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InternationalJournalofAutomotiveTechnology,Vol.13,No.2,pp.273277(2012)DOI10.1007/s1223901200245Copyright©2012KSAE/06311pISSN12299138/eISSN1976-3832273DESIGNOPTIMIZATIONOFANINJECTIONMOLDFORMINIMIZINGTEMPERATUREDEVIATIONJ.-H.CHOI1),S.-H.CHOI1),D.PARK2),C.-H.PARK2),B.-O.RHEE1)*andD.-H.CHOI2)1)GraduateSchoolofMechanicalEngineering,AjouUniversity,Gyeonggi443-740,Korea2)GraduateSchoolofMechanicalEngineering,HanynagUniversity,Seoul133-791,Korea(Received24January2011；Revised15June2011；Accepted17June2011)ABSTRACTThequalityofaninjectionmoldedpartislargelyaffectedbythemoldcooling.Consequently,thismakesitnecessarytooptimizethemoldcoolingcircuitwhendesigningthepartbutpriortodesigningthemold.Variousapproachesofoptimizingthemoldcoolingcircuithavebeenproposedpreviously.Inthiswork,optimizationofthemoldcoolingcircuitwasautomatedbyacommercialprocessintegrationanddesignoptimizationtoolcalledProcessIntegration,AutomationandOptimization(PIAnO),whichisoftenusedforlargeautomotivepartssuchasbumpersandinstrumentpanels.Thecoolingchannelsandbaffletubeswerelocatedontheoffsetprofileequidistantfromthepartsurface.Thelocationsofthecoolingchannelsandthebaffletubeswereautomaticallygeneratedandinputintothemoldcoolingcomputer-aidedengineeringprogram,AutodeskMoldflowInsight2010.Theobjectivefunctionwasthedeviationofthemoldsurfacetemperaturefromagivendesigntemperature.Designvariablesintheoptimizationwerethedepths,distancesanddiametersofthecoolingchannelsandthebaffletubes.Foramorepracticalanalysis,thepressuredropandtemperaturedropwereconsideredthelimitedvalues.Optimizationwasperformedusingtheprogressivequadraticresponsesurfacemethod.Theoptimizationresultedinamoreuniformtemperaturedistributionwhencomparedtotheinitialdesign,andutilizingtheproposedoptimizationmethod,asatisfactorysolutioncouldbemadeatalowercost.KEYWORDS:Injectionmolding,Coolingchannel,Coolinganalysis,PQRSM,Designoptimization1.INTRODUCTIONThecoolingstageisthelongeststageduringthecycletimeoftheinjectionmoldingprocess.Therefore,themosteffectivemethodtoreducethecycletimeistoreducethecoolingtime.Thecoolingtimeisfundamentallydeterminedbythepartthicknessandmoldtemperature,whichcreatesacoolingtimelimitation.Ifthemoldtemperatureandpartthicknessareuniformoverawholepart,thecoolingtimeisnotaconcern；however,non-uniformpartthicknessandmoldtemperaturedistributionlengthentheoverallcoolingtime.Alongercoolingtimemeanspoortemperatureuniformity,whichcancausetheparttowarp.Thisisespeciallytrueforlargeproducts,suchasautomotivebumpersandinstrumentpanels.Itisforthesetypesofpartsthattemperatureuniformitybecomesthemostimportantfactorinmolddesign.Wedevelopedanautomatedoptimizationofthecoolingcircuitforanearlypartdesigninordertocheckthedesignvalidity.Usuallytheearlypartdesignischeckedbythefiling/packingandwarpageanalyseswithoutacoolinganalysis.Thisisbecausetheassumptionisthatthemoldtemperatureisuniform,whichisnotactuallytrue.Providingarapidlyoptimizedcoolingcircuitforthedesignedpartwouldhelppartdesignerscorrecttheirdesign(KoresawaandSuzuki,1999).Theoptimizationwasdesignedtominimizetheparttemperaturedeviationusingdesignvariablessuchasthediametersanddistancesofthecoolingchannelsandbaffletubesandthedepthsofthepartfromthemoldsurfaceofthecoolingchannelsandbaffletubes.Acommercialcomputer-aidedengineering(CAE)tool,AutodeskMoldflowInsight,wasusedforthecoolinganalysis.Wesuccessfullyobtainedanoptimizedcoolingcircuitinatimemuchshorterthancanbeachievedinamanualdesign.Inordertodeveloptheautomatedoptimizationofthecoolingcircuitforthepracticalmolddesign,practicaldesignparameterssuchasthepressuredroplimitandthecoolanttemperaturerisewereconsideredintheoptimization.Theperformanceoftheoptimizationtechniquecanbeaffectedbynumericalnoiseintheresponses.Tofindanoptimumsolutioneffectivelywhennumericalnoiseexists,weperformedanoptimizationbyapplyingaregression-basedsequentialapproximateoptimizerknownastheProgressiveQuadraticResponseSurfaceMethod(PQRSM)(Hongetal.,2000),whichwaspartofacommercialprocessintegrationanddesignoptimization(PIDO)toolknownastheProcessIntegration,AutomationandOptimization(PIAnO)(FRAMAX,2009).*Correspondingauthor.e-mail:rhexajou.ac.kr274J.-H.CHOIetal.2.MODELANDCHANNELCONFIGURATION2.1.ModelConfigurationThemodelusedfortheoptimizationandCAEanalysiswasanautomotivefrontbumper(FB).Thesizeofthepartwas1,800×600mm,theelementtypewastriangularandthenumberofelementsinthemodelwasapproximately26,000,withanaverageaspectratioof1.5.ThemodelisshowninFigure1.2.2.CoolingChannelConfigurationThecoolingcircuitfortheautomotivebumpermoldistypicallydesignedtohaveahorizontalplaneoflinecoolingchannelsandtoinstallbaffletubesfromthelinecoolingchannels.However,inthisdesign,unnecessarilylongbaffletubesattachedatalinecoolingchannelmaycauseahighpressuredropinthecoolingchannel.Thelinecoolingchannelsmaynotcontributetomoldcoolingduetotheirlargedistancefromthepartsurface.Inordertoimprovethedesign,thelinecoolingchannelswerelocatedalongtheoffsetprofileofthepartsurfaceasshowninFigure2.Theendpointsofthebaffletubeswerealsolocatedontheoffsetprofilealongalinecoolingchannel.Eitherthelinecoolingchannelsorbaffletubeswerelocatedontheoffsetprofileswithequalarcdistancesbetweenthem.3.FORMULATION3.1.DesignConstraintsThelimitationofthepressuredropandthetemperaturerisebetweentheinletandoutletofcoolingchannelshouldalsobeconsideredinthedesignofthemoldcoolingcircuit.Ahighpressuredropusuallyoccursinaneedlesslylongcoolingcircuit.Inalongcoolingcircuit,theflowrateofcoolantislow,whichresultsinahighmoldtemperatureandahightemperatureriseattheoutlet.Thedesigndefectcouldeventuallybefoundinthecoolinganalysis；however,theoptimizationisalreadytimeconsuming,soitisbettertoinsteadapplythelimitsasconstraintsintheoptimization.Inthisworkweassumedthat4linecoolingchannelswereconnectedinseriesasacluster,asshowninFigure3.Clustersareconnectedinparallelbyamanifold.Usually,themaximumpressuredropinaclusterislimitedto200kPa,andthemaximumtemperatureriseattheoutletis5oC(Mengesetal.,2001).Inthecoolinganalysis,eachlinecoolingchannelisregardedasaseparateindependentcircuitforconvenience.Becausetherewere4linecoolingchannelsinacircuit,thelimitsonthepressuredropandthetemperatureriseineachlinecoolingchannelwere50kPaand1.25oC,respectively.Wealsohaveanadditionalconstraintduetothefactthatthediameterofthebaffletubemustbegreaterthanorequaltothediameterofthecoolingchannelbecausethebaffletubehaslowerheatremovalefficiencythanthecoolingchannel.ThesethreedesignconstraintscanbeexpressedasEquations(1),(2)and(3),(13)whereG1istheconstraintonpressuredrop,G2istheconstraintontemperaturerise,andG3representsthesubtractionofthediameterofthebaffletubefromthediameterofthecoolingchannel.3.2.DesignVariablesInthiswork,thediameters,distancesanddepthsofthelinecoolingchannelsandbaffletubeswerechosenasdesignvariablesforoptimization.Thetotalnumberofdesignvariableswas6asshowninTable1.Typically,thediametersofthecoolingchannelsandbaffletubesaredeterminedbythemolddesigneraccordingtotheirruleof0PaG150000pa0CoG21.2CoG30mmFigure1.Finiteelementmodeloftheproductusedfortheoptimization.Figure2.Configurationofcoolingchannelslocatedalongtheoffsetprofiles.Figure3.Clustersconsistingof4coolingchannelswithbaffletubes.DESIGNOPTIMIZATIONOFANINJECTIONMOLDFORMINIMIZINGTEMPERATUREDEVIATION275thumb(Rheeetal.,2010).However,ithasbeenexaminedingreatdetailamongthemolddesigners.Table1showsthedesignvariableswiththeirrangesandinitialvalues.Theminimumvaluesforthecoolingchanneldistance,baffledistanceandbaffledepthweredeterminedbytheconstraintsofthemachiningrequirement.Themaximumvaluesofcoolingchanneldistanceandbaffledistanceweredeterminedbytheempiricalmaximumobtainedfromthemolddesigners.ThebaffledistancewasadiscretevariableduetoarestrictionintheautomateduseoftheCAEsoftware.Inthiswork,thebaffledistancesforoptimizationwere60,90and120mm.3.3.ObjectiveFunctionAprincipalpurposeofthemoldcoolingcircuitoptimizationistoachieveuniformtemperaturedistributionoverthepart.Theuniformtemperaturedistributionmeansthatthetemperaturedeviationcausedbythecoolingchannelsisminimized,asshowninFigure4.TheobjectivefunctionintheoptimizationwasthestandarddeviationofparttemperatureasshowninEquation(4).Theparttemperaturewasanarithmeticaverageoftheupperandthelowersurfacesofthemoldhalves.Themoldsurfacetemperaturewascalculatedfromthefiniteelementofthepart.min,(4)whereisthestandarddeviationoftheparttemperature,Eiisthetemperatureofi-thelement,Ewistheaveragetemperatureoftheentiretriangularelements,andNisthenumberofelements.4.OPTIMIZATION4.1.ParametricStudyInordertoexaminetheeffectsofthedesignvariablesontheobjectivefunction,pressuredropandtemperaturerise,parametricstudieswerecarriedout.Aparametricstudywasperformedbychangingavariableinacertainrangewhilekeepingallothervariablesfixed.Figures5-7showtheresultsofparametricstudiesfortheobjectivefunction,pressuredroptemperaturerise,respectively.Ineachfigure,thex-axisindicatesthelevelsofdesignvariables.Everydesignvariablewasdividedinto11levelsfromitslowerboundtoitsupperbound.-5and5meanthelowerandupperbounds,respectively.Whenexaminingthetemperaturedeviation,thediameterofthecoolingchannelsshowslittleinfluencetotheobjectivefunction(seeFigure5.).Thisresultwaspredictablebecausethecoolingchannelaffectstheparttemperaturetoalesserdegreethanthebaffletubesintheautomotivebumpermold.Theautomotivebumpermoldhasadeepcoresothatthemoldcoolingdependsuponthebaffletubesratherthanthecoolingchannels.Anotherreasonofthelackofinfluencecanbethattheflowstateinthecoolingchannelremainsturbulentintherangeoftheparametricstudy.Thecoolingchannelusuallyhasasmallerdiameterthanthebaffletube.Whentheflowinthebaffletubeiskeptintheturbulentstate,theflowinthecoolingchannelwillbeintheturbulentstate.Thediametersofthebaffletubesshowatangibleinfluencewhenitincreasesaboveacertainvalue.Increasingofthediameterchangestheflowinthetubetoalaminarflowstate.Thisisthecauseforthelowerheattransfercoefficientwhencomparedtotheturbulentflowstate.Thisiswhythetemperaturedeviationbecomeslargerwhenthebaffletubediameterincreases.EiEw()2N-i1=N=Figure4.Schemeofthetemperaturefieldbythecoolingchannels.Table1.Lowerandtheupperboundsfordesignvariablesandtheinitialvaluesfortheoptimization(unit:mm).DescriptionLowerInitialUpperX1Channeldiameter103040X2Bafflediameter103040X3Channeldistance6090120X4Baffledistance6060120X5Channeldepth306090X6Bafledepth306090Figure5.Parametricstudyresultoftemperaturedeviation(objectivefunction).276J.-H.CHOIetal.Amongallparameters,thebaffledepthshowsthelargestinfluenceontheobjectivefunction,asshowninFigure5.Asthebaffledepthincreases,theobjectivefunctionincreases.Thismeansthatthedeeperlocationofthebaffletubescausesthetemperaturedeviationtoincrease.Also,itconfirmsthatthecoolingoftheautomotivebumpermolddependsuponthebaffletubes.Thediametersofthecoolingchannelsandthebaffletubeshavethehighestinfluenceonthepressuredropinthecoolingcircuit,whiletheothervariablesshowlittleinfluence(seeFigure6.).Asthediametersincrease,thepressuredropdecreasesafteracertainvalue.Thisisalsoapredictableresultasalargerdiameterdecreasesthepressuredrop.TheinfluencesofthetemperatureriseattheoutletareshowninFigure7.Themostinfluentialparametersarethebafflediameterandthechanneldistance.Theinfluenceofthebafflediametershowsthehighestvaluesintherangefrom-1to3.Inthecaseofthesmallerbafflediameter,thereducedsurfaceareafortheheattransfermaycauseasmallertemperaturerise,whilethelargerbafflediametermaycausethelowerheattransfercoefficientduetothelowerflowrate.Theincreasedchanneldistancemeansthateachcoolingchanneltakesupalargerareaofthepartsurfacewithalargeramountofheatremoval.Thismaygiveaphysicalexplanationtowhytheincreaseofthetemperatureriseincreaseswithchanneldistance.ThefluctuationsshowninFigure7aresupposedtobenumericalnoise.4.2.OptimizationResultsThelargestincreaseinthetemperaturerise(Figure7)isapproximately0.15oC.Thisvalueismuchlessthantheconstraint.Theinfluenceofthevariablesonthetemperatureriseisnottangible.Thebaffledistancewasconsideredthediscretevariableinthiswork；hence,itwasdifficulttoapplyageneraloptimizationmethod.Becausetherewerethreevalues,optimizationswerecarriedout3timeswiththe5designparameters.Thebaffledistancewasfixedineachoptimization.Figures8and9showthetemperaturedeviationsasthechanneldiameter,x1andthechanneldistance,x3changeby0.1%usingtheperturbationmethodaroundtheirinitialdesignvalues.Fromtheseresultswerecognizedthatthevariationsinthetemperaturedeviationsasx1andx3variedincludednumericalnoise.Therefore,wechosePQRSMastheoptimizationmethodthatcouldeffectivelyoptimizetheresponsewithnumericalnoise.ThePQRSMequippedinacommercialFigure6.Parametricstudyresultofthepressuredrop.Figure7.Parametricstudyresultofthetemperaturerise.Figure8.Variationofthetemperaturedeviationw.r.t.x1observedbyusing0.1%perturbationmethod.Figure9.Variationofthetemperaturedeviationw.r.t.x3observedbyusing0.1%perturbationmethod.