FE研發(fā)培訓-設計培訓

FE研發(fā)培訓,設計培訓2024/3/29FE研發(fā)培訓,設計培訓

IntroductionBoundaryValueProblemFundamentalConceptPre-processingProcessingPost-processingParametricModeling

TopicsFE研發(fā)培訓,設計培訓

FEA(FiniteElementAnalysis)isawell- establishednumericalmethodofsolvingfield problems. Commercialsoftwarepackages areavailableto solvefieldproblemsinelectricalmachines, suchasthoseofsynchronousmachines.IntroductionFE研發(fā)培訓,設計培訓

Solutionofaboundaryvalueproblem comprisesthecalculationofthedistribution ofafunctionoveraspecifieddomain.

BoundaryValueProblemFE研發(fā)培訓,設計培訓

Theboundaryvalueproblemisdescribedbya governingequationandboundaryequation.

BoundaryValueProblemFE研發(fā)培訓,設計培訓

Dirichletboundaryequation

NeumannboundaryequationBoundaryValueProblemFE研發(fā)培訓,設計培訓

Fundamentalconceptof FEAisthatany continuousfunctiondefinedoveradomaincan beapproximatedbyadiscretemodelcomposed ofasetofpiecewisecontinuousfunctions definedoverafinitenumberofsubdomains.

FundamentalConceptFE研發(fā)培訓,設計培訓

Consideranexampleoftemperature distributioninabar.

FundamentalConceptFE研發(fā)培訓,設計培訓

ThecontinuousfunctionisT(x)andthe domainisOLalongx-axis.Sixpointsalongx-axisareidentified.Weshall callthesepointsasnodes.Thedomainisdividedintofiveelements.FunctionT(x)isapproximatedbyfive piecewisecontinuouslinearfunctionsdefined overasingleelement.

FundamentalConceptFE研發(fā)培訓,設計培訓

Thepre-processingincludesthestepsof identifyingthedomainofanalysis,derivation ofthegoverningandboundaryequationsand thedivisionofthedomainintosub-domains calledfiniteelements.

Pre-processingFE研發(fā)培訓,設計培訓Considerone-dimensionalbarelement.

Thevalueofafunctionovertheelementiisdefined

Pre-processingFE研發(fā)培訓,設計培訓

Similarly,forelementj

Pre-processingFE研發(fā)培訓,設計培訓

Themostcommontwo-dimensionalelementisatriangle.

Pre-processingFE研發(fā)培訓,設計培訓

Pre-processingFE研發(fā)培訓,設計培訓Thegoverningequationfor2DmagneticfieldproblemcanbederivedfromMaxwell’sequationsbydefiningapotentialfunctionA.

Aresidualisdefinedforanapproximatesolution.

Pre-processingFE研發(fā)培訓,設計培訓Minimizingtheweightedresidualwithrespecttoeachnodalpotential,weobtain

Substitutingfromabove,weobtain.

Pre-processingFE研發(fā)培訓,設計培訓UsingGreen’sidentity,weobtain.

Substituting,weobtainthefollowingequations.

Pre-processingFE研發(fā)培訓,設計培訓Intheprocessingstep,wesolvethesystemofequationsderivedinthepre-processingstep.

ProcessingFE研發(fā)培訓,設計培訓Thecoefficientmatrixforthesystemofequationsis sparseandisusuallysymmetricalalongthediagonal.Fornon-linearmagneticfieldproblems,theentriesinthecoefficientmatrixarefunctionsofpermeability.Aniterativemethod,suchas,Newton-Raphsonisusedforsolutionofthenonlinearsystemofequations.

ProcessingFE研發(fā)培訓,設計培訓TheprincipleoftheNewton-Raphsonmethodistoiterativelyreducethisresidualuntilitissufficientlysmall(ideallyzero).

ProcessingFE研發(fā)培訓,設計培訓ThecommercialsoftwarepackagesMagNetbyInfolyticaofCanadaandMagSoftbyCedretofFranceareusedbyR&DforelectromagneticFEA.AparametricmodelingtechniquehasbeenrecentlydevelopedtoautomaticallymodelsynchronousmachinesbyusingMagNet.Anexampleoftheapplicationfor4poles8500HPmotor2511DAisusedforillustration.

SoftwareFE研發(fā)培訓,設計培訓TherearefourmodulesforcreationofaFEmodelparametrically.

-Stator(modelstatorcore,air) -Rotor(modelrotorpole,spiderandfieldcoil) -Model(createmodelincludingallcomponents) -PhaseSET(createstatorwindingconnection)

ParametricModelingFE研發(fā)培訓,設計培訓Thestatormodelhasfourbuttons.Aftertheparametersareentered,eachbuttoncanbeactivatedtocompletethemodel.Thescaleisthenumberofpolestobemodeled.Thefourbuttonsare -BuildStatorCore -BuildStatorWinding -BuildAir -BuildStator

StatorModelFE研發(fā)培訓,設計培訓

StatorModelFE研發(fā)培訓,設計培訓Therotormodelhassixbuttons.Aftertheparametersareentered,eachbuttoncanbeactivatedtocompletethemodel.Thebuttonsare -BuildFieldPole -BuildAirGap -BuildShaft -BuildDamperBars -BuildCoil

RotorModelFE研發(fā)培訓,設計培訓

PhaseSetFE研發(fā)培訓,設計培訓

ModelFE研發(fā)培訓,設計培訓

MeshFE研發(fā)培訓,設計培訓

AirGapMesh(Close-up)FE研發(fā)培訓,設計培訓

2DFEmodelssolveforfielddistributionover amachinecross-sectionbyneglectingall fringingandendeffects,called3Deffects. Since3Dmodelingrequiresconsiderable computerprogrammingandCPUtime,itisnot yetpracticaltosolverotatingmachinetransient problemsin 3D. Toimprovecorrelationwithtestresults,itis essentialtoincludethe3Deffects.

3DEffectsModelingFE研發(fā)培訓,設計培訓

3Deffectsincludestackingofcore laminations,ventilationairductsfringingflux andpoleandstatorendleakageflux. Somemethodstoinclude3DeffectsinFE modelshavebeendeveloped.

3DEffectsModelingFE研發(fā)培訓,設計培訓

3DEffectsModelingLdwFEsolutionregionFFE研發(fā)培訓,設計培訓

Figureshowsamagneticcircuitinwhichflux F,widthwanddepthdareintheplaneofthe FEsolutionregion,andtheaxiallengthLis perpendiculartotheplaneoftheFEsolution domain. ThepermeancePofthismagneticcircuit

P=mwL/d

3DEffectsModelingFE研發(fā)培訓,設計培訓

ThepermeancePmodofacircuitcomponentin theFEmodelhastobeidenticalwiththeactual permeancePactofthiscomponent

Pact=mactwactLact/dact

Pmod=mmodwmodLmod/dmod WidthanddepthoftheFEmodelagreewith theactualdimensions,whichgivesthescaling equationforthepermeabilitymmod

mmod=mactLact/Lmod=mactfstack

3DEffectsModelingFE研發(fā)培訓,設計培訓

ThescaledpermeabilityisusedintheFE modelbyscalingtheactualB(H)characteristic ofthesteelmaterialineachregionbythe stackingfactor

Hmod=Hact,Bmod=Bactfstack Thefieldsolutionsobtainedusingthis “equivalent”FEmodelarescaledbacktothe actualfluxdensities

Bact=Bmod/fstack

3DEffectsModelingFE研發(fā)培訓,設計培訓

Theductfringingfluxandendleakageflux effectscanbemodeledinastaticmodelto obtaintheleakagecorrectionfactors

3DEffectsModelingFE研發(fā)培訓,設計培訓

FieldSolutionFE研發(fā)培訓,設計培訓OCSolutionat120%RatedVoltage

FE研發(fā)培訓,設計培訓Engineeringparametersofinterestcanbederivedbypost-processingofthefieldsolution.Thesoftwarepost-processinghasmanyoptionstocalculatethedesiredquantities.Thecalculatedquantitiescanbeexportedtoexcelspreadsheetforadditionaldataanalysis.

Post-processingFE研發(fā)培訓,設計培訓

GraphicalPlottingFE研發(fā)培訓,設計培訓OCSaturation

FE研發(fā)培訓,設計培訓 Inintegralslotmachinesthegeometryandthe magneticfielddistributionsrepeateverypolepitch, anditis,therefore,sufficienttoperformthefield analysisusingjustonepolepitch.

Infractionalslotmachinesthestatorcoilsdonot repeateverypolepitch,butonlyaftermultiplepole pitchesdependingonthecoilpattern.

FractionalSlotMachinesFE研發(fā)培訓,設計培訓

InawindingcharacterizedbyA+B/Cslotsperpole perphase,thewindingpatternandmagneticfields repeatonlyafterCpolepitches. Therefore,Cpolepitcheshavetobemodeled, whichresultsinlargeFEmodelsandlong simulationtimes.

FractionalSlotMachinesFE研發(fā)培訓,設計培訓

Theperiodicityofthemagneticfieldsisutilizedto reducetheFEmodelwithperiodicboundary conditionsforthemagneticvectorpotentialA.

Thevectorpotentialofthenodesontheleftradialboundaryhasthesamemagnitudeasthepotentialofthecorrespond