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Copyright©TheMcGraw-HillCompanies,Inc.Permissionrequiredforreproductionordisplay.3-0PowerPointSlidestoaccompanyElectricMachineryFourthEditionStephenJ.ChapmanChapter3ACMachineryFundamentalsCopyright©TheMcGraw-HillCompanies,Inc.Permissionrequiredforreproductionordisplay.3-1Copyright©TheMcGraw-HillCompanies,Inc.Permissionrequiredforreproductionordisplay.3-2ConceptofRotatingMagneticFieldsThreephasemachine.Windingcurrentsarefunctionsoftime.Threewindings.Eachphasewindingaxis(theaxisaroundwhichthecoiliswound)is120degreesspatiallydisplacedfromitsneighboursTheeffectisthatastimeprogressesthepeakcurrentmovesfromRtoYtoBwinding.ThepeakoftheBfieldmovesroundinspacecreatingtheappearanceofarotatingfieldintheairgapRCurrentMaximumYCurrentMaximumBCurrentMaximumTimeDirectionofBCopyright©TheMcGraw-HillCompanies,Inc.Permissionrequiredforreproductionordisplay.3-3ACmachinewindingsACrotatingmachineiscomposedinsynchronousorasynchronousmachines.Generally,thesingleACmachineand3-phaseACmachineareverypopular.Principle1.WaveformsofEMFandMMFinamachineair-gapshouldbetypicallysinusoidal,theharmonicwavesareassmalleraspossible;2.Inathreephasemachine,therearethreevoltagephases,separatedby120electricaldegrees.Copyright©TheMcGraw-HillCompanies,Inc.Permissionrequiredforreproductionordisplay.3-4ElectricAngle&MachineAngleMachineAngle---Spaceangleingeometry,360degreesElectricAngle---Definedas360degreesdividedbythenumberofmechanicphasesNumberofpoleis2pElectricAngle=p×360degree=p×MachineAngleCopyright©TheMcGraw-HillCompanies,Inc.Permissionrequiredforreproductionordisplay.3-5Copyright©TheMcGraw-HillCompanies,Inc.Permissionrequiredforreproductionordisplay.3-6SlotangleZp0360NumberofSlot(perpole&perphase)PmZq2PhasebandThezonecoveredbytheslotswhichbelongstoeachphase.Copyright©TheMcGraw-HillCompanies,Inc.Permissionrequiredforreproductionordisplay.3-7SinglelayerwindingshomocentricwindingchainswindingcrosswindingHomocentricwindingComposedbyhomocentriccoilswithdifferentcoilpitch.Copyright©TheMcGraw-HillCompanies,Inc.Permissionrequiredforreproductionordisplay.3-8Eg:Antwopoles,3-phaseACmachinewith24slots1p24Z122242pZ3m43242pmZqCopyright©TheMcGraw-HillCompanies,Inc.Permissionrequiredforreproductionordisplay.3-9Copyright©TheMcGraw-HillCompanies,Inc.Permissionrequiredforreproductionordisplay.3-10ChainswindingThepitchofchainswindingcoilsissameandisanodd.Copyright©TheMcGraw-HillCompanies,Inc.Permissionrequiredforreproductionordisplay.3-11CrosswindingsCopyright©TheMcGraw-HillCompanies,Inc.Permissionrequiredforreproductionordisplay.3-12DoublelayerwindingsCopyright©TheMcGraw-HillCompanies,Inc.Permissionrequiredforreproductionordisplay.3-13TheMMFofSinglePhaseMMFofDiametricalCoilAccordingtothediagram,itisadiametricalcoilwiththenumberofwindingN,thecurrentitencirclesis:iN.Becausethemagneticpathpassestheairgaptwiceandthepathissymmetrical,thusthediametricalcoilcanbedividedintotwoparts.Thatis:Copyright©TheMcGraw-HillCompanies,Inc.Permissionrequiredforreproductionordisplay.3-14232,2222-,2scCcscCciNfiNfCopyright©TheMcGraw-HillCompanies,Inc.Permissionrequiredforreproductionordisplay.3-15AccordingtoDirichlet,thefunctionofthewaveformcanbeextendedasFourierseries,accordingtothediagram,thediagraphissymmetricalbyaxisXandbyaxisYtoo.Thus,itsFourierseriesonlyhascosine,anditonlyhasodd,sCsCsCsCmFFFFcoscoscos)(531Copyright©TheMcGraw-HillCompanies,Inc.Permissionrequiredforreproductionordisplay.3-161111224coscos224CCCCCsCCcFFINFtINfCopyright©TheMcGraw-HillCompanies,Inc.Permissionrequiredforreproductionordisplay.3-17NoteThat:·TheamplitudeofrespectiveharmonicMMF.·TheamplitudeoffirstharmonicMMFandtheamplitudeoftheharmonicMMFchangewiththetime.TheMMFofthefirstharmonicpulsation)()cos(''1'11tFtFFyyy1''1'121yyyFFFCopyright©TheMcGraw-HillCompanies,Inc.Permissionrequiredforreproductionordisplay.3-18)cos('1tFyThisisalsoaformulaofmovingwave,theamplitudeishalfoftheformerone,butthepositionoftheMMFchangesaccordingtothetime,itisarotationwavefacing+awiththepalstanceω.)(''1tFyThisisalsoaformulaofmovingwave,theamplitudeishalfoftheformerone,andthepositionoftheMMFchangesaccordingtothetime,itisarotationmovefacing–awiththepalstanceω.Copyright©TheMcGraw-HillCompanies,Inc.Permissionrequiredforreproductionordisplay.3-19TheMMFofshort-distancecoilBoththeshort-distancecoefficientoffirst-harmonicandtheshort-distancecoefficientofEMFfirstharmonicisthesame,botharesmallerthan1.EachpolarMMFproducedbydouble-layerwindingisbig.Copyright©TheMcGraw-HillCompanies,Inc.Permissionrequiredforreproductionordisplay.3-20ThefirstharmonicMMFofsingle-phasewindingThefirstharmonicMMFofdouble-layershort-distancecoilassemblyisshownas:151311513122FFFFIPNKFWssssFFFFcoscoscos)(531Copyright©TheMcGraw-HillCompanies,Inc.Permissionrequiredforreproductionordisplay.3-21TheMMFofThree-PhaseInthediagramabovetherearethreecoils,arrangedaroundthestatorofamachinesuchthattheanglebetweeneachofthephasesis120°.Assumingthatthesteelintherotorandstatorisinfinitelypermeable,theMMFproduc
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