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KeywordsInjectionmoldingNumericalsimulationRapidprototyping

1Introduction

Ininjectionmolding,thepolymermeltathightemperatureisinjectedintothemoldunderhighpressure[1].Thus,themoldmaterialneedstohavethermalandmechanicalpropertiescapableofwithstandingthetemperaturesandpressuresofthemoldingcycle.Thefocusofmanystudieshasbeentocreatethe

injectionmolddirectlybyarapidprototyping（RP）process.Byeliminatingmultiplesteps,thismethodoftoolingholdsthebestpromiseofreducingthetimeandcostneededtocreatelow-volumequantitiesofpartsinaproductionmaterial.ThepotentialofintegratinginjectionmoldingwithRPtechnologieshasbeendemonstratedmanytimes.ThepropertiesofRPmoldsareverydifferentfromthoseoftraditionalmetalmolds.Thekeydifferencesarethepropertiesofthermalconductivityandelasticmodulus（rigidity）.Forexample,thepolymersusedinRP-fabricatedstereolithography（SL）moldshaveathermalconductivitythatislessthanonethousandththatofanaluminumtool.InusingRPtechnologiestocreatemolds,theentiremolddesignandinjection-moldingprocessparametersneedtobemodifiedandoptimizedfromtraditionalmethodologiesduetothecompletelydifferenttoolmaterial.However,thereisstillnotafundamentalunderstandingofhowthemodificationstothemoldtoolingmethodandmaterialimpactboththemolddesignandtheinjectionmoldingprocessparameters.Onecannotobtainreasonableresultsbysimplychangingafewmaterialpropertiesincurrentmodels.Also,usingtraditionalapproacheswhenmakingactualpartsmaybegeneratingsub-optimalresults.Sothereisadireneedtostudytheinteractionbetweentherapidtooling（RT）processandmaterialandinjectionmolding,soastoestablishthemolddesigncriteriaandtechniquesforanRT-orientedinjectionmoldingprocess.

Inaddition,computersimulationisaneffectiveapproachforpredictingthequalityofmoldedparts.Commerciallyavailablesimulationpackagesofthetraditionalinjectionmoldingprocesshavenowbecomeroutinetoolsofthemolddesignerandprocessengineer[2].Unfortunately,currentsimulationprogramsforconventionalinjectionmoldingarenolongerapplicabletoRPmolds,becauseofthedramaticallydissimilartoolmaterial.Forinstance,inusingtheexistingsimulationsoftwarewithaluminumandSLmoldsandcomparingwithexperimentalresults,thoughthesimulationvaluesofpartdistortionarereasonableforthealuminummold,resultsareunacceptable,withtheerrorexceeding50%.Thedistortionduringinjectionmoldingisduetoshrinkageandwarpageoftheplasticpart,aswellasthemold.Forordinarilymolds,themainfactoristheshrinkageandwarpageoftheplasticpart,whichismodeledaccuratelyincurrentsimulations.ButforRPmolds,thedistortionofthemoldhaspotentiallymoreinfluence,whichhavebeenneglectedincurrentmodels.Forinstance,[3]usedasimplethree-stepsimulationprocesstoconsiderthemolddistortion,whichhadtoomuchdeviation.

Inthispaper,basedontheaboveanalysis,anewsimulationsystemforRPmoldsisdeveloped.Theproposedsystemfocusesonpredictingpartdistortion,whichisdominatingdefectinRP-moldedparts.ThedevelopedsimulationcanbeappliedasanevaluationtoolforRPmolddesignandprocessoptimization.Oursimulationsystemisverifiedbyanexperimentalexample.

AlthoughmanymaterialsareavailableforuseinRPtechnologies,weconcentrateonusingstereolithography（SL）,theoriginalRPtechnology,tocreatepolymermolds.TheSLprocessusesphotopolymerandlaserenergytobuildapartlayerbylayer.UsingSLtakesadvantageofboththecommercialdominanceofSLintheRPindustryandthesubsequentexpertisebasethathasbeendevelopedforcreatingaccurate,high-qualityparts.Untilrecently,SLwasprimarilyusedtocreatephysicalmodelsforvisualinspectionandform-fitstudieswithverylimitedfunctionalapplications.However,thenewergenerationstereolithographicphotopolymershaveimproveddimensional,mechanicalandthermalpropertiesmakingitpossibletousethemforactualfunctionalmolds.

2Integratedsimulationofthemoldingprocess

2.1Methodology

InordertosimulatetheuseofanSLmoldintheinjectionmoldingprocess,aniterativemethodisproposed.Differentsoftwaremoduleshavebeendevelopedandusedtoaccomplishthistask.ThemainassumptionisthattemperatureandloadboundaryconditionscausesignificantdistortionsintheSLmold.Thesimulationstepsareasfollows:

1Thepartgeometryismodeledasasolidmodel,whichistranslatedtoafilereadablebytheflowanalysispackage.

2Simulatethemold-fillingprocessofthemeltintoaphotopolymermold,whichwilloutputtheresultingtemperatureandpressureprofiles.

3Structuralanalysisisthenperformedonthephotopolymermoldmodelusingthethermalandloadboundaryconditionsobtainedfromthepreviousstep,whichcalculatesthedistortionthatthemoldundergoduringtheinjectionprocess.

4Ifthedistortionofthemoldconverges,movetothenextstep.Otherwise,thedistortedmoldcavityisthenmodeled（changesinthedimensionsofthecavityafterdistortion）,andreturnstothesecondsteptosimulatethemeltinjectionintothedistortedmold.

5Theshrinkageandwarpagesimulationoftheinjectionmoldedpartisthenapplied,whichcalculatesthefinaldistortionsofthemoldedpart.

Inabovesimulationflow,therearethreebasicsimulationmodules.

2.2Fillingsimulationofthemelt

2.2.1Mathematicalmodeling

InordertosimulatetheuseofanSLmoldintheinjectionmoldingprocess,aniterativemethodisproposed.Differentsoftwaremoduleshavebeendevelopedandusedtoaccomplishthistask.ThemainassumptionisthattemperatureandloadboundaryconditionscausesignificantdistortionsintheSLmold.Thesimulationstepsareasfollows:

1.Thepartgeometryismodeledasasolidmodel,whichistranslatedtoafilereadablebytheflowanalysispackage.

2.Simulatethemold-fillingprocessofthemeltintoaphotopolymermold,whichwilloutputtheresultingtemperatureandpressureprofiles.

3.Structuralanalysisisthenperformedonthephotopolymermoldmodelusingthethermalandloadboundaryconditionsobtainedfromthepreviousstep,whichcalculatesthedistortionthatthemoldundergoduringtheinjectionprocess.

4.Ifthedistortionofthemoldconverges,movetothenextstep.Otherwise,thedistortedmoldcavityisthenmodeled（changesinthedimensionsofthecavityafterdistortion）,andreturnstothesecondsteptosimulatethemeltinjectionintothedistortedmold.

5.Theshrinkageandwarpagesimulationoftheinjectionmoldedpartisthenapplied,whichcalculatesthefinaldistortionsofthemoldedpart.

Inabovesimulationflow,therearethreebasicsimulationmodules.

2.2Fillingsimulationofthemelt

2.2.1Mathematicalmodeling

Computersimulationtechniqueshavehadsuccessinpredictingfillingbehaviorinextremelycomplicatedgeometries.However,mostofthecurrentnumericalimplementationisbasedonahybridfinite-element/finite-differencesolutionwiththemiddleplanemodel.TheapplicationprocessofsimulationpackagesbasedonthismodelisillustratedinFig.2-1.However,unlikethesurface/solidmodelinmold-designCADsystems,theso-calledmiddle-plane（asshowninFig.2-1b）isanimaginaryarbitraryplanargeometryatthemiddleofthecavityinthegap-wisedirection,whichshouldbringaboutgreatinconvenienceinapplications.Forexample,surfacemodelsarecommonlyusedincurrentRPsystems（generallySTLfileformat）,sosecondarymodelingisunavoidablewhenusingsimulationpackagesbecausethemodelsintheRPandsimulationsystemsaredifferent.Consideringthesedefects,thesurfacemodelofthecavityisintroducedasdatumplanesinthesimulation,insteadofthemiddle-plane.

Accordingtothepreviousinvestigations[4–6],fillinggoverningequationsfortheflowandtemperaturefieldcanbewrittenas:

wherex,yaretheplanarcoordinatesinthemiddle-plane,andzisthegap-wisecoordinate;

u,v,warethevelocitycomponentsinthex,y,zdirections;

u,varetheaveragewhole-gapthicknesses;

andη,ρ,CP（T）,K（T）representviscosity,density,specificheatandthermalconductiv