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Integratedsimulationoftheinjectionmoldingprocesswithstereolithographymolds
AbstractFunctionalpartsareneededfordesignverificationtesting,fieldtrials,customerevaluation,andproductionplanning.Byeliminatingmultiplesteps,thecreationoftheinjectionmolddirectlybyarapidprototyping（RP）processofinjectionmoldingwithRPdemonstratedmanytimes.Whatismissingisthefundamentalunderstandingofandtheinjectionmoldingprocess.Inaddition,numericalsimulationtechniquesmolding.Butallcurrentsimulationpackagesforconventionalinjectionmoldingarenolongerapplicabletothisnewtypeofinjectionmolds,mainlybecausethepropertyofthemoldmaterialchangesgreatly.Inthispaper,anintegratedapproachtoaccomplishanumericalsimulationofinjectionmoldingintorapid-prototypedmoldsisestablishedandacorrespondingsimulationsystemisdeveloped.Comparisonswithexperimentalresultsareemployedforverification,whichshowthatthepresentschemeiswellsuitedtomoldingNumericalsimulationRapidprototyping
1Introduction
Ininjectionmolding,thepolymermeltattocreatethe
Inthispaper,basedontheaboveanalysis,anewsimulationsystemforRPmoldsisdeveloped.Theproposedsystemfocusesonpredictingpartdistortion,whichisdominatingdefectinRP-moldedparts.ThedevelopedsimulationcanbeappliedasanevaluationtoolforRPmolddesignandprocessoptimization.Oursimulationsystemisverifiedbyanexperimentalexample.
AlthoughmanymaterialsareavailableforuseinRPtechnologies,weconcentrateonusingstereolithography（SL）,theoriginalRPtechnology,tocreatepolymermolds.TheSLprocessusesphotopolymerandlaserenergytobuildapartlayerbylayer.UsingSLtakesadvantageofboththecommercialdominanceofSLintheRPindustryandthesubsequentexpertisebasethatdevelopedforcreatingaccurate,andform-fitstudieswithverylimitedfunctionalapplications.However,thenewergenerationstereolithographicphotopolymersofthemoldingprocess
2.1Methodology
InordertosimulatetheuseofanSLmoldintheinjectionmoldingprocess,aniterativemethodisproposed.Differentsoftwaremodulesdevelopedandusedtoaccomplishthistask.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.Differentsoftwaremodulesdevelopedandusedtoaccomplishthistask.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
Computersimulationtechniquespredictingfillingbehaviorinextremelycomplicatedgeometries.However,mostofthecurrentnumericalimplementationisbasedonawiththemiddleplanemodel.TheapplicationprocessofsimulationpackagesbasedonthismodelisillustratedinFig.2-1.However,unlikethesurfacesolidmodelinmold-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,specificwithmiddle-planemodel.aThe3-DsurfacemodelbThemiddle-planemodelcThemeshedmiddle-planemodeldThedisplayofthesimulationresult
Inaddition,boundaryconditionsinthegap-wisedirectioncanbedefinedas:
whereTWistheconstantwalltemperature（showninFig.2a）.
CombiningEqs.1–4withEqs.5–6,itfollowsthatthedistributionsoftheu,v,T,Patzcoordinatesshouldbesymmetrical,withthemirroraxisbeingz=0,andconsequentlytheu,vaveragedinwholegapthickness.Basedonthischaracteristic,wecandividethewholecavityintotwoequalpartsinthegap-wisedirection,asdescribedbyPartIandPartIIinFig.2b.Atthesametime,triangularfiniteelementsaregeneratedinthesurface（s）ofthecavity（atz=0inFig.2b）,insteadofthemiddle-plane（atz=0inFig.2a）.Accordingly,finite-differenceincrementsinthegapwisedirectionareemployedonlyintheinsideofthesurface（s）（walltomiddlecenter-line）,which,inFig.2b,meansfromz=0toz=b.Thisissingle-sidedinsteadoftwo-sidedwithrespecttothemiddle-plane（i.e.fromthemiddle-linetotwowalls）.Inaddition,thecoordinatesystemischangedfromFig.2atoFig.2btoalterthefinite-elementfinite-differencescheme,asshowninFig.2b.Withtheaboveadjustment,governingequationsarestillEqs.1–4.However,theoriginalboundaryconditionsinthegapwisedirectionarerewrittenas:
Meanwhile,additionalboundaryconditionsmustbeemployedatz=binordertokeeptheflowsatthejunctureofthetwopartsatthesamesectioncoordinate[7]:
wheresubscriptsI,IIrepresenttheparametersofPartIandPartII,respectively,andCm-IandCm-IIindicatethemovingfreemelt-frontsofthesurfacesofthedividedtwopartsinthefillingstage.
Itshouldbenotedthat,unlikeconditionsEqs.7and8,ensuringconditionsEqs.9and10areupheldinnumericalimplementationsbecomesmoredifficultduetothefollowingreasons:
1.Thesurfacesatthesamesectionmeshedrespectively,whichleadstoadistinctivepatternoffiniteelementsatthesamesection.Thus,aninterpolationoperationshouldbeemployedforu,v,T,Pduringthecomparisonbetweenthetwopartsatthejuncture.
2.BecausethetwopartsinFig.2b）atthesamesection,itispossibletofortheformer,whereasassigningoperationforthelatter.
3.Itfollowsthatasmalldifferencebetweenthemelt-frontsispermissible.Thatallowancecanbeimplementedbytimeallowancecontrolorpreferablelocationallowancecontrolofthemelt-frontnodes.
4.Theboundariesoftheflowfieldexpandbyeachmelt-frontadvancement,soitisnecessarytochecktheconditionEq.10aftereachchangeinthemelt-front.
5.Inviewofabove-mentionedanalysis,thephysicalparametersatthenodesofthesamesectionshouldbecomparedandadjusted,sotheinformationdescribingfiniteelementsofthesamesectionshouldbepreparedbeforesimulation,thatis,thematchingoperationamongtheelementsshouldbepreformed.
Fig.2a,b.Illustrativeofboundaryconditionsinthegap-wisedirectionaofthemiddle-planemodelbofthesurfacemodel
2.2.2Numericalimplementation
Pressurefield.Inmodelingviscosityη,whichisafunctionofshearrate,temperatureandpressureofmelt,theshear-thinningbehaviorcanbewellrepresentedbyacross-typemodelsuchas:
wherencorrespondstothepower-lawindex,andτ∗characterizestheshearstresslevelofthetransitionregionbetweentheNewtonianandpower-lawasymptoticlimits.Intermsofan
Arrhenius-typetemperaturesensitivityandexponentialpressuredependence,η0（T,P）canberepresentedwithreasonableaccuracyasf
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