陈敬虎：POM水龙头壳体注塑模设计与制造52附录NumericalFillingSimulationofInjectionMoldingUsingThreeDimensionalModelAbstract：Mostinjectionmoldedpartsarethree-dimensional/withcomplexgeometricalconfigurationsandthickthinwallsectionsA3Dsimulationmodelwillpredictmoreaccuratelythefillingprocessthana2/5Dmode1/Thispapergivesamathematicalmodelandnumericmethodbasedon3Dmodel，inwhichanequal-ordervelocity-pressureinterpolationmethodisemployedsuccessfullyTherelationbetweenvelocityandpressureisobtainedfromthediscretizedmomentumequationsinordertoderivethepressureequationA3DcontrolvolumeschemeisemployedtotracktheflowfrontThevalidityofthemodelhasbeentestedthroughtheananalysisoftheflowincavityKeywords：threedimension；equal-orderinterpolation；simulation；injectionmolding1IntroductionDuringinjectionmolding，thetheologicalresponseofpolymermeltsisgenerallynon-NewtonianandnoisothermalwiththepositionofthemovingflowfrontBecauseoftheseinherentfactors，itisdifficulttoanalyzethefillingprocessTherefore，simplificationsusuallyareusedForexample，inmiddle-planetechniqueanddualdomaintechnique1/becausethemostinjectionmoldedpartshavethecharacteristicofbeingthinbutgenerallyofcomplexshape，theHele-Shawapproximation2isusedwhileananalyzingtheflow/i/e/Thevariationsofvelocityandpressureinthegapwise(thickness)dimensionareneglectedSothesetwotechniquesareboth2/5Dmoldfillingmodels，inwhichthefillingofamoldcavitybecomesa2Dprobleminflowdirectionanda1DprobleminthicknessdirectionHowever/becauseoftheuseoftheHele-Shawapproximation，theinformationthat2/5DmodelscangenerateislimitedandincompleteThevariationinthegapwise(thickness)dimensionofthephysicalquantitieswiththeexceptionofthetemperature，whichissolvedbyfinitedifferencemethod，isneglectedWiththedevelopmentofmoldingtechniques，molded华东交通大学理工学院毕业设计（论文）53partswillhavemoreandmorecomplexgeometryandthedifferenceinthethicknesswillbemoreandmorenotable，sothechangeinthegapwise(thickness)dimensionofthephysicalquantitiescannotbeneglectedInaddition，theflowsimulatedlooksunrealisticinasmuchasthemeltpolymerflowsonlyonsurfacesofcavity/whichappearsmoreobviouswhentheflowsimulationisdisplayedinamouldcavity3DsimulationmodelhasbeenaresearchdirectionandhotspotinthescopeofsimulationforplasticinjectionmoldingIn3Dsimulationmodel，velocityinthegapwise(thickness)dimensionisnotneglectedandthepressurevariesinthedirectionofpartthickness，and3DfiniteelementsareusedtodiscretizethepartgeometryAftercalculating，completedataareobtained(notonlysurfacedatabutalsointernaldataareobtained)Therefore/a3Dsimulationmodelshouldbeabletogeneratecomplementaryandmoredetailedinformationrelatedtotheflowcharacteristicsandstressdistributionsinthinmoldedpartsthantheoneobtainedwhenusinga2/5Dmodel(basedontheHele-Shawapproximation)Ontheotherhand，a3DmodelwillpredictmoreaccuratelythecharacteristicsofmoldedpartshavingthickwalledsectionssuchasencounteredingasassistedinjectionmoldingSeveralflowbehaviorsattheflowfrontsuchas“fountainflow”which2/5Dmodelcannotpredict/canbepredictedby3Dmode1/Meanwhile/theflowsimulationlooksmorerealisticinasmuchastheoverallananalysisresultisdirectlydisplayedin3DpartgeometryortransparentmouldcavityThisPaperpresentsa3Dfiniteelementmodeltodealwiththethreedimensionalflow/whichemploysanequa1-ordervelocity-pressureformulationmethod3/4Therelationbetweenvelocityandpressureisobtainedfromthediscretizedmomentumequations/thensubstitutedintothecontinuityequationtoderivepressureequationA3DcontrolvolumeschemeisemployedtotracktheflowfrontThevalidityofthemodelhasbeentestedthroughtheanalysisoftheflowincavity2GoverningEquationsThepressureofmeltisnotverybigduringfillingthecavity/inaddition，reasonablemoldstructurecanavoidoverbigpressure，sothemeltisconsideredincompressibleInertiaandgravitationareneglectedascomparedtotheviscousforceWiththeaboveapproximation，thegoverningequations，expressedincartesiancoordinates，areasfollowing：陈敬虎：POM水龙头壳体注塑模设计与制造54MomentumequationsContinuityequationEnergyequationwhere/x，y，zarethreedimensionalcoordinatesandu/v，warethevelocitycomponentinthex/y/zdirectionsP，T，anddenotepressure，temperature/densityandviscostyrespectivelyCrossviscositymodelhasbeenusedforthesimulations：where，n/，rarenon-Newtonianexponent，shearrateandmaterialconstantrespectivelyBecausethereisnonotablechangeinthescopeoftemperatureofthemeltpolymerduringfilling，Anheniusmodel5for0isemployedasfollowing：whereB，Tb，arematerialconstants/3NumericalSimulationMethod3/1Velocity-PressureRelationIna3Dmodel，sincethechangeofthephysicalquantitiesarenotneglectedinthegapwise(thickness)dimension，themomentumequationsaremuchmorecomplexthanthoseina2/5Dmode1Itisimpossibletoobtainthevelocitypressurerelationbyintegratingthemomentum华东交通大学理工学院毕业设计（论文）55equationsinthegapwisedimension，whichisdoneina2/5Dmodel/Themomentumequationsmustbefirstdiscretized，andthentherelationbetweenvelocityandpressureisderivedfromit/Inthispaper/themomentumequationsarediscretizedusingGalerkinsmethodwithbilinearvelocity-pressureformulationTheelementequationsareassembledintheconventionalmannertoformthediscretizedglobalmomentumequationsandthevelocitymaybeexpressedasfollowingwherethenodalpressurecoefficientsaredefinedaswhererepresentglobalvelocitycoefficientmatricesinthedirectionofx/y/zcoordinaterespectively/denotethenodalpressurecoefficientsthedirectionofx/y/zcoordinaterespectively/Thenodalvaluesforareobtainedbyassemblingtheelement-by-elementcontributionsintheconventionalmanner/N，iselementinterpolationandimeansglobalnodenumberandj/isforanode/theamountofthenodesaroundit/3/2PressureEquationSubstitutionofthevelocityexpressions(2)intodiscretizedcontinuityequation/whichisdiscretizedusingGalerkinmethod，yieldselementequationforpressure/
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