ATransientUnifiedModelofArc-WeldPoolCouplingsduringPulsedSpotGasTungstenArcWeldingA.Traidia1,2,F.Roger*,11ENSTAParistech,DepartmentofMechanicsUME2AREVANP,TechnicalCenter*Correspondingauthor:ENSTAParistech,DepartmentofMechanicsUME,Chemindelahunière,91761Palaiseau,FRANCE,frederic.roger@ensta-paristech.frAbstract:AtransientfiniteelementmodelhasbeendevelopedtostudytheheattransferandfluidflowduringpulsedspotGTAweldingonstainlesssteel.Temperaturefield,fluidvelocityandelectromagneticfieldsarecomputedinsidethecathode,arc-plasmaandanodeusingaunifiedMHDformulation.Theevolutionoftheheatfluxandcurrentdensityatthetopsurfaceoftheanodearestudiedduringtheweldingprocess.Theelectricheatingfluxattheanodewhichrepresentstheenergyabsorbedbytheworkpiecefromtheelectronscomingfromthecathodeisfoundtobethemajormechanismofheating.Theproposednumericalmodelalsopermitstostudythetimeevolutionoftheweldpooldimensionsforbothconstantandpulsedcurrent.Acomparisonshowsthattheuseofapulsedcurrentweldinggivesawideranddeeperweldshapethanthemeanconstantcurrentwelding.Thepresentworklaysafoundationforthefuturedevelopmentofathree-dimensionalmodelformovingtorcharcwelding.Keywords:Heattransfer,Fluidflow,Arcplasma,Unifiedmodel,Marangonieffect.1、IntroductionDuetothewidespreaduseofGTAweldinginthemanufacturingindustry,thenumericalsimulationofsuchaprocessiscurrentlyingreatprogress.Themaingoalistostudytheimpactoftheweldingparameters(weldingcurrent,arclength,pulsefrequency,weldingspeed…)onthefinalweldshapeinordertoimprovetheweldingqualityandincreaseproductivity.Thecomplexityofthenumericalmodelingisduethestrongcouplingsbetweenmanyphysicsinvolvedinthisprocess.Theionizationoftheshieldinggasensuresthecurrentflowbetweenthetwoelectrodes,thentheheatingJouleeffectcreatesathermalplasmacomposedofelectrons,ionsandneutralspeciesatalargetemperaturerange;from300Ktomorethan20000K.Theworkpieceisthenheatedfromboththearc-plasmaconduction,andtheelectronsflowatthetopsurface.Dependingonthemeltingtemperatureoftheworkpiece,aweldpoolisformedinwhichthefluidflowisgovernedbytheMarangonieffectatthetopsurface,thebuoyancyforcesandtheelectromagneticforcescreatedbythecurrentflow.Thefluidflowinsidetheweldpoolisalsostronglycoupledtothetemperaturefieldandthedeformationofthetopfreesurface.ManynumericalmodelsofspotGTAWareavailableintheliterature[1-5].Mostofthemconsideronlyonepartoftheweldingprocess[14](eitherthecathode,orthearcplasma,ortheanode)whichleadstofixsomeboundaryconditionsthatdonotrepresenttherealsituations.Thebestwaytodealwiththeproblemistotakeintoaccountthethreeparts(anode,cathodeandarc-plasma)inaunifiedformalism.Theinterfacesbetweentheplasmaandtheelectrodesarethenconsideredasinternalboundaries.ThisapproachwasproposedbyLowkeandTanakaetal[5]andgivessatisfyingresultsforconstantcurrentwelding.Inthepresentwork,aunifiedfiniteelementmodelisintroducedtakingintoaccountthethreepartsoftheweldingprocess.Thetime-dependentmodelcansimulatepulsedcurrentweldinginwhichtheweldingcurrentvarieswithtimeatagivenfrequencybetweentwoconstantvalues;thepeakcurrentandthebackgroundcurrent.Thispermitstostudythetransientevolutionofsomephysicalquantitiesatthetransitionbetweenthepeakandbackgroundtimesbutalsotocompareweldingunderpulsedcurrentwithweldingunderthemeancorrespondingconstantcurrent.2.Mathematicalformulation1.1GoverningequationsThemathematicalformulationisbasedonthefollowingassumptions:ThestudyisrestrictedtospotGTAW;anaxisymmetriccoordinatesystemisused.ThearccolumnisassumedtobepureargonatLocalThermodynamicEquilibrium.Thegasplasmaandmoltenmetalareincompressible.AweakcouplingisconsideredbetweenthefreesurfacedeformationandtheMagnetoHydrodynamic(MHD)calculations.Thetemperature,velocityandpressurefieldsarecalculatedinthethreedomainsusingtheclassicalconservationequationswritteninaunifiedtransientformalismasfollows:Whereisvelocity,Tistemperature,ρispressure,ρisdensity,isanequivalentspecificheatthattakesintoaccountthelatentheatoffusionistheliquidfractionassumedtovarylinearlywithtemperatureinthemushyzoneandequals1intheweldpooland0elsewhere.kisthermalconductivityandμistheviscosity.TheBoussinesqapproximationisusedtocomputetheconvectionforcesinsidetheweldpool.βisthemetalthermalexpansionandistakenasthesolidustemperature.IntheweldpoolthevolumetricheatsourceistheJouleeffectandtheenthalpicflux,andinthearcplasmawetakeinadditiontheradiationlosses,usuallyapproximatedby,whereisthenetemissioncoefficientofargonthatvarieswithtemperature.ThedeterminationoftheelectromagneticforcesandthejouleeffectinbotharcplasmaandworkpiecerequiresthecomputationofthecurrentdensityjandthemagneticfluxB.Toachievethis,thecoupledcurrentcontinuityandthemagneticpotentialequationsarecomputedasfunctionoftheelectricpotentialVandthemagneticpotentialvectorAasfollows:Thecurrentdensity,electricfieldandmagneticfluxarethencomputedfromVandAasfollows:Itisimportanttonoticethattheeddycurrentcreatedbythetimevariationoftheweldingcurrentistakenintoaccountintheaboveexpressions.Thefreesurfacedeformationφ(r)isdescribedbythefollowingPDEobtainedfrom[2]:Whereφisthefreesurfacedepression,Paisthearcpressure,γisthemoltenmetalsurfacetensionandλisaLagrangianmultiplierusedtotakeintoaccountthemassconservationconstraint:1.2BoundaryconditionsThecomputationaldomainisshowninFigure1.Asseentheworpieceismadeoftwosubdomainsinordertouseafinermeshsizefortheweldpoolformation.AlltheboundaryconditionsarelistedinTable1;themostimportantpointsarediscussedbelow;Attheinterfacebetweenarcplasmaandtheanode(GD)thefollowingconditionsmustbesatisfied[5]:Figure1.Computationaldomain(dimensionsinmm)Thefirstconditionshowsthatthenormalheatfluxattheanodeiscomposedbytheheatingconductionfluxfromtheplasma,theheatingelectricflux(whichrepresentstheenergytransferredfromtheelectronstotheanode)andthecoolingradiationlosses.istheanodeworkfunctionandistheStefan-Boltzmannconstant.ThesecondconditionmeansthatthetotalshearstressisthesumofthearcdragforceandtheMarangoniforce.andarerespectivelyalocaltangentvectorandthenormalvectortothetopfreesurface(nisdirectedtowardtheplasmadomain).isthesurfacetensioncoefficient,whichhasbeenreportedtohaveabigimpactontheflowdirectionsinsidetheweldpool[1-4].ItsdependenceontemperatureTandsulfuractivityisconsideredusingtheexpressiondevelopedbySahooandDebRoyetal[6]asfollows:Alongtheinterfacebetweenthearcplasmaandthecathode(HIJB),thenormaldiscontinuityoftheheatfluxisexpressedasfollows:WhereiVandcarerespectivelytheargonionizationpotentialandthecathodeworkfunction.ijandejarerespectivelytheioncurrentandelectroncurrentcalculatedfrom:arerespectivelytheRichardson’sconstant,theeffectiveworkfunctionforthermionicemissionandtheelementarycharge.Table1:Boundaryconditions3.NumericalsimulationresultsThenumericalmodelisappliedtoanAISI304stainlesssteeldiskcontaining290ppmsulfurwith8mmthickness.ThethermophysicalpropertiesofAISI304ssarelistedintheappendix.Thepropertiesofpureargonaretakenfrom[7].Thegasinflowrateisfixedto30L/min.Table2liststheotherweldingparameters.Table2:WeldingparametersFigure2presentsthetimeevolutionofthecomputedsolutionattheendofthebackgroundtime(left)andthepeaktime(right)everyfiveperiods.Itisrepresentedthetemperaturefieldandtemperaturecontoursinsidethearcplasmaandtheelectrode,thenormalizedvelocityfieldandstreamlinesinsidethemoltenweldpool.Duringthepeaktimethearcisbell-shapedandthemaximumoftemperatureandvelocityfieldsarehigherthanduringthebackgroundtime.Theobtainedvaluesforthemaximumofplasma-jetvelocityandplasmatemperatureareingoodagreementwiththeliterature,infactfora150Acontinuouscurrentwelding17000Kforthemaximumtemperatureand150m/sforthemaximumvelocityarereviewed[5].Wecanalsonoticethatthevariationsoftemperatureandvelocityfieldsinsidetheplasmacolumnbetweenthepeaktimesarenegligible;thisisalsothecaseforthebackgroundtimes.Thedynamicoftheweldpoolflowisstudiedbyconsideringthestreamlinesofthevelocityfield.WecanclearlyidentifyineachfiguretwovorticesnamedAandB.TheyresultsfromtheMarangonieffectatthetopsurfaceoftheweldpool,thesizeofeachvortexisrelatedtobothtemperaturedistributionatthesurfaceandsulfurcontentoftheworkpiece.Detailsaboutthedynamicvariationofthesevorticesandtheirinfluenceontheweldpoolevolutionareavailableinourpreviousworks[4].Figure3showstheanodicheatfluxdistributionduringthetransitionfromthelastpeaktime(t=14.5s)tothelastpeaktime(15s).Duringthebackgroundtimethemaximumofanodicfluxisaround43W/mm².Thetransitionisthenveryfast;inapproximately15μstheheatfluxseemstostabilizeespeciallyatthecenterofthediskandreachesamaximumof56.6W/mm².Thenumericalmodelpermitstostudytheenergytransferbetweenthearcplasmaandtheworkpiece.Figure4showstheradialevolutionoftheheatfluxattheanodeatthelastpeakandbackgroundtimes(t=14.5sandt=15s).Ineachfigureitisrepresentedthetotalheatfluxanditselementarycontributions,namely;theelectricflux,theconductionfromthearcplasmaandtheradiationlosses.Figure2.MHDsolutionsatbackgroundtimes(left)andpeaktimes(right)fordifferentperiodsFigure3.EvolutionoftheanodicheatfluxatthetransitionbetweenthebackgroundtothepeaktimeFigure4.AnodicheatfluxanditselementarycontributionsatthelastperiodofheatingTheelectricfluxisfoundtobethemostsignificantfactorinbothpeakandbackgroundtimes.Itrepresentsaround80%ofthetotalenergytransferredtotheworkpiece.Thecontributionoftheconductiveheatfluxfromtheplasmarepresentaround30%andthecoolingradiationlossesareunder10%ofthetotalheatflux.Figure5showsthetimeevolutionoftheweldpoolhalf-widthanddepthforthepulsedcurrent80/160Aandthecontinuousmeancurrent120AEventhoughthetwocasesareenergeticallyequivalent,thepulsedcaseproducesadeeperandwiderweldpoolthanthecontinuouscase,especiallyfortheweldpooldepth.Thisconclusiongoeswithwhatiscommonlyobservedbywelders.Figure5.Evolutionoftheweldpoolsizeforthepulsedcurrent80/160Aandthemeancurrent120A4.ConclusionsAtransientunifiedmodelofpulsedspotGTAWhasdevelopedusingCOMSOLMultiphysics.Thenumericalsimulationallowedabetterunderstandingoftheheattransferbetweenthearcplasmaandtheelectrodes.Theheatingthermionicemissionattheanodewasfoundtobethemostimportantheatingeffect.Theresultsshowedthatforagivenlevelofenergy,itismoreinterestingtouseapulsedcurrentweldingthanthemeanconstantcurrenttogetabetterweldsize.5.ReferencesW.H.KimandS.J.Na.Int.J.HeatMassTran.,41,3213-3227(1998)H.G.Fan,H.L.TsaiandS.J.Na.Int.J.HeatMassTran.,44,417-428(2001)F.Lu,S.Yao,S.LouandY.Li.Comput.Mater.Sci.,29,371-378(2004)A.Traidia,F.RogerandE.Guyot.Int.J.Therm.Sci.,49,1197-1208(2010)M.TanakaandJ.J.Lowke.J.Phys.D:Appl.Phys.,40,R1-R23(2007)P.Sahoo,T.DebRoy,M.T.McNallan.Metall.Trans.B.,19B,483-491(1988)P.Fauchais,M.BoulosandE.Pfender,Thermalplasma,fundamentalsandapplications,(1994)6.AcknowledgementsThisresearchwassupportedbytheTechnicalCenterofweldingatAREVANP,FRANCE.TheauthorsaregratefultoLahceneCherfa,AlexanderChidleyandCatherineHolmfortheirhelpontheresultsprocessing.AppendixTable3:Materialpropertiesoftheusedmaterials.免责声明：本页面/内容部分素材来源于互联网公开信息，旨在传递更多信息，不代表本平台立场。版权归原作者或机构所有，如涉及侵权，请通过平台联系我们，我们将在核实后第一时间处理。本平台对转载内容的真实性、准确性不作任何保证，用户需自行判断并承担使用风险。
