3856 motor maxwell2d

7/30/2019 3856 Motor Maxwell2D

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TopicMotorApplicationNote

StudyofaPermanentMagnetMotorwith

MAXWELL2D:

Exampleofthe2004PriusIPMMotor


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Studyofanelectricalmachine

TheElectroMechanicalsoftwarepackageprovidedbyAnsoftenablesextensiveelectricalmalchinesimulation.ThisapplicationnotedetailsthesimulatonofanelectricalmachinewithMaxwel2D.Wewillcoverstaticandtransientsimulations.

Thisapplicationnotewillusethe2004ToyotaPriusmotorasbasis.Itisa8-polepermanentmagnetmotorwithembeddedmagnets.Thesinglelayerwindingsaremadeof3phases.Thestatorhas48slots.Thismotorispublic,wethereforehavethefullsetofparameters.WewillalsouseOakRidgeNationalLaboratorytestingresultsinthisnote.

Note:ThisapplicationhasnotbeendonewiththecollaborationofToyota

References:Report on Toyota/Prius Motor Torque Capability, Torque Property, No-Load Back EMF,and Mechanical Losses,J.S.Hsu,Ph.D.,C.W.Ayers,C.L.Coomer,R.H.Wiles

OakRidgeNationalLaboratory

Report on Toyota/Prius Motor Design and manufacturing AssessmentJ.S.Hsu,C.W.Ayers,C.L.Coomer


Evaluation of 2004 Toyota Prius Hybrid Electric Drive System Interim ReportC.W.Ayers,J.S.Hsu,L.D.Marlino,C.W.Miller,G.W.Ott,Jr.,C.B.Oland



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OverviewoftheStudy:

GETTINGSTARTED

Creatingthe3DModel

Reducingthesizeofthe3DModel

Materialpropertiesofthemachine

ApplyingMaster/SlaveBoundaryCondition

STATICANALYSIS

DYNAMICANALYSIS

COGGINGTORQUE


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GettingStarted

LaunchingMaxwell1. ToaccessMaxwell,clicktheMicrosoftStart button,selectPrograms>Ansoft>Maxwell 12.SettingToolOptions

To set the tool options:Note: Inordertofollowthestepsoutlinedinthisexample,verifythatthefollowingtooloptionsareset :

1. SelectthemenuitemTools > Options > Maxwell 2D Options2. MaxwellOptionsWindow:

1. ClicktheGeneral Options tabUseWizardsfordataentrywhencreatingnewboundaries:CheckedDuplicateboundarieswithgeometry: Checked

2. ClicktheOK button3. SelectthemenuitemTools > O ptions > M odeler Options.4. 3DModelerOptionsWindow:

1. ClicktheOperation tabAutomaticallycoverclosedpolylines: Checked

2. ClicktheDrawing tabEditpropertyofnewprimitives: Checked

3. ClicktheOK button


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OpeningaNewProjectTo open a new project:

1. InanMaxwellwindow,clickthe iconontheStandardtoolbar,orselectthemenuitemFile > New .

2. Rightmouseclickontheprojectname,thenselectthemenuitemRename.ChangetheprojectnametoPrius

3. SelectthemenuitemProject > Insert Maxwell Des ign, orclickontheicon

4. RightmouseclickonMaxwelldesign1andselectRename.Changethenameto1_Whole_Motor

5. ClickonthemenuitemMaxwell 2D > Solution TypeGeometryMode:Cartesion XYMagnetic:Transient

SetModelUnitsSelectthemenuitemModeler > Units. SelectUnits: mm (millimeters)


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Creatingthe2DModel

MaxwellhasnumberofUser Defined Primitives formotorparts.Theseprimitivescandescribeallthemainpartsofmotors.

CreatetheStator:AUserDefinedPrimitivewillbeusedtocreatethestator

Selectthemenuitem Draw > User Defined Primitive > Syslib > Rmxprt >SlotCoreUsethevaluesgiveninthepanelbelowtocreatethestator


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Creatingthe2DModel(Continued)

Clickonthejustcreatedobjectinthedrawingwindowandinthepanelontheleft

changeitsnamefromSlotCore1 toStatorNote:thematerialwillbeappliedafterwards

CreatetheRotor

AUserDefinedPrimitivewillbeusedtocreatetherotor

Selectthemenuitem Draw > User Defined Primitive > Syslib > Rmxprt >IPMCoreUsethevaluesgiveninthepanelnextpagetocreatetherotor


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Clickonthejustcreatedobjectinthedrawingwindowandinthepanelontheleft

changeitsnamefrom IPMCore1 toRotor

CreatetheMagnets

ThesameUserDefinedPrimitivecanbeusedtocreatethemagnets,butwith

differentparameters.UDPscanbecomputedtogeneratedifferenttopologies.

SelecttheobjectRotor.CopyandpastetheobjectusingtheCtrl+C,Ctrl+Vcommands.AnobjectRotor1 iscreated


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Onthemodelertree,doubleclickonthecommandCreateUserDefinedPartoftheobjectRotor1

ChangetheInfoCorelinefrom0(Core)to1(Magnets)

ChangethenameoftheobjectfromRotor1 toMagnetsChangethemagnetscolorfromdefaulttoalightred.


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CreatetheWindings

AnUserDefinedPrimitivewillalsobeusedtocreatethewindings.

Selectthemenuitem Draw > User Defined Primitive > Syslib > Rmxprt > LapCoilUsethevaluesgiveninthepanelbelowtocreatethecoil

ChangetheMaterialfromvacuum toCopperSelecttheobjectLapCoil1,changeitscolortoyellow


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SelecttheobjectLapCoil1,andtoapplyarotationof7.5 degalongtheZ axis,rightmouseclick,andselectthemenuitemEdit > Arrange > R otate orusetheicon.

SelecttheobjectLapCoil1.ThiscoilconstitutesthefirstcoilofPhaseA.WenowduplicatethiscoiltocreatethefirstcoilsofPhaseCandB.RightMouseclick,

andselectthemenuitemEdit > Duplicate > Around Axis orusetheicon.

ChangetheNameofobjectsLapCoil1_1 andLapCoil1_2 toPhaseC andPhaseB.ChangethecolorofPhaseC todarkgreenandthecolorofPhaseB tolightblue.RenameLapcoil1 toPhaseA.


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SelecttheobjectsPhaseA ,PhaseB andPhaseC.RightMouseclick,andselectthemenuitemEdit > Dup licate > Around Axis orusetheicon.Enter45degreesand8 forthetotalnumber.Thiswillcreatealltherequiredcoils.


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Thegeometryofthemotoriscompleted.

Dependingonthesolverandthemotorperformancedatathatwewanttolookat,wemighthavetoaddmoreobjects(formeshingormovementsetting).

Savetheproject.ClickontheMaxwelldesign1_Whole_motor,rightmouseclickandselectCopy.

Clickontheprojectname,rightmouseclickandselectPaste.Changethecopieddesignto2_Partial_motor.Wecantakeadvantageofthetopologyofthemotortoreducethesizeoftheproblem.Thismotorhas8pairofpoles.Wecanonlyuseoneheightofthemotor.Thisisvalidbecausethestatorhas:

48slots(8isadividerof48).

The3-phasewindinghasalsoaperiodicityof45degrees.

Fromnowon,theMaxwelldesign2_Partial_motorwillbeused.Wehavesavedacopyofthewholegeometryasitwillbeusedlaterforotherstudies.


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Reducingthesizeofthe2DModel(Continued)

Selectalltheobjectsfromthemodelertree(oryoucanusethectrl-A command).RightmouseclickandselectEdit > Boo lean > Split orusethetoolbaricon.SelecttheXZ planeandkeepthepositive side.

Note:Duringtheprocess,alotofmessageswillappearinthedialogbox.These

messagesinformthatsomeobjectsnolongerexistastheyentirelylieoutsidethe

remainingmodel.Weobtainhalfofthemotor.Maintaintheobjectsselected,rightmouseclickand

selectEdit > Arrange > Ro tate orselectthetoolbaricon.Enter-45 degfortherotationaroundtheZ axis.

Maintaintheobjectsselected,RightmouseclickandselectEdit > Boolean > Splitorusethetoolbaricon.SelecttheXZ planeandkeepthenegative side.Maintaintheobjectsselected,rightmouseclickandselectEdit > Arrange >Rotate orselectthetoolbaricon.Enter45 degfortherotationaroundtheZaxis


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The3Dmodelnowlookslikebelow

RenamePhaseA toPhaseA1 andPhaseA_7 toPhaseA2.RenamePhaseB ,PhaseB_7,PhaseC andPhaseC_7 toPhaseB1,PhaseB2,PhaseC1 andPhaseC2.WecannowcreatetheRegionaroundthemotor.Mostofthefluxisconcentratedwithinthemotor,sowedonotneedtohavealargeRegion.

SelectDraw > Line1. Usingthecoordinateentryfield,entertheboxposition

X: 0.0, Y: 0.0, Z: 0.0,PresstheEnter key2. Usingthecoordinateentryfield,entertherelativesizeoftheboxdX: 200.0, dY: 0.0, dZ: 0.0,PresstheEnter key3. ClickEnter asecondtimetofinishthedrawing


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SelectPolyline1.RightmouseclickandselectEdit > Sweep > Around Axis.Entertheparametersasspecifiedinthepanelbelow:

RenametheRegionfromPolyline1 toRegion.MakesurethatVacuumistheselectedmaterial.Also,youmightwanttomodifytherenderoftheRegion byincreasingthetransparency.


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Materialpropertiesofthemotor

PermanentMagnetscharacterization.

ThePriusPermanentMagnets(PMs)arehigh-strengthmagnets.

InordertodefinePMsmagnetizationorientation,weneedtocreateseparate

objectsforeachmagnet.SelecttheobjectMagnets.Rightmouseclick,selectEdit > Boolean > S eparate Bodies.RenametheobjectsfromMagnets toPM1andfromMagnets_Separate1 to PM2.Sincethemagnetswillrotate,theorientationcannotbegiventhroughfixedcoordinatesystems(CS).TheuseoffaceCSisrequired.FaceCSareCSthat

areattachedtothefaceofanobject.Whentheobjectmoves,theFaceCSalso

movesalongwiththeobject.

ThePriussPMsareorientedasshownbelow.Therefore,wewillcreateafaceCSforeachmagnet.

SwitchtheselectmodefromObjecttoFacebyclickingonthefbuttonorbyusingthetoolbaricon:


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Materialpropertiesofthemotor(Continued)

ThefaceCSiscreated.ItsdefaultnameisFaceCS1.ChangeitsnamefromFaceCS1 toPM1_CS .

RepeatthesameoperationtocreatethefaceCSPM2_CS attachedtoPM2.MakesuretohavetheXaxislookingtowardtheairgap

ResettheworkingCStotheGlobalCSbyclickingonGlobal asshownbelow.


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EdittheattributesoftheobjectPM1.ModifytheOrientationoftheobjectbyselectingthePM1_CS coordinatesystem.ThisCSwillbethereferenceforthemagnetizationdirection.

Toenterintothematerialdatabase,clickontheMaterialbutton(thedefault

materialisVacuum).ThePriusmagnetisnotpartofthedefaultlibrary,soclickontheAddmaterialbutton


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WehaveaspecialmenutoenterPermanentMagnetparameters.Atthebottom

oftheView/Editmaterialwindow,selectthePermanentMagnetentry.

Enterthevaluesgivenbelowtodefinethemagnetstrength


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ChangethematerialnametoN36Z_20.IfthecoordinatesystemPM1_CS issuchthattheX axis goesintheoppositedirectionoftheairgapaccordinglytotheimagebelow,leavetheXorientationto

1and0fortheYandZcomponents.IftheXaxiswasintheoppositedirection,

youwouldneedtoenter-1fortheXcomponent.

ClickontheValidatebuttonbeforeclosingthewindowtocheckthematerial

definition.

EdittheattributesoftheobjectPM2.ModifytheOrientationoftheobjectbyselectingthePM2_CS coordinatesystem.ThisCSwillbethereferenceforthemagnetizationdirection.IfthedefinitionofPM2_CSisconsistentwithPM1_CS(

Xaxisinthedirectionoftheairgap),youcanusethesamematerialforN36Z_20forPM2.Ifitisnotthecase,youcanclonethematerialN36Z_20 andchangetheorientationtobeconsistentwiththePM2_CS axis.


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Steeldefinition

Thestatorandrotorsharesthesamematerial.SelecttheobjectsStator andRotor.Edittheirattributes,changetheaffectedmaterial.Inthematerialdatabase,addanewmaterialcalledM19_29G.Thesteelisnonlinear.Toenterthenon-linearB-HCharacteristic,changethe

RelativePermeabilityfromSimpletoNonlinear

ClickontheBHcurvebuttonintheValuecolumn.TheBHcurveentrywindowappears


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EntertheB-Hcharacteristicswiththevaluesgivenbelow

H B

0 0

22.28 0.05

25.46 0.1

31.83 0.15

47.74 0.3663.66 0.54

79.57 0.65

159.15 0.99

318.3 1.2

477.46 1.28

636.61 1.33

795.77 1.36

1591.5 1.44

3183 1.52

4774.6 1.58

6366.1 1.63

7957.7 1.67

15915 1.8

31830 1.9

111407 2

190984 2.1

350138 2.3

509252 2.5

560177.2 2.563994494

1527756 3.779889874


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WeneglecttheEddycurrentinthisexample,thereforeweleavetheconductivity

to0.

ValidatethematerialbeforeexitingtheView/Editmaterialwindow

MakesurethatM19_29G isaffectedtotheRotor andStator.


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Coreloss

Thissectionisonlynecessaryifyouwishtocomputethecorelossofthemotor.

IntheTransientsolver,weareabletocomputecoreloss(orhystererisloss),

strandedlossandeddycurrentloss(orproximityloss).Wewillonlyconsider

corelossinthisdocument.

Weneedtoenterthelossvaluesofthesteel.Adedicatedmenuenablestheuser

toenterthedata.

Extendtheprojecttree,anddoubleclicktheMaterialdefinitionoftheSteel

M19_29G

UsethepulldownmenutoenablecorelossforElectrical Steel material


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Coreloss(Continued)

TheMaxwellsolverrequiresthecoefficientsKh,Kc,KeandKdc.Aspecialmenu

allowsthecoefficientstobederivedfrommanufacturercorelossdata

Selectatthebottomofthematerialdefinitionwindowfromthepulldownmenu

CoreLossversusFrequency

TheCoreLossversusFrequencymenupopsup.Weprovidethedataforseveral

frequencies:

1. SelectW/kg fortheCoreLossUnit2. Enter7872 kg/m3 fortheMassdensityoftheSteel3. Enter50 Hz intheEditwindow4. ClickonAdd5. ClickonEdit Dataset intheFrequencyWindow


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Coreloss(Continued)

Thecorelosscoefficientareautomaticallycalculated

Acceptthesetting.Thematerialdefinitionnowincludesthecorelosscoefficients


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ApplyingMaster/SlaveBoundaryCondition

TheMasterandSlaveboundaryconditiontakesadvantageoftheperiodicityof

themotor.Twoplanesaretobedefined:themasterandslaveplanes.TheH-

fieldateverypointontheslavesurfacematchesthe(plusorminus)H-fieldat

everypointonthemastersurface.

SelecttheobjectRegion fromtheactiveview.Rightmouseclick,thenselectView> Show In A ctive View asshownbelow

ChangetheSelectmodetoEdge

SelectoneoftheboundinglineoftheRegion


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ApplyingMaster/SlaveBoundaryCondition(Cond)

Rightmouseclick,selectAssign Boundary > Master

Thevectoruisdefinedcorrectly.Acceptthesetting.

SelecttheoppositeedgeoftheRegion


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ApplyingMaster/SlaveBoundaryCondition(Contd)

Rightmouseclick,selectAssign Boundary > Slave

1. Wefirstneedtogivethereferenceofthemastercondition.FortheMaster

Boundary,sincewehaven'tchangedthedefaultname,SelectMaster12. SelectSwap direction fortheuvectordefinitionifthevectorudoesnot

havethesamedirectionthantheuvectoroftheMastercondition.

3. Themodelrepresentsonepoleoutofheight.Sincewerepresentanodd

numberofpoles,theconditionattheslavesurfaceisSlave=-Master

4. Acceptthesetup


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ApplyingZeroVectorPotentialBoundaryCondition

AtthelimitoftheRegion,selectthefivesegmentsoftheoutsidelimitoftheRegion.UsetheCtrlbuttontoallowmultiselections

RightMouseClick,SelectAssign Boundary > Vector Potential

1. Put0 Weber/mforthevalue2. NametheconditionZero_Flux


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STATICANALYSIS

Wewillstudythedifferentstaticparametersofthemotor.

Savetheproject.ClickontheMaxwelldesign2_Partial_motor,rightmouseclickandselectCopy.

Clickontheprojectname,rightmouseclickandselectPaste.Changethecopied

designto3_Partial_motor_MS.

NoLoadStudy

Thefirstanalysisthatwillbeperformedconsistsincomputingthefieldsdueto

thepermanentmagnets.

TheCoilsarenotneededinthemodelsincenocurrentisdefined.Selectthe6

coils.Then,UnchecktheradiobuttonModelfromthepropertywindow.NotethattheNameofobjectlineisemptysincewehaveselectedseveralobjects.

LeavetheCoilsselected,andHidethecoilsbyselectingthemenuitemView >Hide Selection > Active view orusingthetoolbarbutton


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se

ApplyMeshOperations

Theadaptivemeshingisveryeffective,soitisnotnecessarytoenterdedicatedmeshoperations.However,itisalwaysagoodideatostartwithadecentinitialmeshinordertoreducetimecomputationsinceweknowwherethemeshneedstoberefinedforamotor.Thenonlinearresolutionwillbefasterwithasmallaspectratiosfortheelementsinthesteel.

SelecttheRotor.RightMouseClickandSelectAssign Mesh Operation > InsideSelection > Length Based

Restrictthelengthofelementsto5 mm.RenamethemeshoperationRotor

SelecttheStator.Wewanttominimizethenumberofelementsforthecurvedlineoftheslots.RightMouseClickandSelectAssign Mesh Operation > SurfaceApproximation.

Input30deg fortheMaximumsurfacedeviationSelect5 fortheMaximumaspectRatio.RenamethemeshoperationSA_Stator


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ApplyMeshOperations(Continued)

SelectPM1 andPM2.RightMouseClickandSelectAssign Mesh Operation >Inside Selection > Length Based

Restrictthelengthofelementsto3 mm.RenamethemeshoperationMagnets

ApplyTorquecomputation

SelecttheobjectsPM1,PM2 andRotor.RightmouseclickandselectAssignParameters > Torque


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AddanAnalysisSetup

Fromtheprojectmanager,rightmouseclickonAnalysis andselectAdd So lutionSetup:

1. Enter10forthemaximumnumberofpasses

2. Enter0.1%fortheerror

3. Intheconvergencepanel,enter15%fortherefinement

4. MakesurethattheNonResidualissetto0.0001%.ClickOktorecordthe

analysissetup

Analyse

RightmouseclickonthesetupetselectAnalyzeorclickontheicon.


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Postprocessing

Thecomputationtakes7passestoconverge.TheConvergencepanelcanbe

seenbyrightmouseclickingonSetup1,selectingthemenuitemConvergence

Torque value. SelecttheSolutionstab,thetorqueisgivenforaonemeterdepthmotor.Thetorqueforthefullmotorneedstobemultipliedby8(symmetryfactor),

thenby0.082(toaccountforthemotorlength).Thisgives2.5mN.m,which

soundsreasonable:thevalueisverysmallinregardstothefullloadoperation.

Differentanglesbetweentherotorandthestatorwouldgivedifferentvalues.


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PostProcessing(Contd)

Plot magnetic flux density.SelecttheRotor,Stator,PM1, PM2 rightmouseclick,selectAll Object Faces.Rightmouseclickagainandselect Fields > B > Mag_B.WeobtainthedistributionofB ontheobjects.Thesteelishighlysaturatedclosetothemagnetsasexpected.Thissaturationsappearsjustbecauseofthemagnetsstrengths.

Plot the magnetic flux strength H in the air gap.Weneedtodrawapost-processinglinetoviewthefield:

1. Drawanarc.SelectthemenuitemDraw>Arc>CenterPointorusethecorrespondingtoolbaricon

2. Accepttocontinuetodrawanonmodelobject.Thiswillnotinvalidatetheexistingsolution

3. Enterthecenterofthearc:0,0,0 mm andhitenter


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4. Enterthefirstpointofthearc.Thispointisatthemiddleoftheairgapon

theYZplane.Enter80.575, 0 , 0 mm andhitenter.

5. Enterthelastpointofthearc.ThispointliesontheplaneXY,witha45

anglewiththeX- axis.80.575/2=56.70996().Enter56.70996, 56.70996,0 mm andhitenter.

6. Tofinishthearc,movethemouseonthedrawingarea,rightmouseclick,

andselectthemenuentrydone

7. Namethepolylineairgap_arc andaccepttheobject


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8. AnewfolderLineshasappearedontheobjecttree,containingthenewdefinedarc.

9. Selectthelineairgap_arc,movethemouseonthedrawingarea,rightmouseclick,thenselectthemenuitemFields > H > H_vector.

10. AccepttheFieldplotsetting


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11. ThevectorplotofHappearswiththedefaultsetting.Tocustomizethe

display,doubleclickonthescalezone:

12. Youcanmodifythedefaultsettingsinthedifferenttabslikebelow:


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FullLoadStudy

Savetheproject.ClickontheMaxwelldesign3_Partial_motor_MS ,rightmouseclickandselectCopy.Clickontheprojectname,rightmouseclickandselectPaste.Changethecopieddesignto4_Partial_motor_MS2.Inthisdesign,weapplycurrentinthecoils:weneedtoincludethecoilsinthemodel.Selectthe6coilsfromthemodelertree.Inthepropertywindow,selecttheradiobuttonModel.

UnhidethecoilsbyselectingthemenuitemView> Show se lections> All views

ApplyExcitations

Thecoilsarepartiallyrepresentedinthemodel.Weneedtoenterthecurrentthatflowsinandoutinsideeachcoil.Theexcitationisrealizedthroughabalancedthreephasesystem.Forinstance,inourexample,weapply:

1500AtoPhaseA

-750AtoPhaseB

-750AtoPhaseC.

IntheMagnetosaticsolver,thesourcesaregivenintermsofcurrents.Wedonotneedtomodeleachturnatthisstage;thereforeweonlyenterthetotalcurrentineachphase.Thenumberofturnsandtheelectricaltopologyareonlytakenintoaccountfortheinductancescalculation.


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ApplyExcitations(Contd)

Switchtheselectionmodetoface

EnterExcitationforCoilPhaseA2:1. SelectthePhaseA2

2. Rightmouseclick,selectthemenuitemApply Exc itation > Current3. RenametheExcitationPhaseA24. Enter1500A5. Asthedefaultcurrentdirectionplottedinredisgood,leavePositive6. ValidatetheExcitation


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EnterExcitationforCoilPhaseA11. SelectthePhaseA1

2. Rightmouseclick,selectthemenuitemApply Exc itation > Current3. RenametheExcitationPhaseA14. Enter1500A5. Asthedefaultcurrentdirectionplottedinredisgood,leavePositive6. ValidatetheExcitation


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EnterExcitationforCoilPhaseC21. SelectthePhaseC2

2. Rightmouseclick,selectthemenuitemApply Exc itation > Current3. RenametheExcitationPhaseC24. Enter-750A5. Asthedefaultcurrentdirectionplottedinredisnotgood,chooseNegative6. ValidatetheExcitation


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EnterExcitationforCoilPhaseB21. SelectthePhaseB2

2. Rightmouseclick,selectthemenuitemApply Exc itation > Current3. RenametheExcitationPhaseB24. Enter-750A5. Asthedefaultcurrentdirectionplottedinredisgood,leavePositive6. ValidatetheExcitation


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EnterExcitationforCoilPhaseB11. SelectthePhaseB1

2. Rightmouseclick,selectthemenuitemApply Exc itation > Current3. RenametheExcitationPhaseB14. Enter-750A5. Asthedefaultcurrentdirectionplottedinredisgood,leavePositive6. ValidatetheExcitation


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Inductancecomputation

Weareinterestedbytheinductancescomputation.Thesourcesetupis

independentfromthewindingarrangement:wehaveonlyenteredthe

correspondingamp-turnsforeachterminal.Whenlookingattheinductances,we

obviouslyneedtoenterthenumberofturnsforthecoilsandalsohowthecoils

areelectricallyorganized.

SelectParametersintheprojecttree,rightmouseclickandselectAssign >Matrix

Includethe6phasesinthematrixcomputation.Theinductancesarecomputed

for1turnatthisstage.

SelectthePostProcessingtab.Wedefineinthispanelthenumberofturnsfor

eachcoil.Enter9 forthesixcoils.Wealsowanttogroupallthecoilsofthesamephase.Thiswillenableustohavetheinductanceoftheentirewinding


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Inductancecomputation(Contd)

SelectthePhaseA1_in andPhaseA2_in entries,theyhitthegroupbutton.NameThegroupPhaseA

Repeattheoperationforthe3phases

AnalyseRightmouseclickonthesetupetselectAnalyzeorclickontheicon.


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Postprocessing

Thecomputationtakes6passestoconverge.TheConvergencepanelcanbe

seenbyrightmouseclickingonSetup1,selectingthemenuitemConvergence

Inductancevalues.SelecttheSolutions tab.Theinductanceforeachcoilsappears.Itisassumedthateachcoilhasonlyoneturn.


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Postprocessing(Contd)

SelecttheradiobuttonPost Processed.Theinductanceforeachwindingisdisplayed

Note: itispossibletoexporttheinductancematrixtoSimplorerusingtheExportCircuit button

Torque value. SelecttheSolutionstab,SelectfromthepulldownmenuTorque1.Thetorqueforthefullmotorneedstobemultipliedby8(symmetry

factor),thenmultipliedby0.083(lengthofthemotor).Thisgivesaround47N.m.

Inthiscase,wehavenotsynchronizedthepositionoftherotorpoleswiththe

windingcurrents,sowearefarfromtheoptimizedexcitationvaluetoobtaina

maximumtorque.Differentanglesbetweentherotorandthestatorwouldgive

differentvalues.


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Plot the H field on the plane XY.SelecttheplaneXYbelongingtotheglobalCoordinateSysteminthemodelertree

Movethemousepointertothedrawingarea,rightmouseclickandselectthe

menuitemFields > H > H_vector

Validatethesetting


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Withthedefaultparameters,theHvectorsaretoosmall.Doubleclickonthe

scalezone

OntheColorMaptab,unchecktheReal time mode buttonandchangethenumberofcolorsto50

OntheScaletab,ChecktheUse Limits button,thenEnter1 and1e6 forthelimits.Also,ChecktheLog buttontohavealogscale.


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OntheMarker/Arrowtab,reducethesizeofthearrow,thenunchecktheMapsize andArrow tail buttons.OnthePlotstab,makesuretherightplotcontextisselected,thenmodifytheVectorplotminandmaxto1and5

Weobtainthefollowingplot.TheHfieldisstrongeraroundphaseAastheinput

currentishigher.


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DYNAMICANALYSIS

Wewillstudythetransientcharacteristicofthemotor.

Savetheproject.ClickontheMaxwelldesign2_Partial_motor,rightmouseclickandselectCopy.


designto5_Partial_motor_TR.

Selectthedesignnamefromtheprojectmanager,Rightmouseclickandchange

thesolutiontypefromMagnetostatic toTransient:


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ThetransientsolveractsdifferentlyfromtheMagnetostaticsolvermainly

because:

Thereisnotadaptivemeshing.Sincethegeometrychangesateverytime

step,Maxwelldoesnotre-meshateverytimestepadaptivelyforobvious

timereason.Intransientanalysis,wewillbuildagoodmeshvalidforallthe

rotorpositions.

Thesourcesdefinitionisdifferent.InMagnetostatic,wewereonly

interestedinthetotalcurrentflowingintoconductor.InTransient,weuse

strandedconductors(theexactnumberofconductorsisrequiredforeach

winding)asthecurrentcanbeanarbitrarytimefunction.Weneedtocreate

dedicatedcoilsandwindings.

CreateCoils

Selectthe6coilsPhaseA1, PhaseA2, PhaseB1, PhaseB2, PhaseC1 andPhaseC2.RightmouseclickandselectthemenuitemAssign Exc itation > Coil

1. Leavethedefaultnameasitwillbeautomaticallyaffectedusingthe

objectsname

2. Enter9forthenumberofconductors


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CreateCoils(Contd)

Thesixcoilsdefinitionsareprocessed.

WeneedtochangetheorientationofthecoilsforPhaseC1 andPhaseC2:1. SelectPhaseC1,intheProjectManagerTree2. RightmouseclickandselectProperties

3. SwitchthepolarityfromPositive toNegative4. Repeat1-3withCoilPhaseC2


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Motorexcitation

TheIPMmotorissuchthattherotorisinsynchronismwiththephaseexcitation.

Theexcitationissuchthatthefluxduetothepermanentmagnetismaximizedin

synchronizationwiththerotormovement.

Theexcitationisa3phasebalancedcurrent.ThephasesequenceisA+C-B+

Att=0,theA-phasehastobeintheoppositeaxistothed-axis.Thereforewe

havetomovetheinitialpositionoftherotorby30degsuchthatthepolebe

alignedatthemiddleofA+A-

A+ A+

A-A-

B+B+

B- B-+C+A- A-

C- C-

B-

C+C+

d-axis B-

30

Maxwell modelparts


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CreateParametersforexcitations(Contd)

Thedesignpropertiespanelwilleventuallylooklike:

CreateWindings

Theterminalsaremeanttodefinetheexcitationpathsinandoutofthemodel.

Theactualexcitationisdefinedthroughthedefinitionofwindings.Awinding

needstobedefinedforeachparallelelectricalexcitationofthemotor.

Themotorisexcitedwithabalancedthreephaseconnection.Asinusoidalexcitationisapplied.Ateachtimestep,thephaseshavea120degreeshift.The

loadangleisalsoadded.


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CreateWindings(Contd)

Winding PhaseA..Fromtheprojecttree,rightmouseclickonExcitations,thenselectthemenuitemAdd W inding

1. EnterPhaseA forthename.2. SelectStrandedbecauseeachterminalhas 9 turns3. Enterwindingcurrent:Imax*sin(Omega_rad*Time+Thet). Time isthe

internalreservedvariableforthecurrenttime.

4. ClickonOK

5. RightmouseclickonthewindingPhaseA fromtheprojecttree,selectthemenuitemAdd Coils

6. Selectthe2PhaseA coils(usingtheCtrlbutton)andclickonOK


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CreateWindings(Contd)

Winding PhaseB..Fromtheprojecttree,rightmouseclickonExcitations,thenselectthemenuitemAdd W inding. Repeatthesameoperationusing:

NametheWindingPhaseBThewindingcurrentis Imax*sin(Omega_rad*Time-2*pi/3+Thet). Itisshiftby-120degreesfromPhaseA.

Selectthe2PhaseB tcoils

Winding PhaseC..Fromtheprojecttree,rightmouseclickonExcitations,thenselectthemenuitemAdd W inding. Repeatthesameoperationusing:

NametheWindingPhaseCThewindingcurrentis Imax*sin(Omega_rad*Time+2*pi/3+Thet). Itisshiftby+120degreesfromPhaseA.

Selectthe2PhaseC coils

TheprojecttreeshouldnowhavetheterminalssortedundereachWinding:


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AddCorelosscomputation

Thecorelossarenotactivatedbydefault.Ifyouwishtohavethemconsidered,

expandtheprojecttreewindow,rightmouseclickonExcitations> Set Core Loss

Selectthesteelobjects:Stator,Rotor,Rotor2andRotor3

AccepttheSetting

Note:youneedtohavethecorelossparametersdefinedinthematerialsetup


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AddBandobject

Themovingparts(rotorandpermanentmagnets)needtobeenclosedinanair

object,theband.Thiswillseparatedthemovingpartfromthefixedpartofthe

project.Somerulesapplyforthedefinitionofthebandobjectformotor

applications:

Thebandobjectmustbesomewhatlargerthantherotatingpartsinall

directions(exceptattheboundaries)

Thebandobjectshouldbeafacettedtypecylinderofwedge

Itisveryadvisabletohaveanairobjectthatenclosesallthemovingobject

insidethebandobject.Thiswillfacilitatethemeshhandlingaroundtheairgap

TocreatetheBandobject,wewillclonetheregionandadapttheparameters:

1. SelecttheobjectRegion,RightMouseclick,thenSelectEdit>Copy

2. UsetheCtrl+V keycombinaisontopastetheRegion.3. ChangethenameoftheobjectfromRegion1 toBand4. ExpandthehistorytreeoftheObject


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AddBandobject(Contd)

5. DoubleclickontheCreateLine command.Therotorradiusis80.2mm.Theinnerdiameterofthestator80.95mm.WepickthemiddleforBandobject.

Enter80.575,0,0 mminsteadof200,0,0forPoint2

6. DoubleClickontheSweep A roundAxis command.7. ChangetheNumber of Segments from5 to45 sothateachsegmentofthe

linecoversonedegree

8. LeavethematerialtoVacuum .


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AddBandobject(Contd)

WenowcreateanobjectthatenclosedthemovingobjectsinsidetheBand.SelecttheBand object,rightmouseclick,theselectthemenuitemEdit > CopyoruseCtrl-C.PasteanothercopyoftheBandobjectbyrightmouseclickingandselectingEdit> Paste orwiththeCtrl-V.AnewobjectBand1 hasbeenaddedtotheobjectlist.Expanditshistorytree,thendoubleclickontheCreateLine command

EditthePoint2:Enter80.4, 0, 0 mmThisoperationresizestheobjecttostrictlycovertherotorandthepermanent

magnets

RenametheBand1 objecttoBand_in

Note:Wewillassignthemotionafterthemeshoperationsbecausewewillhavetoaddobjectsdedicatedtothemeshinginthemovingpart


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MeshOperations

Thetransientsolverdoesnotuseadaptivemeshingbecausethiswouldrequire

torefinethemeshateverytimesteps,leadingtoveryhighcomputationtime.

UsingMeshoperations,wewilldefineadecentmeshforthefulltransient

simulation.

TheRotorisdesignedtobehighlysaturatedaroundthepermanentmagnets,

closetotheairgap.Itisrequiredtohaveagoodmeshdensityaroundthisarea.

Toachievethisrequirement,wecreateacoupleofobjectsinsidetherotor,then

meshoperationswillbeappliedtotheseobjectsinordertohaveanicemesh

aroundtheducts.

SelectthemenuitemDraw > Line orselecttheiconfromthetoolbar.1. Enter78.72,0 ,0 mmforthepositionofPoint1andhitEnter2. Enter80.2,0 ,0 mmforthepositionofPoint2andhitEntertwice3. NamethelineRotor2

Highly saturated zones


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MeshOperations(Contd)

Thelinelookslikebelow:

SelecttheRotor2 object,rightmouseclickandselectthemenuitemEdit >Sweep > A round Axis.

Entertheparametersasbelow.NotethatTheRotor objecthasbeencreatedwithanUDPwhichproducestruesurface,thereforeourmesh

objectRotor2 hastohavetruesurfaces.Asaconsequence,weenter0 forthenumberofsegments.


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ChangethematerialpropertyofRotor2 toM19_29G .Also,assignsomecolorandtransparency.

Note:sinceRotor2 isentirelyinsideRotor,wedonotneedtoapplyBooleanoperations.

Note:becauseofthefinitenumberofpixelsonthecomputersscreen,truesurfacesarerepresentedasfacettedsurfaces.Also,forthesamereason,the

objectRotor2 seemstointersectwiththeductsbutthisisnotthecase.Youcanmodifythedefaultvisualizationsettingusing:View > Visualization Setting

RepeatthesameoperationtocreatetheobjectRotor3:1. Drawalinewithdimensions:

2. SweeptherectanglearoundZaxis

3. ChangethematerialpropertytoM19_29G


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SelectthesixcoilsPhaseA1, PhaseA2,PhaseB1,PhaseB2,PhaseC1 andPhaseC2.Rightmouseclick,selectAssign Mesh Operations > Inside Selection >Length Based.

1. NametheoperationCoils2. CheckthebuttonRestrictLengthofElements

3. Enter4mm4. UncheckthebuttonRestricttheNumberofElements

5. Validate

SelectthepermanentmagnetsPM1 and PM2.Rightmouseclick,selectAssignMesh Operations > Inside Selection > Length Based .

1. NametheoperationPMs2. CheckthebuttonRestrictLengthofElements


5. Validate


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SelecttheRotor.Rightmouseclick,selectAssign Mesh Operations > InsideSelection > Length Based.

1. NametheoperationRotor2. CheckthebuttonRestrictLengthofElements


5. Validate

SelecttheStator.Rightmouseclick,selectAssign Mesh Operations > InsideSelection > Length Based.

1. NametheoperationStaor2. CheckthebuttonRestrictLengthofElements


5. Validate


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AssignMovement

SelecttheBand object,rightmouseclickandselectthemenuitemAssignBand

IntheType tab:checktheRotate motionbuttonMakesurethattheGlobal:Z axisisselectedSelectthePositive direction

IntheData tab:Enter30 deg fortheinitialposition.TheinitialpositionofthissynchronousmotorissuchthattheAphaseisoppositetothed-

axis.

A+

A-

d-axis

30


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AssignMovement(Contd)

IntheMechanicaltab:

enter3000 rpm forthespeed.ClickOKtovalidatethesettingoftheBandobject.

RightmouseclickonModel intheProjecttree,thenselectthemenuitemSetSym metry Multiplier

Sincewemodel1/8 th ofthemotor(ourmodelspanson45),Enter8.Theforce,torquewillberescaledtotakeintoaccountthefullmodel.

SelecttheModel Depth tab.Enter83.82mm forthemotordepth.Allquantitieswillbeautomaticallyberescaledtothecorrectsize.

Acceptthesetting


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AddanAnalysisSetup

RightmouseclickonAnalysisintheProjecttreeandselectAddSolutionSetup:

1. OntheGeneral tab enterthestoptimeandthetimestep.At3000rpm,arevolutiontakes20ms(3000rpmmeans50revolutionspersecondor1/50

sforonerevolution).Toachievereasonableaccuracy,wewanttohavea

timestepevery1or2degrees.Inthisstudy,tohavefasterresults,weuse

atimestepof250 us;itcorrespondsto4.5degrees.2. Thetotalsimulationtimeissetto15ms3. OntheSave F ields tab

SelectLinearStep

ForStart,put10ms

ForStop,put15ms

ForStepTime,put250us

ClickonReplaceList

4. IntheSolver Tab,settheNonlinearresidualto1e-6.


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Solvetheproblem

Thesetupiscompleted.ChecktheprojectusingtheValidatebutton

Maxwellchecksthegeometry,excitationdefinitions,meshoperationsandso

one.ThemodelisvalidatedbutsomeWarningisdisplayedinthemessagebox:

Eddyeffectarenottakenintoaccountinourdesignwhichiswhatwe

decided

SelecttheAnalysisSetup1 intheprojecttree,rightmouseclickandselectAnalyse


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PostProcessing

Thefullsimulationtakessomeminutes.

Themeshsizeappearsintheprofileofsimulation.Todisplaytheprofile,selecttheAnalysisSetup,rightmouseclickandselectMesh Statistics.Themeshstatisticsareavailableinthecorrespondingtab

Performancecurvescanbedisplayedduringthesimulation.

Torque versus Time.SelectthemenuitemResults intheprojecttree,rightmouseclick,thenselectthemenuitemCreate Quick Report

ChooseTorqueTheTorqueuptothecurrenttimeisdisplayed.Asthesimulationcontinues,you

canupdatetheplots:rightmouseclickontheTorque Quick Report entryandselectUpdate Report


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AttheendofthesimulationtheTorquelookslikebelow

TheLoadTorque (inred)iszeroasweareinmotormode.WecanseethattherearealotofripplesintheTorque.Theratiobetweenthe

torqueandthetorqueripplesisalmost10percent.Thisisduetotheunique

structureoftheIPMmotor(InternalPermanentMagnets).Tolimittheripple,

somemanufacturersmodifyslightlytherotorshapearoundthemagnetsoradda

secondlayerofinternalmagnets.Alsothecontrolstrategyplaysabigroleintopreventingtheripples.

Thetorquevalueisaround240N.m.Thisvalueiscompatiblewithmeasurement.

Thepeaktorqueforthismotorisabout400N.m

Flux linkage versus Time .SelectthemenuitemResults intheprojecttree,rightmouseclick,thenselectthemenuitemCreate TransientReport >RectangularPlot.

0.00 5.00 10.00 15.00 20.00

Time [ms]

0.00

50.00

100.00

150.00

200.00

250.00

300.00

Y1[NewtonMeter]

Ansoft Corporation 5_Partial_Motor_TRTorque Quick Report1

Curve Info

Moving1.LoadTorque

Setup1 : Transient

Moving1.Torque

Setup1 : Transient


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Toincludethefluxlinkageforeachcoil:

1. SelectWindingintheCategory Column2. SelectFluxLinkage(PhaseA), FluxLinkage(PhaseB), FluxLinkage(PhaseC)

intheQuantity column3. SelectNew R eport4. SelectClose

0.00 5.00 10.00 15.00Time [ms]

-0.40

-0.30

-0.20

-0.10

0.00

0.10

0.20

0.30

0.40

Y1[Wb]

Ansoft Corporation 5_Partial_Motor_TRXY Plot 2

Curve Info

FluxLinkage(PhaseA)

Setup1 : Transient

FluxLinkage(PhaseB)

Setup1 : Transient

FluxLinkage(PhaseC)

Setup1 : Transient


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Induce Voltage versus Time .SelectthemenuitemResults intheprojecttree,rightmouseclick,thenselectthemenuitemCreate TransientReport >Rectangular Plot.UsethesamemethodtoplottheInducedVoltage

Thecurvesarenotreallysmooth.Thereasonisthatthetimestepistoohigh.As

theinducedvoltageisaderivedquantity,Maxwellneedstoderivethetotalflux;

thetimestepsiswaytohightohaveaccurateInducedVoltage.Ifyourerunthe

simulationwithatimestepsof50us(insteadof250us),theInducedVoltagewill

haveamorerealisticshape:

0.00 5.00 10.00 15.00Time [ms]

-500.00

-400.00

-300.00

-200.00

-100.00

0.00

100.00

200.00

300.00

400.00

500.00

Y1[V]

Ansoft Corporation 5_Partial_Motor_TRXY Plot 1

Curve Info

InducedVoltage(PhaseA)

Setup1 : Transient

InducedVoltage(PhaseB)

Setup1 : Transient

InducedVoltage(PhaseC)

Setup1 : Transient

0.00 5.00 10.00 15.00Time [ms]

-500.00

-400.00

-300.00

-200.00

-100.00

0.00

100.00

200.00

300.00

400.00

500.00

Y1[V]

Ansoft Corporation 5_Partial_Motor_TR_smallXY Plot 1

Curve Info

InducedVoltage(PhaseA)

Setup1 : Transient

InducedVoltage(PhaseB)

Setup1 : Transient

InducedVoltage(PhaseC)

Setup1 : Transient


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Plot the Mesh. Selectalltheobject,rightmouseclickandusethe Plot Meshbutton

Plot magnetic flux density.1. SelectthemenuitemView>SetSolutionContextordoubleclickonthe

Time=-1iconinthemodelerwindow

2. Selectthetime0.01s fromthepulldownmenu


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3. SelecttheStator, Stator2, Stator3, PM1 and P M2 objects.RightmouseclickandselectFields > B > Mag B

4. AccepttheSetting

5. TheBfieldat0.01sisdisplayed.

6. ChangethescalebydoubleclickingontheScaleaera

7. GototheScaleTabandenter0 forminand2.2 formax8. ClosetheWindow


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Plot magnetic flux density (Animation). Itispossibletoanimatethefields.SelectMaxwell2D>Fields>Animate.

MakesurethatthesweepvariableisTime

Selectthetimevalues

Acceptthesetting

Theanimationisdisplayedoncetheframesarecalculated.

YoucanexporttheanimationusingtheExport buttonfromtheanimationbutton


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ParametricStudy

Thesetupthathasbeensolvedwaswithaloadangleof20deg.Iftheloadangle

ismodified,thesimulationhastoberestarted.

Aparametricsweepoftheloadanglewillthereforetakealongtime.Wecan

proposetwoapproaches:

RealizeanEquivalentCircuitExtractionofthemotor.Thismethodrequires

thecombinationofparametricsweepsinmagneto-staticandthecircuit

simulatorSimplorer.Wewillnotdiscussthismethodinthiswrite-up.

Realizeaparametrictransientsimulation.Tocutthesimulationtime,the

useoftheDistributiveSolveisnecessary.Thisisthechosenmethod

ClickonOptimetrics intheProjecttree.RightmouseclickandselectthemenuitemAdd > Parametric

Theparametricsetuppanelappears


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ParametricStudy(Contd)

SelecttheAdd buttontoincludeadesignvariableinthesweep

SelectThet_deg fromthepull-downmenu:1. Enter0 deg forthefirstvalue2. Enter60 deg forthelastvalue3. Enter15 deg forthestep4. PushtheAdd button

SelecttheTabletab,theparametricrowsaredisplayed


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SelecttheGeneralTab.Thispanelenablestheusertochangeadesignvariable.Forinstance,ifyouwishtoruntheparametricsweepwithapeak

windingcurrentof400 A,selecttheOverride button,andchangethecurrentvalue.

SelecttheCalculations Tab1. SelecttheSetup Calculations button2. UndertheCategory column,selectTorque3. UndertheQuantity column,selectMoving1.Torque4. selecttheRange Function button.5. SelecttheSpecified radiobutton6. SetecttheMath Category7. Selectavg intheFunctionpulldownmenu8. Clickonok

9. ClickonAdd Calculation10. ClickonDone


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Thesweepsetuppanelcontainsthedesiredquantity

IntheOptionstab,youcanchoosetosavefieldsandmeshsforallthevariations

Acceptthesetup

Run the parametric sweep.Torunthesweep,selecttheParametricsetup1,rightmouseclickandselectthemenuitemAnalyse

Results.RightmouseclickonParametricsetup1,andselectView Analysis Resu lt

Alltheplotsarenowavailableforanyvariation


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COGGINGTORQUE

TheCoggingTorquecorrespondstothetorqueduetotheshapeoftheteethand

thepermanentmagnets,whenallthecoilsexcitationsare0.Thetorqueisavery

smallvalueinregardtothefullloadtorque.Itscomputationisverysensitiveto

themesh,asitsvalueisinthesameorderofmagnitudeofthemeshnoise.

TocomputeaccuratelythecoggingTorque,onecouldsolveaparametricsweep

inMagnetostatic(theinputparameterbeingtheanglebetweenrotorandstator).

Thismethodwillnotleadtoexcellentresultsastheerrorduetothemeshwillbedifferentforeachposition(themeshwillchangeforeveryrow).

Thepreferredmethodistheuseofthetransientsolverwithmotion:

Wewillmovetherotoratthespeedof1deg/s

ThemeshwillremainunchangedforallthepositionsthankstotheBand

object:themeshinsidetheBandobjectwillrotatewiththerotor

Eachtimestepwillbeindependentoftheother

Theadaptivemeshwillnotbeusedthereforethesimulationtimewillbe

shorter

Savetheproject.ClickontheMaxwelldesign5_Partial_motor_TR ,rightmouseclickandselectCopy.


designto6_Partial_motor_CT


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CreationofanairObject

WederivethesetupforthecoggingtorquecalculationfromtheFullloadsetup.

Wewillchangethespeed,theexcitationsandsomemeshingoperations.

Sincethemeshhastobewelldefinedintheairgap,wewilladdanobjectsothat

wehaveenoughlayersofelement:

1. CopyandPastetheObjectBand_in

2. RenametheobjectBand_in1intoBand_out.

3. ExpandthehistorytreeofBand_outandchangetheCreateLinecommand:

Replace80.4,0,0by80.75,0,0mm

Thiscreateathirdlayerintheairgap

Stator

Band_out

Band

Band_in

Rotor2

Rotor3

Rotor


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Increasethesegmentationofairobjects

Forthedynamicanalysis,theojectsBand,Band_in hadonesegmenteverydegre.Inordertoreducemesherror,wereducethespanofeachsegment.

ExpandthehistorytreeoftheobjectsBand,Band_in andBand_out:1. DoubleclickontheSweepAroundAxis commandoftheBand object

2. Changethenumberofsegmentsfrom 45 to1353. Repeat1-2fortheobjectsBand_in, Band_out


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MeshingOperations

WeneedtoreassigntheBand.Expandtheprojecttreeofthecurrentdesign,anddeletetheMotionSetup1

SelecttheObjectBand,rightmouseclick,andselectAssign Band

EnterthefollowingparametersfortheMotionSetup

IntheTypeTab,forMotionType:Rotation around Z axisLeavetheData tabunchangedIntheMechanical tab ,enter1 deg_per_secAccepttheSetting


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MeshingOperations

Wealsoneedtochangethemeshingoperations.Themeshdensitythatwas

goodenoughtocomputethefullloadtorquewontbeaccurateenoughforthecoggingtorque

Expandtheprojecttree,andunderMeshoperations,edittheMeshingoperations

Rotor,Stator:Changethemaximumlengthfrom4mm to3mm

SelecttheobjectsRotor,Rotor2 ,Rotor3 andStator.RightmouseclickandselectAssignMeshOperation>SurfaceApproximation

NamethemeshingoperationSA_Rotor_Stator

Settheminimumnormaldeviationto1deg

Ignoretheothersettings


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Analyse

Fromtheprojecttree,rightmouseclickonSetup1,andselectAnalyse.Ittakesacoupleofminutestosolve

Fromtheprojecttree,rightmouseclickonResults,andselectCreate TransientReport > Rectangular plot. TheTracewindowpopsup

FromtheCategory columnselectTorqueFromtheQuantity column,selectMoving1.TorqueSelectNew R eportSelectClose

TheTorquetraceappears.Asexpected,thecoggingtorqueisperiodical.The

peak value is about

3856 motor maxwell2d

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