英语写作.docx
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英语写作.docx
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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),wecanseethefinalfillareaofthegrooveportionintheoverflow,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
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