comsol涡流模块

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1、-InductionCurrentsfromCircularCoilsIntroductionAtime-varyingcurrentinducesavaryingmagneticfield.Thisfieldinducescurrentsin neighboringconductors.Theinducedcurrentsarecallededdycurrents.Thefollowingmodelillustratesthis phenomenonbya time-harmonicfieldsimulationas wellasatransientanalysis,whichprovide

2、sastudyoftheeddycurrentsresultingfromswitchingonthesource.Twocurrent-carryingcoilsareplacedaboveacopperplate.Theyaresurrounded byair,andthereisasmallairgapbetweenthecoilsandthemetalplate.Apotentialdifferenceprovides thee*ternalsource.Toobtainthetotalcurrentdensityin thecoilsyoumusttaketheinducedcurr

3、entsintoaccount.Thetime-harmoniccaseshowstheskineffect,thatis,thatthecurrentdensityishighclosetothesurfaceanddecreasesrapidlyinsidetheconductor.ModelDefinitionEQUATIONTosolvetheproblem,useaquasi-staticequationforthemagneticpotentialA:-A-+(11A) = Vcoi-l. z.-t0 r2r. z.-Here0isthepermeabilityofvacuum,r

4、the relativepermeability,theelectricconductivity,andVcoilthevoltageoveroneturnin thecoil.Inthetime-harmoniccasetheequationreducesto. z.-1 1Vcoil=-. z.-jA+(0 rA)2r. z.-FORCESThetotalelectromagneticforceactingonregionofspace canbeobtainedbyintegratingMa*wellsstresstensor onthedelimitingboundary :F= Tn

5、dSTheForceCalculationfeatureautomaticallyperformstheintegralalongtheboundariesofthedesiredregion,consideringalsothea*isymmetricgeometryoftheproblem.Theputedforcewillbeavailableinresultsprocessingasaglobalvariable.ResultsandDiscussionInthetime-harmonicregime,thevaryingmagneticfieldinduceselectricalcu

6、rrentsin themetallicplate.Thecurrents,inturn,actassourcesofanopposingmagneticfieldshieldingtheplatefromthemagneticfield.Asaresultofthisphenomenon,theregioninwhichelectricalcurrentsaregeneratedisconfinedinpro*imityofthesurfaceandreducesinsizewithincreasingfrequency.Figure1andFigure2showtheinducedcurr

7、entdensityat10Hzand300Hz,respectively.Inthismodel,atime-domainstudyisperformedtoinvestigatethestepresponseofthesystem.Figure 3displaysasnapshotoftheinducedcurrentdensityandmagneticflu*densityforthetransientsolutioninabinedsurfaceandarrowplot.Finally,Figure4showsthetotala*ialforcebetweenthecoilsandth

8、eplateasafunctionoftimeputedbytheForceCalculationfeature.Forthechosencurrentdirection,theforceisrepulsive(negative). z.-Figure1:Theponentoftheinducedcurrentdensityforthetime-harmonicsolutionplottedtogetherwithacontourplotofthemagneticvectorpotentialatafrequencyof10Hz.Figure2:Plotofthesamequantitiesa

9、tafrequencyof300Hz. z.-Figure3:Snapshotoftheinducedcurrentdensity(surfaceplot)andthemagneticflu*density(arrowplot)duringthetransientstudy. z.-Figure4:Totalforceactingonthecopperplateplottedasafunctionoftime.ModelLibrarypath:ACDC_Module/Inductive_Devices_and_Coils/coil_above_plateModelingInstructions

10、FrequencyDomainFromtheFilemenu,chooseNew.NEW1IntheNewwindow,clicktheModelWizardbutton.MODEL WIZA RD1 IntheModelWizardwindow,clickthe2DA*isymmetricbutton.2 IntheSelectphysicstree,selectAC/DCMagneticFields(mf).3 ClicktheAddbutton. z.-4 ClicktheStudybutton.5 Inthetree,selectPresetStudiesFrequencyDomain

11、.6 ClicktheDonebutton.GEOMETRY 1Square11 IntheModelBuilderwindow,underponent1right-clickGeometry1andchooseSquare.2 IntheSquaresettingswindow,locatetheSizesection.3 IntheSidelengtheditfield,type0.1.4 LocatethePositionsection.Inthezeditfield,type-0.05.Rectangle11 IntheModelBuilderwindow,right-clickGeo

12、metry1andchooseRectangle.2 IntheRectanglesettingswindow,locatetheSizesection.3 IntheWidtheditfield,type0.08.4 IntheHeighteditfield,type0.02.5 LocatethePositionsection.Inthezeditfield,type-0.021.Circle11 Right-clickGeometry1andchooseCircle.2 IntheCirclesettings window,locatethe SizeandShapesection.3

13、IntheRadiuseditfield,type0.0025.4 LocatethePositionsection.Inthereditfield,type0.0125.5 Inthezeditfield,type0.0025.Circle21 Right-clickGeometry1andchooseCircle.2 IntheCirclesettings window,locatethe SizeandShapesection.3 IntheRadiuseditfield,type0.0025.4 LocatethePositionsection.Inthereditfield,type

14、0.0185.5 Inthezeditfield,type0.0025. z.-6 ClicktheBuildAllObjectsbutton.Thegeometryisnowplete.Ne*t,addthematerialsrelevanttothemodel.MATER IALSOntheHometoolbar,clickAddMaterial.ADD MATERIAL1 GototheAddMaterialwindow.2 Inthetree,selectBuilt-InAir.3 IntheAdd Materialwindow,clickAddtoponent.MATER IALSA

15、DD MATERIAL1 GototheAddMaterialwindow.2 Inthetree,selectBuilt-InCopper.3 IntheAdd Materialwindow,clickAddtoponent.4 ClosetheAddMaterialwindow. z.-MATERIALSCopper1 IntheModelBuilderwindow,underponent1MaterialsclickCopper.2 SelectDomains24only.MAGNETIC FIELDSSingle-TurnCoil11 OnthePhysicstoolbar,click

16、DomainsandchooseSingle-TurnCoil.2 SelectDomains3and4only.3 IntheSingle-TurnCoilsettingswindow,locatetheSingle-TurnCoilsection.4 FromtheCoile*citationlist,chooseVoltage.5 IntheVcoileditfield,type0.1mV.Withthissetting,theSingle-TurnCoilfeatureappliesaloopvoltageof0.1mVtoeach ofthe coilloops.Now,adda F

17、orceCalculation featurethatputes thetotal forceactingon theplate.Force Calculation11 OnthePhysicstoolbar,clickDomainsandchooseForceCalculation.2 SelectDomain2only.3 IntheForceCalculationsettingswindow,locatetheForceCalculationsection.4 IntheForcenameeditfield,typeplate.STUDY 1Step1:FrequencyDomain1

18、In the ModelBuilderwindow, underStudy1clickStep1:FrequencyDomain.2 IntheFrequencyDomainsettingswindow,locatetheStudySettingssection.3 IntheFrequencieseditfield,type10Hz,100Hz,300Hz.Disabletheautomaticplotgeneration.4 IntheModelBuilderwindow,clickStudy1.5 IntheStudysettingswindow,locatetheStudySettin

19、gssection.6 CleartheGeneratedefaultplotscheckbo*.7 OntheStudytoolbar,clickpute.Whenthesolutionprocessispleted,createplotgroupstovisualizetheresults. z.-RES ULTS2DPlotGroup11 OntheResultstoolbar,click2DPlotGroup.2 Onthe2DPlotGroup1toolbar,clickSurface.3 IntheSurfacesettingswindow,clickReplace E*press

20、ionintheupper-rightcorneroftheE*pressionsection.Fromthemenu,chooseMagneticFieldsCurrentsandchargeInducedcurrentdensityInducedcurrentdensity,phiponent(mf.Jiphi).Addacontourplottoshowthefieldlinesofthemagneticflu*density.Ina*ialsymmetry,thoselinescanbeobtainedbyplottingtheisolinesofthemagneticvectorpo

21、tentialmultipliedbytheradialcoordinate,r.4 Onthe2DPlotGroup1toolbar,clickContour.5 In the Contoursettings window,locatetheE*pressionsection.6 IntheE*pressioneditfield,typeAphi*r.7 IntheModelBuilderwindow,click2DPlotGroup1.8 Inthe2DPlotGroupsettingswindow, locatetheData section.9 FromtheParametervalu

22、e(freq)list,choose10.10 Onthe2DPlotGroup1toolbar,clickPlot.Theplotshowstheinducedcurrentdensityintheplate.Plottingtheothersolutionsshowshowtheregioninwhichthecurrentsareinduceddecreaseswithincreasingfrequency.11 FromtheParametervalue(freq)list,choose100,thenclickPlot.12 FromtheParametervalue(freq)li

23、st,choose300,thenclickPlot.TransientAnalysisTosetupatime-dependentstudytoinvestigatethestepresponseofthesystemrequiresonlyafewadditionalsteps.TheInitialValuesfeatureautomaticallyincludedintheMagneticFieldsinterfacespecifiestheinitialvalueforthemagneticvectorpotential,defaultedtozero.Atthebeginningof

24、thetransientsimulation(t=0),a0.1mVvoltageisappliedtothecoil.Thiscorrespondstoe*citingfromanune*cited statethesystemwithastepfunction.1OntheStudytoolbar,clickAddStudy. z.-ADD STUDY1 GototheAddStudywindow.2 FindtheStudiessubsection.Inthetree,selectPresetStudiesTimeDependent.3 IntheAddstudywindow,click

25、AddStudy.4 ClosetheAddStudywindow.STUDY 2Step 1:TimeDependent1 In theModelBuilderwindow, underStudy2click Step1:TimeDependent.2 IntheTimeDependentsettingswindow,locatetheStudySettingssection.3 IntheTimeseditfield,type0,10(range(-4,1/3,-1).4 SelecttheRelativetolerancecheckbo*.5 Intheassociatededitfie

26、ld,type0.001.6 IntheModelBuilderwindow,clickStudy2.7 IntheStudysettingswindow,locatetheStudySettingssection.8 CleartheGeneratedefaultplotscheckbo*.9 OntheStudytoolbar,clickpute.RESULTS2DPlotGroup21 OntheResultstoolbar,click2DPlotGroup.2 In the2DPlotGroup settingswindow, locate theDatasection.3 Fromt

27、heDatasetlist,chooseSolution2.4 FromtheTime(s)list,choose0.002154.5 Onthe2DPlotGroup2toolbar,clickSurface.6 IntheSurfacesettingswindow,clickReplace E*pressionintheupper-rightcorneroftheE*pressionsection.Fromthemenu,chooseMagneticFieldsCurrentsandchargeInducedcurrentdensityInducedcurrentdensity,phipo

28、nent(mf.Jiphi).7 IntheModelBuilderwindow,right-click2DPlotGroup2andchooseArrowSurface.8 IntheArrowSurfacesettingswindow,locatetheArrowPositioningsection.9 Findthergridpointssubsection.InthePointseditfield,type50.10 Findthezgridpointssubsection.InthePointseditfield,type50.11 LocatetheColoringandStyle

29、section.FromtheColorlist,chooseWhite. z.-12 Onthe2DPlotGroup2toolbar,clickPlot.TheForceCalculationfeatureautomaticallyputedthetotalforceactingontheplateandcreatedaglobalvariablethatcanbeplottedasafunctionoftime.1DPlotGroup31 OntheResultstoolbar,click1DPlotGroup.2 Inthe1DPlotGroupsettingswindow, loca

30、tetheData section.3 FromtheDatasetlist,chooseSolution2.4 Clicktoe*pandtheLegendsection.FromthePositionlist,chooseLowerright.5 Onthe1DPlotGroup3toolbar,clickGlobal.6 IntheGlobalsettingswindow,clickReplaceE*pressionintheupper-rightcornerofthey-a*isdatasection.Fromthemenu,chooseMagneticFieldsMechanical

31、ElectromagneticforceElectromagneticforce,zponent(mf.Forcez_plate).7 Onthe1DPlotGroup3toolbar,clickPlot.Theplotshowsthatarepulsiveforceactsontheplateduringthetransient.Thefollowinginstructionse*plainhowtouseaRevolveddatasettoobtaina3Dplotfromthe2Da*isymmetricmodel. z.-DataSets1 OntheResultstoolbar,cl

32、ickMoreDataSetsandchooseSolution.2 IntheModelBuilderwindow,underResultsDataSetsright-clickSolution3andchooseAddSelection.3 IntheSelectionsettingswindow,locatetheGeometricEntitySelectionsection.4 FromtheGeometricentitylevellist,chooseDomain.5 SelectDomains24only.6 OntheResultstoolbar,clickMoreDataSet

33、sandchooseRevolution2D.7 IntheRevolution2Dsettingswindow,locatetheDatasection.8 FromtheDatasetlist,chooseSolution3.9 Clicktoe*pandtheRevolution layerssection.LocatetheRevolution Layerssection.IntheStartangleeditfield,type-90.10 IntheRevolutionangleeditfield,type255.3DPlotGroup41 OntheResultstoolbar,

34、click3DPlotGroup.2 Onthe3DPlotGroup4toolbar,clickSurface.3 IntheSurfacesettingswindow,clickReplace E*pressionintheupper-rightcorneroftheE*pressionsection.Fromthemenu,chooseMagneticFieldsCurrentsandchargeInducedcurrentdensityInducedcurrentdensity,phiponent(mf.Jiphi).4 IntheModelBuilder window,click3DPlotGroup4.5 In the3DPlotGroup settingswindow, locate theDatasection.6 FromtheParametervalue(freq)list,choose10.7 Onthe1DPlotGroup4toolbar,clickPlot. z.-8 ClicktheZoomInbuttonontheGraphicstoolbar. z.-. z.