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OpticsLaserTechnology40ofInstitute1lossspeed.KeywordsTaguchimethodLaserbeamcuttingHybridapproachindustriestoachievecomplexshapes/profileswithclosemethodinwhichsheetmaterialiscutmainlyduetomeltingandvaporisation.Themoltenmaterialisejectedwiththehelpofhighpressureassistgasjet4.TheschematicoftheInmostoftheexperimentalinvestigationsoftheLBCresearchershaveincorporateddesignofexperimentsmethodologiessuchastheresponsesurfacemethodologyRSMandTaguchimethodologyTMduringexperiARTICLEINPRESSmentalstudyofLBCprocess.Tametal.11appliedtheTaguchimethodtostudythelasercuttingprocessfor4.5mmthickmildsteelsheet.The00303992/seefrontmatterr2007ElsevierLtd.Allrightsreserved.doi10.1016/j.optlastec.2007.09.002C3Correspondingauthor.Tel.915322271812fax915322445101.Emailaddressavanishdubeyyahoo.comA.KumarDubey.tolerancesforcuttingofsteelsheets3.ThemostwidelyusedindustriallasersforcuttingofsheetmetalsaregaseousCO2andsolidstateNdYAG.TherehasbeengrowinginterestinrecentyearsintheuseofpulsedNdYAGlasersforprecisioncuttingofthinsheetmetalsbecauseofitshighintensity,lowmeanbeampower,goodfocusingcharacteristics,andnarrowheataffectedzoneHAZ.LBCisathermalenergybasednonconventionalcuttingprocess,researchershavevariedonefactoratatimetoanalysetheeffectofinputprocessparametersonoutputqualitycharacteristicsorresponses5–10.Butthistechniquerequiresalargenumberofexperimentalrunsbecauseonlyonefactorisvariedineachrun,keepingallotherfactorsconstant.Also,inthistechnique,theinteractioneffectsamongvariousinputprocessparametersarenotconsidered.Toovercometheseproblems,some1.IntroductionThelaserwasinventedin1960sandhaswideapplicationsinthefieldoffinecuttingofsheetmetalsduetoitsprecisionandhighintensity1,2.LaserbeamcuttingLBCcanbesuccessfullyusedforthecuttingofconductiveandnonconductivedifficulttocutadvancedengineeringmaterialssuchasreflectivemetals,plastics,rubbers,ceramicsandcomposites.Apartfromcuttingdifficulttocutmaterials,LBCismostwidelyusedinLBCprocesshasbeenshowninFig.1.Sinceitsintroduction,LBChasalwaysbeenamajorresearchareaforgettingtheexceptionallygoodqualityofcut.Thequalityofcutsolelydependsonthesettingofprocessparameterssuchaslaserpower,typeandpressureofassistgas,sheetmaterialthicknessanditscomposition,cuttingspeed,andmodeofoperationcontinuouswaveorpulsedmode.Alotofexperimentalinvestigationhasbeenundertakenwiththeaimofanalysingtheeffectofprocessparametersoncutgeometry,andcutsurfacequality.MultiobjectiveoptimisationAvanishKumarDubeyDepartmentofMechanicalEngineering,MotilalNehruNationalReceived31July2007receivedinrevisedformAbstractThispaperpresentsahybridTaguchimethodandresponsesurfacebeamcuttingprocess.TheapproachfirstusestheTaguchiqualitysuchasassistgaspressure,pulsewidth,pulsefrequencyandcuttingcentralvaluesintheresponsesurfacemethodtodevelopandoptimiseKerfwidthKW,andmaterialremovalrateMRR,thatareofdifferentthehigherthebettertype,havebeenselectedforsimultaneousoptimisation.qualitycharacteristicswhenthehybridapproachisused,ascomparedr2007ElsevierLtd.Allrightsreserved.2008562–570laserbeamcuttingprocessC3,VinodYadavaofTechnology,Teliarganj,Allahabad,UP211004,IndiaSeptember2007accepted7September2007methodTMRSMforthemultiresponseoptimisationofalaserfunctiontofindtheoptimumlevelofinputcuttingparametersTheoptimuminputparametervaluesarefurtherusedasthethesecondorderresponsemodel.ThetwoqualitycharacteristicsnatureKWisofthesmallerthebettertype,whileMRRisofTheresultsshowconsiderableimprovementinboththetheresultsofasingleapproach.www.elsevier.com/locate/optlastecARTICLEINPRESSNomenclaturebregressioncoefficientDcompositedesirabilitydindividualdesirabilityknumberofresponsesorqualitycharacteristicsLijthequalitylossfortheithqualitycharacteristicatthejthtrialconditionorrunLimaximumqualitylossfortheithqualitycharacteristicamongalltheexperimentalrunsmMeanofmultipleS/NratiosofallexperimentalrunsnnumberofexperimentalrunspnumberofcontrolfactorsorinputprocessparametersA.KumarDubey,V.Yadava/OpticsLasersignaltonoiseS/Nratioofoverallfigureofmeritwasconsideredasqualityfunction.ThisqualityfunctionintegratestheweightedeffectsofqualitycharacteristicsKerfwidthKW,surfaceroughness,microhardness,slopeofcutedgeandHAZandcostcomponentscuttingspeed,oxygenpressureandbeampower.Limetal.12haveappliedthesameapproachforthestudyofthesurfaceroughnessobtainedduringhighspeedlasercuttingofstainlesssteelsheets.Lietal.13havealsoappliedTaguchisrobustdesignmethodologytostudythewidthofcutandHAZduringlasercuttingofquadflatnoQFNleadpackagesusingadiodepumpedsolidstatelaserDPSSLsystem.Thecuttingparameterstakenarelasercurrent,laserfrequencyandcuttingspeed.Mathewetal.14performedparametricstudiesonpulsedNdYAGlasercuttingoffibrereinforcedplasticcompositesheet2mmthick.AcentralcompositedesignCCDwithuniformprecisionwasusedforexperimentaldesignandasecondorderresponsesurfacemodelforHAZGASJETDRAGLINESMELTINGORSLAGNOZZLEGASFOCUSINGOPTICSLASERBEAMCUTTINGEDGEONWORKPIECEFig.1.Schematicoflaserbeamcutting.andKerftaperwasdeveloped.Theinputprocessparameterswerecuttingspeed,pulseenergy,pulseduration,pulserepetitionrateandgaspressure.Almeidaetal.15appliedfactorialdesignapproachtodeterminetheeffectsofpulseenergy,overlappingrateandtypeofassistgasonthesurfaceroughnessanddrossformationedgeirregularityduringNdYAGlasercuttingofpuretitaniumandtitaniumalloyTi6Al4V.ThedesignofexperimentsbasedstudiesonLBCprocesssofarhavebeenmainlyaimedattheoptimisationofthesinglequalitycharacteristicatatime.Ithasbeenfoundthattheoptimumparametersettingsforonequalitycharacteristicmaydeteriorateotherqualitycharacteristics.Astheaimofamanufacturingprocessisalwaystoimprovetheoverallqualityofaproductitisnecessarytooptimisethemultiplequalitycharacteristicssimultaneously.Antony16hasdemonstratedaTaguchiqualitylossfunctionbasedmultiobjectiveoptimisationtechniqueformanufacturingprocessestakinganexampleofelectrowiweightingfactorassignedtoithresponseorqualitycharacteristicxiithinputprocessparameterorcontrolfactorYjtotalnormalisedqualitylossvalueinjthexperimentalrunyiresponseorobservedqualityvalueinithexperimentalrunyijnormalisedqualitylossvalueforithexperimentalrunandjthqualitycharacteristicZS/NratioZopredictedmultipleS/NratioatoptimumparameterlevelsZejmultipleS/NratioofjthtrialconditionorexperimentalrunTechnology402008562–570563nicassemblyproblem.Hehasfoundconsiderableimprovementinmultiplequalitycharacteristics,incomparisontosinglequalitycharacteristics.Differenthybridapproacheshaverecentlybeenusedfortheoptimisationofdifferentmachiningprocesses.Taguchimethodwithfuzzylogic17orwithgreyrelationalanalysis18hasbeenusedtooptimisetheelectricaldischargemachiningprocessanonconventionalthermalbasedmachiningprocesswithmultiplemachiningperformance.Chiadamrong19hassuggestedasequentialintegrationapproachofTMandRSMtooptimisethequalitycharacteristicsinmanufacturingsystem.Hedemonstratedthehybridmethodologybytakingacasestudyofprintedcircuitboardmanufacturingplantandfoundasignificantreductioninqualityloss.ThehybridapproachofTMandRSMhasyetnotbeenappliedinthestudyofLBCprocesswithsingleormultipleperformancemeasures.InthepresentpaperahybridTaguchimethodandresponsesurfacemethodTMRSMapproachhasbeenusedtodeveloptheresponsemodelsandtooptimisetheselectionofOAisbasedonthetotaldegreeoffreedomdofofARTICLEINPRESSLasertheprocess.Mathematically,thedofcanbecomputedas22dof¼ðnumberoflevelsC01Þforeachcontrolfactor½þðnumberoflevelsforAC01ÞC2ðnumberoflevelsforBC01Þforeachinteractionþ1C138,ð1Þwhere,AandBaretheinteractingcontrolfactors.IntheTaguchimethod,theS/NratioZisusedtorepresentthequalitycharacteristicsfortheobserveddataorresponses.Here,thesignalrepresentsthedesirablevalueandthenoiserepresentstheundesirablevalueandS/Nratioexpressesthescatteraroundthedesiredvalue.ThelargertheS/Nratio,smallerwillbethescatter.Dependingontheexperimentalobjectives,thereareseveralqualitycharacteristics.Inthepresentcase,asmallervalueofKWandahighervalueofMRRaredesirable.IntheTaguchimethodthesecharacteristicsaretermedSBtypeandHBtyperespectively.Mathematically,theS/NratiosZforSBandHBtypequalitycharacteristicscanbecomputedas21–22LBCprocessformultiplequalitycharacteristicssuchasKW,andmaterialremovalrateMRR.ApulsedNdYAGlaserbeamisusedforcuttingofthinsheetsofmagneticmaterialgrainorientedhighsiliconalloysteelsheetsusedintransformers.ThequalitycharacteristicsoftwodifferentnatureKWisofsmallerthebetterSBtypeandMRRisofhigherthebetterHBtypewithunequalweightingfactorKW80,andMRR20havebeenselected.Firstly,TMisappliedtodeterminetheoptimumprocessparametersformultiplequalitycharacteristicsi.e.forminimumKWandmaximumMRR.TheoutputoptimumparametervaluesfromTMisfurtherusedascentralvalueinRSM.ThesecondorderresponsemodelforKWandMRRhasbeendevelopedbyperformingtheexperimentsusingthecentralcompositerotatabledesignCCRDmatrix20.TheMINITABsoftwarehasbeenusedtocalculatethefinalresultsofmultiobjectiveoptimisation.TheresultsofmultiobjectiveoptimisationusingTaguchisqualitylossfunctiononlyhavealsobeencomparedwiththeresultsfromhybridapproach.2.Experimentalplanningmethods2.1.TaguchimethodIntheTaguchimethod,theoptimumlevelofinputprocessparametersorcontrolfactorsaredecidedonthebasisofstatisticalanalysisofexperimentalresultsthatmakestheprocessinsensitivetotheeffectofvariationsduetouncontrollableornoisefactorssuchasenvironmentaltemperature,humidityandvibration.Inthismethod,theexperimentsareperformedasperspeciallydesignedexperimentalmatrixknownasorthogonalarrayOA21–22.TheA.KumarDubey,V.Yadava/Optics564Z¼C010log10ðMSDÞ,2where,MSDmeansquaredeviationfromthedesiredvalueandcommonlyknownasqualitylossfunction.ForSBC0typeMSD¼1nXni¼1y2i,3ForHBC0typeMSD¼1nXni¼11y2i,4where,yiistheobservedresponseorqualityvalueattheithtrialorexperimentalrunandnisthenumberoftrialsatsameparameterlevel.Inmultiobjectiveoptimisation,asingleoverallS/NratioforallqualitycharacteristicsiscomputedinplaceofseparateS/Nratiosforeachofthequalitycharacteristic.ThisoverallS/NratioisknownwiththenameofmultipleS/NratioMSNR.TheMSNRforjthtrialðZejÞiscomputedasgivenbelow16.Zej¼C010log10ðYjÞ,5Yj¼Xki¼1wiyij,6yij¼LijLiC3,7whereYjisthetotalnormalisedqualitylossinjthtrial,wirepresentstheweightingfactorfortheithqualitycharacteristic,kisthetotalnumberofqualitycharacteristicsandyijisthenormalisedqualitylossassociatedwiththeithqualitycharacteristicatthejthtrialcondition,anditvariesfromaminimumofzerotoamaximumof1.LijisthequalitylossorMSDfortheithqualitycharacteristicatthejthtrial,andLiisthemaximumqualitylossfortheithqualitycharacteristicamongalltheexperimentalruns.2.2.ResponsesurfacemethodRSMisacollectionofstatisticalandmathematicalmethodsthatareusefulforthemodellingandoptimisationoftheengineeringscienceproblems.Inthistechnique,themainobjectiveistooptimisetheresponsesthatareinfluencedbyvariousinputprocessparameters.RSMalsoquantifiestherelationshipbetweenthecontrollableinputparametersandtheobtainedresponses.InmodellingandoptimisationofmanufacturingprocessesusingRSM,thesufficientdataiscollectedthroughdesignedexperimentation.Ingeneral,asecondorderregressionmodelisdevelopedbecausefirstordermodelsoftengivelackoffit23.AccordingtoRSM,alltheinputprocessparametersareassumedtobemeasurable,thecorrespondingresponsescanbeexpressedasfollowsy¼fðx1x2xpÞ,8where,x1,x2,y,xpareinputprocessparametersandyisTechnology402008562–570theresponsewhichisrequiredtobeoptimised.Here,itisassumedthattheindependentvariablesinputprocessNozzlediameter1.0mm,nozzletipdistance1.0mm,andsheetmaterialthickness0.5mmwerekeptconstantthroughouttheexperimentation.ThetwoqualitycharacteristicsanalysedareKWandMRR.Thegrainorientedhighsiliconalloysteelsheetamagneticmaterialsheetusedintransformercoreswasusedintheexperimentsassheetmaterial.Twocutseachof15mmlengthwereARTICLEINPRESSLaserTechnology402008562–570565parametersarecontinuousandcontrollablebyexperimentswithnegligibleerrors.Itisalsorequiredtofindasuitableapproximationforthetruefunctionalrelationshipbetweenindependentvariablesandresponses.Usually,asecondorderregressionmodelasgivenbelowisutilisedinRSM.y¼b0þXpi¼1bixiþXpi¼1biix2iþXiXjbijxixj,9where,allbsareregressioncoefficientsdeterminedbyleastsquaremethod23.Inordertoestimatetheregressioncoefficientsinthismodeleachvariableximustbetakenatleastthreedifferentlevels.Thisrequires3pnumberofexperimentsinfactorialdesignbutitisatediousjobwithlargenumberoffactors.ForfittingsecondordermodelanewdesignknownasCCDisgenerallyused20.Itrequiresexperimentationwith2pnumberofexperimentsoffactorialdesignand2p1combinationofadditionalfactors.Thesecombinationsaretakenasgivenbelowð00...0ÞðC0a0...0Þða0...0Þð0C0a...0Þð0a...0Þ...ð00...C0aÞð00...aÞHere,thevalueofcodeaisequalto2p1/4,anditisintroducedtoprovidetheorthogonalpropertytoarray.Thecodedlevel0representsthecentralvalueofinputprocessparameters.Itisimportantforasecondordermodeltoprovideoptimumpredictionabouttheprocessbehaviourwithinthespecifiedrangeofallinputprocessparameters.Sothemodelshouldhaveareasonablyconsistentandstablepredictionofresponsesatpointsofinterestxi.ThiscanbeachievedbyCCRD.AccordingtoCCRDmethodology,standarderroriskeptsameforallpointsthatareatthesamedistancefromthecentreoftheregion.Thiscanbestatedmathematicallyasfollows20x21þx22þC1C1C1þx2p¼constant10CCRDrequiresminimumfivelevelsofallfactorsforthecalculationofregressioncoefficients.Inthissituation,thetotalnumberofcombinationsorrunsrequiredbecomes2p2pmorethanonerunsatcentre.InpresentcaseoffourcontrolfactorsanstandardCCRDmatrixwith7centralpointrunshasbeenselected20.Thedevelopedresponsemodelisusedforfindingoptimumlevelofinputprocessparameters.Thisisobtainedbylocationofstationarypointsthatwillleadtoapointofmaximumorminimumresponse23.3.ExperimentalprocedureandoperatingparametersTheexperimentalstudieswereperformedona200WpulsedNdYAGlaserbeammachiningsystemwithCNCworktable.Theoxygenisusedasanassistgas.ThevariableinputprocessparametersorcontrolfactorsA.KumarDubey,V.Yadava/Opticstakenareassistgaspressure,pulsewidth,pulsefrequency,andcuttingspeed.Focallengthoflensusedis50.0mm.obtainedineachexperimentalrun.TheKWwasmeasuredusingtheToolMakersMicroscopeModelRTM900,RADICALInstruments,Indiaat10C2magnification.TheKWmmtakenisthemathematicalaverageoftwocutscorrespondingtosameexperimentalrun.KWofeachcuthasbeenmeasuredatthreedifferentplacesatthetopofthesheet.AverageofthesethreemeasurementsrepresentstheKWofeachcut.TheMRRmg/miniscalculatedbyusingthefollowingformulaMRR¼ðLossofmassduringeachcutC2cuttingspeedÞlengthofcut.11TheMRRcalculatedisalsotakenasaverageoftwocuts.ThelossofmasswasobtainedbyweighingthespecimenbeforeandafterthecuttingusingElectronicBalanceModelAC2120,ShimandzuCorporation,Japan.Thecontrolfactorstakenarethegaspressure1.5–3.5kg/cm2,pulsewidthorpulseduration1.0–1.4ms,pulsefrequency20–28Hz,andcuttingspeed25–75mm/min.ThenumericalvaluesoffactorsatdifferentlevelsareshowninTable1.Anexhaustivepilotexperimentationisdonetodecidetheparameterrangeforqualitycut.Here,thequalitycutbasicallyrepresentsthecompletethroughanddrossfreecuttingwithoutanyburningeffectaspervisualinspectionthroughnakedeye.Forexample,theminimumpulsewidth,maximumcuttingspeedandgaspressurewerefoundtobe0.6ms,125mm/minand4.5kg/cm2,respectivelyforcompletethroughcuttingbut,belowthepulsewidthof1.0ms,andbeyondthecuttingspeedof75mm/minandgaspressureof3.5kg/cm2,thecuttingwasnotfreefromburningeffectand/ordrossadhesiontothebottomsurfaceofthesheet.ThequalitycharacteristicsmeasuredareKWandMRR.TheinitialsettingofinputparametersisgaspressureC01.5kg/cm2,pulsewidthC01.0ms,pulsefrequencyC020Hz,andcuttingspeedC025mm/min.Inpresentcaseoffourparametersatthreedifferentlevelsassumingnointeractionbetweenfactors,thedofhasTable1ControlfactorsandtheirlevelsusedinOAdesignmatrixSymbolFactorsUnitLevel1Level2Level3AGaspressurekg/cm21.52.53.5BPulsewidthms1.01.21.4CPulsefrequencyHz202428DCuttingspeedmm/min255075
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