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外文翻译--三维注射成型流动模拟的研究.doc

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外文翻译--三维注射成型流动模拟的研究.doc

陈敬虎POM水龙头壳体注塑模设计与制造52附录NumericalFillingSimulationofInjectionMoldingUsingThreeDimensionalModelAbstractMostinjectionmoldedpartsarethreedimensional,withcomplexgeometricalconfigurationsandthick/thinwallsections.A3Dsimulationmodelwillpredictmoreaccuratelythefillingprocessthana2.5Dmode1.Thispapergivesamathematicalmodelandnumericmethodbasedon3Dmodel,inwhichanequalordervelocitypressureinterpolationmethodisemployedsuccessfully.Therelationbetweenvelocityandpressureisobtainedfromthediscretizedmomentumequationsinordertoderivethepressureequation.A3Dcontrolvolumeschemeisemployedtotracktheflowfront.Thevalidityofthemodelhasbeentestedthroughtheananalysisoftheflowincavity.Keywordsthreedimensionequalorderinterpolationsimulationinjectionmolding1IntroductionDuringinjectionmolding,thetheologicalresponseofpolymermeltsisgenerallynonNewtonianandnoisothermalwiththepositionofthemovingflowfront.Becauseoftheseinherentfactors,itisdifficulttoanalyzethefillingprocess.Therefore,simplificationsusuallyareused.Forexample,inmiddleplanetechniqueanddualdomaintechnique1,becausethemostinjectionmoldedpartshavethecharacteristicofbeingthinbutgenerallyofcomplexshape,theHeleShawapproximation2isusedwhileananalyzingtheflow,i.e..Thevariationsofvelocityandpressureinthegapwisethicknessdimensionareneglected.Sothesetwotechniquesareboth2.5Dmoldfillingmodels,inwhichthefillingofamoldcavitybecomesa2Dprobleminflowdirectionanda1Dprobleminthicknessdirection.However,becauseoftheuseoftheHeleShawapproximation,theinformationthat2.5Dmodelscangenerateislimitedandincomplete.Thevariationinthegapwisethicknessdimensionofthephysicalquantitieswiththeexceptionofthetemperature,whichissolvedbyfinitedifferencemethod,isneglected.Withthedevelopmentofmoldingtechniques,molded华东交通大学理工学院毕业设计(论文)53partswillhavemoreandmorecomplexgeometryandthedifferenceinthethicknesswillbemoreandmorenotable,sothechangeinthegapwisethicknessdimensionofthephysicalquantitiescannotbeneglected.Inaddition,theflowsimulatedlooksunrealisticinasmuchasthemeltpolymerflowsonlyonsurfacesofcavity,whichappearsmoreobviouswhentheflowsimulationisdisplayedinamouldcavity.3Dsimulationmodelhasbeenaresearchdirectionandhotspotinthescopeofsimulationforplasticinjectionmolding.In3Dsimulationmodel,velocityinthegapwisethicknessdimensionisnotneglectedandthepressurevariesinthedirectionofpartthickness,and3Dfiniteelementsareusedtodiscretizethepartgeometry.Aftercalculating,completedataareobtainednotonlysurfacedatabutalsointernaldataareobtained.Therefore,a3Dsimulationmodelshouldbeabletogeneratecomplementaryandmoredetailedinformationrelatedtotheflowcharacteristicsandstressdistributionsinthinmoldedpartsthantheoneobtainedwhenusinga2.5DmodelbasedontheHeleShawapproximation.Ontheotherhand,a3Dmodelwillpredictmoreaccuratelythecharacteristicsofmoldedpartshavingthickwalledsectionssuchasencounteredingasassistedinjectionmolding.Severalflowbehaviorsattheflowfront.suchasfountainflow.which2.5Dmodelcannotpredict,canbepredictedby3Dmode1.Meanwhile,theflowsimulationlooksmorerealisticinasmuchastheoverallananalysisresultisdirectlydisplayedin3Dpartgeometryortransparentmouldcavity.ThisPaperpresentsa3Dfiniteelementmodeltodealwiththethreedimensionalflow,whichemploysanequa1ordervelocitypressureformulationmethod3,4.Therelationbetweenvelocityandpressureisobtainedfromthediscretizedmomentumequations,thensubstitutedintothecontinuityequationtoderivepressureequation.A3Dcontrolvolumeschemeisemployedtotracktheflowfront.Thevalidityofthemodelhasbeentestedthroughtheanalysisoftheflowincavity.2GoverningEquationsThepressureofmeltisnotverybigduringfillingthecavity,inaddition,reasonablemoldstructurecanavoidoverbigpressure,sothemeltisconsideredincompressible.Inertiaandgravitationareneglectedascomparedtotheviscousforce.Withtheaboveapproximation,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,zdirections.P,T,ρandηdenotepressure,temperature,densityandviscostyrespectively.Crossviscositymodelhasbeenusedforthesimulationswhere,n,γ,rarenonNewtonianexponent,shearrateandmaterialconstantrespectively.Becausethereisnonotablechangeinthescopeoftemperatureofthemeltpolymerduringfilling,Anheniusmodel5forη0isemployedasfollowingwhereB,Tb,βarematerialconstants.3NumericalSimulationMethod3.1VelocityPressureRelationIna3Dmodel,sincethechangeofthephysicalquantitiesarenotneglectedinthegapwisethicknessdimension,themomentumequationsaremuchmorecomplexthanthoseina2.5Dmode1.Itisimpossibletoobtainthevelocitypressurerelationbyintegratingthemomentum华东交通大学理工学院毕业设计(论文)55equationsinthegapwisedimension,whichisdoneina2.5Dmodel.Themomentumequationsmustbefirstdiscretized,andthentherelationbetweenvelocityandpressureisderivedfromit.Inthispaper,themomentumequationsarediscretizedusingGalerkinsmethodwithbilinearvelocitypressureformulation.Theelementequationsareassembledintheconventionalmannertoformthediscretizedglobalmomentumequationsandthevelocitymaybeexpressedasfollowingwherethenodalpressurecoefficientsaredefinedaswhererepresentglobalvelocitycoefficientmatricesinthedirectionofx,y,zcoordinaterespectively.denotethenodalpressurecoefficientsthedirectionofx,y,zcoordinaterespectively.Thenodalvaluesforareobtainedbyassemblingtheelementbyelementcontributionsintheconventionalmanner.N,iselementinterpolationandimeansglobalnodenumberandj,isforanode,theamountofthenodesaroundit.3.2PressureEquationSubstitutionofthevelocityexpressions2intodiscretizedcontinuityequation,whichisdiscretizedusingGalerkinmethod,yieldselementequationforpressure

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