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INTERNATIONALJOURNALOFAUTOMOTIVETECHNOLOGY,VOL13,NO2,PP273−2772012DOI101007/S12239−012−0024−5COPYRIGHT2012KSAE/063−11PISSN1229−9138/EISSN19763832273DESIGNOPTIMIZATIONOFANINJECTIONMOLDFORMINIMIZINGTEMPERATUREDEVIATIONJHCHOI1,SHCHOI1,DPARK2,CHPARK2,BORHEE1ANDDHCHOI21GRADUATESCHOOLOFMECHANICALENGINEERING,AJOUUNIVERSITY,GYEONGGI443740,KOREA2GRADUATESCHOOLOFMECHANICALENGINEERING,HANYNAGUNIVERSITY,SEOUL133791,KOREARECEIVED24JANUARY2011;REVISED15JUNE2011;ACCEPTED17JUNE2011ABSTRACT−THEQUALITYOFANINJECTIONMOLDEDPARTISLARGELYAFFECTEDBYTHEMOLDCOOLINGCONSEQUENTLY,THISMAKESITNECESSARYTOOPTIMIZETHEMOLDCOOLINGCIRCUITWHENDESIGNINGTHEPARTBUTPRIORTODESIGNINGTHEMOLDVARIOUSAPPROACHESOFOPTIMIZINGTHEMOLDCOOLINGCIRCUITHAVEBEENPROPOSEDPREVIOUSLYINTHISWORK,OPTIMIZATIONOFTHEMOLDCOOLINGCIRCUITWASAUTOMATEDBYACOMMERCIALPROCESSINTEGRATIONANDDESIGNOPTIMIZATIONTOOLCALLEDPROCESSINTEGRATION,AUTOMATIONANDOPTIMIZATIONPIANO,WHICHISOFTENUSEDFORLARGEAUTOMOTIVEPARTSSUCHASBUMPERSANDINSTRUMENTPANELSTHECOOLINGCHANNELSANDBAFFLETUBESWERELOCATEDONTHEOFFSETPROFILEEQUIDISTANTFROMTHEPARTSURFACETHELOCATIONSOFTHECOOLINGCHANNELSANDTHEBAFFLETUBESWEREAUTOMATICALLYGENERATEDANDINPUTINTOTHEMOLDCOOLINGCOMPUTERAIDEDENGINEERINGPROGRAM,AUTODESKMOLDFLOWINSIGHT2010THEOBJECTIVEFUNCTIONWASTHEDEVIATIONOFTHEMOLDSURFACETEMPERATUREFROMAGIVENDESIGNTEMPERATUREDESIGNVARIABLESINTHEOPTIMIZATIONWERETHEDEPTHS,DISTANCESANDDIAMETERSOFTHECOOLINGCHANNELSANDTHEBAFFLETUBESFORAMOREPRACTICALANALYSIS,THEPRESSUREDROPANDTEMPERATUREDROPWERECONSIDEREDTHELIMITEDVALUESOPTIMIZATIONWASPERFORMEDUSINGTHEPROGRESSIVEQUADRATICRESPONSESURFACEMETHODTHEOPTIMIZATIONRESULTEDINAMOREUNIFORMTEMPERATUREDISTRIBUTIONWHENCOMPAREDTOTHEINITIALDESIGN,ANDUTILIZINGTHEPROPOSEDOPTIMIZATIONMETHOD,ASATISFACTORYSOLUTIONCOULDBEMADEATALOWERCOSTKEYWORDSINJECTIONMOLDING,COOLINGCHANNEL,COOLINGANALYSIS,PQRSM,DESIGNOPTIMIZATION1INTRODUCTIONTHECOOLINGSTAGEISTHELONGESTSTAGEDURINGTHECYCLETIMEOFTHEINJECTIONMOLDINGPROCESSTHEREFORE,THEMOSTEFFECTIVEMETHODTOREDUCETHECYCLETIMEISTOREDUCETHECOOLINGTIMETHECOOLINGTIMEISFUNDAMENTALLYDETERMINEDBYTHEPARTTHICKNESSANDMOLDTEMPERATURE,WHICHCREATESACOOLINGTIMELIMITATIONIFTHEMOLDTEMPERATUREANDPARTTHICKNESSAREUNIFORMOVERAWHOLEPART,THECOOLINGTIMEISNOTACONCERN;HOWEVER,NONUNIFORMPARTTHICKNESSANDMOLDTEMPERATUREDISTRIBUTIONLENGTHENTHEOVERALLCOOLINGTIMEALONGERCOOLINGTIMEMEANSPOORTEMPERATUREUNIFORMITY,WHICHCANCAUSETHEPARTTOWARPTHISISESPECIALLYTRUEFORLARGEPRODUCTS,SUCHASAUTOMOTIVEBUMPERSANDINSTRUMENTPANELSITISFORTHESETYPESOFPARTSTHATTEMPERATUREUNIFORMITYBECOMESTHEMOSTIMPORTANTFACTORINMOLDDESIGNWEDEVELOPEDANAUTOMATEDOPTIMIZATIONOFTHECOOLINGCIRCUITFORANEARLYPARTDESIGNINORDERTOCHECKTHEDESIGNVALIDITYUSUALLYTHEEARLYPARTDESIGNISCHECKEDBYTHEFILING/PACKINGANDWARPAGEANALYSESWITHOUTACOOLINGANALYSISTHISISBECAUSETHEASSUMPTIONISTHATTHEMOLDTEMPERATUREISUNIFORM,WHICHISNOTACTUALLYTRUEPROVIDINGARAPIDLYOPTIMIZEDCOOLINGCIRCUITFORTHEDESIGNEDPARTWOULDHELPPARTDESIGNERSCORRECTTHEIRDESIGNKORESAWAANDSUZUKI,1999THEOPTIMIZATIONWASDESIGNEDTOMINIMIZETHEPARTTEMPERATUREDEVIATIONUSINGDESIGNVARIABLESSUCHASTHEDIAMETERSANDDISTANCESOFTHECOOLINGCHANNELSANDBAFFLETUBESANDTHEDEPTHSOFTHEPARTFROMTHEMOLDSURFACEOFTHECOOLINGCHANNELSANDBAFFLETUBESACOMMERCIALCOMPUTERAIDEDENGINEERINGCAETOOL,AUTODESKMOLDFLOWINSIGHT,WASUSEDFORTHECOOLINGANALYSISWESUCCESSFULLYOBTAINEDANOPTIMIZEDCOOLINGCIRCUITINATIMEMUCHSHORTERTHANCANBEACHIEVEDINAMANUALDESIGNINORDERTODEVELOPTHEAUTOMATEDOPTIMIZATIONOFTHECOOLINGCIRCUITFORTHEPRACTICALMOLDDESIGN,PRACTICALDESIGNPARAMETERSSUCHASTHEPRESSUREDROPLIMITANDTHECOOLANTTEMPERATURERISEWERECONSIDEREDINTHEOPTIMIZATIONTHEPERFORMANCEOFTHEOPTIMIZATIONTECHNIQUECANBEAFFECTEDBYNUMERICALNOISEINTHERESPONSESTOFINDANOPTIMUMSOLUTIONEFFECTIVELYWHENNUMERICALNOISEEXISTS,WEPERFORMEDANOPTIMIZATIONBYAPPLYINGAREGRESSIONBASEDSEQUENTIALAPPROXIMATEOPTIMIZERKNOWNASTHEPROGRESSIVEQUADRATICRESPONSESURFACEMETHODPQRSMHONGETAL,2000,WHICHWASPARTOFACOMMERCIALPROCESSINTEGRATIONANDDESIGNOPTIMIZATIONPIDOTOOLKNOWNASTHEPROCESSINTEGRATION,AUTOMATIONANDOPTIMIZATIONPIANOFRAMAX,2009CORRESPONDINGAUTHOREMAILRHEXAJOUACKR274JHCHOIETAL2MODELANDCHANNELCONFIGURATION21MODELCONFIGURATIONTHEMODELUSEDFORTHEOPTIMIZATIONANDCAEANALYSISWASANAUTOMOTIVEFRONTBUMPERFBTHESIZEOFTHEPARTWAS1,800600MM,THEELEMENTTYPEWASTRIANGULARANDTHENUMBEROFELEMENTSINTHEMODELWASAPPROXIMATELY26,000,WITHANAVERAGEASPECTRATIOOF15THEMODELISSHOWNINFIGURE122COOLINGCHANNELCONFIGURATIONTHECOOLINGCIRCUITFORTHEAUTOMOTIVEBUMPERMOLDISTYPICALLYDESIGNEDTOHAVEAHORIZONTALPLANEOFLINECOOLINGCHANNELSANDTOINSTALLBAFFLETUBESFROMTHELINECOOLINGCHANNELSHOWEVER,INTHISDESIGN,UNNECESSARILYLONGBAFFLETUBESATTACHEDATALINECOOLINGCHANNELMAYCAUSEAHIGHPRESSUREDROPINTHECOOLINGCHANNELTHELINECOOLINGCHANNELSMAYNOTCONTRIBUTETOMOLDCOOLINGDUETOTHEIRLARGEDISTANCEFROMTHEPARTSURFACEINORDERTOIMPROVETHEDESIGN,THELINECOOLINGCHANNELSWERELOCATEDALONGTHEOFFSETPROFILEOFTHEPARTSURFACEASSHOWNINFIGURE2THEENDPOINTSOFTHEBAFFLETUBESWEREALSOLOCATEDONTHEOFFSETPROFILEALONGALINECOOLINGCHANNELEITHERTHELINECOOLINGCHANNELSORBAFFLETUBESWERELOCATEDONTHEOFFSETPROFILESWITHEQUALARCDISTANCESBETWEENTHEM3FORMULATION31DESIGNCONSTRAINTSTHELIMITATIONOFTHEPRESSUREDROPANDTHETEMPERATURERISEBETWEENTHEINLETANDOUTLETOFCOOLINGCHANNELSHOULDALSOBECONSIDEREDINTHEDESIGNOFTHEMOLDCOOLINGCIRCUITAHIGHPRESSUREDROPUSUALLYOCCURSINANEEDLESSLYLONGCOOLINGCIRCUITINALONGCOOLINGCIRCUIT,THEFLOWRATEOFCOOLANTISLOW,WHICHRESULTSINAHIGHMOLDTEMPERATUREANDAHIGHTEMPERATURERISEATTHEOUTLETTHEDESIGNDEFECTCOULDEVENTUALLYBEFOUNDINTHECOOLINGANALYSIS;HOWEVER,THEOPTIMIZATIONISALREADYTIMECONSUMING,SOITISBETTERTOINSTEADAPPLYTHELIMITSASCONSTRAINTSINTHEOPTIMIZATIONINTHISWORKWEASSUMEDTHAT4LINECOOLINGCHANNELSWERECONNECTEDINSERIESASACLUSTER,ASSHOWNINFIGURE3CLUSTERSARECONNECTEDINPARALLELBYAMANIFOLDUSUALLY,THEMAXIMUMPRESSUREDROPINACLUSTERISLIMITEDTO200KPA,ANDTHEMAXIMUMTEMPERATURERISEATTHEOUTLETIS5OCMENGESETAL,2001INTHECOOLINGANALYSIS,EACHLINECOOLINGCHANNELISREGARDEDASASEPARATEINDEPENDENTCIRCUITFORCONVENIENCEBECAUSETHEREWERE4LINECOOLINGCHANNELSINACIRCUIT,THELIMITSONTHEPRESSUREDROPANDTHETEMPERATURERISEINEACHLINECOOLINGCHANNELWERE50KPAAND125OC,RESPECTIVELYWEALSOHAVEANADDITIONALCONSTRAINTDUETOTHEFACTTHATTHEDIAMETEROFTHEBAFFLETUBEMUSTBEGREATERTHANOREQUALTOTHEDIAMETEROFTHECOOLINGCHANNELBECAUSETHEBAFFLETUBEHASLOWERHEATREMOVALEFFICIENCYTHANTHECOOLINGCHANNELTHESETHREEDESIGNCONSTRAINTSCANBEEXPRESSEDASEQUATIONS1,2AND3,13WHEREG1ISTHECONSTRAINTONPRESSUREDROP,G2ISTHECONSTRAINTONTEMPERATURERISE,ANDG3REPRESENTSTHESUBTRACTIONOFTHEDIAMETEROFTHEBAFFLETUBEFROMTHEDIAMETEROFTHECOOLINGCHANNEL32DESIGNVARIABLESINTHISWORK,THEDIAMETERS,DISTANCESANDDEPTHSOFTHELINECOOLINGCHANNELSANDBAFFLETUBESWERECHOSENASDESIGNVARIABLESFOROPTIMIZATIONTHETOTALNUMBEROFDESIGNVARIABLESWAS6ASSHOWNINTABLE1TYPICALLY,THEDIAMETERSOFTHECOOLINGCHANNELSANDBAFFLETUBESAREDETERMINEDBYTHEMOLDDESIGNERACCORDINGTOTHEIRRULEOF0PAG150000PA≤≤0COG212CO≤≤G30MM≤FIGURE1FINITEELEMENTMODELOFTHEPRODUCTUSEDFORTHEOPTIMIZATIONFIGURE2CONFIGURATIONOFCOOLINGCHANNELSLOCATEDALONGTHEOFFSETPROFILESFIGURE3CLUSTERSCONSISTINGOF4COOLINGCHANNELSWITHBAFFLETUBESDESIGNOPTIMIZATIONOFANINJECTIONMOLDFORMINIMIZINGTEMPERATUREDEVIATION275THUMBRHEEETAL,2010HOWEVER,ITHASBEENEXAMINEDINGREATDETAILAMONGTHEMOLDDESIGNERSTABLE1SHOWSTHEDESIGNVARIABLESWITHTHEIRRANGESANDINITIALVALUESTHEMINIMUMVALUESFORTHECOOLINGCHANNELDISTANCE,BAFFLEDISTANCEANDBAFFLEDEPTHWEREDETERMINEDBYTHECONSTRAINTSOFTHEMACHININGREQUIREMENTTHEMAXIMUMVALUESOFCOOLINGCHANNELDISTANCEANDBAFFLEDISTANCEWEREDETERMINEDBYTHEEMPIRICALMAXIMUMOBTAINEDFROMTHEMOLDDESIGNERSTHEBAFFLEDISTANCEWASADISCRETEVARIABLEDUETOARESTRICTIONINTHEAUTOMATEDUSEOFTHECAESOFTWAREINTHISWORK,THEBAFFLEDISTANCESFOROPTIMIZATIONWERE60,90AND120MM33OBJECTIVEFUNCTIONAPRINCIPALPURPOSEOFTHEMOLDCOOLINGCIRCUITOPTIMIZATIONISTOACHIEVEUNIFORMTEMPERATUREDISTRIBUTIONOVERTHEPARTTHEUNIFORMTEMPERATUREDISTRIBUTIONMEANSTHATTHETEMPERATUREDEVIATIONCAUSEDBYTHECOOLINGCHANNELSISMINIMIZED,ASSHOWNINFIGURE4THEOBJECTIVEFUNCTIONINTHEOPTIMIZATIONWASTHESTANDARDDEVIATIONOFPARTTEMPERATUREASSHOWNINEQUATION4THEPARTTEMPERATUREWASANARITHMETICAVERAGEOFTHEUPPERANDTHELOWERSURFACESOFTHEMOLDHALVESTHEMOLDSURFACETEMPERATUREWASCALCULATEDFROMTHEFINITEELEMENTOFTHEPARTMIN,4WHEREΣISTHESTANDARDDEVIATIONOFTHEPARTTEMPERATURE,EIISTHETEMPERATUREOFITHELEMENT,EWISTHEAVERAGETEMPERATUREOFTHEENTIRETRIANGULARELEMENTS,ANDNISTHENUMBEROFELEMENTS4OPTIMIZATION41PARAMETRICSTUDYINORDERTOEXAMINETHEEFFECTSOFTHEDESIGNVARIABLESONTHEOBJECTIVEFUNCTION,PRESSUREDROPANDTEMPERATURERISE,PARAMETRICSTUDIESWERECARRIEDOUTAPARAMETRICSTUDYWASPERFORMEDBYCHANGINGAVARIABLEINACERTAINRANGEWHILEKEEPINGALLOTHERVARIABLESFIXEDFIGURES57SHOWTHERESULTSOFPARAMETRICSTUDIESFORTHEOBJECTIVEFUNCTION,PRESSUREDROPTEMPERATURERISE,RESPECTIVELYINEACHFIGURE,THEXAXISINDICATESTHELEVELSOFDESIGNVARIABLESEVERYDESIGNVARIABLEWASDIVIDEDINTO11LEVELSFROMITSLOWERBOUNDTOITSUPPERBOUND5AND5MEANTHELOWERANDUPPERBOUNDS,RESPECTIVELYWHENEXAMININGTHETEMPERATUREDEVIATION,THEDIAMETEROFTHECOOLINGCHANNELSSHOWSLITTLEINFLUENCETOTHEOBJECTIVEFUNCTIONSEEFIGURE5THISRESULTWASPREDICTABLEBECAUSETHECOOLINGCHANNELAFFECTSTHEPARTTEMPERATURETOALESSERDEGREETHANTHEBAFFLETUBESINTHEAUTOMOTIVEBUMPERMOLDTHEAUTOMOTIVEBUMPERMOLDHASADEEPCORESOTHATTHEMOLDCOOLINGDEPENDSUPONTHEBAFFLETUBESRATHERTHANTHECOOLINGCHANNELSANOTHERREASONOFTHELACKOFINFLUENCECANBETHATTHEFLOWSTATEINTHECOOLINGCHANNELREMAINSTURBULENTINTHERANGEOFTHEPARAMETRICSTUDYTHECOOLINGCHANNELUSUALLYHASASMALLERDIAMETERTHANTHEBAFFLETUBEWHENTHEFLOWINTHEBAFFLETUBEISKEPTINTHETURBULENTSTATE,THEFLOWINTHECOOLINGCHANNELWILLBEINTHETURBULENTSTATETHEDIAMETERSOFTHEBAFFLETUBESSHOWATANGIBLEINFLUENCEWHENITINCREASESABOVEACERTAINVALUEINCREASINGOFTHEDIAMETERCHANGESTHEFLOWINTHETUBETOALAMINARFLOWSTATETHISISTHECAUSEFORTHELOWERHEATTRANSFERCOEFFICIENTWHENCOMPAREDTOTHETURBULENTFLOWSTATETHISISWHYTHETEMPERATUREDEVIATIONBECOMESLARGERWHENTHEBAFFLETUBEDIAMETERINCREASESΣEIEW–2NI1N∑FIGURE4SCHEMEOFTHETEMPERATUREFIELDBYTHECOOLINGCHANNELSTABLE1LOWERANDTHEUPPERBOUNDSFORDESIGNVARIABLESANDTHEINITIALVALUESFORTHEOPTIMIZATIONUNITMMDESCRIPTIONLOWERINITIALUPPERX1CHANNELDIAMETER103040X2BAFFLEDIAMETER103040X3CHANNELDISTANCE6090120X4BAFFLEDISTANCE6060120X5CHANNELDEPTH306090X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