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外文翻译--三维注射成型流动模拟的研究.doc外文翻译--三维注射成型流动模拟的研究.doc -- 5 元

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编号:201311171107015710    大小:544.14KB    格式:DOC    上传时间:2013-11-17
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陈敬虎:POM水龙头壳体注塑模设计与制造52附录NumericalFillingSimulationofInjectionMoldingUsingThree—DimensionalModelAbstract:Mostinjectionmoldedpartsarethree-dimensional,withcomplexgeometricalconfigurationsandthick/thinwallsections.A3Dsimulationmodelwillpredictmoreaccuratelythefillingprocessthana2.5Dmode1.Thispapergivesamathematicalmodelandnumericmethodbasedon3Dmodel,inwhichanequal-ordervelocity-pressureinterpolationmethodisemployedsuccessfully.Therelationbetweenvelocityandpressureisobtainedfromthediscretizedmomentumequationsinordertoderivethepressureequation.A3Dcontrolvolumeschemeisemployedtotracktheflowfront.Thevalidityofthemodelhasbeentestedthroughtheananalysisoftheflowincavity.Keywords:threedimension;equal-orderinterpolation;simulation;injectionmolding1IntroductionDuringinjectionmolding,thetheologicalresponseofpolymermeltsisgenerallynon-Newtonianandnoisothermalwiththepositionofthemovingflowfront.Becauseoftheseinherentfactors,itisdifficulttoanalyzethefillingprocess.Therefore,simplificationsusuallyareused.Forexample,inmiddle-planetechniqueanddualdomaintechnique[1],becausethemostinjectionmoldedpartshavethecharacteristicofbeingthinbutgenerallyofcomplexshape,theHele-Shawapproximation[2]isusedwhileananalyzingtheflow,i.e..Thevariationsofvelocityandpressureinthegapwise(thickness)dimensionareneglected.Sothesetwotechniquesareboth2.5Dmoldfillingmodels,inwhichthefillingofamoldcavitybecomesa2Dprobleminflowdirectionanda1Dprobleminthicknessdirection.However,becauseoftheuseoftheHele-Shawapproximation,theinformationthat2.5Dmodelscangenerateislimitedandincomplete.Thevariationinthegapwise(thickness)dimensionofthephysicalquantitieswiththeexceptionofthetemperature,whichissolvedbyfinitedifferencemethod,isneglected.Withthedevelopmentofmoldingtechniques,molded华东交通大学理工学院毕业设计(论文)53partswillhavemoreandmorecomplexgeometryandthedifferenceinthethicknesswillbemoreandmorenotable,sothechangeinthegapwise(thickness)dimensionofthephysicalquantitiescannotbeneglected.Inaddition,theflowsimulatedlooksunrealisticinasmuchasthemeltpolymerflowsonlyonsurfacesofcavity,whichappearsmoreobviouswhentheflowsimulationisdisplayedinamouldcavity.3Dsimulationmodelhasbeenaresearchdirectionandhotspotinthescopeofsimulationforplasticinjectionmolding.In3Dsimulationmodel,velocityinthegapwise(thickness)dimensionisnotneglectedandthepressurevariesinthedirectionofpartthickness,and3Dfiniteelementsareusedtodiscretizethepartgeometry.Aftercalculating,completedataareobtained(notonlysurfacedatabutalsointernaldataareobtained).Therefore,a3Dsimulationmodelshouldbeabletogeneratecomplementaryandmoredetailedinformationrelatedtotheflowcharacteristicsandstressdistributionsinthinmoldedpartsthantheoneobtainedwhenusinga2.5Dmodel(basedontheHele-Shawapproximation).Ontheotherhand,a3Dmodelwillpredictmoreaccuratelythecharacteristicsofmoldedpartshavingthickwalledsectionssuchasencounteredingasassistedinjectionmolding.Severalflowbehaviorsattheflowfront.suchas“fountainflow”.which2.5Dmodelcannotpredict,canbepredictedby3Dmode1.Meanwhile,theflowsimulationlooksmorerealisticinasmuchastheoverallananalysisresultisdirectlydisplayedin3Dpartgeometryortransparentmouldcavity.ThisPaperpresentsa3Dfiniteelementmodeltodealwiththethree—dimensionalflow,whichemploysanequa1-ordervelocity-pressureformulationmethod[3,4].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.Crossviscositymodelhasbeenusedforthesimulations:where,n,γ,rarenon-Newtonianexponent,shearrateandmaterialconstantrespectively.Becausethereisnonotablechangeinthescopeoftemperatureofthemeltpolymerduringfilling,Anheniusmodel[5]forη0isemployedasfollowing:whereB,Tb,βarematerialconstants.3NumericalSimulationMethod3.1Velocity-PressureRelationIna3Dmodel,sincethechangeofthephysicalquantitiesarenotneglectedinthegapwise(thickness)dimension,themomentumequationsaremuchmorecomplexthanthoseina2.5Dmode1.Itisimpossibletoobtainthevelocity—pressurerelationbyintegratingthemomentum华东交通大学理工学院毕业设计(论文)55equationsinthegapwisedimension,whichisdoneina2.5Dmodel.Themomentumequationsmustbefirstdiscretized,andthentherelationbetweenvelocityandpressureisderivedfromit.Inthispaper,themomentumequationsarediscretizedusingGalerkin’smethodwithbilinearvelocity-pressureformulation.Theelementequationsareassembledintheconventionalmannertoformthediscretizedglobalmomentumequationsandthevelocitymaybeexpressedasfollowingwherethenodalpressurecoefficientsaredefinedaswhererepresentglobalvelocitycoefficientmatricesinthedirectionofx,y,zcoordinaterespectively.denotethenodalpressurecoefficientsthedirectionofx,y,zcoordinaterespectively.Thenodalvaluesforareobtainedbyassemblingtheelement-by-elementcontributionsintheconventionalmanner.N,iselementinterpolationandimeansglobalnodenumberandj,isforanode,theamountofthenodesaroundit.3.2PressureEquationSubstitutionofthevelocityexpressions(2)intodiscretizedcontinuityequation,whichisdiscretizedusingGalerkinmethod,yieldselementequationforpressure:
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