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GJOURNALOFMECHANICALSCIENCEANDTECHNOLOGY212007789798JOURNALOFMECHANICALSCIENCEANDTECHNOLOGYMICROGENETICALGORITHMBASEDOPTIMALGATEPOSITIONINGININJECTIONMOLDINGDESIGNJONGSOOLEE,JONGHUNKIMSCHOOLOFMECHANICALENGINEERINGYONSEIUNIVERSITY,SEOUL120749KOREAMANUSCRIPTRECEIVEDDECEMBER12,2006REVISEDMARCH26,2007ACCEPTEDMARCH26,2007ABSTRACTTHEPAPERDEALSWITHTHEOPTIMIZATIONOFRUNNERSYSTEMININJECTIONMOLDINGDESIGNTHEDESIGNOBJECTIVEISTOLOCATEGATEPOSITIONSBYMINIMIZINGBOTHMAXIMUMINJECTIONPRESSUREATTHEINJECTIONPORTANDMAXIMUMPRESSUREDIFFERENCEAMONGALLTHEGATESONAPRODUCTWITHCONSTRAINTSONSHEARSTRESSAND/ORWELDLINETHEANALYSISOFFILLINGPROCESSISCONDUCTEDBYAFINITEELEMENTBASEDPROGRAMFORPOLYMERFLOWMICROGENETICALGORITHMMGAISUSEDASAGLOBALOPTIMIZATIONTOOLDUETOTHENATUREOFINHERENTNONLINEARLITYINFLOWANALYSISFOURDIFFERENTDESIGNAPPLICATIONSININJECTIONMOLDSAREEXPLOREDTOEXAMINETHEPROPOSEDDESIGNSTRATEGIESTHEPAPERSHOWSTHEEFFECTIVENESSOFMGAINTHECONTEXTOFOPTIMIZATIONOFRUNNERSYSTEMININJECTIONMOLDINGDESIGNGKEYWORDSMICROGENETICALGORITHMDESIGNOPTIMIZATIONFILLINGINJECTIONMOLD1INTRODUCTIONINJECTIONMOLDINGPROCESSHASBEENRECOGNIZEDASONEOFTHEMOSTEFFICIENTMANUFACTURINGTECHNOLOGIESSINCEHIGHPERFORMANCEPOLYMERMATERIALSCANBEUTILIZEDTOACCURATELYMANUFACTUREAPRODUCTWITHCOMPLICATEDSHAPECHIANG,ETAL,1991CHANGANDYANG,2001HIMASEKHAR,ETAL,1992KWONANDPARK,2004ALSO,THEDEMANDONINJECTIONMOLDEDPRODUCTSSUCHASFROMCONVENTIONALPLASTICGOODSTOMICROOPTICALDEVICESISBEINGDRAMATICALLYINCREASEDOVERTHERECENTYEARSPIOTTER,ETAL,2001KANG,ETAL,2000INGENERAL,THEINJECTIONMOLDPROCESSISINITIATEDBYTHEFILLINGSTAGEWHERETHEPOLYMERMATERIALSFILLINTOACAVITYUNDERTHEINJECTIONTEMPERATUREAFTERTHECAVITYISCOMPLETELYFILLED,THEPOSTFILLINGSTAGE,THATIS,THEPACKINGSTAGEISCONDUCTEDTOBEADDITIONALLYFILLEDWITHTHEHIGHPRESSUREPOLYMER,THEREBYRESULTINGINTHEAVOIDANCEOFMATERIALSHRINKAGESUBSEQUENTLY,THECOOLINGSTAGEISREQUIREDFORAMOLDEDPRODUCTTOBEEJECTEDWITHOUTANYDEFORMATIONITISIMPORTANTTOACCOMMODATETHEMOLDINGCONDITIONSINTHEFILLINGSTAGESINCEITISTHEFIRSTSTAGEINTHEOVERALLINJECTIONMOLDINGDESIGNZHOUANDDLI,2001AFTERTHAT,ONECANSUCCESSFULLYEXPECTMOREIMPROVEDMOLDINGCONDITIONSDURINGPOSTFILLINGSTAGESSUCHASPACKING,COOLINGSTAGESTHEPAPERDEALSWITHOPTIMALCONDITIONSOFTHEFILLINGINJECTIONMOLDINGDESIGNINWHICHTHEFLOWPATTERNANDPRESSUREFORTHEPOLYMERMATERIALSTOBEFILLEDTHROUGHGATESOFARUNNERAREOFSIGNIFICANTTHATIS,ONEOFDESIGNREQUIREMENTSARESUCHTHATWHENTHEPOLYMERCOMESINTOACAVITYTHROUGHANUMBEROFGATESLOCATEDATDIFFERENTPOSITIONS,PRESSURELEVELSONTHESURFACEOFAPRODUCTSHOULDBEASUNIFORMASPOSSIBLESUCHDESIGNCANBEPERFORMEDTHROUGHTHEINTELLIGENTGATEPOSITIONINGTOGENERATETHEMORECORRESPONDINGAUTHORTEL82221234474FAX8223622736EMAILADDRESSJLEEJYONSEIACKR790JONGSOOLEEANDJONGHUNKIM/JOURNALOFMECHANICALSCIENCEANDTECHNOLOGY212007740749UNIFORMDISTRIBUTIONOFINJECTIONPRESSUREOVERTHEPRODUCTSURFACETHEREHAVEBEENANUMBEROFSTUDIESOFOPTIMALGATELOCATIONINTHECONTEXTOFCAEFILLINGINJECTIONMOLDINGDESIGNPROBLEMSWHEREVARIOUSKINDSOFOPTIMIZERHAVEBEENEMPLOYEDTOCONDUCTDESIGNOPTIMIZATIONKIMETAL,1996YOUNG,1994PANDELIDISANDZOU,2004LIN,2001LIANDSHEN,1995THEPAPEREXPLORESTHEDESIGNOFINJECTIONMOLDSYSTEMUSINGMICROGENETICALGORITHMMGAGENETICALGORITHMCONVENTIONALGAISBASEDONTHEDARWINSTHEORYOFTHESURVIVALOFTHEFITTEST,ANDADOPTSTHECONCEPTOFNATURALEVOLUTIONTHECOMPETITIVEDESIGNSWITHMOREFITARESURVIVEDBYSELECTION,ANDTHENEWDESIGNSARECREATEDBYCROSSOVERANDMUTATIONLEE,1996LEEANDHAJELA,1996ACONVENTIONALGAWORKSWITHAMULTIPLENUMBEROFDESIGNSINAPOPULATIONHANDLINGWITHSUCHDESIGNSRESULTSININCREASINGAHIGHERPROBABILITYOFLOCATINGAGLOBALOPTIMUMASWELLASMULTIPLELOCALOPTIMAGAISALSOADVANTAGEOUSWHENTHEDESIGNPROBLEMISREPRESENTEDBYAMIXTUREOFINTEGER/DISCRETEANDCONTINUOUSDESIGNVARIABLESNEVERTHELESS,ITREQUIRESEXPENSIVECOMPUTATIONALCOSTSESPECIALLYWHENCOMBININGWITHFINITEELEMENTBASEDCAEANALYSISTOOLSACONVENTIONALGADETERMINESTHEPOPULATIONSIZEDEPENDINGUPONTHESTRINGLENGTHOFACHROMOSOMETHATISACODEDVALUEOFASETOFDESIGNVARIABLESTHEMAINDIFFERENCEBETWEENACONVENTIONALGAANDMGARESIDESONTHEPOPULATIONSIZETHEPOPULATIONSIZEINMGAISBASEDONGOLDBERGSCONCEPTSUCHTHATEVOLUTIONPROCESSISPOSSIBLEWITHSMALLPOPULATIONSTOREDUCETHECOSTOFFITNESSFUNCTIONEVALUATIONGOLDBERG,1988THISIMPLIESTHATMGAEMPLOYSAFEWNUMBEROFPOPULATIONSFORGAEVOLUTIONREGARDLESSOFTHENUMBEROFDESIGNVARIABLESANDTHECOMPLEXITYOFDESIGNPARAMETERSKRISHNAKUMAR,1989DENNISANDDULIKRAVICH,2001THEPAPERDISCUSSESTHEDESIGNREQUIREMENTSOFFILLINGINJECTIONMOLDOPTIMIZATIONTOCONSTRUCTTHEPROPEROBJECTIVEFUNCTIONSANDDESIGNCONSTRAINTSFOURDIFFERENTDESIGNAPPLICATIONSININJECTIONMOLDSAREEXPLOREDTOEXAMINETHEPROPOSEDDESIGNSTRATEGIESTHEPAPERSHOWSTHEEFFECTIVENESSOFMGAINTHECONTEXTOFOPTIMIZATIONOFRUNNERSYSTEMININJECTIONMOLDINGDESIGN2MOLDFLOWANALYSISTHEFLOWOFAPOLYMERININJECTIONMOLDINGPROCESSOBEYSTHEFOLLOWINGGOVERNINGEQUATIONS220PPSSXXYYWWWWWWWW1222PXYTTTTCKTXYZUQQKJWWWWWWWW2WHERE,220HZSDZKINTHEABOVEEQUATIONS,PISAFLOWPRESSURE,TISATEMPERATUREOFPOLYMER,ANDTISDENOTEDASTIMEPARAMETERSK,J,ANDKAREVISCOSITY,SHEARRATEANDTHERMALCONDUCTIVITY,RESPECTIVELYLEE,2003ITISASSUMEDTHATPOLYMERISANONCOMPACTIONSUBSTANCEINTHEFILLINGANALYSISTHEFLOWANALYSISINTHEPRESENTSTUDYISCONDUCTEDBYCOMPUTERAIDEDPLASTICSAPPLICATIONCAPAKOO,2003,AFINITEELEMENTBASEDCOMMERCIALCODEFORPOLYMERFLOWOFINJECTIONMOLDINGTHERUNNERSYSTEMININJECTIONMOLDCOVERSTHEPASSAGEOFMOLTENPOLYMERFROMINJECTIONPORTTOGATESTHEPRESENTSTUDYDEVELOPSTWODIFFERENTRUNNERSYSTEMSWHEREACOLDSYSTEMREQUIRESTHECHANGEINPOLYMERTEMPERATURE,ANDAHOTSYSTEMKEEPITUNCHANGEDWHILETHEFLOWPASSESTHROUGHTHERUNNERFORTHEHOTRUNNERSYSTEMHASAGEOMETRICALLYCONSISTENTTHICKNESSDUETOTHECONSTANTTEMPERATUREASSHOWNINFIG1AHOWEVER,THECAERESULTOFACOLDRUNNERSYSTEMDEPENDSONTHETHICKNESSANDSHAPETABLE1TENBARTRUSSDESIGNRESULTSMICROGACONVENTIONALGACASE1CASE2CASE3CASE1CASE2CASE3REFERENCE20X1786815785815730781790X2041018019010083045010X3838799815820877837810X4505383389397327416390X5012096015110075055010X6041025025010082030010X7641567587584674630580X8523629552568506526551X9383385505507289386368OPTIMALAREAX10050025025040116042014OPTIMALWEIGHT1599158715881593159015851499OFFUNCTIONEVALUATIONS575405423025335788946949773533JONGSOOLEEANDJONGHUNKIM/JOURNALOFMECHANICALSCIENCEANDTECHNOLOGY212007789798791AHOTRUNNERSYSTEMBCOLDRUNNERSYSTEMFIG1MODELINGOFRUNNERSYSTEMSHAPEOFARUNNERTHETYPICALILLUSTRATIONOFTHEGEOMETRICMODELINACOLDRUNNERSYSTEMISSHOWNINFIG1BWHERETHERUNNERTHICKNESSISCHANGEDACCORDINGTOTHETEMPERATUREGRADIENT3MOLDINGDESIGNREQUIREMENTS31OBJECTIVEFUNCTIONSONEOFTHEMOSTSIGNIFICANTFACTORSCONSIDEREDINTHEINJECTIONMOLDINGDESIGNISAFLOWPATTERN,WHICHIMPLIESTHATABALANCEDFLOWSHOULDBEMAINTAINEDWHILEAPOLYMERARRIVESATEACHPARTOFADESIGNPRODUCTONCETHEIMPROVEMENTONFLOWBALANCEISOBTAINED,THEFLOWOFMOLTENPOLYMERSMOOTHESANDTHEMAXIMUMINJECTIONPRESSUREISDECREASEDWITHTHESAMEORATLEASTEVENLYDISTRIBUTEDINJECTIONPRESSURELEVELATEACHGATEINACASEWHERETHECERTAINPARTOFAPRODUCTWITHINTHEMOLDISFILLEDUPEARLIERTHANOTHERPARTS,EACHPARTWOULDFALLINTOOVERPACKINGANDUNDERPACKINGSITUATIONSDURINGTHEFILLINGPROCESSOFAPOLYMERINTOMOLDSUCHPROBLEMFURTHEREVOKESAMALFORMATIONLIKETWISTINGANDBENDING,RESULTINGFROMTHEDIFFERENCEINCONTRACTIONRATEDURINGTHECOURSEOFCOOLINGOFFTHEDIFFERENCEINPRESSURETRIGGERSTHEFLOWOFPOLYMERDURINGTHEFILLINGPROCESS,INWHICHTHEMAXIMUMINJECTIONPRESSUREISDETECTEDATTHEINJECTIONPORTOFPOLYMERTHEPOLYMERALWAYSFLOWSFROMHIGHPRESSUREREGIONTOLOWPRESSUREONEWHENAFLOWPATTERNIMPROVES,THEFLOWOFPOLYMERGETSSMOOTHERWITHTHEMAXIMUMINJECTIONPRESSUREDECREASEDHOWEVER,THEFLOWINSTABILITYSOMETIMESHAPPENS,THEREBYREQUIRINGAHIGHERPRESSURETOFILLUPTHATIS,THEMAXIMUMINJECTIONPRESSURENEEDSTOBEREDUCEDINORDERTOIMPROVETHEFLOWINSTABILITYTHEPRESSUREGAPIE,THEHIGHESTANDLOWESTPRESSUREVALUESAMONGALLOFGATESISALSOTAKENASANOTHEROBJECTIVEFUNCTIONTODETERMINEWHETHERTHEWHOLEMOLDISBEINGFILLEDATONCEMOSTCOMMONLYACCEPTEDDESIGNSTRATEGYTOIMPROVETHEFLOWPATTERNISTHEADJUSTMENTOFGATELOCATIONTHEPRESENTSTUDYCONTROLSTHEFLOWPATTERNBYDEVELOPINGTHEOPTIMALGATEPOSITIONINGPROBLEMSWITHPROPEROBJECTIVEFUNCTIONSANDDESIGNCONSTRAINTSOBJECTIVEFUNCTIONSFORINJECTIONMOLDINGDESIGNARECONSIDEREDASBOTHMAXIMUMINJECTIONPRESSUREMIPANDMAXIMUMPRESSUREDIFFERENCEMPDITSHOULDBENOTEDTHATTHEMAXIMUMINJECTIONPRESSUREISCALCULATEDATTHEINJECTIONPORTANDTHEMAXIMUMPRESSUREDIFFERENCEISANUMERICALDIFFERENCEBETWEENTHEHIGHESTANDLOWESTVALUESOFPRESSUREAMONGALLOFGATESTHEAFOREMENTIONEDSTATEMENTSCOULDBEINTERPRETEDASAMULTIOBJECTIVEDESIGNPROBLEM,HENCETHEPRESENTSTUDYSIMPLYEMPLOYSAWEIGHTINGMETHODASFOLLOWSMIPXMPDXFXMIPMPDDE3WHERE,DANDEAREWEIGHTINGFACTORSASDE1,ANDXISASETOFDESIGNVARIABLESWHICHARECARTESIANCOORDINATESOFGATESONAPRODUCTEACHCOMPONENTINTHEABOVEEQUATIONISNORMALIZEDBYOPTIMALSINGLEOBJECTIVEFUNCTIONVALUE,IE,MIP,MPDITISMENTIONEDTHATTHENUMBEROFGATESISCONSIDEREDASAPROBLEMPARAMETERINTHESTUDY31CONSTRAINTSWELDLINESAREEASILYDETECTEDWHENMORETHANTWOFLOWFRONTSHAVINGDIFFERENTTEMPERATUREVALUESMEETDURINGTHEFILLINGPROCESSTHEWELDLINEISONEOFTHEWEAKESTPOINTSINMOLDEDPRODUCTITISVERY792JONGSOOLEEANDJONGHUNKIM/JOURNALOFMECHANICALSCIENCEANDTECHNOLOGY212007740749VULNERABLETOASHOCKANDSUBSEQUENTLYCAUSESEXTERNALDEFECTSOFAVERYGLOSSYPOLYMERTHEWELDLINESHOULDBEMOVEDINTOALESSWEAKREGIONBYADJUSTINGTHEWIDTHOFAPRODUCT,THESIZEAND/ORSHAPEOFGATESANDRUNNERS,ANDTHEPOSITIONOFGATES,ETCTHEPRESENTSTUDYCONSIDERSTHEPOSITIONOFAWELDLINEASACONSTRAINTINOPTIMALGATEPOSITIONINGOFMOLDDESIGNONCEADESIGNERSPECIFIESAREASWHEREWELDLINESSHOULDNOTBEGENERATED,ALLOFTHEFINITEELEMENTNODESINSUCHAREASARECONSTRAINEDNOTTOFORMTHEWELDLINESSHEARSTRESSISDEFINEDASASHEARFORCEIMPOSEDONTHEWALLOFAMOLDBYTHESHEARFLOWOFAPOLYMERTHEMAGNITUDEOFSHEARSTRESSISPROPORTIONALTOTHEPRESSUREGRADIENTOFEACHPOSITIONINGENERAL,THESHEARSTRESSISZEROATTHECENTEROFAMOLDEDPRODUCT,ANDREACHESAMAXIMUMVALUEONTHEWALLHIGHSHEARSTRESSTRIGGERSTHEMOLECULECULTIVATIONONTHESURFACEOFAMOLDEDPRODUCTFLOWINSTABILITYSUCHASMELTFRACTUREHASACLOSERELATIONSHIPWITHTHESHEARSTRESSTHECLEARSURFACEOFAMOLDEDPRODUCTCANBEOBTAINEDBYREDUCINGTHEMAGNITUDEOFSHEARSTRESSTHATIS,SHEARSTRESSSHOULDBEMINIMIZEDDURINGTHEMOLDFILLINGPROCESSINORDERTOIMPROVETHEQUALITYOFAMOLDEDPRODUCT,PARTICULARLYONITSSURFACEMAXIMUMALLOWABLESHEARSTRESSDEPENDSONTHEKINDSOFPOLYMER,ANDISGENERALLYTAKENAS1OFTENSILESTRENGTHOFAPOLYMERSHEARSTRESSAFFECTINGTHEQUALITYOFENDPRODUCTISCONSIDEREDASANOTHERCONSTRAINT33FORMULATIONOFOPTIMI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MIZATIONRESULTSOFVEHICLEDASHBOARDMAXIMUMPRESSUREMPAMAXIMUMDIFFERENCEMPAINITIALDESIGN242692026MIPONLY184733508MPDONLY231221244OBJECTIVEBOTHMIPANDMPD229921258TABLE3OPTIMIZATIONRESULTSOFTVMONITORMAXIMUMPRESSUREMPAMAXIMUMDIFFERENCEMPASHEARSTRESS05MPAINITIALDESIGN80551371045MIPONLY6846406043MPDONLY7227304045OBJECTIVEBOTHMIPANDMPD6846406043OFMPDONLYINTERMSOFGATELOCATIONSFROMFIGS7AND8ANDTHEPERCENTILEIMPROVEMENTINTABLE2AWEIGHTEDSUMMETHODISUSEDTOOBTAINTHEMULTIOBJECTIVEOPTIMALSOLUTIONSBYCHANGINGDANDESIMULTANEOUSLY,BUTYIELDSTHESAMERESULTSOUTOFATOTALOF11WEIGHTINGFACTORBASEDTRIALSTHEREASONWHYAFEWNUMBEROFPARETOSOLUTIONSAREDETECTEDISSUCHTHATTHEMAXIMUMPRESSUREISNOTCOUNTERTOPRESSUREDISTRIBUTIONINTHEFILLINGINJECTIONMOLDINGINOTHERWORDS,WHENTHEOVERALLPRESSUREDISTRIBUTIONISIMPROVEDTHANKSTOTHEENHANCEMENTOFFLOWBALANCEANDTHESMOOTHNESSOFPOLYMERFLOW,THEMAXIMUMPRESSUREISCONSEQUENTLYDECREASEDASFARASTHEPRESSUREDISTRIBUTIONOFAMODELEDPRODUCTISCONCERNED,THECHANGEINGATEPOSITIONISNOTICEABLEGATE_5OFOPTIMIZEDMODELSMOVESFROMRIGHTTOLEFTREGIONCOMPAREDWITHANINITIALMODEL52TVMONITORTHEMODELOFATVMONITOREQUIPPEDWITH4GATESISNOWOPTIMIZEDUSINGOBJECTIVEFUNCTIONSANDTHEUPPERLIMITONSHEARSTRESSCONSTRAINT,WHERETHESHEARSTRESSALLOWABLEIS05MPATHEINITIALDESIGNWITH4DISCRETEDESIGNSPACESISDISPLAYEDINFIG9,ANDOPTIMIZEDPRESSUREDISTRIBUTIONSARESHOWNINFIGS10AND11DESIGNRESULTSFORSINGLEOBJECTIVEANDMULTIOBJECTIVEOPTIMIZATIONARETABULATEDINTABLE3INCASEOFMIPONLYGENERATESTHESAMERESULTASWEIGHTINGMETHODBASEDMULTIOBJECTIVESOLUTIONSOFBOTHMIPANDMPDINCASEOFMPDONLY,THEMAXIJONGSOOLEEANDJONGHUNKIM/JOURNALOFMECHANICALSCIENCEANDTECHNOLOGY212007789798795FIG9INITIALGATELOCATIONOFTVMONITORFIG10OPTIMIZEDDESIGNOFTVMONITORMPDONLYFIG11OPTIMIZEDDESIGNOFTVMONITORMIPONLYBOTHMIPANDMPDMUMINJECTIONPRESSUREANDMAXIMUMPRESSUREDIFFERENCEHAVEBEENIMPROVEDBY103AND778,RESPECTIVELYITISEXPECTEDTHATTHEENHANCEMENTONFLOWBALANCEANDSMOOTHNESSMAYBEMADEPOSSIBLEBYOPTIMIZINGTHEGATEPOSITIONS53CDTRAYTHECDTRAYUSEINALAPTOPCOMPUTERHAS4GATESFORINJECTIONMOLDINGTHEOPTIMIZATIONONTHISMODELFIG12CDTRAYLEFTANDITSINITIALGATELOCATIONRIGHTFIG13OPTIMIZEDDESIGNOFCDTRAYMIPONLYFIG14OPTIMIZEDDESIGNOFCDTRAYMPDONLYISCONDUCTEDWITHASHEARSTRESSCONSTRAINT,WHERETHEUPPERLIMITONSHEARSTRESSALLOWABLEIS15MPAINITIALANDOPTIMIZEDRESULTSFORPRESSUREDISTRIBUTIONARESHOWNINFIGS12TO15FROMTHESUMMARYOFTABLE4,THEDESIGNSOLUTIONSOFOPTIMALOBJECTIVEFUN796JONGSOOLEEANDJONGHUNKIM/JOURNALOFMECHANICALSCIENCEANDTECHNOLOGY212007740749FIG15OPTIMIZEDDESIGNOFCDTRAYBOTHMIPANDMPDTABLE4OPTIMIZATIONRESULTSOFCDTRAYMAXIMUMPRESSUREMPAMAXIMUMDIFFERENCEMPASHEARSTRESS15MPAINITIALDESIGN82661192122MIPONLY73917085126MPDONLY80440332112OBJECTIVEBOTHMIPANDMPD78790376114CTIONVALUESINTHISPROBLEMAREQUITESIMILARTOTHATINTHEVEHICLEDASHBOARDINCASEOFMIPONLY,THEMAXIMUMPRESSUREDIFFERENCEVALUEGETSWORSETH