2_Electromagnetic fundamentals.pdf

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1、2.2.ElectromagneticfundamentalsElectromagneticfundamentalsDARMSTADTDept.ofElectricalEnergyConversionUNIVERSITYOF2/1TECHNOLOGYProf.A.BinderAMPERE´slaw:ExcitationofmagneticfieldbyelectriccurrentExample:TwodifferentcurrentsI,Iwith12rrtwodifferent∫H⋅ds=Θnumbersofturns1a

2、ndNandtwoCdifferentflowdirections:AmpereturnsΘ:Θ=NI-I12•TheintegrationofmagneticfieldstrengthHalongclosedloop(curveC),whichspanstheareaA,isequaltotheresultingcurrentflow(AmpereturnsΘ)penetratingthroughtheareaA.•Positivefielddirectionisconnectedtopositivecurrentflowd

3、irectionbyRIGHTHANDRULE.DARMSTADTDept.ofElectricalEnergyConversionUNIVERSITYOF2/2TECHNOLOGYProf.A.BinderLawofmagneticfluxonclosedsurfaces•ThetotalmagneticfluxΦonclosedsurfaceAofvolumeVisalwaysZERO!rr∫B⋅dA=Φ=0AB:Magneticfluxdensity•NormalcomponentofB-vectoronbothside

4、sofsurfaceAisidentical:Bn,1=Bn,2•Magneticfieldhasalwaysnorth-ANDsouthpoles:NOmagneticmonopoles!•Minimumpolenumberis2:Onenorthandonesouthpole(Example:Earthmagneticfield!•Numberofmagneticpoles2p(polepairnumberp=1,2,3,...means2,4,6,...poles).DARMSTADTDept.ofElectricalE

5、nergyConversionUNIVERSITYOF2/3TECHNOLOGYProf.A.BinderMagneticfieldofcurrentexcitedcoilinairgaprr•AMPERE´slaw:H⋅ds=2H∆+2Hδ=2Hδ=Θ∫FeFeδδC−7•Bδ=BFe⇒HFer=BrFe/µFe=0(µFe=∞)undHδ=Bδ/µ0(µ0=Vs/Am)4π⋅10•FieldvectorsH,Binairgap:onlydominatingradialcomponentsconsidered!ΘNcIc•N

6、umberofturnsofcoilN,coilcurrentI:B=µH=µ=µccδ0δ002δ2δDARMSTADTDept.ofElectricalEnergyConversionUNIVERSITYOF2/4TECHNOLOGYProf.A.BinderMagnetomotive“force”V(x)andcurrentlayerA(x)•AsH=0(µ→∞):fieldlinesofHstartandendatironsurfaces:FeFeδV(x)δ“magnetomotiveforceV"inairgap:

7、V=H⋅δ⇒B(x)=µ0δδδδΘ•”currentlayer"A(x):A=liminslotregion,Aintoothregion=0b→0bb:slotwidth:hereb=0forsimplification!•CalculationofBwithuseofcurrentlayerA(x):δxµ0µ0()Bδ(x)=µ0Hδ(x)=∫A(x)dx=V(x)−V0δδ0•TotalmagneticfluxatclosedsurfaceAHsurroundingrotorinairgapiszero⇒Thisde

8、terminesintegrationconstantV.0rr2pτpB⋅dA=lB(x)dx=0∫Fe∫δAHx=0DARMSTADTDept.ofElectricalEnergyConversionUNIVERSITYOF2/5TECHNOLOGYProf.A.Bind