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InternationalJournalofAutomotiveTechnology,Vol.13,No.2,pp.273−2772012DOI10.1007/s12239−012−0024−5Copyright©2012KSAE/063−11pISSN1229−9138/eISSN19763832273DESIGNOPTIMIZATIONOFANINJECTIONMOLDFORMINIMIZINGTEMPERATUREDEVIATIONJ.H.CHOI1,S.H.CHOI1,D.PARK2,C.H.PARK2,B.O.RHEE1andD.H.CHOI21GraduateSchoolofMechanicalEngineering,AjouUniversity,Gyeonggi443740,Korea2GraduateSchoolofMechanicalEngineering,HanynagUniversity,Seoul133791,KoreaReceived24January2011Revised15June2011Accepted17June2011ABSTRACT−Thequalityofaninjectionmoldedpartislargelyaffectedbythemoldcooling.Consequently,thismakesitnecessarytooptimizethemoldcoolingcircuitwhendesigningthepartbutpriortodesigningthemold.Variousapproachesofoptimizingthemoldcoolingcircuithavebeenproposedpreviously.Inthiswork,optimizationofthemoldcoolingcircuitwasautomatedbyacommercialprocessintegrationanddesignoptimizationtoolcalledProcessIntegration,AutomationandOptimizationPIAnO,whichisoftenusedforlargeautomotivepartssuchasbumpersandinstrumentpanels.Thecoolingchannelsandbaffletubeswerelocatedontheoffsetprofileequidistantfromthepartsurface.Thelocationsofthecoolingchannelsandthebaffletubeswereautomaticallygeneratedandinputintothemoldcoolingcomputeraidedengineeringprogram,AutodeskMoldflowInsight2010.Theobjectivefunctionwasthedeviationofthemoldsurfacetemperaturefromagivendesigntemperature.Designvariablesintheoptimizationwerethedepths,distancesanddiametersofthecoolingchannelsandthebaffletubes.Foramorepracticalanalysis,thepressuredropandtemperaturedropwereconsideredthelimitedvalues.Optimizationwasperformedusingtheprogressivequadraticresponsesurfacemethod.Theoptimizationresultedinamoreuniformtemperaturedistributionwhencomparedtotheinitialdesign,andutilizingtheproposedoptimizationmethod,asatisfactorysolutioncouldbemadeatalowercost.KEYWORDSInjectionmolding,Coolingchannel,Coolinganalysis,PQRSM,Designoptimization1.INTRODUCTIONThecoolingstageisthelongeststageduringthecycletimeoftheinjectionmoldingprocess.Therefore,themosteffectivemethodtoreducethecycletimeistoreducethecoolingtime.Thecoolingtimeisfundamentallydeterminedbythepartthicknessandmoldtemperature,whichcreatesacoolingtimelimitation.Ifthemoldtemperatureandpartthicknessareuniformoverawholepart,thecoolingtimeisnotaconcernhowever,nonuniformpartthicknessandmoldtemperaturedistributionlengthentheoverallcoolingtime.Alongercoolingtimemeanspoortemperatureuniformity,whichcancausetheparttowarp.Thisisespeciallytrueforlargeproducts,suchasautomotivebumpersandinstrumentpanels.Itisforthesetypesofpartsthattemperatureuniformitybecomesthemostimportantfactorinmolddesign.Wedevelopedanautomatedoptimizationofthecoolingcircuitforanearlypartdesigninordertocheckthedesignvalidity.Usuallytheearlypartdesignischeckedbythefiling/packingandwarpageanalyseswithoutacoolinganalysis.Thisisbecausetheassumptionisthatthemoldtemperatureisuniform,whichisnotactuallytrue.ProvidingarapidlyoptimizedcoolingcircuitforthedesignedpartwouldhelppartdesignerscorrecttheirdesignKoresawaandSuzuki,1999.Theoptimizationwasdesignedtominimizetheparttemperaturedeviationusingdesignvariablessuchasthediametersanddistancesofthecoolingchannelsandbaffletubesandthedepthsofthepartfromthemoldsurfaceofthecoolingchannelsandbaffletubes.AcommercialcomputeraidedengineeringCAEtool,AutodeskMoldflowInsight,wasusedforthecoolinganalysis.Wesuccessfullyobtainedanoptimizedcoolingcircuitinatimemuchshorterthancanbeachievedinamanualdesign.Inordertodeveloptheautomatedoptimizationofthecoolingcircuitforthepracticalmolddesign,practicaldesignparameterssuchasthepressuredroplimitandthecoolanttemperaturerisewereconsideredintheoptimization.Theperformanceoftheoptimizationtechniquecanbeaffectedbynumericalnoiseintheresponses.Tofindanoptimumsolutioneffectivelywhennumericalnoiseexists,weperformedanoptimizationbyapplyingaregressionbasedsequentialapproximateoptimizerknownastheProgressiveQuadraticResponseSurfaceMethodPQRSMHongetal.,2000,whichwaspartofacommercialprocessintegrationanddesignoptimizationPIDOtoolknownastheProcessIntegration,AutomationandOptimizationPIAnOFRAMAX,2009.Correspondingauthor.emailrhexajou.ac.kr274J.H.CHOIetal.2.MODELANDCHANNELCONFIGURATION2.1.ModelConfigurationThemodelusedfortheoptimizationandCAEanalysiswasanautomotivefrontbumperFB.Thesizeofthepartwas1,800600mm,theelementtypewastriangularandthenumberofelementsinthemodelwasapproximately26,000,withanaverageaspectratioof1.5.ThemodelisshowninFigure1.2.2.CoolingChannelConfigurationThecoolingcircuitfortheautomotivebumpermoldistypicallydesignedtohaveahorizontalplaneoflinecoolingchannelsandtoinstallbaffletubesfromthelinecoolingchannels.However,inthisdesign,unnecessarilylongbaffletubesattachedatalinecoolingchannelmaycauseahighpressuredropinthecoolingchannel.Thelinecoolingchannelsmaynotcontributetomoldcoolingduetotheirlargedistancefromthepartsurface.Inordertoimprovethedesign,thelinecoolingchannelswerelocatedalongtheoffsetprofileofthepartsurfaceasshowninFigure2.Theendpointsofthebaffletubeswerealsolocatedontheoffsetprofilealongalinecoolingchannel.Eitherthelinecoolingchannelsorbaffletubeswerelocatedontheoffsetprofileswithequalarcdistancesbetweenthem.3.FORMULATION3.1.DesignConstraintsThelimitationofthepressuredropandthetemperaturerisebetweentheinletandoutletofcoolingchannelshouldalsobeconsideredinthedesignofthemoldcoolingcircuit.Ahighpressuredropusuallyoccursinaneedlesslylongcoolingcircuit.Inalongcoolingcircuit,theflowrateofcoolantislow,whichresultsinahighmoldtemperatureandahightemperatureriseattheoutlet.Thedesigndefectcouldeventuallybefoundinthecoolinganalysishowever,theoptimizationisalreadytimeconsuming,soitisbettertoinsteadapplythelimitsasconstraintsintheoptimization.Inthisworkweassumedthat4linecoolingchannelswereconnectedinseriesasacluster,asshowninFigure3.Clustersareconnectedinparallelbyamanifold.Usually,themaximumpressuredropinaclusterislimitedto200kPa,andthemaximumtemperatureriseattheoutletis5oCMengesetal.,2001.Inthecoolinganalysis,eachlinecoolingchannelisregardedasaseparateindependentcircuitforconvenience.Becausetherewere4linecoolingchannelsinacircuit,thelimitsonthepressuredropandthetemperatureriseineachlinecoolingchannelwere50kPaand1.25oC,respectively.Wealsohaveanadditionalconstraintduetothefactthatthediameterofthebaffletubemustbegreaterthanorequaltothediameterofthecoolingchannelbecausethebaffletubehaslowerheatremovalefficiencythanthecoolingchannel.ThesethreedesignconstraintscanbeexpressedasEquations1,2and3,13whereG1istheconstraintonpressuredrop,G2istheconstraintontemperaturerise,andG3representsthesubtractionofthediameterofthebaffletubefromthediameterofthecoolingchannel.3.2.DesignVariablesInthiswork,thediameters,distancesanddepthsofthelinecoolingchannelsandbaffletubeswerechosenasdesignvariablesforoptimization.Thetotalnumberofdesignvariableswas6asshowninTable1.Typically,thediametersofthecoolingchannelsandbaffletubesaredeterminedbythemolddesigneraccordingtotheirruleof0PaG150000pa≤≤0CoG21.2Co≤≤G30mm≤Figure1.Finiteelementmodeloftheproductusedfortheoptimization.Figure2.Configurationofcoolingchannelslocatedalongtheoffsetprofiles.Figure3.Clustersconsistingof4coolingchannelswithbaffletubes.DESIGNOPTIMIZATIONOFANINJECTIONMOLDFORMINIMIZINGTEMPERATUREDEVIATION275thumbRheeetal.,2010.However,ithasbeenexaminedingreatdetailamongthemolddesigners.Table1showsthedesignvariableswiththeirrangesandinitialvalues.Theminimumvaluesforthecoolingchanneldistance,baffledistanceandbaffledepthweredeterminedbytheconstraintsofthemachiningrequirement.Themaximumvaluesofcoolingchanneldistanceandbaffledistanceweredeterminedbytheempiricalmaximumobtainedfromthemolddesigners.ThebaffledistancewasadiscretevariableduetoarestrictionintheautomateduseoftheCAEsoftware.Inthiswork,thebaffledistancesforoptimizationwere60,90and120mm.3.3.ObjectiveFunctionAprincipalpurposeofthemoldcoolingcircuitoptimizationistoachieveuniformtemperaturedistributionoverthepart.Theuniformtemperaturedistributionmeansthatthetemperaturedeviationcausedbythecoolingchannelsisminimized,asshowninFigure4.TheobjectivefunctionintheoptimizationwasthestandarddeviationofparttemperatureasshowninEquation4.Theparttemperaturewasanarithmeticaverageoftheupperandthelowersurfacesofthemoldhalves.Themoldsurfacetemperaturewascalculatedfromthefiniteelementofthepart.min,4whereσisthestandarddeviationoftheparttemperature,Eiisthetemperatureofithelement,Ewistheaveragetemperatureoftheentiretriangularelements,andNisthenumberofelements.4.OPTIMIZATION4.1.ParametricStudyInordertoexaminetheeffectsofthedesignvariablesontheobjectivefunction,pressuredropandtemperaturerise,parametricstudieswerecarriedout.Aparametricstudywasperformedbychangingavariableinacertainrangewhilekeepingallothervariablesfixed.Figures57showtheresultsofparametricstudiesfortheobjectivefunction,pressuredroptemperaturerise,respectively.Ineachfigure,thexaxisindicatesthelevelsofdesignvariables.Everydesignvariablewasdividedinto11levelsfromitslowerboundtoitsupperbound.5and5meanthelowerandupperbounds,respectively.Whenexaminingthetemperaturedeviation,thediameterofthecoolingchannelsshowslittleinfluencetotheobjectivefunctionseeFigure5..Thisresultwaspredictablebecausethecoolingchannelaffectstheparttemperaturetoalesserdegreethanthebaffletubesintheautomotivebumpermold.Theautomotivebumpermoldhasadeepcoresothatthemoldcoolingdependsuponthebaffletubesratherthanthecoolingchannels.Anotherreasonofthelackofinfluencecanbethattheflowstateinthecoolingchannelremainsturbulentintherangeoftheparametricstudy.Thecoolingchannelusuallyhasasmallerdiameterthanthebaffletube.Whentheflowinthebaffletubeiskeptintheturbulentstate,theflowinthecoolingchannelwillbeintheturbulentstate.Thediametersofthebaffletubesshowatangibleinfluencewhenitincreasesaboveacertainvalue.Increasingofthediameterchangestheflowinthetubetoalaminarflowstate.Thisisthecauseforthelowerheattransfercoefficientwhencomparedtotheturbulentflowstate.Thisiswhythetemperaturedeviationbecomeslargerwhenthebaffletubediameterincreases.σEiEw–2Ni1N∑Figure4.Schemeofthetemperaturefieldbythecoolingchannels.Table1.Lowerandtheupperboundsfordesignvariablesandtheinitialvaluesfortheoptimizationunitmm.DescriptionLowerInitialUpperX1Channeldiameter103040X2Bafflediameter103040X3Channeldistance6090120X4Baffledistance6060120X5Channeldepth306090X6Bafledepth306090Figure5.Parametricstudyresultoftemperaturedeviationobjectivefunction.276J.H.CHOIetal.Amongallparameters,thebaffledepthshowsthelargestinfluenceontheobjectivefunction,asshowninFigure5.Asthebaffledepthincreases,theobjectivefunctionincreases.Thismeansthatthedeeperlocationofthebaffletubescausesthetemperaturedeviationtoincrease.Also,itconfirmsthatthecoolingoftheautomotivebumpermolddependsuponthebaffletubes.Thediametersofthecoolingchannelsandthebaffletubeshavethehighestinfluenceonthepressuredropinthecoolingcircuit,whiletheothervariablesshowlittleinfluenceseeFigure6..Asthediametersincrease,thepressuredropdecreasesafteracertainvalue.Thisisalsoapredictableresultasalargerdiameterdecreasesthepressuredrop.TheinfluencesofthetemperatureriseattheoutletareshowninFigure7.Themostinfluentialparametersarethebafflediameterandthechanneldistance.Theinfluenceofthebafflediametershowsthehighestvaluesintherangefrom1to3.Inthecaseofthesmallerbafflediameter,thereducedsurfaceareafortheheattransfermaycauseasmallertemperaturerise,whilethelargerbafflediametermaycausethelowerheattransfercoefficientduetothelowerflowrate.Theincreasedchanneldistancemeansthateachcoolingchanneltakesupalargerareaofthepartsurfacewithalargeramountofheatremoval.Thismaygiveaphysicalexplanationtowhytheincreaseofthetemperatureriseincreaseswithchanneldistance.ThefluctuationsshowninFigure7aresupposedtobenumericalnoise.4.2.OptimizationResultsThelargestincreaseinthetemperatureriseFigure7isapproximately0.15oC.Thisvalueismuchlessthantheconstraint.Theinfluenceofthevariablesonthetemperatureriseisnottangible.Thebaffledistancewasconsideredthediscretevariableinthisworkhence,itwasdifficulttoapplyageneraloptimizationmethod.Becausetherewerethreevalues,optimizationswerecarriedout3timeswiththe5designparameters.Thebaffledistancewasfixedineachoptimization.Figures8and9showthetemperaturedeviationsasthechanneldiameter,x1andthechanneldistance,x3changeby0.1usingtheperturbationmethodaroundtheirinitialdesignvalues.Fromtheseresultswerecognizedthatthevariationsinthetemperaturedeviationsasx1andx3variedincludednumericalnoise.Therefore,wechosePQRSMastheoptimizationmethodthatcouldeffectivelyoptimizetheresponsewithnumericalnoise.ThePQRSMequippedinacommercialFigure6.Parametricstudyresultofthepressuredrop.Figure7.Parametricstudyresultofthetemperaturerise.Figure8.Variationofthetemperaturedeviationw.r.t.x1observedbyusing0.1perturbationmethod.Figure9.Variationofthetemperaturedeviationw.r.t.x3observedbyusing0.1perturbationmethod.