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JournalofMaterialsProcessingTechnology170(2005)1116ApplicationofresponsesurfacemethodologyintheoptimizationofcuttingconditionsforsurfaceroughnessH.Oktema,T.Erzurumlub,H.KurtaranbaDepartmentofMechanicalEngineering,UniversityofKocaeli,41420Kocaeli,TurkeybDepartmentofDesignandManufacturingEngineering,GIT,41400Gebze,Kocaeli,TurkeyReceived16July2004；receivedinrevisedform12March2005；accepted12April2005AbstractThispaperfocusesonthedevelopmentofaneffectivemethodologytodeterminetheoptimumcuttingconditionsleadingtominimumsurfaceroughnessinmillingofmoldsurfacesbycouplingresponsesurfacemethodology(RSM)withadevelopedgeneticalgorithm(GA).RSMisutilizedtocreateanefficientanalyticalmodelforsurfaceroughnessintermsofcuttingparameters:feed,cuttingspeed,axialdepthofcut,radialdepthofcutandmachiningtolerance.Forthispurpose,anumberofmachiningexperimentsbasedonstatisticalthree-levelfullfactorialdesignofexperimentsmethodarecarriedoutinordertocollectsurfaceroughnessvalues.Aneffectivefourthorderresponsesurface(RS)modelisdevelopedutilizingexperimentalmeasurementsinthemoldcavity.RSmodelisfurtherinterfacedwiththeGAtooptimizethecuttingconditionsfordesiredsurfaceroughness.TheGAreducesthesurfaceroughnessvalueinthemoldcavityfrom0.412H9262mto0.375H9262mcorrespondingtoabout10%improvement.OptimumcuttingconditionproducedfromGAisverifiedwiththeexperimentalmeasurement.2005ElsevierB.V.Allrightsreserved.Keywords:Milling；Cuttingconditions；Surfaceroughness；Injectionmolding；Responsesurfacemethodology；Geneticalgorithm1.tribMillingducingpartsT6aircraftastensileticoffsurffirre0924-0136/$doi:10.1016/j.jmatprotec.2005.04.096IntroductionRecentdevelopmentsinmanufacturingindustryhavecon-utedtotheimportanceofCNCmillingoperations1,2.processisrequiredtomakemoldpartsusedforpro-plasticproducts.ItisalsopreferredinmachiningmoldmadeofAluminum7075-T6material.Aluminum7075-materialaschoseninthisstudyiscommonlyutilizedinanddie/moldindustriesduetosomeadvantagessuchhighresistance,goodtransmission,heattreatableandhighstrength3,4.Thequalityofplasticproductsmanufacturedbyplas-injectionmoldingprocessishighlyinfluencedbythatmoldsurfacesobtainedfromthemillingprocess.Sur-acequalityoftheseproductsisgenerallyassociatedwithaceroughnessandcanbedeterminedbymeasuringsur-aceroughness5.SurfaceroughnessisexpressedasthegularitiesofmaterialresultedfromvariousmachiningCorrespondingauthor.Tel.:+902627423290；fax:+902627424091.E-mailaddress:.tr(H.Oktem).operations.fsymbol,meticmeananSurftingsuchwditionsmachiningthisditionssuchmodelstoolinbeen718seefrontmatter2005ElsevierB.V.Allrightsreserved.Inquantifyingsurfaceroughness,averagesur-aceroughnessdefinition,whichisoftenrepresentedwithRaiscommonlyused.Theoretically,Raisthearith-averagevalueofdepartureoftheprofilefromthelinethroughoutthesamplinglength6.Raisalsoimportantfactorincontrollingmachiningperformance.aceroughnessisinfluencedbytoolgeometry,feed,cut-conditionsandtheirregularitiesofmachiningoperationsastoolwear,chatter,tooldeflections,cuttingfluid,andorkpieceproperties7,11,16.Theeffectofcuttingcon-(feed,cuttingspeed,axialradialdepthofcutandtolerance)onsurfaceroughnessisdiscussedinstudy.Severalresearchershavestudiedtheeffectofcuttingcon-inmillingandplasticinjectionmoldingprocessesasinvacuum-sealedmoldingprocess5.Analyticalhavebeencreatedtopredictsurfaceroughnessandlifeintermsofcuttingspeed,feedandaxialdepthofcutmillingsteelmaterial8,9.AneffectiveapproachhasalsopresentedtooptimizesurfacefinishinmillingInconel10.12Processingforsurfoped.methodologymodeldegeneticleadingisaxialradialdictedepresentture.polynomialnatesGAs.optimizationtions.2.2.1.thementsesideringaxialingcarriedcuttingisbasedMillingconditionsmillingfrom2.2.10TLodesignCuttingFeed,CuttingAxialRadialMachiningFig.1.Moldpart.isPVDAlTiNcoatedwithsolidcarbide.Ithasthehelixangleof45andrakeangleof10.Machiningexperimentsareperformedinthemoldcavityonaluminum(7075-T6)blockwithdimensionsof120mm120mm50mm.Thechemicalcompositionofworkpiecematerialisgiveninthefollowingspecification(wt.%):1.6Cu,2.5Mg,0.23Cr,5.40Zn.Thehardnessofworkpieceismeasuredas150BHN.Themechanicalpropertiesofaluminummaterialare:ten-silestrengthof570MPa,yieldstrengthof505MPa,shearstrengthof330MPaandelongationof11%.SurfaceroughnessismeasuredwithSurftest301pro-H.Oktemetal./JournalofMaterialsInthisstudy,afourthorderresponsesurface(RS)modelpredictingsurfaceroughnessvaluesinmillingthemoldacesmadeofAluminum(7075-T6)materialisdevel-IngeneratingtheRSmodelstatisticalresponsesurface(RSM)isutilized.TheaccuracyoftheRSisverifiedwiththeexperimentalmeasurement.ThevelopedRSmodelisfurthercoupledwithadevelopedalgorithm(GA)tofindtheoptimumcuttingconditiontotheleastsurfaceroughnessvalue.Cuttingconditionrepresentedwithcuttingparametersoffeed,cuttingspeed,depthofcutandmachiningtolerance.Thepre-optimumcuttingconditionbyGAisvalidatedwithanxperimentalmeasurement.TheRSmodelandGAdevelopedandutilizedinthisstudyseveraladvantagesoverothermethodsinthelitera-TheRSmodelisahigherorderandmoresophisticatedmodelwithsufficientaccuracy.TheGAelimi-thedifficultyofuser-definedparametersoftheexistingDetailsoftheRSmodelgenerationbyRSMandtheprocessbyGAaregiveninthefollowingsec-ExperimentalproceduresPlanofexperimentsAnimportantstageofRSmodelgenerationbyRSMisplanningofexperiments.Inthisstudy,cuttingexperi-areplannedusingstatisticalthree-levelfullfactorialxperimentaldesign.Cuttingexperimentsareconductedcon-fivecuttingparameters:feed(ft),cuttingspeed(Vc),depthofcut(aa),radialdepthofcut(ar)andmachin-tolerance(mt).Overall35=243cuttingexperimentsareout.Lowmiddlehighlevelofcuttingparametersinspaceforthree-levelfullfactorialexperimentaldesignshowninTable1.RangesofcuttingparametersareselectedonrecommendationofSandvikToolCatalogue12.operationsareperformedatthedeterminedcuttingonaDECKELMAHODMU60PfiveaxisCNCmachine.Surfaceroughness(Ra)valuesaremeasuredthemoldsurfaces.ToolandmaterialCuttingtoolusedinexperimentshasthediameterofmmflatendmillwithfourteeth.Thematerialofthetoolable1wmiddlehighlevelsofcuttingparametersinthree-levelfullfactorialofexperimentparametersThree-levelvaluesft(mm/tooth)0.080.1050.13speed,Vc(m/min)100200300depthofcut,ar(mm)depthofcut,ar(mm)11.52tolerance,mt(mm)0.0010.00550.01filometerpling.mathematicalvastimes.model.2.3.thecations.utilizedpositionandminumOrthoseis2.4.manufgratedCNCfTechnology170(2005)1116attraverselengthof2.5mmalongcenterlineofsam-Convertingthemeasurementintoanumericalvalue,definitionofRaisused.Sincethiswayofcon-ersioniscommonintheliteratureitisadoptedinthisstudywell79.EachRameasurementisrepeatedatleastthreeAverageofthreeRavaluesissavedtoestablishRSMoldpartsThemoldpartusedinthisstudyisutilizedtoproducecomponentsofanorthosepartinbiomechanicalappli-ItisshowninFig.1.Orthosepartsaregenerallyinwalkingapparatusthatholdshumanlegsinstableduringwalking.Itbindsthekneecapregionoflegisequippedwithcylindricalbarsthataremadeofalu-materialindiameterof12mmandlengthof300mm.partconsistsofthreemaincomponents；oneofthememployedastheworkingmodelinthisstudy.ManufacturingthecomponentsoforthosepartThreemachiningprocessesareimplementedinordertoactureeachcomponentoftheorthosepartinaninte-manner.Firstly,theselectedcomponentismachinedinmillingmachine.Ravaluesarethentakenfromthesur-acesinthemoldcavity.Secondly,plasticproductisinjectedProcessinginacetalmaterial.sityviscosityFinallyingillustrated3.surfstatisticalniquephase.H.Oktemetal./JournalofMaterialsFig.2.ThepartsobtainedfromthreeFig.3.ThestagestakenincreatingaresponsesurfacemodelbyRSM.plasticinjectionmachineproducedbyARBURG.Poly-(POM)C9021materialisusedtoinjectthepolymerThepropertiesofpolymermaterialhastheden-ofsolution1.2g/cm3,theejectedtemperatureof165C,of50Pasandmeltflow-fillrateof0.8cm3/min.,netcastingprocessisappliedforproducingdiecast-part.Moldpart,plasticproductanddiecastingpartareinFig.2.ResponsesurfacemodelforsurfaceroughnessRSmodel,whichisananalyticalfunction,inpredictingaceroughnessvaluesisdevelopedusingRSM.RSMusesdesignofexperiment(experimentaldesign)tech-andleast-squarefittingmethodinmodelgenerationItissummarizedinFig.3.RSMwasoriginallydevel-opedandisfwhereoftoMAingAllmodelsgeneratedbecreatingminedfordatatrainingdatalizedvrathersetfroughnesstheFig.4.ComparisonofexperimentalmeasurementsTechnology170(2005)111613machiningprocess.forthemodelfittingofphysicalexperimentsbyBoxDraper13andlateradoptedinotherfields.RSmodelformulatedasfollowingpolynomialfunction:nsummationdisplaynsummationdisplaynsummationdisplay=a0+i=1aixi+i=1j=1aijxixj+(1)a0,aiandaijaretuningparametersandnisthenumbermodelparameters(cessparameters).Inthisstudy,createRSmodel,acomputerprogramhasbeenwritteninTLABprogramminglanguage.TheRSprogramdevelopedhasthecapabilityofcreat-RSpolynomialsupto10thorderifsufficientdataexist.crossterms(eractionsbetweenparameters)inthecanbetakenintoaccount.RSmodelscanalsobeintermsofinverseofparameters.Thatis,xicanreplacedas1xi(i.e.inversely)inRSmodelifdesired,intheRSmodels,243surfaceroughnessvaluesdeter-basedonthree-levelfullfactorialexperimentaldesignfiveparameters(ft,Vc,aa,arandmt)areusedThe243setsforsurfaceroughnessaredividedintotwoparts；datasetandthecheck(i.e.test)dataset.Trainingsetincludes236surfaceroughnessvaluesandisuti-inmodelfittingprocedure.Becauseoflargenumberofaluesandtosavespace,trainingdataisshowninFig.4,thaninatable.InFig.4,abscissaindicatesthedatanumberandtheordinateindicatesthecorrespondingsur-aceroughnessvalue.CheckdatasetsincludesevensurfacevaluesandareusedincheckingtheaccuracyofRSmodel.CheckdatasetsareshowninTable2.TheywithRSpredictionforsurfaceroughness.14ProcessingTTheSet1234567TTheReciprocalareinchecktoprogram.withTaofRfitsThedata2.05%.accuraccutting4.r4.1.surfpossible.H.Oktemetal./JournalofMaterialsable2datasetusedforcheckingtheaccuracyofRSmodelnumberCuttingconditionsftVcaaarmt0.1052000.710.0010.105200010.1052000.310.00550.082000550.081000.720.00550.0820010.1052000.520.01able3accuracyerrorofseveralRSmodelsflagFirstorderSecondorderThirdorderFourthorder000002774.82.70010025.97.285.82.950000152.410.94.02.991100027.26.634.82.050110025.97.05.52.550001154.91110025.87.035.72.50111027.57.05.92.81111153.03selectedfrom243datasetstoshowagooddistributionthecuttingparametersspaceandtherebytohaveagoodontheaccuracyoftheRSmodel.Inthisstudy,RSmodelsofvaryingordersfromfirstorderfourthorderarecreatedandtestedwiththedevelopedSeveralRSmodelcreatedaredemonstratedalongtheiraccuracyerrorsinTable3.Inreciprocalsectioninable3,0indicatesaparameter(xi),1indicatestheinverseofparameter(1xi).Thefullfourthorderpolynomialfunctiontheform:a=a0+a11ft+a21Vc+a3aa+a4ar+a5mt+anparenleftbigg1ft1Vcaaarmtparenrightbigg4+am(mt)4(2)best(withminimumfittingerror)tothetrainingdataset.accuracyoftheRSmodelwascheckedusingthecheckset.ThemaximumaccuracyerrorisfoundtobeaboutThisindicatesthatRSmodelgeneratedhassufficientyinpredictingsurfaceroughnesswithintherangeofparameters.OptimizationofcuttingconditionsforsurfaceoughnessOptimizationproblemformulationSinceitisindicatorofsurfacequalityinmillingofmoldaces,surfaceroughnessvalueisdesiredtobeaslowasLowsurfaceroughnessvaluescanbeachievedeffi-cientlyappropriatemizationinFindMinimizeSubjectedfmizationforcedsearchestheroughnesscuttingon4.2.couplingalgorithmiterati(Darwincedure,rankFig.surfTechnology170(2005)1116Ra(H9262m)MeasurementresultsRSMmodelMaximum