Reactances研发培训,设计培训

ReactanceofInductionMachinesFundamentalConceptsdtdieL•L=InstantaneousInductanceofCoil(Henries)•e=Instantaneousvalueofvoltageinducedinthecoilbythechangeofcurrent(Volts)•di/dt=InstantaneousvalueoftherateofchangeofthecurrentwhichflowsthroughthecoilFaraday’sLawdtddepath•epath=inducedvoltagearoundanenclosedpath•E=VectorofElectricFieldaroundthepath•dl=Vectorofenclosedpath•d/dt=RateofChangeofFluxenclosedbythepathdtndexxPATH•AmoreusefulformofFaraday’slaw:•wherexxn•IsthesumofallfluxesxlinkingcorrespondingturnsnxofthecoilCombiningEquationsdidLReactanceofaninductivecircuitX=2fL(Ohms)f=freqencyofvoltageacrossinductance(Hz)dindLxxorAmpere’sCircuitLawAdAJdH•H=VectorofMagneticFieldIntensity(Amp/meter)•dl=Vectoralongthelengthofthepath•J=Vectorfieldofcurrentdensityenclosedbypath•dA=areaenclosedbythepathToapplyAmpere’sCircuitlaw,considerthesimplemagneticcircuitofatoruswithanon-ferromagneticcoreAdAJdHHr(2r)=NirNiHr2•B=uruoH•B=VectorQuantityofMagneticFluxDensity(Tesla)•uo=constantrelatingFluxDensitytoFluxIntensityinfreespaceornon-ferrousmaterials=4x10-7(T•m/A)•ur=proportionalityconstantforferromagneticmaterials(unit-less)Rearranging:Also:Amp/meter•Theintegrationoffluxdensityoveraunitareagivestotalflux.Foratorroid=BAWebers•CombiningEquationsforLand,theinductanceofthecoilisshowntobedeterminedentirelybythedimensionsofthecoilandindependentofthecurrentinthewire.lAuNLo2ThereactanceofthetorroidisthenlAufNXo22ForFerromagneticMaterials,avalueofroisreadfromaSaturationCurveEffectofSaturationonInductanceEquivalentCircuitofInductionMotor•R1Primaryresistance•X1Leakagereactanceofprimarywinding•XMMagnetizingReactance•gh=Resistancepathtoaccountforcoreloss•X2Secondaryleakagereactance•R2/sResistanceofsquirrelcagewinding•Thereisnostandardmethodforreactancecalculationsassimplifyingassumptionsaremadeatmanystepsintheircalculation.Theformulastofollowhavemanysimplifyingassumptions(suchasnosaturation)thatIwilltrytopointoutaswegoalong.However,thedependencyofreactancetophysicalparametersisthesameforallcalculationmethods.MagnetizingReactanceXM22319.0PKgKLDTXgWM•T=ReactanceFactor•D=StatorBoreDiameter(I.D.)•L=CoreLengthinInches•KW=StatorWindingFactorKdxKp•g=singleairgapinches•Kg=Carter’sAirGapCoefficient•P=#Poles•T=ReactanceFactor=82102ZmfT•Where•f=frequency•m=#ofphases•Z=#statorconductorsinseriesperphasephasesuitstatorcircilturnspercosStatorslotZ####•TheresultantvoltageintheairgapavailabletocreatetherotatingmagneticfieldislessthanthepeakvoltageofthesinewaveatthemotorterminalsBecauseof2factors:1Kp:Accountsforthepitchofthewinding2Kd:Accountsforthedistributionofthewinding•Toaccountfortheslotopeningsofthestatorandrotorsurface,agapfactorisusedasamultipliertocreatean“effective”airgap.Thisfactoriscalledthe“Carter’sCoefficient”KgKW=Kp•KdTotalLeakageReactanceX1+X21ThePrimaryslotreactance2TheSecondaryslotreactance3Thezig-zagreactance4Thebelt-leakagereactance5TheCoilEndLeakageReactance6Theperipheralleakage•Becauserelativelyfewstatorsorrotorsareskewed,theleakagereactancecausedbyeitheraskewedstatororskewedrotorwillnotbeconsidered.Itissufficienttoknowthatanadditionalleakagereactanceexistsforskewedmotors.•Reactance3and4aresometimescombinedandcalledDifferentialLeakage•StatorSlotLeakageReactancesssKSLTX1•T=ReactanceFactor•L=Lengthofstatorcore•S=#statorSlots•Ks=Factortoaccountforcoilsofdifferentphasesbeinginthesameslot•1=PermeanceFactorofStatorSlotBasedonslotgeometry141321211133.2WhWhWWhWh484743635233.2WhWhWWhWh•ForStator:•ForRotor:RotorSlotLeakageReactance22WSRKRLTX•XSR=RotorSlotLeakageReactanceReferredtotheStator•T=ReactanceFactor•L=Lengthofrotorcore•R=#rotorSlots•Kw=statorwindingfactor•2=PermeanceFactorofrotorslotBasedonslotgeometryRotorLeakageReactanceCont.ThevalueofXSRiseffectedbytheoperatingconditionofthemotor.Thevaluecalculatedisfor“running”conditionswhenrotorfrequencyis1-2Hzandrotorcurrentisrelativelylow.Duringrunningconditions,therotorbarcurrentcanbethoughofasdistributingevenlythroughoutthebar.Duringlockedrotor,therotorfrequencyis60Hzandduetothe“DeepBarEffect”thecurrentcrowdstowardthetopofthebar.ThecurrentcrowdingalongwiththesaturationeffectsofthehighinrushcurrentcausethestartingvalueofXSRtobesignificantlyreduced.DifferentialLeakage•Besidesthefundamentalairgapfluxwaveformthereareharmonicwaveformsthataremultiplesofthenumberofpolesandrotateatsub-multiplesofsynchronousspeed.Theseharmonicsinducevoltagesinthewindingsthatproducedthemandthereforeaddtothereactanceofthewinding.•Thedifferentialleakageissometimesbrokeintotwocomponents:Thezig-zagandphasebeltleakage.Thefollowingnotationcombinesthebeltleakagewiththezig-zag.21122822.WSKPRKPSmzzKKXXgRgS•XM=MagnetizingReactance•S=#StatorSlots•P=#Poles•R+#RotorSlots•KgSCarter’sairgapcoefficientforthestator•KgRCarter’sairgapcoefficientfortherotor•KSShortPitchCorrectionFactor•KWStatorWindingCorrectionFactorCoilendLeakageReactancesESAPTX123.2123.WRERKAPTX•Stator•Rotor•AS=Meanstatoroverhang•AR=MeanRotorOv