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英语写作

Progressonnumericalsimulationofmoldfillingandsolidificationprocessesofshapedcastings

XIONGShouMei,LIUBaiCheng,XUQingYan,KANGJinWu

DepartmentofMechanicalEngineering,TsinghuaUniversity,Beijing100084,China

Abstract:

Thelatestprogressonnumericalsimulationofmoldfillingandsolidificationprocessesofshaped-castingwasreviewed.Thecomposedsplittingmethodwasimplementedinsolidificationsimulationandanewmethodwasproposedtooptimizethecomputationalarea.Thecomputationalefficiencywasstudiedbypracticalapplications.AnewcriterionwasproposedtopredicttheshrinkagedefectofS.G.ironcastingsandacombinedFDM/FEMmethodwasproposedtopredicttheshrinkagedefectofS.G.ironcastingsandacombinedFDM/FEMmethodwasusedtosimulatethethermalstressesofcastings.

Keywords:

castings；moldfilling；solidificationprocesses；numericalsimulation

1Introduction

Thecomputersimulationofmoldfillingandsolidificationprocessisthedisciplinedevelopmentfrontier,istheonlywaytotransformetraditionalcastingindustry.Afterdecadesofeffort,thecomputersimulationofmoldfillingandsolidificationprocesshasenteredthestageofpracticalengineering,castingproductionisbeingusedbyexperiencetoscientifictheoreticalguidance.Thecomputersimulationofmoldfillingandsolidificationprocesscanhelpstaffdetecteffectivellyforallkindsofpossibledefectsandsize,location,andthetimeofoccurrenceinthecastingprocessdesignstage,thuswecanoptimizethedesignofcastingandensurethequality,shortentheproductioncycle,reduceproductioncosts[1、2].Thispaperfocusesontheanalysisandresearchofmoldfillingandsolidificationprocessofcastingsandshrinkageprediction,progressofthestress.

2Thefluidflowandheattransferinfillingprocess

Moldfillingprocesshaveagreaterinfluenceonthequalityofcastings.Improperfillingprocesscanleadtocastingdefectssuchasgasvolumeandmisrunandcoldinsulation.Inmanycases,thefillingprocesscanalsoinfluencethesolidificationprocessofthesubsequent.Inrecentyears,peoplehavemadeunremittingeffortsinthenumericalsimulationoffillingprocess.avarietyofcomputationalfluiddynamicstechnologyisusedinthesimulationprocess,suchasMAC,SMAC,andSOLA-VOFandothermethods[3、4].ThisstudyusedtheSOLA-VOFmethod,andhasbeenimprovedonthefreesurfacetreatment,turbulencemodelandcomputationaltechniquesetc.

1.1Thegoverningequation

Inthemoldfillingprocess,inordertogetaccuratespeeddistribution,wemustsolvethemasterequationincludesthecontinuityequation,momentumandenergyequations.FreesurfacetreatmentusinganimprovedVOFmethod.Fortheturbulencemodel,theK-εtwo-equationturbulencemodelismoreusedcurrently.Flowandheattransferequations,theKequationofturbulentkineticenergyandtheεequationofturbulencedissipationrateintheK-εturbulencemodel,andtheVolumefunctionequationforthefreesurfacetreatmentcanbeexpressedbyaunifiedtransportequationintheCartesiancoordinatesystemasfollows.

Xj———Coordinatecomponent;j=1,2,3

uj———Xjupwardvelocitycomponent

Φ———flux

гΦ———Transmissioncoefficient

SΦ———Thesourceterm

∙ForthespecificmeaningsofΦ,specificгΦandSΦ.

1.2Parallelcomputingtechnology

Becausetheflowcontrolofthediscreteequationsolutionisaniterativeprocess,andittakesalongtime.Thisstudyusedaparallelcomputingtechnologytospeedupthecalculationprocess,especiallyforlarge-scaleproblemsolving.ThroughtheparallelprocessingoftheimprovedSOLA-VOFalgorithm,thefluidflowsimulationtimecanbegreatlyreduced,andwiththeparticipationofthenetworkconnectedinparallelcomputingvarythenumberofcomputers.

1.3DieCastingPartsfillingprocesssimulation

InSP2parallelmachine,TheMotorcycleCrankcaseCoverfillingprocessofcastingswassimulated,andhascarriedontheanalysistothedesignoftwodifferentchannelfillmode[4],Theresultsareshowninfigure1.InFigure1（a）,itshowstheoriginalgatesolutioneventuallyfillthelocation,attheupperleftcornerofthecastingshasafluidregion.FromtheimproveddesignofthefillinggatesimulationresultsinFigure1（b）,wecanseethefinalfillareaof​​thegrooveportionintheoverflow,sothatthereisnogasinthecastinginvolvement.Byusingthemethodofincompleteinjection,moldfillingsimulationoftwokindsofgatingschemeresultswerevalidated.

（a）Theoriginalfourgateprocessscheme（b）Improvedtwogateprocessscheme

FIG.1Resultofmould-fillingprocesssimulationofmotorcyleparts

3Solidificationsimulation

Asthesolidificationprocessofcastingwascloselyrelatedwiththeshrinkagedefects,sincethe1960s,manystudieshavebeenfocusedontheuseofnumericalsimulationonthesolidificationprocesstopredictshrinkagedefects,putforwardalotofdefectpredictionmethodandcriterion,andqualitativelyfortheactualcasting.Thisarticlefocusesonusingthefractionalstepmethodforsolidificationsimulationanalysisandtheresearchofductileironshrinkageprediction.

2.1Componentwisesplittingmethodforheatconductionproblems

ThebasicprincipleofComponentwisesplittingmethod[5]isthebasicprincipleofthedifferentialoperatorbyacomplexconsistingofpartialdifferentialequationsintoasimpledifferentialoperatorconstitutedbyaseriesofsimplepartialdifferentialequation.AsinthenumericalsolutionprocessrequiresonlydiscreteschemeasawholetomeettheoriginalPDEcompatibilityconditionsandthestabilitycondition.whichcanbedecomposedonthebasisofpartialdifferentialequationsconstituteaseriesofcomponentwisesplittingdiscretizationscheme,andbycomponentwisesplittingdiscretizationschemeasawholetomeettheconditionsoftheoriginalequationofcompatibilityandstabilitycriteria.

Forheatconductionproblemintheprocessofsolidificationfollowtheenergyconservationequation,canbesimplifiedas:

TypeAiscalledthethermaldiffusioncoefficientorguideinthetemperaturecoefficient.

Fortheheatconductionequation,accordingtotheprinciplesoftheComponentwisesplittingmethodcanbeconstructedwithaweightedformatFactional

StepDifferenceFormat:

FormulaofAjx、Ajy、Ajzrespectivelywhenτj≤t≤τj+1;

τ——Eachfractionalsteptimestep；

j——Calculationtimestepj=1,2,3……

Equation（3）isabsolutelystable,withasecondorderaccuracy,andthatbothcanbeusedchasingmethodtosolve.

Sincethealgorithmisunconditionallystable,sohere'sthetimestepcanbewithinacertainrange（mainlytoensurethereasonablenessofcalculatedresults）arbitrarychoice,itcangreatlyacceleratethecalculationspeedandimprovecomputationalefficiency.

2.2Solidificationsimulationoptimizationcomputingarea

Componentwisesplittingmethodfornumericalsolutionbecausethereisnotimesteplimit,therefore,wecanconsiderinthesolidificationsimulationareapartitioningandusingdifferenttimestepstocalculatesoastoachievethepurposeofimprovingthecomputationalefficiency.Intheprocessofcastingsolidification,somecloserfromthecastingmoldunitsinvolvedintheintenseheattransferprocess,andsomerelativelyfarawayfromthecastingmoldunitsheattransfertendstoweaken,Therefore,thecastingmoldcanbedividedintotwocalculatedareas,internalandexternalareas,asshowninfigure2.Internalareaincludescastingsandcastingcastaroundthearea,internalcastingareaisdecidedbythethicknessofthecastingsurfacealongthenormaldirection.externalareaisrelativelyfarawayfromthecastingmoldforallareas[6].Theexternalareasmayusethelargertimesteprelativedtotheinternal,atthesametime,duetothecalculatedareasoftheinternalareaismuchlessthantheallareas,thusitwillgreatlyimprovethecomputationalefficiency.

Atypicalcastingweresimulatedbyusingthecomponentwisesplittingmethodanddistrictcomputingtechnology.Figure3showsthetemperaturedistributionafterthestartofsolidificationatacertaintime,itdisplayedthemayoccurhotspotdefectpositionofcastingsolidification.theauthorstudiedtheeffiiciencyofsolidificationsimulationinthreedifferentgridconditionsandcalculatingconditions,inordertotheefficiencyofthecomponentwisesplittingmethodanddistrictcomputingtechnology.Themeshsizeandnumberasshownintable1.Asisshownintable3,thenon-uniformgridcaneffectivelyreducethetotalnumberofgridcasting,whileafterusingpartitionmethodincomputingsysteminternalnumberofgridcomputingareaisreducedgreatly.

Table3liststhecomparisonofcastingsolidificationsimulationcomputationtimeandthecalculatedsolidificationtimeindifferentgridschemeanddifferentcalculationparametersconditions.AscanbeseenfromTable2:

underthesameconditionsofthegridschemeandpartitioningcalculations,thecalculationtimedecreaseswiththetimestepincreasing,andarelativelylargetimestephaslittleeffecttotheresults.Meanwhile,itcangreatlyreducethecomputingtimebyusingpartitionmethodinthesamegridandtimestep,thus,wecanimprovethecomputationalefficiency.

Tab.1Dissectionschemeofthegridmeshandmeshquantityofatypicalcasting

Meshsize（mm）TotalmeshCastinggridnumberInternalregionalgrid

227000004018188238

2/5（non-uniform）8447364018188238

5172800258910880

Tab.2Calculatedtimeandresultedsolidificationtimefromdifferentmeshscheme

ProjectGridschemeInternalmouldExternalareaTimeStep