comsol電磁場-線圈載荷激勵施加方式

Single-turnandmulti-turncoil

domainsin3D?2012COMSOL.Allrightsreserved.IntroductionThistutorialshowshowtousetheSingle-TurnCoilDomainandMulti-TurnCoilDomainfeaturesinCOMSOL’sMagneticFieldsinterfaceformodelingcoilsin3DThesefeaturesareavailableonlywiththeAC/DCModuleTheyaresuitableforcomputationallyefficientmodelingofcurrent-carryingconductorscreatingmagneticfieldAdditionalinformationrelatedtosuitabilityofusingthesecoilmodelingfeaturesinDCandACareprovidedWeshouldhaveaclosedcurrentloopUseaclosedgeometrySpecifyaclosedcurrentpathusingappropriatemodelingtechniquesWhenmodelingmagneticfield,weneedtohaveaclosedcurrentloopUseappropriateboundaryconditionsforopengeometriesOverviewThistutorialdescribeshowtousethefollowingfeaturesSingle-turncoildomainGapfeedBoundaryfeedMulti-turncoildomainLinearcoilCircularcoilNumericcoilUsingsymmetryUser-definedcoilSingle-turncoildomainModeltheactualconductortocomputemagnitudeanddirectionofcurrentflowUsethisinformationtofindthemagneticfieldinandaroundtheconductorUsefulwhenyouhaveafewturnsAlsowhenyouwanttoresolvethecurrentdistributioninindividualwiresandturnsNote:YouneedtomodelanairdomainaroundtheconductorSingle-turntoroidalcoilModelinginfrequencydomain-ACAlwaysusethiswhenthesignalisperiodic(e.g.sinusoidal,squarewave)Canbeusedforsingle-turncoildomainaslongastheskindepthisnottoosmallcomparedtotheconductorthicknessWhentheskindepthissmallerthantheconductorthickness,useaboundarylayermeshWhentheskindepthissignificantlysmaller(<1/20th)thantheconductorthicknessthenwecannotusesingle-turncoildomainanymoreModelingintimedomain-TransientCannotbeusedforsingle-turncoildomainCOMSOLusesanA-Vformulationlocallywithinthesingle-turncoilSolvesforbothmagneticvectorpotential(A)andelectricpotential(V)TransientsimulationisnotsupportedforsuchcasesbecauseVisnotuniquelydefinedateachpointinspaceIntimedomainanalysis,thevoltage(V)isdefinedasapathintegralbetweentwopointsinspaceFordetailsontheA-Vformulation,refertotheAC/DCModuleUser’sGuideSingle-turncoil–GapfeedSingle-turncoilLeadsarenotmodeledGeometrymustformaclosedloopCrosssectionandshapecanbearbitraryCoilexcitationmethodExcitationsourceismodeledasaninternalcrosssectionboundarycalledgapfeedWeneedtobecarefulwhiledrawingthegeometrysothatwecreatethisinternalboundaryGapfeedSpecifythevoltageacrossthisboundarySpecifythecurrentthroughthisboundaryOptionstoconnecttolumpedelectricalcircuitModelinginCOMSOLFordetailedmodelingsteps,seethefollowingfile:single_coil_gap_feed.mphThismodelshowsbothDCandACcasesUsingsingle-turncoildomainwithgapfeedResults–Magneticfluxdensity(DC)Inductance=1.17e-8HResults–CurrentdensityDCsolutionResistance=1.65e-4ΩHighercurrentdensityalongtheinnerradiusindicatesthatmorecurrentisconcentratedalongashorterconductionpathAC(20kHz)solutionImpedance=2.3e-4+0.001iΩCurrentdistributionclearlyshowstheskineffectUsinggapfeedinACsingle-turncoilGapfeedinACindicatesaconnectiontoatransmissionlineInrealitythereisacapacitivecouplingbetweenthetwoendsofthis“gap”feedCapacitivecouplingismoresignificantathigherfrequenciesWecannotmodelitsinceweassumethegapfeedtobeazerothicknesssurfaceGapimpedancewilldependontheactualgapthicknessandmaterialpropertyofthe“gap”GapfeedisperfectlyaccurateforDCmodelsbutagoodapproximationonlyforlowfrequencyACmodelsSingle-turncoil–BoundaryfeedSingle-turncoilLeadsaremodeledGeometrydoesnotformaclosedloopCrosssectionandshapecanbearbitraryYoucanusethistomodelmorethanasingleturnCoilexcitationmethodDirectionofcurrentflowismodeledbyspecifyingagroundsurfaceandaboundaryfeedThesesurfacesshouldtouchtheexternalwallsoftheairdomainsurroundingtheconductorBoundaryfeedSpecifythevoltageatthisboundarySpecifythecurrentthroughthisboundaryOptionstoconnecttolumpedelectricalcircuitGroundUsingsingle-turncoildomainwithgroundandboundaryfeedResults–Magneticfluxdensity(DC)Inductance=3.16e-8HModelinginCOMSOLFordetailedmodelingsteps,seethefollowingfile:single_coil_boundary_feed.mphThismodelshowsbothDCandACcasesResults–CurrentdensityDCsolutionResistance=3.25e-4ΩHighercurrentdensityalongtheinneredgesindicatesthatmorecurrentisconcentratedalongashorterconductionpathAC(10kHz)solutionImpedance=3.83e-4+0.002iΩCurrentdistributionclearlyshowstheskineffectMeshingconsiderationsDefaultfreetetrahedralmeshissuitablefortheDCproblemBoundarylayermeshisbettertoresolvetheskineffectforACproblemswheretheskindepthissmallerthantheconductorcrosssectionResolvingtheskineffectinconductorsusingboundarylayermeshComputeskindepth:Iftheskindepthislessthan?thethicknessoftheconductor,considerusingaboundarylayermeshTwolayersofmesharoundtheconductorwallisgoodenoughEachlayerhasthesamethicknessastheskindepthMulti-turncoildomainModelahomogenizedcurrentcarryingregiontocomputemagnitudeanddirectionofcurrentflowUsethisinformationtofindthemagneticfieldinandaroundtheconductorUsefulwhenyouhavealotofturnsEachindividualwireisinsulated–hencenoshortingbetweenconductorsIndividualwireandmultiplelayersarenotresolvedNote:YoustillneedtomodelanairdomainaroundtheconductorHomogenizedmulti-turncoilModelinginfrequencyandtimedomainAlwaysusefrequencydomainwhenthesignalisharmonic(i.e.sinusoidal)LinearproblemRelativelyeasytosolveCanbeusedformulti-turncoildomainaslongastheskindepthismuchlargerthantheindividualwirediameterUsetimedomainonlyifthesignalisnotharmonic(e.g.pulse)NonlinearproblemRequiresmorecomputationaltimeandmemoryConvergencetipswhenusing3DMulti-TurnCoilDomaininfrequencydomainmodelsUseasmallnon-zeroelectricalconductivityforAirThisisrequiredtoavoidcreatingasingularstiffnessmatrixAvalueof1[S/m]isagoodguessUsingsmallervalueswouldincreasecomputationtimeCannotuseaveryhighvaluebecausethatwouldaffectthe“physics”ofthemodelMayneedGaugefixingAddGaugeFixingtoAmpere’sLawAddGaugeFixingtoMulti-TurnCoilDomainRequiredtogetauniquenumericalsolutionMulti-turncoil–LinearMultipleparallelstraightwiresbundledinasleeveLeadsaremodeledGeometryshouldnotformaclosedloopandmusthaveastraightlongitudinalaxisCrosssectioncanbearbitraryCoilexcitationmethodDirectionofcurrentflowismodeledbyspecifyingareferenceedgeAlsothetwoendsurfacesshouldtouchtheexternalwallsoftheairdomainsurroundingtheconductorReferenceedgeModelinginCOMSOLFordetailedmodelingsteps,seethefollowingfile:multi_coil_linear.mphThismodelshowsonlytheDCcaseNoteoncoilpropertiesThisistheelectricalconductivityofthewirematerial.ThisisthecrosssectionareaofeachwireCOMSOLusestheseforcomputingcoilresistanceTherelativepermeabilityandrelativepermittivityvaluesareforthehomogenizedcoildomainUsingmulti-turncoildomain:LinearOptionsforwirecrosssectionDefaultissettoUserdefinedcrosssectionareaCanspecifythewirediameterofroundwireCanalsospecifyAWGorSWGnumberNote:WearestillnotgeometricallyresolvingthewiresResults–MagneticfluxdensityInductance=1.02e-6HResults–CurrentdensityResistance=0.003ΩMulti-turncoil–CircularMultiplewiresarrangedasacircularcoilandplacedinapottingmaterialLeadsarenotmodeledGeometrymustformaclosedloopandmusthaveastraightlongitudinalaxisCrosssectionmustbecircularCoilexcitationmethodDirectionofcurrentflowismodeledbyspecifyingareferenceedge(typicallymorethanoneedge)thatshouldformaclosedcurveReferenceedgesModelinginCOMSOLFordetailedmodelingsteps,seethefollowingfile:multi_coil_circular.mphThismodelshowsbothDCandACcasesTheACmodelshowstheeffectofinducedcurrentinaconductorplacedintheACmagneticfieldcreatedbythemultiturncoilUsingmulti-turncoildomain:CircularResults–Magneticfluxdensity(DC)Inductance=6.05e-6HResults–CurrentdensityDCsolutionResistance=0.052ΩUniformcurrentdensityinthehomogenizedcoildomainAC(100Hz)solutionImpedance=0.061+0.001iΩUniformcurrentdensityincoildomainbutskineffectisvisibleinthecoppercoreThearrowsshowthatthecurrentdirectionisoppositeinthecoilandthecorebecauseofinductioneffectNoteonreferenceedgeForcircularcoil,the“referenceedge”isusedfor:DefiningthecurrentdirectionDefiningthetotallength(L)ofthewirewhere:Theeffectivecoilresistance(R)iscomputedas:N=numberofturnsσcoil=electricalconductivityofwiresAcoil=cross-sectionareaofindividualwireChoiceofreferenceedgeChoiceofreferenceedgecanaffecttheaccuracyofcomputedcoilresistanceifthecrosssectionisappreciablythickChoosingasetofedgeswhichrunthroughthemiddleofthethicknesswillgiveabetterestimateofresistanceChoosingasetofedgeswhichrunaroundtheouterorinnerperipherywillgiveanoverestimateorunderestimaterespectivelyofresistanceMulti-turncoil–NumericMultiplewiresarrangedasacoilandplacedinapottingmaterialLeadsarenotmodeledGeometrymustformaclosedloopCrosssectioncanhavearbitraryshapeMusthaveconstantcross-sectionperpendiculartocurrentdirectionPreferablenottohavesharpcornersinthecrosssectionUsefilletsCoilexcitationmethodExcitationsourceismodeledasaninternalcrosssectionboundarycalledan

InputNeedtotakecarewhiledrawingthegeometrysothatwecreatethisinternalboundaryOtherboundariesofthemulti-turncoildomainshouldbeassignedtoElectricinsulationCurrentflowsparalleltothesesurfacesNeedtoaddaCoilCurrentCalculationstudystepInputModelinginCOMSOLFordetailedmodelingsteps,seethefollowingfile:multi_coil_numeric.mphThismodelshowstheDCcaseUsingmulti-turncoildomain:NumericResults–MagneticfluxdensityInductance=2.88e-6HStudysettingsfornumericmulti-turncoilAddthisstepmanuallyfromStudy1>StudyStepsDragthisstepupandensurethatitislocatedabove

Step2:StationaryundertheStudybranchCOMSOLwillautomaticallysetuptheappropriatesolversAneigenvaluesolverwillfirstcomputethedirectionofcurrentflowinthecoildomainThisinformationwillbethenusedinthestationarysolverResults–CurrentdensityResistance=0.039Ωxy-viewUsingsymmetry–1/2Coilresistanceandinductanceis2timesthecomputedvalueNeedtousethreeboundaryconditionsforanumericmulti-turncoildomainElectricinsulation:currentisparalleltothesesurfacesInput:inletsurfaceforcurrentflowOutput:outletsurfaceforcurrentflowInputOutputModelinginCOMSOLFordetailedmodelingsteps,seethefollowingfile:multi_coil_numeric_symmetry_half.mphThismodelshowstheDCcaseUsingmulti-turncoildomain:NumericAllothersettingsareidenticaltothefull3DmodelResults–MagneticfluxdensityInductance=2.88e-6HResults–CurrentdensityResistance=0.039Ωxy-viewUsingsymmetry–1/8thmodelCoilresistanceandinductanceis8timesthecomputedvalueNeedtousethreeboundaryconditionsforanumericmulti-turncoildomainElectricinsulation:currentisparalleltothesesurfacesInput:inletsurfaceforcurrentflowOutput:outletsurfaceforcurrentflowInputOutputModelinginCOMSOLFordetailedmodelingsteps,seethefollowingfile:multi_coil_numeric_symmetry_octant.mphThismodelshowstheDCcaseUsingmulti-turncoildomain:NumericUsehalfthenumberofturnssincewehavecutthegeometrybyhalfalongthelengthofthecoilResults–MagneticfluxdensityInductance=2.88e-6HResults–CurrentdensityResistance=0.039ΩNoteoncrosssectionareaLongitudinalcross-sectionareamustbeconstantCoilCurrent