutionsintheisolatedregionofthesearchspaceareidentifiedbasedontheξvalue,andasolutionwithahigherrankandhigherξvalueisconsideredasthebestsolutioninthenextgeneration.Thus,theothersolutionsinthepopula‐tionwillbedirectedtowardsthegoodsolutionwhichliesinthelesspopulous(isolated)regionof thesearchspace in thenextgeneration.Thiswillprevent thealgorithmfromconvergingtosingleoptimumsolutionandensurediversityamongthesolutions.Forthispurposeasolutionfromthemoreisolatedregionofsearchspaceisgivenmorepreferencethanthesolutioninthecrowdedregionofthesearchspace.IntheMO‐Jayaalgorithm,amongthetwocompetingsolu‐tions i and j, primarily, the solutionwithahigher rank ispreferred. If the two solutionshaveequalrankthenthesolutionwithahigherξvalueispreferred.

ThenextsectiondescribestheexperimentsperformedonthePAM,EDMandµ‐EDMprocess‐es.TheexperimentsareperformedattheManufacturingScienceLaboratoryofIITKanpur,IndiabytheteamofProfessorJ.Ramkumar(co‐authorofthispaper)andvalidationtestsarealsoper‐formedfortheconsideredmachiningprocesses.

4. Case studies

TheMOOPsofPAM,EDMandµ‐EDMprocessesaredescribedinthefollowingsub‐sectionsandthesamearesolvedusingMO‐Jayaalgorithm. Inorder togetasetof50Pareto‐efficientsolu‐tionsapopulationsizeof50ischosenforMO‐Jayaalgorithm.InordertoprovideenoughchanceforthesearchprocesstoevolveandconvergeatthePareto‐efficientsetofsolutions,allowableiterationsaresetto100.Allthesimulationsareperformedonacomputerwith2.93GHzproces‐sorand4GBRAM.ThecodeforMO‐JayaalgorithmisdevelopedinMATLABR2009a.

4.1 Optimization of plasma arc machining process

Thiswork aims to improve the performance of PAMprocess bymeans of process parameteroptimization.Theregressionmodelsformaterialremovalrate‘MRR’(g/s)anddrossformationrate‘DFR’(g/s)aredevelopedusingthedatacollectedbymeansofactualexperimentation,andthesameareusedasfitnessfunctionsforMO‐Jayaalgorithminordertoobtainmultipletrade‐offsolutions.

The experimental setup consisted ofmainly four components i.e. power supply unit, steeltrailer,plasmatorch,awork‐tableandavibrationsetup.Thepowersupplyunitisusedtocon‐trol thecurrentandpressureofgas.Thesteel trailer isused tomove theplasma torchon2Dsurface.Theplasmatorch isused toconvert thegas intoplasmaand theworktable isused toholdtheworkpieceavibrationsetupisalsomountedontheworktable.Thevibrationsetupcon‐sistsoftwoRMsliderassembly,amovingplateandafixedplate,aninductionmotor,avariablefrequencydrivetocontrolthespeedofthemotorandacamandspringassembly.

The experiments are performed atManufacturing Science Laboratory of IIT Kanpur, IndiaandAISI4340steel(0.16‐0.18%ofC) isusedasworkmaterial.Theexperimentsareplannedaccordingtothecentralcompositedesign(CCD)and4processparameterssuchasthicknessofworkpiece‘T’(mm),current‘I’(Amp),arcgapvoltage‘Vg’(V)andspeed‘S’(mm/min)arecon‐sideredeachat5levels.Table1givestheplanofexperimentsbasedonCCD.



Table1DesignofexperimentsandvaluesofMRRandDFRmeasuredafterexperimentationS.No. T(mm) I(A) Vg(V) S(mm/min) MRR(g/s) DFR(g/s)1 2 40 135 500 0.1514 0.11642 1.5 35 145 600 0.1269 0.16233 1.5 45 145 600 0.3088 0.00584 2 30 135 700 0.2476 0.025 2 40 155 700 0.3529 0.02176 1 40 135 700 0.1495 0.04287 1.5 25 145 600 0.1367 0.08948 1.5 35 145 600 0.2537 0.02049 2 40 135 700 0.3206 0.006510 2.5 35 145 600 0.2939 0.064311 1 40 155 500 0.0696 0.112012 1 40 155 700 0.1958 0.042713 1 30 155 700 0.1571 0.049514 1.5 35 145 400 0.1230 0.079915 2 40 155 500 0.2530 0.048416 2 30 135 500 0.1791 0.033017 1 40 135 500 0.0447 0.080418 0.5 35 145 600 0.0023 0.085819 1.5 35 145 600 0.15 0.126020 2 30 155 500 0.1516 0.109521 1.5 35 145 800 0.3106 0.023522 1.5 35 125 600 0.1389 0.089923 2 30 155 700 0.1351 0.192124 1.5 35 145 600 0.1693 0.114425 1 30 135 700 0.1330 0.021826 1.5 3555 145 600 0.1440 0.127427 1.5 35 165 600 0.1308 0.188528 1 30 135 500 0.0580 0.067929 1.5 35 145 600 0.1711 0.108430 1 30 155 500 0.0236 0.1363

ThirtyexperimentalrunsareperformedandMRRandDFRaremeasuredandrecorded.The

weightofeachtestspecimenismeasuredbeforeandafterperforminganexperimentalrun,withdrossandwithoutdrossandtheMRRandDFRaredeterminedaccordingtoEq.3toEq.5.

/ (3)/ (4)

60/ (5)

Wherew1istheweightoftheworkpieceingramsbeforecutting;w2istheweightofthework‐pieceingramsaftercuttingwithdross;w3istheweightoftheworkpieceaftercuttingingramswithoutdross;t isthecuttingtimeinsandL isthelengthofcutoneachworkpiece(125mm)andSisthecuttingspeed(mm/min).Thereafter,regressionmodelsforMRRandDFRaredevel‐opedusingalogarithmicscaleandareexpressedbyEq.6andEq.7. exp 202.0963939 26.97654873 log 115.7823 log 36.5388 log 32.2698 log 2.3015 log 3.07499 log 10.03049 log 2.5766 log 0.70759 log log 0.25221 log log 3.92965 log log 17.92577 log log 0.91766 log log 0.07549 log log

0.95

(6)

exp 310.030243 7.0437 log 311.642 log 169.3030 log 56.3056 log 0.5839 log 16.1736 log 17.4766 log 8.15487 log 4.90491 log log 4.68153 log log 0.17082 log log 28.2996 log log 8.91918 log log 15.42233 log log

0.7

(7)

NowMO‐JayaalgorithmisappliedtomaximizetheMRRandminimizetheDFR,simultaneously.TheregressionmodelsforMRRandDFRexpressedbyEq.6andEq.7areusedasfitnessfunc‐tionforMO‐Jayaalgorithm.TheprocessparameterslimitsareexpressedbyEqs.8to11.



0.5 ≤ T ≤ 2.5 (8)25 ≤ I≤ 45 (9)

125 ≤ Vg ≤ 165 (10)400 ≤ S ≤ 800 (11)

ThesetofPareto‐efficientsolutionsprovidedbyMO‐JayaalgorithmisreportedTable2andthePareto‐front is shown in Fig. 3. TheMO‐Jaya algorithm required8 iterations to obtain 50Pareto‐efficient solutions.TheCPU time requiredbyMO‐Jayaalgorithm toperform100 itera‐tionsis7.2s.

TheresultsofMO‐Jayaalgorithmhaverevealedthat,theoptimalvalueforcurrentandspeedare45(A)and800(mm/min)toachieveatrade‐offbetweenMRRandDFR.TheMRRincreasescontinuously fromaminimumvalueof0.2342(g/s) to1.0769(g/s)as thearcgapvoltage in‐creasesfrom128.2032(V)to165(V).However,theincreaseinMRRisachievedontheexpenseof increase inDFR.Therefore, thebestcompromisedvalues forDFR lie in therangeof0.0004(g/s)to0.0026(g/s).TheDFRshowsaninversetrendwithrespecttothicknessofworkpiece.However,asthearcgapvoltageincreasestheDFRalsoincreases(refertoTable2).

Table2ParetooptimalsolutionsetprovidedbyMO‐JayaalgorithminasinglesimulationrunforPAMprocessS.No. x1(mm) x2(A) x3(V) x4(mm/min) MRR(g/s) DFR(g/s)1 2.5 45 128.2032 800 0.2342 0.00042 2.5 45 130.0663 800 0.2573 0.00043 2.5 45 134.3141 800 0.3127 0.00044 2.5 45 137.139 800 0.3508 0.00055 2.5 45 140.1553 800 0.392 0.00056 2.5 45 141.3426 800 0.4082 0.00057 2.5 45 142.5303 800 0.4243 0.00058 2.4048 45 142.5775 800 0.4589 0.00069 2.4115 45 144.2314 800 0.4804 0.000610 2.3928 45 144.823 800 0.4961 0.000611 2.3038 45 143.0715 800 0.5033 0.000612 2.4004 45 147.4697 800 0.5308 0.000713 2.3995 45 148.7112 800 0.5483 0.000714 2.3583 45 148.559 800 0.564 0.000715 2.2949 45 148.3905 800 0.5889 0.000816 2.3668 45 150.6993 800 0.5898 0.000817 2.3144 45 151.253 800 0.6215 0.000818 2.268 45 150.9664 800 0.6388 0.000819 2.0579 45 146.8665 800 0.6613 0.000920 2.1508 45 150.1631 800 0.6794 0.000921 2.1876 45 152.6231 800 0.7005 0.00122 2.1182 45 151.5029 800 0.7152 0.00123 2.0995 45 152.0345 800 0.7319 0.00124 2.0861 45 153.623 800 0.7628 0.001125 2.0661 45 153.5103 800 0.7701 0.001126 2.0207 45 153.3698 800 0.788 0.001127 1.985 45 153.4289 800 0.804 0.001228 1.9782 45 154.6089 800 0.8259 0.001229 1.8797 45 153.3452 800 0.8429 0.001330 1.9448 45 155.8998 800 0.8601 0.001331 2.0101 45 158.4338 800 0.8681 0.001432 1.8571 45 155.9489 800 0.8943 0.001433 1.8422 45 156.0147 800 0.9005 0.001534 1.7788 45 155.7694 800 0.9156 0.001535 1.8493 45 157.9314 800 0.928 0.001636 1.8344 45 158.1038 800 0.9358 0.001637 1.901 45 160.6495 800 0.9464 0.001738 1.8744 45 160.3258 800 0.9528 0.001739 1.8186 45 159.9524 800 0.9681 0.001740 1.8681 45 161.9012 800 0.9757 0.001841 1.8435 45 162.0781 800 0.9874 0.001842 1.6871 45 160.0925 800 1.004 0.001943 1.6935 45 160.9864 800 1.0155 0.00244 1.7365 45 162.4991 800 1.0263 0.00245 1.7111 45 163.0979 800 1.0397 0.002146 1.7012 45 163.4105 800 1.0457 0.002247 1.7513 45 165 800 1.0518 0.002248 1.7091 45 165 800 1.0624 0.002349 1.6118 45 165 800 1.076 0.002550 1.5829 45 165 800 1.0769 0.0026



Fig.3Pareto‐frontobtainedbyMO‐JayaalgorithmforPAMprocessinasinglesimulationrun

4.2 Optimization of electro‐discharge machining process

ThisworkaimstomaximizetheMRR(mg/min),minimizetoolwearrate‘TWR’(mg/min),min‐imize taper angle Ɵ (degree) and minimize delamination factor ‘DF’, simultaneously, by themeansofprocessparameteroptimization.Forthispurpose,experimentsareperformedandthedatacollectedisusedtodevelopregressionmodelsforMRR,TWR ,ƟandDFandthesameareusedasfitnessfunctionsforMO‐Jayaalgorithm.

ThesurveyofliteraturerevealedthattherearenumberofprocessparameterswhichcontroltheperformanceoftheEDMprocesssuchaspulsecurrent,pulseontime,gapvoltage,%dutycycle,Zdepth,sensitivity,anti‐arcsensitivity,work‐time,lifttime,prepulsesparkingcurrent,Xdisplacement, Y displacement, polarity and tool rotation. Therefore, preliminary experimentswereconductedtofindoutthemostcriticalparameterslikethegapvoltage‘Vg’(V),pulsecur‐rent‘Ip’(A),pulse‐ontime‘Ton’(µs)andtoolrotationspeed‘N’(rpm).

Designofexperimentsisusedasatooltogeneratetheexperimentalprocedure.Theexperi‐mentsareplannedaccordingtotherotational‐centralcompositedesign(RCCD)andregressionmodelsforMRR,TWR,taperangleandDFaredeveloped.Theexperimentsareconductedwith4process parameters considering each at 5 levels. The values of other process parameters aremaintainedasconstantsuchasdutycycle40%,Zdepth15mm,sensitivity8,anti‐arcsensitivity7,worktime8.0s,lifttime0.2s,prepulsesparkingcurrent0Aandstraightpolarity.

TheexperimentsareperformedintheManufacturingScienceslaboratoryofIITKanpur,In‐dia.ZNCElectronicaEDMmachinewithacoppertoolof3mmdiameterisusedforthepurposeof experimentation. Carbon‐carbon compositematerialswith6%gradewith approximatedi‐mensionsas155mm×75mm×3.5mmisusedastheworkpiecematerial.Acopperrodof3mm diameter and 7mm length is used as tool. The tool is given negative polarity while theworkpiece isgivenpositivepolarity.30experimentswith6replicatesof centrepointareper‐formed.Table3givestheexperimentalplanandresults.

Foreachexperimenttheinitialandfinalweightsoftoolandworkpiecematerialismeasuredusingaweighingscale(CitizenCY204),careistakentocompletelyremovethemoisturefromtheworkpiecematerialbeforemeasurement.TheMRRiscalculatedbytakingtheratioofdiffer‐encebetweeninitialandfinalweightsofworkpiecetothemachiningtimeofthroughhole.TheTWRiscalculatedbytakingtheratioofdifferencebetweeninitialandfinalweightsofthetooltothemachiningtimeofthroughhole.

IntheEDMprocessasthematerial isremovedfromtoolaswellastheworkpieceallholesmachinedhaveasignificanttaperangle.TocalculatetaperanglethenominaldiametersofupperandlowerpartofthemachinedholearemeasuredwiththehelpofdigitalmicroscopeandDino‐litesoftware.Further,thetaperangleiscalculatedasfollows.

tan2

(12)



WhereDtopandDbotarenominaldiametersoftopandbottomsurfacesofthemachinedholeandtisthethicknessofworkpiece.

Thedelaminationfactoriscalculatedastheratioofmaximumdiameteroftheheataffectedzonetothenominaldiameterofthemachinedhole.TheregressionmodelsforMRR,TWR,ƟandDFdevelopedusinga logarithmicscalewithuncodedvaluesofmachiningparametersandareexpressedbyEq.13toEq.16.

Table3DesignofexperimentsandvaluesofMRR,TWR,ƟandDFmeasuredafterexperimentation

S.No. Vg(V) Ip(A) Ton(µs) N(rpm) MRR(mg/min) TWR(mg/min) Ɵ(degree) DF1 40 20 500 250 11.774 15.56 0.49896 1.137652 80 20 500 250 18.429 28.071 0.94956 1.174073 40 40 500 250 17.984 87.5 2.14977 1.194774 80 40 500 250 23.818 169.129 2.93734 1.287565 40 20 1000 250 10.485 9.706 1.01307 1.14836 80 20 1000 250 21.755 35.145 1.44775 1.188427 40 40 1000 250 17.957 89.586 2.34904 1.203878 80 40 1000 250 25.836 189.062 3.03773 1.295919 40 20 500 350 9.409 12.994 1.21824 1.1256710 80 20 500 350 14.73 22.858 1.45351 1.1621111 40 40 500 350 14.251 87.553 2.47527 1.1869312 80 40 500 350 17.152 141.074 2.73688 1.2714313 40 20 1000 350 7.567 13.593 1.43657 1.1306214 80 20 1000 350 12.739 26.774 1.58195 1.1655615 40 40 1000 350 13.983 88.552 1.86935 1.1838516 80 40 1000 350 16.643 145.738 2.11996 1.275317 25 30 750 300 7.135 13.344 1.56341 1.1576818 95 30 750 300 17.791 97.223 2.05367 1.2050819 60 10 750 300 16.462 2.123 0.609447 1.116820 60 45 750 300 23.262 189.031 1.93848 1.2350421 60 30 300 300 19.481 90.738 1.2623 1.2347822 60 30 2000 300 11.879 63.277 2.5361 1.2053923 60 30 750 200 23.644 92.36 1.75735 1.2425324 60 30 750 400 4.167 8.568 1.45485 1.2199225 60 30 750 300 22.61 76.726 1.54156 1.2170426 60 30 750 300 22.532 80.963 1.51356 1.2199627 60 30 750 300 21.873 75.491 1.50756 1.2289228 60 30 750 300 22.095 79.266 1.53274 1.2245529 60 30 750 300 20.032 75.118 1.53498 1.211930 60 30 750 300 22.263 76.726 1.52827 1.2338

exp 264.7311 14.62835 log 0.633896 log 8.67444 log 74.465 log 1.0053 log 0.2317 log 0.3459 log 5.83289 log 0.63041 log log 0.16643 log log 0.87394 log log 0.12709 log log 0.94153 log log

0.855

(13)


0.926

(14)


0.892

(15)


0.898

(16)



NowMO‐JayaalgorithmisusedtomaximizetheMRR,minimizeTWR,minimizetaperangleandminimizeDF,simultaneously.TheregressionmodelsexpressedbyEq.13toEq.16areusedasfitnessfunctionsforMO‐Jayaalgorithm.TheprocessparameterboundsareexpressedbyEq.17toEq.20asfollows.

25 ≤ Vg ≤ 95 (17)10 ≤ Ip≤ 45 (18)

300 ≤ Ton ≤ 2000 (19)200 ≤ N ≤ 400 (20)

ThesetofPareto‐efficientsolutionsprovidedbyMO‐Jayaalgorithminasinglerunofsimula‐tionisreportedinTable4forall4objectives.Astheoptimizationproblemishaving4objectivesitisnoteasytoshowthe4‐dimensionalParetofrontandhencetheParetofrontforMRR,TWRandƟisshownasFig.4(a)andtheParetofrontforTWR,ƟandDFisshownasFig.4(b).

Table4ParetooptimalsolutionsetprovidedbyMO‐JayaalgorithminasinglesimulationrunforEDMprocess

S.No. Vg(V) Ip(A) Ton(µs) N(rpm) MRR(0.1mg/s) TWR(0.1mg/s) Ɵ(degree) DF1 25 10 1913.724 200 1.2453 0.0965 3.3476 1.15742 25.0495 10 1844.116 200 1.2865 0.0986 3.0562 1.15583 25 10 1757.623 200 1.3199 0.0996 2.7192 1.15364 26.2683 10 2000 200 1.4191 0.1162 3.7259 1.16035 25 10 300 200 1.4245 0.2215 0.0811 1.0796 31.7003 10 2000 200 2.5179 0.2405 3.8046 1.16297 28.5 10 932.73 212.1907 3.0999 0.2672 0.6472 1.12598 33.8835 10 980.8407 214.6995 5.0426 0.4827 0.7417 1.139 39.4565 10 1366.835 200 5.5058 0.5499 1.7016 1.148810 39.5125 10 893.006 200 6.1636 0.6041 0.6878 1.132511 43.1006 10 785.4233 214.3395 9.0452 1.0027 0.5488 1.123812 60.5423 10 300 200 9.4074 1.871 0.159 1.094913 50.252 10 951.2899 200 10.0145 1.1314 0.943 1.134714 50.4624 10 1094.945 209.8391 11.047 1.3154 1.1924 1.135915 95 10 300 370.8176 11.201 1.547 0.5758 1.074916 53.9205 10 1193.568 203.7774 11.3644 1.3979 1.5711 1.140417 61.7591 10 417.817 200 11.776 1.8677 0.269 1.105418 52.3786 10 997.8612 216.286 12.7649 1.5735 0.9942 1.130219 59.0602 10 1199.503 212.3769 14.2355 1.9259 1.6368 1.135720 62.0647 10 782.3541 212.8126 16.3417 2.1735 0.7642 1.121421 57.6466 10 899.7264 241.1095 17.1198 2.3377 0.8244 1.118722 78.1695 10 300 303.9107 18.6777 3.184 0.3371 1.081723 63.9669 10 721.4555 233.2439 19.5525 2.7339 0.6496 1.112924 81.4454 10.4816 300 263.1196 20.3185 4.6091 0.3181 1.088925 82.047 10.242 300 276.3105 20.4793 4.1102 0.3279 1.084926 81.5354 10 407.3847 289.2469 22.0527 3.4706 0.4306 1.086327 93.3095 10 460.6347 290.8624 23.1194 3.5922 0.5781 1.083728 77.2987 10 847.0946 243.5197 23.7081 3.6683 1.0182 1.109729 84.271 11.0556 628.0503 247.9736 24.8563 5.7193 0.7768 1.110830 95 10 680.5518 230.7705 25.9749 4.2886 1.0235 1.10131 95 10 726.217 247.0427 26.8204 4.4199 1.0638 1.098332 63.1759 35.7338 815.4502 250.6803 26.8784 141.1848 1.9473 1.246133 46.8665 45 704.2118 262.2001 26.8928 168.1049 2.1411 1.237734 66.0972 36.3491 644.0377 251.924 27.032 153.657 1.8928 1.252235 63.4694 37.0986 865.4543 259.8581 27.2314 155.9124 2.0329 1.248936 65.7791 37.3432 876.1797 259.7034 27.5357 164.2039 2.1005 1.253137 48.7786 45 750.8355 259.6498 27.6576 176.157 2.1703 1.243138 53.8153 45 571.8286 249.4247 27.9858 200.6127 2.1753 1.258139 55.3277 45 591.4365 277.3743 28.3591 208.3648 2.2865 1.256840 52.1831 45 875.1416 246.9805 28.454 185.9188 2.3039 1.25441 55.6714 45 867.8184 251.2169 29.5533 205.7847 2.3407 1.260842 56.978 45 895.9178 245.2088 29.6352 208.5368 2.4141 1.26543 59.1992 45 664.6343 264.8876 29.8885 224.7545 2.3068 1.266244 58.1049 45 835.4176 253.878 30.121 218.1782 2.3559 1.265345 60.3879 45 738.0855 255.0349 30.42 228.327 2.3521 1.2746 62.1815 45 846.2731 248.4064 30.6445 233.4057 2.473 1.274547 64.936 45 937.1024 251.8109 30.7501 246.4366 2.577 1.27848 64.7866 45 770.7681 249.6904 30.8257 243.3128 2.4831 1.279249 69.817 45 810.0259 259.0902 30.8293 260.9632 2.5826 1.284950 68.0958 45 836.1816 252.7234 31.0207 256.4056 2.5864 1.2836



(a)MRRvsTWRand (b)TWRvsandDF

Fig.4 Pareto‐optimalsolutionobtainedbyMO‐JayaalgorithmforEDMprocessinasinglesimulationrun

TheMO‐Jayaalgorithmrequired20iterationsanditrequiredaCPUtimeof7.77stoperform100 iterations. The results show that the optimumvalue ofMRR lies in the range of 0.12453(mg/s)to3.10207(mg/s).TheMRR increaseswithincreaseingapvoltageandcurrentduetoincreaseinenergyinputperpulsewhichcausesmoremeltingoftheworkpiecematerial.How‐ever,ahighenergyinputalsoresultsinmeltingoftoolmaterialincreasingtheTWR.Therefore,theTWR increaseswiththeincrease inMRR.ThebestcompromisevalueforTWRachievedbyMO‐Jayaalgorithmliesintherangeof0.00965mg/sto25.64mg/s.

ItisobservedthatMRRincreasessteadilyasthecurrentincreasesfrom10Ato45A.Howev‐er,TWR islowatlowervalueofcurrent(10A)butatahighervalueofcurrent(45A)thetoolwear rate increasesdrastically.As thepulse‐on time increases, due tomore energy inputperpulseMRRalsoincreases.However,beyondalimitingvalueofpulse‐ontimetheMRRdecreaseswithfurtherincreaseinpulse‐ontimebecausewithinfixedpulsedurationtheincreaseinpulse‐ontimeiscompensatedwithdecreaseinpulse‐offtime.Thisresultsinimproperflushingofde‐bris by the electrolyte. The accumulationof debris reduces the arc gap and thus theMRR de‐creases.Furthermore,accumulationofdebrisinthearcgapcausestheformationofarcbetweenworkpiecedebrisandthetoolresultinginincreaseinTWRwithoutremovalofmaterialfromthetool.Further,withincreaseinpulse‐on‐timelesstimeisavailableforcoolingofthetoolwhichfurtherincreasestheTWR.

Thetaperangleincreaseswithincreaseinpulseontimebecausetheworkpiecedebrisresultinabrasiveactionon thewallsof theworkpieceduring flushing.The increase in inputenergyincreasesthetaperangleduetosecondarydischargecausedduetoincreaseintemperatureofdielectricfluidandincreaseinworkpiecedebris.ThebestcompromisedvaluesfortaperanglesuggestedbyMO‐Jayaalgorithmliesintherangeof0.0811degreesto3.8046degrees.ThebestcompromisedvaluesfordelaminationfactorsuggestedbyMO‐Jayaalgorithmliesintherangeof1.0749to1.2849.

4.3 Optimization of micro‐EDM process

The objective of this work is to improve the performance of micro‐EDM milling process bymeansofprocessparameteroptimization.TheregressionmodelsforMRR(mm3/min)andTWR(mm3/min)aredevelopedbasedonactualdatacollectedbymeansofexperimentationandthesame as used as fitness functions forMO‐Jaya algorithm in order to obtainmultiple trade‐offsolutions.TheexperimentsareperformedatManufacturingScienceLaboratoryof IITKanpur,IndiaandDT110highprecision,CNCcontrolled,micro‐machiningsetupwithintegratedmulti‐processmachinetoolwasusedforthepurposeofexperimentation.Theworkpieceisdiemateri‐alEN24,cylindricaltungstenelectrode(dia.500µm)isusedastoolandconventionalEDMoilisusedasdieelectric.Thefeatureshapeconsideredforthestudyisaµ‐channelofwidthapproxi‐matelyequaltothediameterofthetool,lengthofcut1700µm,thedepthofchannelisconsid‐eredas1000µm.

Inthepresentstudythebulkmachiningapproachforµ‐EDMmillingisused.Asthebulkma‐chining approach results in excessive toolwear intermittent tool dressingwith block electro‐



dischargegrinding(EDG)processisused.Reviewofliteratureshowsthatthereareanumberofprocess parameters that affect the performance of µ‐EDMmilling process. Therefore prior toactual experimentation dimensional analysis is performed to identify themost influential pa‐rametersoftheprocesssuchasEnergy‘E’(µJ),feedrate‘F’(µm/s),toolrotationspeed‘S’(rpm)andaspectratio‘A’.Theusefullevelsoftheseparametersisidentifiedusingonefactoratatime(OFAT)analysisand2levelsofenergy,4levelsoffeedrate,3 levelsofrotationalspeed,and4levelsofaspectratioareidentified.ThemeasurementofMRRandTWRduringexperimentationiscarriedoutbymeansofaCADsoftwareslikeSolidworksandAutoCADalongwithimagesofcrosssectionattheentryandexitofthemicrochannelwhicharerecordedusingaUSBmicro‐scopewith adigital scale interface. The amountof re‐depositionon themicrochannel surfacewasstudiedbymeansofchemicalanalysisonchannelsurfaceusingenergydispersiveanalysisX‐raytechnique(EDAX).

TheregressionmodelsforMRRandTWRareformulatedbyconsideringafullfactorialexper‐imentaldesign, consideringall combinationofprocessparametervaluesa totalnumberof96experimentsareconducted.ThevaluesofMRR(mm3/min)andTWR(mm3/min)aremeasuredandrecordedasshowninTable5.TheregressionmodelsforMRRandTWRaredevelopedusingtheexperimentaldata,usingalogarithmicscale,andareexpressedbyEq.21andEq.22intheuncodedformofprocessparameters.

exp 11.15134 1.79325 log 3.20333 log 0.114931 log 0.072533 log 0.06657 log 0.251122 log 0.16314 log 0.21496 log log 0.099501 log log 0.16903 log log 0.040721 log log 0.11206 log log 0.07489 log log

0.94

(21)

Table5Designofexperimentsformicro‐EDMprocessandvaluesofMRRandTWRmeasuredafterexperimentationS.No. E(µJ) F(µm/s) S(rpm) A MRR(10‐3mm3/min) TWR(10‐3mm3/min)1 2000 60 100 1 9.16 1.992 2000 60 800 1 23.48 5.163 500 60 800 1 12.88 3.24 500 60 100 1 6.26 0.925 500 10 100 1 4.53 0.746 2000 10 800 1 12.58 2.297 500 10 800 1 8.48 1.488 500 10 500 1.5 7.06 1.089 500 25 800 1.5 10.14 1.6710 500 45 500 1.5 9.92 1.5511 500 45 800 0.5 9.39 1.4312 500 10 500 2 5.97 1.0513 500 25 100 0.5 3.6 0.5414 2000 45 500 2 16 3.6615 2000 60 500 1 19.01 4.4816 500 45 100 2 4.05 0.8317 2000 10 100 2 6.05 1.1118 500 60 500 1 9.91 2.1519 500 60 100 1.5 6.57 1.0120 500 10 800 0.5 7.34 1.1921 2000 60 800 1.5 28.17 5.8722 2000 25 800 2 19.68 3.8323 500 25 800 2 11.69 1.6124 500 25 500 0.5 6.32 0.8125 2000 10 100 1 4.24 0.5326 500 60 100 0.5 5.52 1.2727 2000 60 100 2 12.08 3.5628 2000 10 500 1 5.28 1.3429 500 25 100 1 4.56 0.7930 2000 25 500 1 10.15 2.4531 500 60 800 0.5 12.71 2.8432 500 45 500 1 9.2 1.9233 2000 60 800 2 25.39 5.1434 500 45 100 1.5 5.72 1.0235 2000 10 500 2 7.66 1.8736 500 10 500 1 6.69 1.23



Table5Designofexperimentsformicro‐EDMprocessandvaluesofMRRandTWRmeasuredafterexperimentation(continuation) 37 500 25 800 1 9.86 1.6438 2000 45 800 2 23.75 5.0639 2000 25 800 1 21 3.3340 500 60 800 2 12.02 2.141 500 60 100 2 5.62 0.9342 2000 45 100 2 11.62 3.1243 500 45 800 2 12.62 1.9644 500 60 500 0.5 9.26 1.4945 2000 25 500 1.5 15 3.3246 2000 25 500 0.5 6.7 1.1347 2000 10 800 1.5 13.32 2.7748 500 10 800 1.5 9.03 1.3649 2000 60 500 0.5 16.12 3.3350 500 45 500 2 10.63 1.7351 500 45 100 1 5.55 0.7352 2000 45 500 1 17.65 4.4953 2000 60 500 2 17.46 3.8454 500 10 100 2 4.52 0.7355 2000 45 800 1.5 29.84 6.456 500 60 500 1.5 10.08 2.0657 2000 45 500 1.5 22.29 5.0458 2000 60 100 0.5 7.32 1.1359 2000 45 100 0.5 4.84 0.9760 2000 45 800 0.5 23.2 3.8461 500 45 800 1.5 12.7 1.9762 500 45 100 0.5 5.3 1.0263 2000 10 800 0.5 9.88 1.7964 2000 25 100 1 6.13 1.2165 2000 60 800 0.5 25.64 3.5866 500 10 100 0.5 3.99 0.6367 2000 25 800 1.5 25.55 4.2368 2000 45 100 1 6.93 1.3769 500 10 500 0.5 6.02 0.9770 500 10 100 1.5 5.28 0.9371 2000 25 100 1.5 7.1 1.4472 2000 60 500 1.5 22.68 5.373 500 60 800 1.5 13.8 2.574 500 25 500 1.5 7.82 1.1975 2000 10 500 1.5 7.9 1.7376 2000 10 500 0.5 3.95 0.6477 500 25 500 2 8.48 1.3378 500 45 500 0.5 7.55 1.1179 2000 60 100 1.5 11.41 3.8280 2000 10 100 1.5 6.79 0.9581 2000 45 800 1 24.61 5.8282 500 25 100 2 4.75 0.7883 500 45 800 1 11.25 2.3384 2000 45 100 1.5 9.73 2.1485 2000 10 800 2 15.46 3.4786 500 10 800 2 11.33 1.4387 500 60 500 2 10.34 1.8388 2000 10 100 0.5 2.73 0.3189 2000 25 500 2 13.21 3.4690 500 25 100 1.5 5.31 0.8291 2000 25 100 0.5 3 0.4492 2000 25 100 2 7.88 1.8693 500 25 800 0.5 8.54 1.0794 2000 45 500 0.5 13.38 1.7995 500 25 500 1 7.44 1.5796 2000 25 800 0.5 17.29 1.79

exp 5.68347 2.22795 log 1.77173 log 1.29611 log 0.07152 log 0.175929 log 0.13946 log 0.34761 log 0.23781 log log 0.1005 log log 0.380612 log log 0.015495 log log 0.120799 log log 0.096066 log log

0.933

(22)

NowMO‐JayaalgorithmisusedtomaximizetheMRRandminimizetheTWR,simultaneously.TheregressionmodelsforMRRandTWRexpressedbyEq.21andEq.22,respectivelyareused



asfitnessfunctionsforMO‐Jayaalgorithms.TheprocessparameterboundsareexpressedbyEq.23toEq.26asfollows.

500 ≤ E ≤ 2000 (23)10 ≤ F≤ 60 (24)100 ≤ S ≤ 800 (25)0.5 ≤ A ≤ 2.0 (26)

ThePareto‐efficientsetofsolutionsobtainedusingMO‐JayaalgorithminasinglesimulationrunisshownTable6andthePareto‐frontisshowninFig.5.TheMO‐Jayaalgorithmrequired11iterationstoobtainthePareto‐efficientsetofsolutions.TheMO‐Jayaalgorithmrequired6.086stoperform100iterations.Table6ParetooptimalsolutionsetprovidedbyMO‐Jayaalgorithminasinglesimulationrunformicro‐EDMprocessS.No. E(µJ) F(µm/s) S(rpm) A MRR(10‐3mm3/min) TWR(10‐3mm3/min)

1 2000 10 100 0.5 2.6219 0.33072 2000 12.9182 100.0819 0.5 2.9267 0.37093 2000 19.5363 100.2894 0.5 3.561 0.46894 2000 22.5177 100 0.6364 4.4926 0.68375 2000 15.471 100 0.8852 4.6108 0.76716 2000 11.1055 525.5919 0.5 5.6157 0.84317 2000 14.9048 494.173 0.5018 6.2136 0.92658 2000 17.4029 520.7207 0.5028 7.0729 1.05119 2000 12.1938 660.3727 0.5 7.2438 1.053410 2000 16.9822 648.2183 0.5023 8.5232 1.230811 2000 15.3951 800 0.5 9.9806 1.38912 1999.999 16.3754 800 0.5 10.3308 1.435413 2000 18.2665 800 0.5 10.9949 1.526514 2000 23.1415 729.9279 0.5 11.4719 1.634715 2000 22.9902 800 0.5 12.6004 1.761416 2000 25.9902 781.586 0.5 13.2492 1.877317 1999.999 26.7446 800 0.5 13.8351 1.955118 2000 29.8817 793.8799 0.5 14.7207 2.107219 2000 31.589 800 0.5022 15.4229 2.223320 2000 33.7982 800 0.5 16.0848 2.334321 2000 37.0695 800 0.5 17.1046 2.516722 2000 37.6695 800 0.5 17.2904 2.550723 2000 40.8566 800 0.5033 18.3284 2.75124 2000 42.1834 800 0.5 18.6761 2.810325 2000 45.1411 800 0.5 19.5745 2.984726 2000 48.3518 800 0.5 20.5423 3.177827 2000 50.9093 779.8629 0.5 20.7107 3.262228 2000 50.6162 800 0.5 21.2207 3.316329 2000 52.5044 800 0.5 21.7841 3.433430 2000 54.6281 800 0.5 22.4155 3.566731 2000 56.967 800 0.5 23.1082 3.715432 2000 60 800 0.5 24.0027 3.911533 2000 60 800 0.5253 24.5151 4.093934 2000 60 800 0.5524 25.0289 4.281435 2000 60 800 0.5779 25.4824 4.450836 2000 60 794.4076 0.6082 25.7814 4.614837 2000 60 800 0.6292 26.3089 4.768738 2000 60 800 0.652 26.6441 4.901139 2000 60 800 0.6732 26.9399 5.019740 2000 60 800 0.686 27.1113 5.089141 1999.999 60 800 0.7105 27.4242 5.217242 1999.999 60 800 0.7441 27.8258 5.384343 2000 60 800 0.8279 28.6992 5.75844 2000 60 800 0.8464 28.8696 5.832645 1999.999 60 800 0.891 29.2525 6.002346 2000 60 800 0.9016 29.3378 6.040447 2000 60 800 0.9574 29.7536 6.228748 2000 60 800 1.0504 30.3372 6.49949 2000 60 800 1.1582 30.8707 6.752650 2000 60 800 1.906 32.1458 7.404



Fig.5Pareto‐frontobtainedbyMO‐Jayaalgorithmformicro‐EDMprocessinasinglesimulationrun

The results ofMO‐Jaya algorithmhave revealed that, in order to achieve a trade‐off betweenMRRandTWRtheoptimalsettingforpulseenergyis2000µJandanydeviationfromthisvaluemayresultinnon‐optimalvaluesofMRRandTWR.Withaspectratiofixedat0.5anincreaseinMRRisobservedwithincreaseinfeedrateandspeed.However,atextremevaluesoffeedrateandspeedtheMRR increaseswithincreaseinaspectratio.Alowvalueoffeedrate,speedandaspectratioresultsinminimumtoolwear(TWR=0.3307×10‐3mm3/min,refersolution1,Ta‐ble 6). On the other hand, a high value of feed rate, speed and aspect ratio gives a highMRR(32.1458×10‐3mm3/min,refersolution50,Table6)butattheexpenseofsignificantincreaseinTWR(7.040×10‐3mm3/min).

5. Conclusion

Multi‐objectiveoptimizationaspectsofplasmaarcmachining,electro‐dischargemachining,andmicro‐electro‐dischargemachiningprocessesareconsideredinthepresentwork.Mathematicalmodelsaredevelopedbasedontheactualexperimentaldataandthesemodelsareusedasfit‐nessfunctionsforMO‐Jayaalgorithm.

InthecaseofPAMprocess,theMO‐JayaalgorithmisappliedtooptimizesimultaneouslytheMRR andDFR.TheMO‐Jayaalgorithmhasprovided50 trade‐off solutions in8 iterations.Theresultsofoptimizationshowthatinordertoachieveatrade‐offbetweenMRRandDFRthepro‐cess planner should choose the values of current and speed close to their respective upperbounds(45Aand800mm/min).However,thevaluesofotherparameterssuchasthicknessandarcgapvoltagemustbeselectedoptimallyintherangeof1.58mmto2.5mmand128Vto165V,respectively.TheParetofrontobtainedbyMO‐Jayaalgorithmisconvexinnaturewithmaxi‐mumMRRequalto1.0769(g/s)andminimumDFRequalto0.0004(g/s).

InthecaseofEDMprocess,theMO‐JayaalgorithmisappliedtooptimizetheMRR,TWR,taperangleandDF,simultaneously.TheMO‐Jayaalgorithmhasobtained50trade‐offsolutionsin20iterations.TheMO‐Jaya algorithmcouldachieve a valueofMRR ashighas3.10207 (mg/min)and values of TWR, taper angle and DF as low as 0.00965 (mg/min), 0.0811 (degrees) and1.0749,respectively.

Inthecaseofmicro‐EDMprocess,theMO‐Jayaalgorithmrequired11iterationstoobtain50trade‐offsolutionsforMRRandTWR.Theresultsshowthat inordertoachieveatrade‐offbe‐tweenMRRandTWRahighervalueofpulseenergyisdesired.Therefore,pulseenergymaybesettoitsrespectiveupperbound(2000µJ)However,thefeedrateandrotationspeedmustbesetoptimallywithintheirrespectiveranges.TheParetofrontobtainedbyMO‐JayaalgorithmiscontinuousandconvexinnaturewiththevalueofMRRashighas0.03214(mm3/min)andTWRaslowas0.3307×10‐3(mm3/min).

ThemainadvantagesoftheMO‐Jayaalgorithmarethat:(1)thealgorithmdoesnotbur‐dentheuserwiththetaskoftuningthealgorithm‐specificparameters,and(2)thealgorithmissimpletoimplementasthesolutionsareupdatedinsinglephaseusingasingleequationandhaslowcomputationalandtimecomplexities.Theeffectofthebestandworstsolutionsinthecur‐rent population are considered simultaneouslywhich gives a high convergence speed toMO‐


Jaya algorithm without trapping into local optima. The ranking mechanism based on the concept of non-dominance relation between the solutions helps MO-Jaya algorithm to maintain the good solutions in every generation and guides the search process towards the Pareto-optimal set.

The population size in MO-Jaya algorithm is fixed at the beginning of the algorithm and is maintained constant in every generation throughout the simulation run. However, increasing or reducing the population size adaptively in every generation may save a considerable number of function evaluations which would otherwise be spent in updating a large population.

The Pareto-efficient solutions provided by MO-Jaya algorithm can be used as ready reference by the process engineer in order to set the parameter values at their optimal levels for best per-formance of machining process with sustainability. Thus the results presented in this work are very useful for real manufacturing environment. The application of MO-Jaya algorithm may be extended to other modern machining processes.

Acknowledgement The Authors are thankful to the Department of Science and Technology (DST), Ministry of Science & Technology, of the Republic of India and the Slovenian Research Agency (ARRS), Ministry of Education, Science and Sport of the Re-public of Slovenia for providing the financial support for the project entitled “Optimization of Sustainable Advanced Manufacturing Processes”.

References [1] De Wolf, D., Cardon, L., Balic, J. (2010). Parameters effecting the quality of the electrical discharge machining

process, Advances in Production Engineering and Management, Vol. 5, No. 4, 245-252. [2] Aich, U., Banerjee, S. (2016). Application of teaching learning based optimization procedure for the development

of SVM learned EDM process and its pseudo Pareto optimization, Applied Soft Computing, Vol. 39, 64-83, doi: 10.1016/j.asoc.2015.11.002.

[3] Zhang, T.Y., Owodunni, O., Gao, J. (2015). Scenarios in multi-objective optimization of process parameters for sustainable machining, Procedia CIRP, Vol. 26, 373-378, doi: 10.1016/j.procir.2014.07.186.

[4] Gupta, M.K., Sood, P.K., Sharma, V.S. (2016). Optimization of machining parameters and cutting fluids during nano-fluid based minimum quantity lubrication turning of titanium alloy by using evolutionary techniques, Journal of Cleaner Production, Vol. 135, 1276-1288, doi: 10.1016/j.jclepro.2016.06.184.

[5] Chandrasekaran, M., Muralidhar, M., Krishna, C.M., Dixit, U.S. (2010). Application of soft computing techniques in machining performance prediction and optimization : A literature review, The International Journal of Advanced Manufacturing Technology, Vol. 46, No. 5, 445-464, doi: 10.1007/s00170-009-2104-x.

[6] Jiang, Z., Zhou, F., Zhang, H, Wang, Y., Sutherland, J.W. (2015). Optimization of machining parameters considering minimum cutting fluid consumption, Journal of Cleaner Production, Vol. 108 (part A), 183-191, doi: 10.1016/ j.jclepro.2015.06.007.

[7] Yusup, N., Zain, A.M., Hashim, S.Z.M. (2012). Evolutionary techniques in optimizing machining parameters: Re-view and recent applications (2007-2011), Expert Systems with Applications, Vol. 39, No. 10, 9909-9927, doi: 10.1016/j.eswa. 2012.02.109.

[8] Rao, R.V., Kalyankar, V.D. (2014) Optimization of modern machining processes using advanced optimization techniques: A review, The International Journal of Advanced Manufacturing Technology, Vol. 73, No. 5, 1159-1188, doi: 10.1007/s00170-014-5894-4.

[9] Goswami, D., Chakraborty, S. (2015), Parametric optimization of ultrasonic machining process using gravita-tional search and fireworks algorithms, Ain Shams Engineering Journal, Vol. 6, No. 1, 315-331, doi: 10.1016/ j.asej.2014.10.009.

[10] Saha, A., Mondal, S.C. (2016). Multi-objective optimization in WEDM process of nanostructured hardfacing mate-rials through hybrid techniques, Measurement, Vol. 94, 46-59, doi: 10.1016/j.measurement.2016.07.087.

[11] Maity, K.P., Bagal, D.K. (2015). Effect of process parameters on cut quality of stainless steel of plasma arc cutting using hybrid approach, The International Journal of Advanced Manufacturing Technology, Vol. 78, No. 1, 161-175, doi: 10.1007/s00170-014-6552-6.

[12] Rao, R.V., Rai, D.P., Balic, J. (2016). Multi-objective optimization of machining and micro-machining processes using non-dominated sorting teaching-learning-based optimization algorithm, Journal of Intelligent Manufactur-ing, doi:10.1007/s10845-016-1210-5.

[13] Li, C., Xiao, Q., Tang, Y., Li, L. (2016). A method integrating Taguchi, RSM and MOPSO to CNC machining parame-ters optimization for energy saving, Journal of Cleaner Production, Vol. 35, 263-275, doi: 10.1016/j.jclepro. 2016.06.097.

[14] Rao, R.V. (2016). Jaya: A simple and new optimization algorithm for solving constrained and unconstrained optimization problems, International Journal of Industrial Engineering Computations, Vol. 7, No. 1, 19-34, doi: 10.5267/j.ijiec.2015.8.004.


http://dx.doi.org/10.1016/j.asoc.2015.11.002

http://dx.doi.org/10.1016/j.asoc.2015.11.002

https://doi.org/10.1016/j.procir.2014.07.186

http://www.sciencedirect.com/science/article/pii/S095965261630871X

http://www.sciencedirect.com/science/article/pii/S095965261630871X

https://doi.org/10.1016/j.jclepro.2016.06.184

https://doi.org/10.1007/s00170-009-2104-x

http://www.sciencedirect.com/science/article/pii/S0959652615007192




https://doi.org/10.1016/j.eswa.2012.02.109

https://doi.org/10.1016/j.eswa.2012.02.109

https://doi.org/10.1007/s00170-014-5894-4



https://doi.org/10.1016/j.asej.2014.10.009

https://doi.org/10.1016/j.asej.2014.10.009



https://doi.org/10.1016/j.measurement.2016.07.087

https://doi.org/10.1007/s00170-014-6552-6

https://doi.org/10.1007/s10845-016-1210-5





https://doi.org/10.5267/j.ijiec.2015.8.004

https://doi.org/10.5267/j.ijiec.2015.8.004

Documents

R.V.a,* D.P. - APEM journalapem-journal.org/Archives/2016/APEM11-4_271-286.pdf · Rao, Rai, Ramkumar, Balic 272 Advances in Production Engineering & Management 11(4) 2016 mization