电机学（第七版）（修订版）课件 Chapter-1-Magnetic-Circuits-and-Magnetic-Materials

Chapter1MagneticCircuitsandMagneticMaterials7/10/2024MagneticCircuitsandMagneticMaterials1IntroductionThemagneto-quasi-staticformofMaxwell’sequationsareusedatlowfrequenciestypicalofenergy-conversiondevicesAmpere’slawandGauss’slaw:7/10/2024MagneticCircuitsandMagneticMaterials2CoilorwindingofNturnsonamagneticcoreofhighpermeabilitym>>moFluxismostlyconfinedtothecoreSimplifyAmpere’slaw:coilMMF=Ni7/10/2024MagneticCircuitsandMagneticMaterials3Gauss’slaw:fluxlinesareclosed,sonetfluxisfluxdensityBctimecross-sectionalareaAc Fc=BcAcSinceweareusingaveragefluxdensityBcthenthecorrespondingaveragemagneticfieldintensityHcwillbeapproximately7/10/2024MagneticCircuitsandMagneticMaterials4lcistheaverage(mean)corelengthwhichisperpendiculartothecross-sectionalareaAcThematerialpropertiesgivetherelationbetweenBandH,suchasB=mHforalinearmaterial7/10/2024MagneticCircuitsandMagneticMaterials5Magneticcircuitwithairgap7/10/2024MagneticCircuitsandMagneticMaterials6AnalogybetweenDCelectriccircuit(a)andmagneticcircuit(b):VoltageVisanalogoustoMMFFCurrentIisanalogoustofluxfResistanceRisanalogoustoreluctanceRFluxlinkage,inductanceandenergyFluxlinkageofacoilisl=NfwherethefluxfisassumedtolinkallNturns,thenAmpere’slawgivesthecoilinducedvoltagee=dl/dtCoilonprecedingslidehasNturnsandinductance

L=l/i=N2/Rtot

whereRtot=Rc+RgPowertothecoilp=ei=idl/dtEnergystoredinmagneticfieldW=pdt7/10/2024MagneticCircuitsandMagneticMaterials7PropertiesofmagneticmaterialsFerromagneticmaterialssuchasironhaveveryhighpermeabilitym,

idealforfocusingmagneticfluxinmachineryalsohighlynonlinearifdrivenintosaturation7/10/2024MagneticCircuitsandMagneticMaterials8HysteresisinBversusHforferromagneticmaterialACoperationMagneticcoreunderACexcitation,havingsinusoidalflux,willhaveanon-sinusoidalexcitationcurrentif7/10/2024MagneticCircuitsandMagneticMaterials9Hysteresisandeddy-currentlossesTheenergyperunitvolumelostpercycleistheareaenclosedbythehysteresisloopThereisadditionalenergylostduetoeddycurrentsinducedintheironbythetime-varyingfluxdensityEddy-currentlossisminimizedbylaminatedcores,builtupfromsheetselectricalsheetsteelFiguresinthetextillustratepropertiesofM-5grainorientedsheetsteel(propertiesareobtainedbytherollingprocessesusedinthemill)7/10/2024MagneticCircuitsandMagneticMaterials10PermanentmagnetsPermanentmagnetresidualmagnetismBrandcoercivityHcareshowninthefigureBrgivesthefluxdensitywithnodemagnetizingmmfHcgivesthedemagnetizingfieldneededtoreduceBtozeroTheloadlineshownillustratestheeffectofcuttinganairgapinthemagneticcore(seeExample1.9)SecondquadranthysteresisloopforAlnico57/10/2024MagneticCircuitsandMagneticMaterials117/10/2024MagneticCircuitsandMagneticMaterials12ThenumericalsolutionforExample1.9(seetheloadlineshownonthepreviousslide):Bg=0.30TNoticethattheair-gapfluxdensityisabout¼ofBrApplicationofpermanentmagnetsOperatingapermanent-magnetdevicewillsubjectittodemagnetizingforcesThefigureshowstheeffectsofthisasaminorhysteresiscurve,approximatedasarecoilline7/10/2024MagneticCircuitsandMagneticMaterials13SummaryThetheoryofmagneticcircuitsisdevelopedandusedforanalysisofwindingsonmagneticcoresThenon