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毕业论文中英文资料外文翻译文献INTEGRATEDSIMULATIONOFTHEINJECTIONMOLDINGPROCESSWITHSTEREOLITHOGRAPHYMOLDSABSTRACTFUNCTIONALPARTSARENEEDEDFORDESIGNVERICATIONTESTING,ELDTRIALS,CUSTOMEREVALUATION,ANDPRODUCTIONPLANNINGBYELIMINATINGMULTIPLESTEPS,THECREATIONOFTHEINJECTIONMOLDDIRECTLYBYARAPIDPROTOTYPINGRPPROCESSHOLDSTHEBESTPROMISEOFREDUCINGTHETIMEANDCOSTNEEDEDTOMOLDLOWVOLUMEQUANTITIESOFPARTSTHEPOTENTIALOFTHISINTEGRATIONOFINJECTIONMOLDINGWITHRPHASBEENDEMONSTRATEDMANYTIMESWHATISMISSINGISTHEFUNDAMENTALUNDERSTANDINGOFHOWTHEMODICATIONSTOTHEMOLDMATERIALANDRPMANUFACTURINGPROCESSIMPACTBOTHTHEMOLDDESIGNANDTHEINJECTIONMOLDINGPROCESSINADDITION,NUMERICALSIMULATIONTECHNIQUESHAVENOWBECOMEHELPFULTOOLSOFMOLDDESIGNERSANDPROCESSENGINEERSFORTRADITIONALINJECTIONMOLDINGBUTALLCURRENTSIMULATIONPACKAGESFORCONVENTIONALINJECTIONMOLDINGARENOLONGERAPPLICABLETOTHISNEWTYPEOFINJECTIONMOLDS,MAINLYBECAUSETHEPROPERTYOFTHEMOLDMATERIALCHANGESGREATLYINTHISPAPER,ANINTEGRATEDAPPROACHTOACCOMPLISHANUMERICALSIMULATIONOFINJECTIONMOLDINGINTORAPIDPROTOTYPEDMOLDSISESTABLISHEDANDACORRESPONDINGSIMULATIONSYSTEMISDEVELOPEDCOMPARISONSWITHEXPERIMENTALRESULTSAREEMPLOYEDFORVERICATION,WHICHSHOWTHATTHEPRESENTSCHEMEISWELLSUITEDTOHANDLERPFABRICATEDSTEREOLITHOGRAPHYSLMOLDSKEYWORDSINJECTIONMOLDINGNUMERICALSIMULATIONRAPIDPROTOTYPING1INTRODUCTIONININJECTIONMOLDING,THEPOLYMERMELTATHIGHTEMPERATUREISINJECTEDINTOTHEMOLDUNDERHIGHPRESSURE1THUS,THEMOLDMATERIALNEEDSTOHAVETHERMALANDMECHANICALPROPERTIESCAPABLEOFWITHSTANDINGTHETEMPERATURESANDPRESSURESOFTHEMOLDINGCYCLETHEFOCUSOFMANYSTUDIESHASBEENTOCREATETHEINJECTIONMOLDDIRECTLYBYARAPIDPROTOTYPINGRPPROCESSBYELIMINATINGMULTIPLESTEPS,THISMETHODOFTOOLINGHOLDSTHEBESTPROMISEOFREDUCINGTHETIMEANDCOSTNEEDEDTOCREATELOWVOLUMEQUANTITIESOFPARTSINAPRODUCTIONMATERIALTHEPOTENTIALOFINTEGRATINGINJECTIONMOLDINGWITHRPTECHNOLOGIESHASBEENDEMONSTRATEDMANYTIMESTHEPROPERTIESOFRPMOLDSAREVERYDIFFERENTFROMTHOSEOFTRADITIONALMETALMOLDSTHEKEYDIFFERENCESARETHEPROPERTIESOFTHERMALCONDUCTIVITYANDELASTICMODULUSRIGIDITYFOREXAMPLE,THEPOLYMERSUSEDINRPFABRICATEDSTEREOLITHOGRAPHYSLMOLDSHAVEATHERMALCONDUCTIVITYTHATISLESSTHANONETHOUSANDTHTHATOFANALUMINUMTOOLINUSINGRPTECHNOLOGIESTOCREATEMOLDS,THEENTIREMOLDDESIGNANDINJECTIONMOLDINGPROCESSPARAMETERSNEEDTOBEMODIEDANDOPTIMIZEDFROMTRADITIONALMETHODOLOGIESDUETOTHECOMPLETELYDIFFERENTTOOLMATERIALHOWEVER,THEREISSTILLNOTAFUNDAMENTALUNDERSTANDINGOFHOWTHEMODICATIONSTOTHEMOLDTOOLINGMETHODANDMATERIALIMPACTBOTHTHEMOLDDESIGNANDTHEINJECTIONMOLDINGPROCESSPARAMETERSONECANNOTOBTAINREASONABLERESULTSBYSIMPLYCHANGINGAFEWMATERIALPROPERTIESINCURRENTMODELSALSO,USINGTRADITIONALAPPROACHESWHENMAKINGACTUALPARTSMAYBEGENERATINGSUBOPTIMALRESULTSSOTHEREISADIRENEEDTOSTUDYTHEINTERACTIONBETWEENTHERAPIDTOOLINGRTPROCESSANDMATERIALANDINJECTIONMOLDING,SOASTOESTABLISHTHEMOLDDESIGNCRITERIAANDTECHNIQUESFORANRTORIENTEDINJECTIONMOLDINGPROCESSINADDITION,COMPUTERSIMULATIONISANEFFECTIVEAPPROACHFORPREDICTINGTHEQUALITYOFMOLDEDPARTSCOMMERCIALLYAVAILABLESIMULATIONPACKAGESOFTHETRADITIONALINJECTIONMOLDINGPROCESSHAVENOWBECOMEROUTINETOOLSOFTHEMOLDDESIGNERANDPROCESSENGINEER2UNFORTUNATELY,CURRENTSIMULATIONPROGRAMSFORCONVENTIONALINJECTIONMOLDINGARENOLONGERAPPLICABLETORPMOLDS,BECAUSEOFTHEDRAMATICALLYDISSIMILARTOOLMATERIALFORINSTANCE,INUSINGTHEEXISTINGSIMULATIONSOFTWAREWITHALUMINUMANDSLMOLDSANDCOMPARINGWITHEXPERIMENTALRESULTS,THOUGHTHESIMULATIONVALUESOFPARTDISTORTIONAREREASONABLEFORTHEALUMINUMMOLD,RESULTSAREUNACCEPTABLE,WITHTHEERROREXCEEDING50THEDISTORTIONDURINGINJECTIONMOLDINGISDUETOSHRINKAGEANDWARPAGEOFTHEPLASTICPART,ASWELLASTHEMOLDFORORDINARILYMOLDS,THEMAINFACTORISTHESHRINKAGEANDWARPAGEOFTHEPLASTICPART,WHICHISMODELEDACCURATELYINCURRENTSIMULATIONSBUTFORRPMOLDS,THEDISTORTIONOFTHEMOLDHASPOTENTIALLYMOREINUENCE,WHICHHAVEBEENNEGLECTEDINCURRENTMODELSFORINSTANCE,3USEDASIMPLETHREESTEPSIMULATIONPROCESSTOCONSIDERTHEMOLDDISTORTION,WHICHHADTOOMUCHDEVIATIONINTHISPAPER,BASEDONTHEABOVEANALYSIS,ANEWSIMULATIONSYSTEMFORRPMOLDSISDEVELOPEDTHEPROPOSEDSYSTEMFOCUSESONPREDICTINGPARTDISTORTION,WHICHISDOMINATINGDEFECTINRPMOLDEDPARTSTHEDEVELOPEDSIMULATIONCANBEAPPLIEDASANEVALUATIONTOOLFORRPMOLDDESIGNANDPROCESSOPTIMIZATIONOURSIMULATIONSYSTEMISVERIEDBYANEXPERIMENTALEXAMPLEALTHOUGHMANYMATERIALSAREAVAILABLEFORUSEINRPTECHNOLOGIES,WECONCENTRATEONUSINGSTEREOLITHOGRAPHYSL,THEORIGINALRPTECHNOLOGY,TOCREATEPOLYMERMOLDSTHESLPROCESSUSESPHOTOPOLYMERANDLASERENERGYTOBUILDAPARTLAYERBYLAYERUSINGSLTAKESADVANTAGEOFBOTHTHECOMMERCIALDOMINANCEOFSLINTHERPINDUSTRYANDTHESUBSEQUENTEXPERTISEBASETHATHASBEENDEVELOPEDFORCREATINGACCURATE,HIGHQUALITYPARTSUNTILRECENTLY,SLWASPRIMARILYUSEDTOCREATEPHYSICALMODELSFORVISUALINSPECTIONANDFORMTSTUDIESWITHVERYLIMITEDFUNCTIONALAPPLICATIONSHOWEVER,THENEWERGENERATIONSTEREOLITHOGRAPHICPHOTOPOLYMERSHAVEIMPROVEDDIMENSIONAL,MECHANICALANDTHERMALPROPERTIESMAKINGITPOSSIBLETOUSETHEMFORACTUALFUNCTIONALMOLDS2INTEGRATEDSIMULATIONOFTHEMOLDINGPROCESS21METHODOLOGYINORDERTOSIMULATETHEUSEOFANSLMOLDINTHEINJECTIONMOLDINGPROCESS,ANITERATIVEMETHODISPROPOSEDDIFFERENTSOFTWAREMODULESHAVEBEENDEVELOPEDANDUSEDTOACCOMPLISHTHISTASKTHEMAINASSUMPTIONISTHATTEMPERATUREANDLOADBOUNDARYCONDITIONSCAUSESIGNICANTDISTORTIONSINTHESLMOLDTHESIMULATIONSTEPSAREASFOLLOWS1THEPARTGEOMETRYISMODELEDASASOLIDMODEL,WHICHISTRANSLATEDTOALEREADABLEBYTHEOWANALYSISPACKAGE2SIMULATETHEMOLDLLINGPROCESSOFTHEMELTINTOAPHOTOPOLYMERMOLD,WHICHWILLOUTPUTTHERESULTINGTEMPERATUREANDPRESSUREPROLES3STRUCTURALANALYSISISTHENPERFORMEDONTHEPHOTOPOLYMERMOLDMODELUSINGTHETHERMALANDLOADBOUNDARYCONDITIONSOBTAINEDFROMTHEPREVIOUSSTEP,WHICHCALCULATESTHEDISTORTIONTHATTHEMOLDUNDERGODURINGTHEINJECTIONPROCESS4IFTHEDISTORTIONOFTHEMOLDCONVERGES,MOVETOTHENEXTSTEPOTHERWISE,THEDISTORTEDMOLDCAVITYISTHENMODELEDCHANGESINTHEDIMENSIONSOFTHECAVITYAFTERDISTORTION,ANDRETURNSTOTHESECONDSTEPTOSIMULATETHEMELTINJECTIONINTOTHEDISTORTEDMOLD5THESHRINKAGEANDWARPAGESIMULATIONOFTHEINJECTIONMOLDEDPARTISTHENAPPLIED,WHICHCALCULATESTHENALDISTORTIONSOFTHEMOLDEDPARTINABOVESIMULATIONOW,THEREARETHREEBASICSIMULATIONMODULES22FILLINGSIMULATIONOFTHEMELT221MATHEMATICALMODELINGINORDERTOSIMULATETHEUSEOFANSLMOLDINTHEINJECTIONMOLDINGPROCESS,ANITERATIVEMETHODISPROPOSEDDIFFERENTSOFTWAREMODULESHAVEBEENDEVELOPEDANDUSEDTOACCOMPLISHTHISTASKTHEMAINASSUMPTIONISTHATTEMPERATUREANDLOADBOUNDARYCONDITIONSCAUSESIGNIFICANTDISTORTIONSINTHESLMOLDTHESIMULATIONSTEPSAREASFOLLOWS1THEPARTGEOMETRYISMODELEDASASOLIDMODEL,WHICHISTRANSLATEDTOAFILEREADABLEBYTHEFLOWANALYSISPACKAGE2SIMULATETHEMOLDFILLINGPROCESSOFTHEMELTINTOAPHOTOPOLYMERMOLD,WHICHWILLOUTPUTTHERESULTINGTEMPERATUREANDPRESSUREPROFILES3STRUCTURALANALYSISISTHENPERFORMEDONTHEPHOTOPOLYMERMOLDMODELUSINGTHETHERMALANDLOADBOUNDARYCONDITIONSOBTAINEDFROMTHEPREVIOUSSTEP,WHICHCALCULATESTHEDISTORTIONTHATTHEMOLDUNDERGODURINGTHEINJECTIONPROCESS4IFTHEDISTORTIONOFTHEMOLDCONVERGES,MOVETOTHENEXTSTEPOTHERWISE,THEDISTORTEDMOLDCAVITYISTHENMODELEDCHANGESINTHEDIMENSIONSOFTHECAVITYAFTERDISTORTION,ANDRETURNSTOTHESECONDSTEPTOSIMULATETHEMELTINJECTIONINTOTHEDISTORTEDMOLD5THESHRINKAGEANDWARPAGESIMULATIONOFTHEINJECTIONMOLDEDPARTISTHENAPPLIED,WHICHCALCULATESTHEFINALDISTORTIONSOFTHEMOLDEDPARTINABOVESIMULATIONFLOW,THEREARETHREEBASICSIMULATIONMODULES22FILLINGSIMULATIONOFTHEMELT221MATHEMATICALMODELINGCOMPUTERSIMULATIONTECHNIQUESHAVEHADSUCCESSINPREDICTINGFILLINGBEHAVIORINEXTREMELYCOMPLICATEDGEOMETRIESHOWEVER,MOSTOFTHECURRENTNUMERICALIMPLEMENTATIONISBASEDONAHYBRIDFINITEELEMENT/FINITEDIFFERENCESOLUTIONWITHTHEMIDDLEPLANEMODELTHEAPPLICATIONPROCESSOFSIMULATIONPACKAGESBASEDONTHISMODELISILLUSTRATEDINFIG21HOWEVER,UNLIKETHESURFACE/SOLIDMODELINMOLDDESIGNCADSYSTEMS,THESOCALLEDMIDDLEPLANEASSHOWNINFIG21BISANIMAGINARYARBITRARYPLANARGEOMETRYATTHEMIDDLEOFTHECAVITYINTHEGAPWISEDIRECTION,WHICHSHOULDBRINGABOUTGREATINCONVENIENCEINAPPLICATIONSFOREXAMPLE,SURFACEMODELSARECOMMONLYUSEDINCURRENTRPSYSTEMSGENERALLYSTLFILEFORMAT,SOSECONDARYMODELINGISUNAVOIDABLEWHENUSINGSIMULATIONPACKAGESBECAUSETHEMODELSINTHERPANDSIMULATIONSYSTEMSAREDIFFERENTCONSIDERINGTHESEDEFECTS,THESURFACEMODELOFTHECAVITYISINTRODUCEDASDATUMPLANESINTHESIMULATION,INSTEADOFTHEMIDDLEPLANEACCORDINGTOTHEPREVIOUSINVESTIGATIONS46,FILLINGGOVERNINGEQUATIONSFORTHEFLOWANDTEMPERATUREFIELDCANBEWRITTENASWHEREX,YARETHEPLANARCOORDINATESINTHEMIDDLEPLANE,ANDZISTHEGAPWISECOORDINATEU,V,WARETHEVELOCITYCOMPONENTSINTHEX,Y,ZDIRECTIONSU,VARETHEAVERAGEWHOLEGAPTHICKNESSESAND,CPT,KTREPRESENTVISCOSITY,DENSITY,SPECIFICHEATANDTHERMALCONDUCTIVITYOFPOLYMERMELT,RESPECTIVELYFIG21ADSCHEMATICPROCEDUREOFTHESIMULATIONWITHMIDDLEPLANEMODELATHE3DSURFACEMODELBTHEMIDDLEPLANEMODELCTHEMESHEDMIDDLEPLANEMODELDTHEDISPLAYOFTHESIMULATIONRESULTINADDITION,BOUNDARYCONDITIONSINTHEGAPWISEDIRECTIONCANBEDEFINEDASWHERETWISTHECONSTANTWALLTEMPERATURESHOWNINFIG2ACOMBININGEQS14WITHEQS56,ITFOLLOWSTHATTHEDISTRIBUTIONSOFTHEU,V,T,PATZCOORDINATESSHOULDBESYMMETRICAL,WITHTHEMIRRORAXISBEINGZ0,ANDCONSEQUENTLYTHEU,VAVERAGEDINHALFGAPTHICKNESSISEQUALTOTHATAVERAGEDINWHOLEGAPTHICKNESSBASEDONTHISCHARACTERISTIC,WECANDIVIDETHEWHOLECAVITYINTOTWOEQUALPARTSINTHEGAPWISEDIRECTION,ASDESCRIBEDBYPARTIANDPARTIIINFIG2BATTHESAMETIME,TRIANGULARFINITEELEMENTSAREGENERATEDINTHESURFACESOFTHECAVITYATZ0INFIG2B,INSTEADOFTHEMIDDLEPLANEATZ0INFIG2AACCORDINGLY,FINITEDIFFERENCEINCREMENTSINTHEGAPWISEDIRECTIONAREEMPLOYEDONLYINTHEINSIDEOFTHESURFACESWALLTOMIDDLE/CENTERLINE,WHICH,INFIG2B,MEANSFROMZ0TOZBTHISISSINGLESIDEDINSTEADOFTWOSIDEDWITHRESPECTTOTHEMIDDLEPLANEIEFROMTHEMIDDLELINETOTWOWALLSINADDITION,THECOORDINATESYSTEMISCHANGEDFROMFIG2ATOFIG2BTOALTERTHEFINITEELEMENT/FINITEDIFFERENCESCHEME,ASSHOWNINFIG2BWITHTHEABOVEADJUSTMENT,GOVERNINGEQUATIONSARESTILLEQS14HOWEVER,THEORIGINALBOUNDARYCONDITIONSINTHEGAPWISEDIRECTIONAREREWRITTENASMEANWHILE,ADDITIONALBOUNDARYCONDITIONSMUSTBEEMPLOYEDATZBINORDERTOKEEPTHEFLOWSATTHEJUNCTUREOFTHETWOPARTSATTHESAMESECTIONCOORDINATE7WHERESUBSCRIPTSI,IIREPRESENTTHEPARAMETERSOFPARTIANDPARTII,RESPECTIVELY,ANDCMIANDCMIIINDICATETHEMOVINGFREEMELTFRONTSOFTHESURFACESOFTHEDIVIDEDTWOPARTSINTHEFILLINGSTAGEITSHOULDBENOTEDTHAT,UNLIKECONDITIONSEQS7AND8,ENSURINGCONDITIONSEQS9AND10AREUPHELDINNUMERICALIMPLEMENTATIONSBECOMESMOREDIFFICULTDUETOTHEFOLLOWINGREASONS1THESURFACESATTHESAMESECTIONHAVEBEENMESHEDRESPECTIVELY,WHICHLEADSTOADISTINCTIVEPATTERNOFFINITEELEMENTSATTHESAMESECTIONTHUS,ANINTERPOLATIONOPERATIONSHOULDBEEMPLOYEDFORU,V,T,PDURINGTHECOMPARISONBETWEENTHETWOPARTSATTHEJUNCTURE2BECAUSETHETWOPARTSHAVERESPECTIVEFLOWFIELDSWITHRESPECTTOTHENODESATPOINTAANDPOINTCASSHOWNINFIG2BATTHESAMESECTION,ITISPOSSIBLETOHAVEEITHERBOTHFILLEDORONEFILLEDANDONEEMPTYTHESETWOCASESSHOULDBEHANDLEDSEPARATELY,AVERAGINGTHEOPERATIONFORTHEFORMER,WHEREASASSIGNINGOPERATIONFORTHELATTER3ITFOLLOWSTHATASMALLDIFFERENCEBETWEENTHEMELTFRONTSISPERMISSIBLETHATALLOWANCECANBEIMPLEMENTEDBYTIMEALLOWANCECONTROLORPREFERABLELOCATIONALLOWANCECONTROLOFTHEMELTFRONTNODES4THEBOUNDARIESOFTHEFLOWFIELDEXPANDBYEACHMELTFRONTADVANCEMENT,SOITISNECESSARYTOCHECKTHECONDITIONEQ10AFTEREACHCHANGEINTHEMELTFRONT5INVIEWOFABOVEMENTIONEDANALYSIS,THEPHYSICALPARAMETERSATTHENODESOFTHESAMESECTIONSHOULDBECOMPAREDANDADJUSTED,SOTHEINFORMATIONDESCRIBINGFINITEELEMENTSOFTHESAMESECTIONSHOULDBEPREPAREDBEFORESIMULATION,THATIS,THEMATCHINGOPERATIONAMONGTHEELEMENTSSHOULDBEPREFORMEDFIG2A,BILLUSTRATIVEOFBOUNDARYCONDITIONSINTHEGAPWISEDIRECTIONAOFTHEMIDDLEPLANEMODELBOFTHESURFACEMODEL222NUMERICALIMPLEMENTATIONPRESSUREFIELDINMODELINGVISCOSITY,WHICHISAFUNCTIONOFSHEARRATE,TEMPERATUREANDPRESSUREOFMELT,THESHEARTHINNINGBEHAVIORCANBEWELLREPRESENTEDBYACROSSTYPEMODELSUCHASWHERENCORRESPONDSTOTHEPOWERLAWINDEX,ANDCHARACTERIZESTHESHEARSTRESSLEVELOFTHETRANSITIONREGIONBETWEENTHENEWTONIANANDPOWERLAWASYMPTOTICLIMITSINTERMSOFANARRHENIUSTYPETEMPERATURESENSITIVITYANDEXPONENTIALPRESSUREDEPENDENCE,0T,PCANBEREPRESENTEDWITHREASONABLEACCURACYASFOLLOWSEQUATIONS11AND12CONSTITUTEAFIVECONSTANTN,B,TB,REPRESENTATIONFORVISCOSITYTHESHEARRATEFORVISCOSITYCALCULATIONISOBTAINEDBYBASEDONTHEABOVE,WECANINFERTHEFOLLOWINGFILLINGPRESSUREEQUATIONFROMTHEGOVERNINGEQS14WHERESISCALCULATEDBYSB0/BZ2DZAPPLYINGTHEGALERKINMETHOD,THEPRESSUREFINITEELEMENTEQUATIONISDEDUCEDASWHEREL_TRAVERSESALLELEMENTS,INCLUDINGNODEN,ANDWHEREIANDJREPRESENTTHELOCALNODENUMBERINELEMENTL_CORRESPONDINGTOTHENODENUMBERNANDN_INTHEWHOLE,RESPECTIVELYTHEDL_IJISCALCULATEDASFOLLOWSWHEREAL_REPRESENTSTRIANGULARFINITEELEMENTS,ANDLL_IISTHEPRESSURETRIALFUNCTIONINFINITEELEMENTSTEMPERATUREFIELDTODETERMINETHETEMPERATUREPROFILEACROSSTHEGAP,EACHTRIANGULARFINITEELEMENTATTHESURFACEISFURTHERDIVIDEDINTONZLAYERSFORTHEFINITEDIFFERENCEGRIDTHELEFTITEMOFTHEENERGYEQUATIONEQ4CANBEEXPRESSEDASWHERETN,J,TREPRESENTSTHETEMPERATUREOFTHEJLAYEROFNODENATTIMETTHEHEATCONDUCTIONITEMISCALCULATEDBYWHERELTRAVERSESALLELEMENTS,INCLUDINGNODEN,ANDIANDJREPRESENTTHELOCALNODENUMBERINELEMENTLCORRESPONDINGTOTHENODENUMBERNANDN_INTHEWHOLE,RESPECTIVELYTHEHEATCONVECTIONITEMISCALCULATEDBYFORVISCOUSHEAT,ITFOLLOWSTHATSUBSTITUTINGEQS1720INTOTHEENERGYEQUATIONEQ4,THETEMPERATUREEQUATIONBECOMES23STRUCTURALANALYSISOFTHEMOLDTHEPURPOSEOFSTRUCTURALANALYSISISTOPREDICTTHEDEFORMATIONOCCURRINGINTHEPHOTOPOLYMERMOLDDUETOTHETHERMALANDMECHANICALLOADSOFTHEFILLINGPROCESSTHISMODELISBASEDONATHREEDIMENSIONALTHERMOELASTICBOUNDARYELEMENTMETHODBEMTHEBEMISIDEALLYSUITEDFORTHISAPPLICATIONBECAUSEONLYTHEDEFORMATIONOFTHEMOLDSURFACESISOFINTERESTMOREOVER,THEBEMHASANADVANTAGEOVEROTHERTECHNIQUESINTHATCOMPUTINGEFFORTISNOTWASTEDONCALCULATINGDEFORMATIONWITHINTHEMOLDTHESTRESSESRESULTINGFROMTHEPROCESSLOADSAREWELLWITHINTHEELASTICRANGEOFTHEMOLDMATERIALTHEREFORE,THEMOLDDEFORMATIONMODELISBASEDONATHERMOELASTICFORMULATIONTHETHERMALANDMECHANICALPROPERTIESOFTHEMOLDAREASSUMEDTOBEISOTROPICANDTEMPERATUREINDEPENDENTALTHOUGHTHEPROCESSISCYCLIC,TIMEAVERAGEDVALUESOFTEMPERATUREANDHEATFLUXAREUSEDFORCALCULATINGTHEMOLDDEFORMATIONTYPICALLY,TRANSIENTTEMPERATUREVARIATIONSWITHINAMOLDHAVEBEENRESTRICTEDTOREGIONSLOCALTOTHECAVITYSURFACEANDTHENOZZLETIP8THETRANSIENTSDECAYSHARPLYWITHDISTANCEFROMTHECAVITYSURFACEANDGENERALLYLITTLEVARIATIONISOBSERVEDBEYONDDISTANCESASSMALLAS25MMTHISSUGGESTSTHATTHECONTRIBUTIONFROMTHETRANSIENTSTOTHEDEFORMATIONATTHEMOLDBLOCKINTERFACEISSMALL,ANDTHEREFOREITISREASONABLETONEGLECTTHETRANSIENTEFFECTSTHESTEADYSTATETEMPERATUREFIELDSATISFIESLAPLACESEQUATION2T0ANDTHETIMEAVERAGEDBOUNDARYCONDITIONSTHEBOUNDARYCONDITIONSONTHEMOLDSURFACESAREDESCRIBEDINDETAILBYTANGETAL9ASFORTHEMECHANICALBOUNDARYCONDITIONS,THECAVITYSURFACEISSUBJECTEDTOTHEMELTPRESSURE,THESURFACESOFTHEMOLDCONNECTEDTOTHEWORKTABLEAREFIXEDINSPACE,ANDOTHEREXTERNALSURFACESAREASSUMEDTOBESTRESSFREETHEDERIVATIONOFTHETHERMOELASTICBOUNDARYINTEGRALFORMULATIONISWELLKNOWN10ITISGIVENBYWHEREUK,PKANDTARETHEDISPLACEMENT,TRACTIONANDTEMPERATURE,REPRESENTTHETHERMALEXPANSIONCOEFFICIENTANDPOISSONSRATIOOFTHEMATERIAL,ANDR|YX|CLKXISTHESURFACECOEFFICIENTWHICHDEPENDSONTHELOCALGEOMETRYATX,THEORIENTATIONOFTHECOORDINATEFRAMEANDPOISSONSRATIOFORTHEDOMAIN11THEFUNDAMENTALDISPLACEMENTULKATAPOINTYINTHEXKDIRECTION,INATHREEDIMENSIONALINFINITEISOTROPICELASTICDOMAIN,RESULTSFROMAUNITLOADCONCENTRATEDATAPOINTXACTINGINTHEXLDIRECTIONANDISOFTHEFORMWHERELKISTHEKRONECKERDELTAFUNCTIONANDISTHESHEARMODULUSOFTHEMOLDMATERIALTHEFUNDAMENTALTRACTIONPLK,MEASUREDATTHEPOINTYONASURFACEWITHUNITNORMALN,ISDISCRETIZINGTHESURFACEOFTHEMOLDINTOATOTALOFNELEMENTSTRANSFORMSEQ22TOWHERENREFERSTOTHENTHSURFACEELEMENTONT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