外文翻译--多目标优化激光切割工艺 英文版.pdf

Optics&LaserTechnology40ofInstitute1lossspeed.Keywords:Taguchimethod；Laserbeamcutting；Hybridapproachindustriestoachievecomplexshapes/profileswithclosemethodinwhichsheetmaterialiscutmainlyduetomeltingandvaporisation.Themoltenmaterialisejectedwiththehelpofhigh-pressureassistgasjet4.TheschematicoftheInmostoftheexperimentalinvestigationsoftheLBCresearchershaveincorporateddesignofexperimentsmethodologiessuchastheresponsesurfacemethodology(RSM)andTaguchimethodology(TM)duringexperi-ARTICLEINPRESSmentalstudyofLBCprocess.Tametal.11appliedtheTaguchimethodtostudythelasercuttingprocessfor4.5mmthickmildsteelsheet.The0030-3992/$-seefrontmatterr2007ElsevierLtd.Allrightsreserved.doi:10.1016/j.optlastec.2007.09.002C3Correspondingauthor.Tel.:+915322271812；fax:+915322445101.E-mailaddress:(A.KumarDubey).tolerancesforcuttingofsteelsheets3.ThemostwidelyusedindustriallasersforcuttingofsheetmetalsaregaseousCO2andsolidstateNd:YAG.TherehasbeengrowinginterestinrecentyearsintheuseofpulsedNd:YAGlasersforprecisioncuttingofthinsheetmetalsbecauseofitshighintensity,lowmeanbeampower,goodfocusingcharacter-istics,andnarrowheataffectedzone(HAZ).LBCisathermalenergybasednon-conventionalcuttingprocess,researchershavevariedonefactoratatimetoanalysetheeffectofinputprocessparametersonoutputqualitycharacteristicsorresponses510.Butthistechniquerequiresalargenumberofexperimentalrunsbecauseonlyonefactorisvariedineachrun,keepingallotherfactorsconstant.Also,inthistechnique,theinteractioneffectsamongvariousinputprocessparametersarenotconsidered.Toovercometheseproblems,some1.IntroductionThelaserwasinventedin1960sandhaswideapplica-tionsinthefieldoffinecuttingofsheetmetalsduetoitsprecisionandhighintensity1,2.Laserbeamcutting(LBC)canbesuccessfullyusedforthecuttingofconductiveandnonconductivedifficult-to-cutadvancedengineeringmaterialssuchasreflectivemetals,plastics,rubbers,ceramicsandcomposites.Apartfromcuttingdifficult-to-cutmaterials,LBCismostwidelyusedinLBCprocesshasbeenshowninFig.1.Sinceitsintroduction,LBChasalwaysbeenamajorresearchareaforgettingtheexceptionallygoodqualityofcut.Thequalityofcutsolelydependsonthesettingofprocessparameterssuchaslaserpower,typeandpressureofassistgas,sheetmaterialthicknessanditscomposition,cuttingspeed,andmodeofoperation(continuouswaveorpulsedmode).Alotofexperimentalinvestigationhasbeenundertakenwiththeaimofanalysingtheeffectofprocessparametersoncutgeometry,andcutsurfacequality.Multi-objectiveoptimisationAvanishKumarDubeyDepartmentofMechanicalEngineering,MotilalNehruNationalReceived31July2007；receivedinrevisedformAbstractThispaperpresentsahybridTaguchimethodandresponsesurfacebeamcuttingprocess.TheapproachfirstusestheTaguchiqualitysuchasassistgaspressure,pulsewidth,pulsefrequencyandcuttingcentralvaluesintheresponsesurfacemethodtodevelopandoptimiseKerfwidth(KW),andmaterialremovalrate(MRR),thatareofdifferentthehigherthebettertype),havebeenselectedforsimultaneousoptimisation.qualitycharacteristicswhenthehybridapproachisused,ascomparedr2007ElsevierLtd.Allrightsreserved.(2008)562570laserbeamcuttingprocessC3,VinodYadavaofTechnology,Teliarganj,Allahabad,UP211004,IndiaSeptember2007；accepted7September2007method(TMRSM)forthemulti-responseoptimisationofalaserfunctiontofindtheoptimumlevelofinputcuttingparametersTheoptimuminputparametervaluesarefurtherusedasthethesecond-orderresponsemodel.Thetwoqualitycharacteristicsnature(KWisofthesmaller-the-bettertype,whileMRRisofT/locate/optlastecARTICLEINPRESSNomenclaturebregressioncoefficientDcompositedesirabilitydindividualdesirabilityknumberofresponsesorqualitycharacteristicsLijthequalitylossfortheithqualitycharacteristicatthejthtrialconditionorrunLi*maximumqualitylossfortheithqualitycharacteristicamongalltheexperimentalrunsmMeanofmultipleS/NratiosofallexperimentalrunsnnumberofexperimentalrunspnumberofcontrolfactorsorinputprocessparametersA.KumarDubey,V.Yadava/Optics&Lasersignal-to-noise(S/N)ratioofoverallfigure-of-meritwasconsideredasqualityfunction.Thisqualityfunctionintegratestheweightedeffectsofqualitycharacteristics(Kerfwidth(KW),surfaceroughness,micro-hardness,slopeofcutedgeandHAZ)andcostcomponents(cuttingspeed,oxygenpressureandbeampower).Limetal.12haveappliedthesameapproachforthestudyofthesurfaceroughnessobtainedduringhigh-speedlasercuttingofstainlesssteelsheets.Lietal.13havealsoappliedTaguchisrobustdesignmethodologytostudythewidthofcutandHAZduringlasercuttingof(quadflatno(QFN)lead)packagesusingadiodepumpedsolidstatelaser(DPSSL)system.Thecuttingparameterstakenare:lasercurrent,laserfrequencyandcuttingspeed.Mathewetal.14performedparametricstudiesonpulsedNd:YAGlasercuttingoffibrereinforcedplasticcompositesheet(2mmthick).Acentralcompositedesign(CCD)withuniformprecisionwasusedforexperimentaldesignandasecond-orderresponsesurfacemodelforHAZGASJETDRAGLINESMELTINGORSLAGNOZZLEGASFOCUSINGOPTICSLASERBEAMCUTTINGEDGEONWORKPIECEFig.1.Schematicoflaserbeamcutting.andKerftaperwasdeveloped.Theinputprocessparameterswerecuttingspeed,pulseenergy,pulsedura-tion,pulserepetitionrateandgaspressure.Almeidaetal.15appliedfactorialdesignapproachtodeterminetheeffectsofpulseenergy,overlappingrateandtypeofassist-gasonthesurfaceroughnessanddrossformation(edgeirregularity)duringNd:YAGlasercuttingofpuretitaniumandtitaniumalloy(Ti6Al4V).ThedesignofexperimentsbasedstudiesonLBCprocesssofarhavebeenmainlyaimedattheoptimisationofthesinglequalitycharacteristicatatime.Ithasbeenfoundthattheoptimumparametersettingsforonequalitycharacteristicmaydeteriorateotherqualitycharacteristics.Astheaimofamanufacturingprocessisalwaystoimprovetheoverallqualityofaproductitisnecessarytooptimisethemultiplequalitycharacteristicssimulta-neously.Antony16hasdemonstratedaTaguchiqualitylossfunctionbasedmulti-objectiveoptimisationtechniqueformanufacturingprocessestakinganexampleofelectro-wiweightingfactorassignedtoithresponseorqualitycharacteristicxiithinputprocessparameterorcontrolfactorYjtotalnormalisedqualitylossvalueinjthexperimentalrunyiresponseorobservedqualityvalueinithexperimentalrunyijnormalisedqualitylossvalueforithexperi-mentalrunandjthqualitycharacteristicZS/NratioZopredictedmultipleS/NratioatoptimumparameterlevelsZejmultipleS/NratioofjthtrialconditionorexperimentalrunTechnology40(2008)562570563nicassemblyproblem.Hehasfoundconsiderableim-provementinmultiplequalitycharacteristics,incomparisontosinglequalitycharacteristics.Differenthybridapproacheshaverecentlybeenusedfortheoptimisationofdifferentmachiningprocesses.Taguchimethodwithfuzzylogic17orwithgreyrelationalanalysis18hasbeenusedtooptimisetheelectricaldischargemachiningprocess(anon-conventionalthermalbasedmachiningprocess)withmultiplemachiningperformance.Chiadamrong19hassuggestedasequentialintegrationapproachofTMandRSMtooptimisethequalitycharacteristicsinmanufacturingsystem.Hedemonstratedthehybridmethodologybytakingacasestudyofprintedcircuitboardmanufacturingplantandfoundasignificantreductioninqualityloss.ThehybridapproachofTMandRSMhasyetnotbeenappliedinthestudyofLBCprocesswithsingleormultipleperformancemeasures.InthepresentpaperahybridTaguchimethodandresponsesurfacemethod(TMRSM)approachhasbeenusedtodeveloptheresponsemodelsandtooptimisetheselectionofOAisbasedonthetotaldegreeoffreedom(dof)ofARTICLEINPRESS&Lasertheprocess.Mathematically,thedofcanbecomputedas22:dofnumberoflevelsC01foreachcontrolfactornumberoflevelsforAC01C2numberoflevelsforBC01foreachinteraction1C138,1where,AandBaretheinteractingcontrolfactors.IntheTaguchimethod,theS/Nratio(Z)isusedtorepresentthequalitycharacteristicsfortheobserveddataorresponses.Here,thesignalrepresentsthedesirablevalueandthenoiserepresentstheundesirablevalueandS/Nratioexpressesthescatteraroundthedesiredvalue.ThelargertheS/Nratio,smallerwillbethescatter.Dependingontheexperimentalobjectives,thereareseveralqualitycharacteristics.Inthepresentcase,asmallervalueofKWandahighervalueofMRRaredesirable.IntheTaguchimethodthesecharacteristicsaretermedSBtypeandHBtyperespectively.Mathematically,theS/Nratios(Z)forSBandHBtypequalitycharacteristicscanbecomputedas2122:LBCprocessformultiplequalitycharacteristicssuchasKW,andmaterialremovalrate(MRR).ApulsedNd:YAGlaserbeamisusedforcuttingofthinsheetsofmagneticmaterial(grainorientedhighsilicon-alloysteelsheetsusedintransformers).Thequalitycharacteristicsoftwodifferentnature(KWisofsmaller-the-better(SB)typeandMRRisofhigher-the-better(HB)type)withunequalweightingfactor(KW:80%,andMRR:20%)havebeenselected.Firstly,TMisappliedtodeterminetheoptimumprocessparametersformultiplequalitycharacteristics(i.e.forminimumKWandmaximumMRR).Theoutput(optimumparametervalues)fromTMisfurtherusedascentralvalueinRSM.Thesecond-orderresponsemodelforKWandMRRhasbeendevelopedbyperformingtheexperimentsusingthecentralcompositerotatabledesign(CCRD)matrix20.TheMINITABsoftwarehasbeenusedtocalculatethefinalresultsofmulti-objectiveoptimisation.Theresultsofmulti-objectiveoptimisationusingTaguchisqualitylossfunctiononlyhavealsobeencomparedwiththeresultsfromhybridapproach.2.Experimentalplanningmethods2.1.TaguchimethodIntheTaguchimethod,theoptimumlevelofinputprocessparametersorcontrolfactorsaredecidedonthebasisofstatisticalanalysisofexperimentalresultsthatmakestheprocessinsensitivetotheeffectofvariationsduetouncontrollableornoisefactorssuchasenvironmentaltemperature,humidityandvibration.Inthismethod,theexperimentsareperformedasperspeciallydesignedexperi-mentalmatrixknownasorthogonalarray(OA)2122.TheA.KumarDubey,V.Yadava/Optics564ZC010log10MSD,(2)where,MSD=meansquaredeviationfromthedesiredvalueandcommonlyknownasqualitylossfunction.ForSBC0type；MSD1=nXni1y2i#,(3)ForHBC0type；MSD1=nXni11=y2i#,(4)where,yiistheobservedresponseorqualityvalueattheithtrialorexperimentalrunandnisthenumberoftrialsatsameparameterlevel.Inmulti-objectiveoptimisation,asingleoverallS/NratioforallqualitycharacteristicsiscomputedinplaceofseparateS/Nratiosforeachofthequalitycharacteristic.ThisoverallS/NratioisknownwiththenameofmultipleS/Nratio(MSNR).TheMSNRforjthtrialZejiscomputedasgivenbelow16.ZejC010log10Yj,(5)YjXki1wiyij,(6)yijLijLiC3,(7)whereYjisthetotalnormalisedqualitylossinjthtrial,wirepresentstheweightingfactorfortheithqualitycharacteristic,kisthetotalnumberofqualitycharacter-isticsandyijisthenormalisedqualitylossassociatedwiththeithqualitycharacteristicatthejthtrialcondition,anditvariesfromaminimumofzerotoamaximumof1.LijisthequalitylossorMSDfortheithqualitycharacteristicatthejthtrial,andLi*isthemaximumqualitylossfortheithqualitycharacteristicamongalltheexperimentalruns.2.2.ResponsesurfacemethodRSMisacollectionofstatisticalandmathematicalmethodsthatareusefulforthemodellingandoptimisationoftheengineeringscienceproblems.Inthistechnique,themainobjectiveistooptimisetheresponsesthatareinfluencedbyvariousinputprocessparameters.RSMalsoquantifiestherelationshipbetweenthecontrollableinputparametersandtheobtainedresponses.InmodellingandoptimisationofmanufacturingprocessesusingRSM,thesufficientdataiscollectedthroughdesignedexperimentation.Ingeneral,asecond-orderregressionmodelisdevelopedbecausefirst-ordermodelsoftengivelack-of-fit23.AccordingtoRSM,alltheinputprocessparametersareassumedtobemeasurable,thecorrespondingresponsescanbeexpressedasfollows:yfx1；x2；:；xp,(8)where,x1,x2,y,xpareinputprocessparametersandyisTechnology40(2008)562570theresponsewhichisrequiredtobeoptimised.Here,itisassumedthattheindependentvariables(inputprocessNozzlediameter(1.0mm),nozzletipdistance(1.0mm),andsheetmaterialthickness(0.5mm)werekeptconstantthroughouttheexperimentation.Thetwoqualitychar-acteristicsanalysedareKWandMRR.Thegrainorientedhighsilicon-alloysteelsheet(amagneticmaterialsheetusedintransformercores)wasusedintheexperimentsassheetmaterial.Twocutseachof15mmlengthwereARTICLEINPRESS&LaserTechnology40(2008)562570565parameters)arecontinuousandcontrollablebyexperi-mentswithnegligibleerrors.Itisalsorequiredtofindasuitableapproximationforthetruefunctionalrelationshipbetweenindependentvariablesandresponses.Usually,asecond-orderregressionmodelasgivenbelowisutilisedinRSM.yb0Xpi1bixiXpi1biix2iXiXjbijxixj,(9)where,allbsareregressioncoefficientsdeterminedbyleastsquaremethod23.Inordertoestimatetheregressioncoefficientsinthismodeleachvariableximustbetakenatleastthreedifferentlevels.Thisrequires3pnumberofexperimentsinfactorialdesignbutitisatediousjobwithlargenumberoffactors.Forfittingsecond-ordermodelanewdesignknownasCCDisgenerallyused20.Itrequiresexperimentationwith2pnumberofexperimentsoffactorialdesignand2p+1combinationofadditionalfactors.Thesecombinationsaretakenasgivenbelow:0；0.；0；C0a；0；.；0；a；0.；0；0；C0a；.；0；0；a.；0.0；0；.；C0a；0；0.；a:Here,thevalueofcodeaisequalto(2p)1/4,anditisintroducedtoprovidetheorthogonalpropertytoarray.Thecodedlevel0representsthecentralvalueofinputprocessparameters.Itisimportantforasecond-ordermodeltoprovideoptimumpredictionabouttheprocessbehaviourwithinthespecifiedrangeofallinputprocessparameters.Sothemodelshouldhaveareasonablyconsistentandstablepredictionofresponsesatpointsofinterestxi.ThiscanbeachievedbyCCRD.AccordingtoCCRDmethodology,standarderroriskeptsameforallpointsthatareatthesamedistancefromthecentreoftheregion.Thiscanbestatedmathematicallyasfollows20:x21x22C1C1C1x2pconstant:(10)CCRDrequiresminimumfivelevelsofallfactorsforthecalculationofregressioncoefficients.Inthissituation,thetotalnumberofcombinationsorrunsrequiredbecomes2p+2p+morethanonerunsatcentre.InpresentcaseoffourcontrolfactorsanstandardCCRDmatrixwith7centralpointrunshasbeenselected20.Thedevelopedresponsemodelisusedforfindingoptimumlevelofinputprocessparameters.Thisisobtainedbylocationofstationarypointsthatwillleadtoapointofmaximumorminimumresponse23.3.ExperimentalprocedureandoperatingparametersTheexperimentalstudieswereperformedona200WpulsedNd:YAGlaserbeammachiningsystemwithCNCworktable.Theoxygenisusedasanassistgas.Thevariableinputprocessparameters(orcontrolfactors)A.KumarDubey,V.Yadava/Opticstakenareassistgaspressure,pulsewidth,pulsefrequency,andcuttingspeed.Focallengthoflensusedis50.0mm.obtainedineachexperimentalrun.TheKWwasmeasuredusingtheToolMakersMicroscope(ModelRTM-900,RADICALInstruments,India)at10C2magnification.TheKW(mm)takenisthemathematicalaverageoftwocutscorrespondingtosameexperimentalrun.KWofeachcuthasbeenmeas