FE研发培训,设计培训

SynchronousMachinesElectromagneticFiniteElementAnalysisHaranKarmakerJune1,2006•Introduction•BoundaryValueProblem•FundamentalConcept•Pre-processing•Processing•Post-processing•ParametricModelingTopics•FEA(FiniteElementAnalysis)isawell-establishednumericalmethodofsolvingfieldproblems.•Commercialsoftwarepackagesareavailabletosolvefieldproblemsinelectricalmachines,suchasthoseofsynchronousmachines.Introduction•Solutionofaboundaryvalueproblemcomprisesthecalculationofthedistributionofafunctionoveraspecifieddomain.BoundaryValueProblem•Theboundaryvalueproblemisdescribedbyagoverningequationandboundaryequation.BoundaryValueProblem•Dirichletboundaryequation•NeumannboundaryequationBoundaryValueProblem•FundamentalconceptofFEAisthatanycontinuousfunctiondefinedoveradomaincanbeapproximatedbyadiscretemodelcomposedofasetofpiecewisecontinuousfunctionsdefinedoverafinitenumberofsubdomains.FundamentalConcept•Consideranexampleoftemperaturedistributioninabar.FundamentalConcept•ThecontinuousfunctionisT(x)andthedomainisOLalongx-axis.•Sixpointsalongx-axisareidentified.Weshallcallthesepointsasnodes.•Thedomainisdividedintofiveelements.•FunctionT(x)isapproximatedbyfivepiecewisecontinuouslinearfunctionsdefinedoverasingleelement.FundamentalConcept•Thepre-processingincludesthestepsofidentifyingthedomainofanalysis,derivationofthegoverningandboundaryequationsandthedivisionofthedomainintosub-domainscalledfiniteelements.Pre-processing•Considerone-dimensionalbarelement.•ThevalueofafunctionovertheelementiisdefinedPre-processing•Similarly,forelementjPre-processing•Themostcommontwo-dimensionalelementisatriangle.Pre-processingPre-processing•Thegoverningequationfor2DmagneticfieldproblemcanbederivedfromMaxwell’sequationsbydefiningapotentialfunctionA.•Aresidualisdefinedforanapproximatesolution.Pre-processing•Minimizingtheweightedresidualwithrespecttoeachnodalpotential,weobtain•Substitutingfromabove,weobtain.Pre-processing•UsingGreen’sidentity,weobtain.•Substituting,weobtainthefollowingequations.Pre-processing•Intheprocessingstep,wesolvethesystemofequationsderivedinthepre-processingstep.Processing•Thecoefficientmatrixforthesystemofequationsissparseandisusuallysymmetricalalongthediagonal.•Fornon-linearmagneticfieldproblems,theentriesinthecoefficientmatrixarefunctionsofpermeability.•Aniterativemethod,suchas,Newton-Raphsonisusedforsolutionofthenonlinearsystemofequations.Processing•TheprincipleoftheNewton-Raphsonmethodistoiterativelyreducethisresidualuntilitissufficientlysmall(ideallyzero).ProcessingR(A)R(A)AkAk+1kdAA•ThecommercialsoftwarepackagesMagNetbyInfolyticaofCanadaandMagSoftbyCedretofFranceareusedbyR&DforelectromagneticFEA.•AparametricmodelingtechniquehasbeenrecentlydevelopedtoautomaticallymodelsynchronousmachinesbyusingMagNet.•Anexampleoftheapplicationfor4poles8500HPmotor2511DAisusedforillustration.Software•TherearefourmodulesforcreationofaFEmodelparametrically.-Stator(modelstatorcore,air)-Rotor(modelrotorpole,spiderandfieldcoil)-Model(createmodelincludingallcomponents)-PhaseSET(createstatorwindingconnection)ParametricModeling•Thestatormodelhasfourbuttons.Aftertheparametersareentered,eachbuttoncanbeactivatedtocompletethemodel.Thescaleisthenumberofpolestobemodeled.•Thefourbuttonsare-BuildStatorCore-BuildStatorWinding-BuildAir-BuildStatorStatorModelStatorModel•Therotormodelhassixbuttons.Aftertheparametersareentered,eachbuttoncanbeactivatedtocompletethemodel.•Thebuttonsare-BuildFieldPole-BuildAirGap-BuildShaft-BuildDamperBars-BuildCoilRotorModelPhaseSetModelMeshAirGapMesh(Close-up)•2DFEmodelssolveforfielddistributionoveramachinecross-sectionbyneglectingallfringingandendeffects,called3Deffects.•Since3DmodelingrequiresconsiderablecomputerprogrammingandCPUtime,itisnotyetpracticaltosolverotatingmachinetransientproblemsin3D.•Toimprovecorrelationwithtestresults,itisessentialtoincludethe3Deffects.3DEffectsModeling•3Deffectsincludestackingofcorelaminations,ventilationairductsfringingfluxandpoleandstatorendleakageflux.•Somemethodstoinclude3DeffectsinFEmodelshavebeendeveloped.3DEffectsModeling3DEffectsModelingLdwFEsolutionregionF•FigureshowsamagneticcircuitinwhichfluxF,widthwanddepthdareintheplaneoftheFEsolutionregion,andtheaxiallengthLisperpendiculartotheplaneoftheFEsolutiondomain.•ThepermeancePofthismagneticcircuitP=mwL/d3DEffectsModeling•ThepermeancePmodofacircuitcomponentintheFEmodelhastobeidenticalwiththeactualpermeancePactofthiscomponentPact=mactwactLact/dactPmod=mmodwmodLmod/dmod•WidthanddepthoftheFEmodelagreewiththeactualdimensions,whichgivesthescalingequationforthepermeabilitymmodmmod=mactLact/Lmod=mactfstack3DEffectsModeling•ThescaledpermeabilityisusedintheFEmodelbyscalingtheactualB(H)characteristicofthesteelmaterialineachregionbythestackingfactorHmod=Hact,Bmod=Bactfstack•Thefieldsolutionsobtainedusingthis“equivalent”FEmodelarescaledbacktotheactualfluxdensitiesBact=Bmod/fstack3DEffectsModeling•Theductfringingfluxandendleakagefluxeffectscanbemodeledinastaticmodeltoobtaintheleakagecorrectionfactors3DEffectsModelingFieldSolutionOCSolutionat120%RatedVoltag