Fundamentals研发培训,设计培训

ReviewofFundamentals1ReviewofFundamentalsHaranKarmakerAugust4,2005ReviewofFundamentals2TopicsVectorsandScalarsPartialDifferentialEquationsElectromagneticConceptsMaxwell’sEquationsElectricandMagneticCalculationsPrinciplesofMachineOperationMathematicalModelingMagneticFieldsTwo-ReactionTheoryReviewofFundamentals3VectorsandScalarsVectorsandscalarsaremathematicalrepresentationsofphysicalquantities.Vectorshavebothmagnitudesanddirections.Scalarshaveonlymagnitudes,nodirections.Forexample,locationofapointinspacefromtheoriginisdefinedbyapositionvectorwiththreecomponentsalongthex,yandzaxes.Thedistanceofthepointfromtheoriginisascalarquantitywithoutanydirection.xPole-faceToothedmemberAirgapzygdtsxPole-faceToothedmemberAirgapzygdtsReviewofFundamentals4VectorRepresentationIntheexample,thefluxdensityintheairgapwillhavecomponentsintheradial,tangentialandaxialdirectionsandisavector.Theairgapfluxoveranareaisascalar.Anotherexampleofascalaristheroomtemperaturewhichhasnodirection.Thegradientofascalaristherateofchangeofthescalaralongadirection.Thegradientisavectorquantity.ReviewofFundamentals5VectorRepresentationThedivergenceofavectorquantityrepresentsthenetflowofthequantitythroughavolume.Thedivergenceisascalarfunctionofavectorfield.Thecurlofavectorisameasureofcirculationofthevectorfield.Stoke’stheoremrelatestheintegralofavectorfieldalongaclosedpathtotheintegralofthecurlofthefieldonthesurfacedefinedbytheclosedpath.Thethreevectorfunctions,gradient,divergenceandcurldescribethenatureofvariationofallphysicalquantitiesintheuniverse.ReviewofFundamentals6PartialDifferentialEquationsThenatureofdistributionofaphysicalphenomenonisgovernedbyequationsincludingthechangeinmultiplevariablescalledpartialdifferentialequations.ThemostcommongoverningequationsareLaplace,Poisson,diffusionandwaveequations.Solutionofmostengineeringproblemscanbeformulatedasboundaryvalueproblems,whichrequiregoverningequationsandboundaryconditionsfortheirsolutions.Oncetheboundaryvalueproblemhasbeenformulated,itcanbesolvedbyanalyticalornumericalmethods.ReviewofFundamentals7ElectromagneticConceptsElectrostaticfieldsarecausedbystationaryelectriccharges.In1785,Coulombinvestigatedthenatureofforcebetweentwochargedbodiesandformulatedthefollowingequationfromexperiments.F=Q1*Q2/(4*π*ε*r2)whereF=ForceinNewtonsQ1,Q2=ChargesinCoulombε=Permittivityofthemediuminfarads/mr=DistancebetweenchargesinmetersReviewofFundamentals8ElectromagneticConceptsElectricfieldintensityduetoachargeQisdefinedasE=Q/(4*π*ε*r2)ElectricfieldintensityisavectorwhosemagnitudeisinunitsofNewtonsperCoulomb,whichcanbeconvertedtotheunitsofvolts/meter.Therefore,thevectorEcanbetreatedasaforcefieldthatactsonacharge.Itcanalsobetreatedasagradientofavoltage.ReviewofFundamentals9ElectromagneticConceptsElectricfluxdensityisdefinedasD=εEIthasunitsofchargeperareaorCoulombspersquaremeter.AccordingtoGauss’slaw,theintegralofelectricfluxdensityoveraclosedsurfaceisequaltothefreechargeenclosedbythesurface.ReviewofFundamentals10ElectromagneticConceptsThegoverningequationsforelectricfieldproblemsareoftendescribedbyapotentialfunctiondefinedasE=-VMathematicalrepresentationofGauss’slawgives.D=ρwhereρischargedensity.Therefore,-.(εV)=ρV=-ρ/εPoisson’sequationV=0Laplace’sequation22ReviewofFundamentals11Faraday’sLawFaraday’sLawstatesthatachangingmagneticfieldwillinduceanelectricfield.Theelectricfieldexistsinspaceregardlessofwhetheraconductorispresentornot.Whenaconductorispresent,acurrentwillflow.ThedifferentialformofFaraday’sLawiscurltBEReviewofFundamentals12Faraday’sLawInducedvoltagearoundastationaryclosedcontourClinkedbyachangingmagneticfieldisgivenbythelineintegralofelectricfieldThemagneticfluxisTheintegralformofFaraday’sLawisdsB.dlEV.).(/.dSBtdlEReviewofFundamentals13Ampere’sLawAvectorcalledmagneticfieldintensityisdefinedasThedifferentialformofAmpere’sLawisBHcurlHJReviewofFundamentals14Ampere’sLawIntegralformofAmpere’sLawisobtainedbyapplyingStoke’stheoremAmpere’sLawinintegralformstatesthatthelineintegraloffieldintensityaroundacontourisequaltothenetcurrentenclosedbythecontour.SSIdSJdlHdScurlH...ReviewofFundamentals15Maxwell’sEquationsMaxwell’sequationsdescribethetheoryofelectromagnetismbyunifyingalllaws.curlHJcurltBEBHJEdivD=ρdivB=0D=εEReviewofFundamentals16SymbolsinMaxwell’sEquationsPermeabilityisaphysicalpropertyofamaterialrelatingfluxdensityBtofieldintensityH.Permeabilityoffreespaceis4Пx1E-7Henry/m.Formagneticsteel,permeabilityvarieswithfluxdensityorfieldintensity.Electricconductivityisreciprocalofresistivityandvarieswithtemperature.ReviewofFundamentals17ElectricandMagneticCalculationsFormanymagneticapplications,goodapproximatesolutionscanbeobtainedbyacircuitanalysissimilartothatofad.c.circuitcomposedofseriesandparallelcombinationsofresistors.Forexample,consideratoroidwithNturnscarryingcurrentI.ReviewofFundamentals18ElectricandMagneticCalculationsThemagneticfieldintensityinthetoroidiscontinuous.Thefluxdensityismuchgreaterinsidethanoutsidebecauseofthe