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JournalofMaterialsProcessingTechnology170200511–16ApplicationofresponsesurfacemethodologyintheoptimizationofcuttingconditionsforsurfaceroughnessH.¨Oktema,∗,T.Erzurumlub,H.KurtaranbaDepartmentofMechanicalEngineering,UniversityofKocaeli,41420Kocaeli,TurkeybDepartmentofDesignandManufacturingEngineering,GIT,41400Gebze,Kocaeli,TurkeyReceived16July2004receivedinrevisedform12March2005accepted12April2005AbstractThispaperfocusesonthedevelopmentofaneffectivemethodologytodeterminetheoptimumcuttingconditionsleadingtominimumsurfaceroughnessinmillingofmoldsurfacesbycouplingresponsesurfacemethodologyRSMwithadevelopedgeneticalgorithmGA.RSMisutilizedtocreateanefficientanalyticalmodelforsurfaceroughnessintermsofcuttingparametersfeed,cuttingspeed,axialdepthofcut,radialdepthofcutandmachiningtolerance.Forthispurpose,anumberofmachiningexperimentsbasedonstatisticalthreelevelfullfactorialdesignofexperimentsmethodarecarriedoutinordertocollectsurfaceroughnessvalues.AneffectivefourthorderresponsesurfaceRSmodelisdevelopedutilizingexperimentalmeasurementsinthemoldcavity.RSmodelisfurtherinterfacedwiththeGAtooptimizethecuttingconditionsfordesiredsurfaceroughness.TheGAreducesthesurfaceroughnessvalueinthemoldcavityfrom0.412H9262mto0.375H9262mcorrespondingtoabout10improvement.OptimumcuttingconditionproducedfromGAisverifiedwiththeexperimentalmeasurement.©2005ElsevierB.V.Allrightsreserved.KeywordsMillingCuttingconditionsSurfaceroughnessInjectionmoldingResponsesurfacemethodologyGeneticalgorithm1.tribMillingducingpartsT6aircraftastensileticoffsurffirre09240136/doi10.1016/j.jmatprotec.2005.04.096IntroductionRecentdevelopmentsinmanufacturingindustryhaveconutedtotheimportanceofCNCmillingoperations1,2.processisrequiredtomakemoldpartsusedforproplasticproducts.ItisalsopreferredinmachiningmoldmadeofAluminum7075T6material.Aluminum7075materialaschoseninthisstudyiscommonlyutilizedinanddie/moldindustriesduetosomeadvantagessuchhighresistance,goodtransmission,heattreatableandhighstrength3,4.Thequalityofplasticproductsmanufacturedbyplasinjectionmoldingprocessishighlyinfluencedbythatmoldsurfacesobtainedfromthemillingprocess.Suracequalityoftheseproductsisgenerallyassociatedwithaceroughnessandcanbedeterminedbymeasuringsuraceroughness5.Surfaceroughnessisexpressedasthegularitiesofmaterialresultedfromvariousmachining∗Correspondingauthor.Tel.902627423290fax902627424091.Emailaddresshoktemkou.edu.trH.¨Oktem.operations.fsymbol,meticmeananSurftingsuchwditionsmachiningthisditionssuchmodelstoolinbeen718–seefrontmatter©2005ElsevierB.V.Allrightsreserved.Inquantifyingsurfaceroughness,averagesuraceroughnessdefinition,whichisoftenrepresentedwithRaiscommonlyused.Theoretically,Raisthearithaveragevalueofdepartureoftheprofilefromthelinethroughoutthesamplinglength6.Raisalsoimportantfactorincontrollingmachiningperformance.aceroughnessisinfluencedbytoolgeometry,feed,cutconditionsandtheirregularitiesofmachiningoperationsastoolwear,chatter,tooldeflections,cuttingfluid,andorkpieceproperties7,11,16.Theeffectofcuttingconfeed,cuttingspeed,axial–radialdepthofcutandtoleranceonsurfaceroughnessisdiscussedinstudy.Severalresearchershavestudiedtheeffectofcuttingconinmillingandplasticinjectionmoldingprocessesasinvacuumsealedmoldingprocess5.Analyticalhavebeencreatedtopredictsurfaceroughnessandlifeintermsofcuttingspeed,feedandaxialdepthofcutmillingsteelmaterial8,9.AneffectiveapproachhasalsopresentedtooptimizesurfacefinishinmillingInconel10.12Processingforsurfoped.methodologymodeldegeneticleadingisaxial–radialdictedepresentture.polynomialnatesGAs.optimizationtions.2.2.1.thementsesideringaxialingcarriedcuttingisbasedMillingconditionsmillingfrom2.2.10TLodesignCuttingFeed,CuttingAxialRadialMachiningFig.1.Moldpart.isPVDAlTiNcoatedwithsolidcarbide.Ithasthehelixangleof45◦andrakeangleof10◦.Machiningexperimentsareperformedinthemoldcavityonaluminum7075T6blockwithdimensionsof120mm120mm50mm.Thechemicalcompositionofworkpiecematerialisgiveninthefollowingspecificationwt.1.6Cu,2.5Mg,0.23Cr,5.40Zn.Thehardnessofworkpieceismeasuredas150BHN.Themechanicalpropertiesofaluminummaterialaretensilestrengthof570MPa,yieldstrengthof505MPa,shearstrengthof330MPaandelongationof11.SurfaceroughnessismeasuredwithSurftest301proH.¨Oktemetal./JournalofMaterialsInthisstudy,afourthorderresponsesurfaceRSmodelpredictingsurfaceroughnessvaluesinmillingthemoldacesmadeofAluminum7075T6materialisdevelIngeneratingtheRSmodelstatisticalresponsesurfaceRSMisutilized.TheaccuracyoftheRSisverifiedwiththeexperimentalmeasurement.ThevelopedRSmodelisfurthercoupledwithadevelopedalgorithmGAtofindtheoptimumcuttingconditiontotheleastsurfaceroughnessvalue.Cuttingconditionrepresentedwithcuttingparametersoffeed,cuttingspeed,depthofcutandmachiningtolerance.ThepreoptimumcuttingconditionbyGAisvalidatedwithanxperimentalmeasurement.TheRSmodelandGAdevelopedandutilizedinthisstudyseveraladvantagesoverothermethodsintheliteraTheRSmodelisahigherorderandmoresophisticatedmodelwithsufficientaccuracy.TheGAelimithedifficultyofuserdefinedparametersoftheexistingDetailsoftheRSmodelgenerationbyRSMandtheprocessbyGAaregiveninthefollowingsecExperimentalproceduresPlanofexperimentsAnimportantstageofRSmodelgenerationbyRSMisplanningofexperiments.Inthisstudy,cuttingexperiareplannedusingstatisticalthreelevelfullfactorialxperimentaldesign.Cuttingexperimentsareconductedconfivecuttingparametersfeedft,cuttingspeedVc,depthofcutaa,radialdepthofcutarandmachintolerancemt.Overall35243cuttingexperimentsareout.Low–middle–highlevelofcuttingparametersinspaceforthreelevelfullfactorialexperimentaldesignshowninTable1.RangesofcuttingparametersareselectedonrecommendationofSandvikToolCatalogue12.operationsareperformedatthedeterminedcuttingonaDECKELMAHODMU60PfiveaxisCNCmachine.SurfaceroughnessRavaluesaremeasuredthemoldsurfaces.ToolandmaterialCuttingtoolusedinexperimentshasthediameterofmmflatendmillwithfourteeth.Thematerialofthetoolable1w–middle–highlevelsofcuttingparametersinthreelevelfullfactorialofexperimentparametersThreelevelvaluesftmm/tooth0.08–0.105–0.13speed,Vcm/min100–200–300depthofcut,armm0.3–0.5–0.7depthofcut,armm1–1.5–2tolerance,mtmm0.001–0.0055–0.01filometerpling.mathematicalvastimes.model.2.3.thecations.utilizedpositionandminumOrthoseis2.4.manufgratedCNCfTechnology170200511–16attraverselengthof2.5mmalongcenterlineofsamConvertingthemeasurementintoanumericalvalue,definitionofRaisused.Sincethiswayofconersioniscommonintheliteratureitisadoptedinthisstudywell7–9.EachRameasurementisrepeatedatleastthreeAverageofthreeRavaluesissavedtoestablishRSMoldpartsThemoldpartusedinthisstudyisutilizedtoproducecomponentsofanorthosepartinbiomechanicalappliItisshowninFig.1.Orthosepartsaregenerallyinwalkingapparatusthatholdshumanlegsinstableduringwalking.Itbindsthekneecapregionoflegisequippedwithcylindricalbarsthataremadeofalumaterialindiameterof12mmandlengthof300mm.partconsistsofthreemaincomponentsoneofthememployedastheworkingmodelinthisstudy.ManufacturingthecomponentsoforthosepartThreemachiningprocessesareimplementedinordertoactureeachcomponentoftheorthosepartinanintemanner.Firstly,theselectedcomponentismachinedinmillingmachine.Ravaluesarethentakenfromthesuracesinthemoldcavity.Secondly,plasticproductisinjectedProcessinginacetalmaterial.sityviscosityFinallyingillustrated3.surfstatisticalniquephase.H.¨Oktemetal./JournalofMaterialsFig.2.ThepartsobtainedfromthreeFig.3.ThestagestakenincreatingaresponsesurfacemodelbyRSM.plasticinjectionmachineproducedbyARBURG.PolyPOMC9021materialisusedtoinjectthepolymerThepropertiesofpolymermaterialhasthedenofsolution1.2g/cm3,theejectedtemperatureof165◦C,of50Pasandmeltflowfillrateof0.8cm3/min.,netcastingprocessisappliedforproducingdiecastpart.Moldpart,plasticproductanddiecastingpartareinFig.2.ResponsesurfacemodelforsurfaceroughnessRSmodel,whichisananalyticalfunction,inpredictingaceroughnessvaluesisdevelopedusingRSM.RSMusesdesignofexperimentexperimentaldesigntechandleastsquarefittingmethodinmodelgenerationItissummarizedinFig.3.RSMwasoriginallydevelopedandisfwhereoftoMAingAllmodelsgeneratedbecreatingminedfordatatrainingdatalizedvrathersetfroughnesstheFig.4.ComparisonofexperimentalmeasurementsTechnology170200511–1613machiningprocess.forthemodelfittingofphysicalexperimentsbyBoxDraper13andlateradoptedinotherfields.RSmodelformulatedasfollowingpolynomialfunctionnsummationdisplaynsummationdisplaynsummationdisplaya0i1aixii1j1aijxixj1a0,aiandaijaretuningparametersandnisthenumbermodelparametersi.e.processparameters.Inthisstudy,createRSmodel,acomputerprogramhasbeenwritteninTLABprogramminglanguage.TheRSprogramdevelopedhasthecapabilityofcreatRSpolynomialsupto10thorderifsufficientdataexist.crosstermsi.e.interactionsbetweenparametersinthecanbetakenintoaccount.RSmodelscanalsobeintermsofinverseofparameters.Thatis,xicanreplacedas1xii.e.inverselyinRSmodelifdesired,intheRSmodels,243surfaceroughnessvaluesdeterbasedonthreelevelfullfactorialexperimentaldesignfiveparametersft,Vc,aa,arandmtareusedThe243setsforsurfaceroughnessaredividedintotwopartsdatasetandthechecki.e.testdataset.Trainingsetincludes236surfaceroughnessvaluesandisutiinmodelfittingprocedure.Becauseoflargenumberofaluesandtosavespace,trainingdataisshowninFig.4,thaninatable.InFig.4,abscissaindicatesthedatanumberandtheordinateindicatesthecorrespondingsuraceroughnessvalue.CheckdatasetsincludesevensurfacevaluesandareusedincheckingtheaccuracyofRSmodel.CheckdatasetsareshowninTable2.TheywithRSpredictionforsurfaceroughness.14ProcessingTTheSet1234567TTheReciprocalareinchecktoprogram.withTaofRfitsThedata2.05.accuraccutting4.r4.1.surfpossible.H.¨Oktemetal./JournalofMaterialsable2datasetusedforcheckingtheaccuracyofRSmodelnumberCuttingconditionsftVcaaarmt0.1052000.710.0010.1052000.71.50.0010.1052000.310.00550.082000.71.50.00550.081000.720.00550.082000.31.50.010.1052000.520.01able3accuracyerrorofseveralRSmodelsflagFirstorderSecondorderThirdorderFourthorder000002774.82.70010025.97.285.82.950000152.410.94.02.991100027.26.634.82.050110025.97.05.52.550001154.910.53.72.71110025.87.035.72.50111027.57.05.92.81111153.0310.54.72.7selectedfrom243datasetstoshowagooddistributionthecuttingparametersspaceandtherebytohaveagoodontheaccuracyoftheRSmodel.Inthisstudy,RSmodelsofvaryingordersfromfirstorderfourthorderarecreatedandtestedwiththedevelopedSeveralRSmodelcreatedaredemonstratedalongtheiraccuracyerrorsinTable3.Inreciprocalsectioninable3,0indicatesaparameterxi,1indicatestheinverseofparameter1xi.Thefullfourthorderpolynomialfunctiontheformaa0a11fta21Vca3aaa4ara5mtanparenleftbigg1ft1Vcaaarmtparenrightbigg4ammt42bestwithminimumfittingerrortothetrainingdataset.accuracyoftheRSmodelwascheckedusingthecheckset.ThemaximumaccuracyerrorisfoundtobeaboutThisindicatesthatRSmodelgeneratedhassufficientyinpredictingsurfaceroughnesswithintherangeofparameters.OptimizationofcuttingconditionsforsurfaceoughnessOptimizationproblemformulationSinceitisindicatorofsurfacequalityinmillingofmoldaces,surfaceroughnessvalueisdesiredtobeaslowasLowsurfaceroughnessvaluescanbeachievedefficientlyappropriatemizationinFindMinimizeSubjectedfmizationforcedsearchestheroughnesscuttingon4.2.couplingalgorithmiteratiDarwincedure,rankFig.surfTechnology170200511–16RaH9262mMeasurementresultsRSMmodelMaximumtesterror0.5910.5892.050.6290.6270.7810.7750.8990.8950.9780.9961.6741.7061.8561.893byadjustingcuttingconditionswiththehelpofannumericaloptimizationmethod.Forthis,miniofsurfaceroughnessproblemmustbeformulatedthestandardmathematicalformatasbelowft,Vc,aa,ar,mt3aRaft,Vc,aa,ar,mt3btoconstraintsRa≤0.412H9262m3cWithinranges0.08mm≤ft≤0.13mm100mm≤Vc≤300mm0.3mm≤aa≤0.7mm1mm≤ar≤2mm0.001mm≤mt≤0.01mm.InEq.3,RaistheRSmodeldevelopedinSection3.t,Vc,aa,arandmtarethecuttingparameters.Intheoptiproblemdefinitionabove,abettersolutionisalsothroughtheconstraintdefinition.ConstraintdefinitionasurfaceroughnessvalueRa,whichislessthanlowestvaluein243datasetifpossible.Minimumsurfacevaluein243datasetis0.412H9262m.TherangesofparametersinoptimizationhavebeenselectedbasedtherecommendationofSandvikToolCatalogue.OptimizationproblemsolutionTheoptimizationproblemexpressedinEq.3issolvedbythedevelopedRSmodelwiththedevelopedgeneticasshowninFig.5.Thegeneticalgorithm14solvesoptimizationproblemvelybasedohbiologicalevolutionprocessinnaturestheoryofsurvivalofthefittest.Inthesolutionproasetofparametervaluesisrandomlyselected.Setisedbashedontheirsurfaceroughnessvaluesi.e.fitness5.Interactionofexperimentalmeasurements,RSmodelandGAduringaceroughnessoptimization.
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