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首页 The Induction Motor by Beherend 1967s124s 7.1m…

The Induction Motor by Beherend 1967s124s 7.1mb.pdf

The Induction Motor by Beherend…

上传者: xieros_ltdal 2012-09-12 评分 0 0 0 0 0 0 暂无简介 简介 举报

简介:本文档为《The Induction Motor by Beherend 1967s124s 7.1mbpdf》,可适用于工程科技领域,主题内容包含UNIVERSITYOFTORONTOLIBRARYAcmeLibraryCardPocketUnderPat"RefIndexFile"Madeb符等。

UNIVERSITYOFTORONTOLIBRARYAcmeLibraryCardPocketUnderPat"RefIndexFile"MadebyLIBRAETBUfiEAUPROPERTYOFELECTRICALLABORATORY,FACULTYOFAPPLIEDSCIENCEDatePROPERTYOFELECTRICALLABORATORY,FACULTYOFAPPLIEDSCIENCEDatePROPERTYOFELECTRICALLABORATOfiT"FACULTYOFAPPLIEDSCIENCEI)THEINDUCTIONMOTORAShortTreatiseonitsTheoryandDesign,withNumerousExperimentalDataandDiagramsBABEHRENDiMiii!herlustCE,MemberInstE,GermanyMemberlustEE,Switzerland',AssociateMemberAmericanInstK'FormerlyAssistantChiffElectricianoftheOerlikonEngineeringWorks,Switzerland"Theabsenceofanalyticaldifficultiesallowsattentiontobemarteasilycon,entratedanthephysicalaspects<>thequestion,andthusgirtsthestudentamurerii'iiiideaandamureinanaxeablegraspojthesubjectthanhfwould<<likelytoattainifhemerelyregardedelectricalphfnonteiiiithroughacloudoa>talyticaIsymbols"IITlloM'isNEWYORKMiGKAWPUBLISHINGCOMPANYIIBHKTYSTREETCOPYRIGHTED,,BYELECTRICALWORLDANDENGINEER(INCORPORATED)TOMYFRIENDANDTEACHERMRGISBERTKAPPIINSCRIBETHISWORKPREFACETheliteratureofelectricalengineeringhasbecomesovastandextensivethatitisimpossibleforanymantokeeppacewithallthatiswrittenonelectricalsubjectsHewhoproducesanewbookthataddstotheswellingtideofnewpublications,mayjustlybeaskedforhiscredentialsMyjustificationforwritingthistractwillbefoundinthefactthat,thoughalmostallbranchesofappliedelectricityhaveenlistedtheindustryofauthors,theinductionmotorhasreceivedcomparativelylittleattentionfromcompetentengineersThefewwhoseexperienceandknowledgewouldentitlethemtospeakwithauthorityonthissubjectaredeterredfrompublishingbycommercialreasonsIhavemadetheinductionmotorthesubjectofearlyandspecialstudies,andacomparisonofmytreatmentofitstheorywiththepurelyanalyticaltheorieswillshowhowfarIhavesucceededinsimplifyingandelucidatingsocomplexasubjectThegraphicaltreatmentofabstrusenaturalphenomenaisconstantlygainingground,andIquotewithsatisfactionthewordsofsogreatamathematicianasProfGeorgeHowardDarwin,FellowofTrinityCollege,Cambridge,whosaysonpofthesecondvolumeofLordKelvinandProfTail'sTreatiseonNaturalPhilosophythat"thesimplicitywithwhichcomplicatedmechanicalinteractionsmaybethustracedoutgeometricallytotheirresultsappearstrulyremarkable"AllthroughthislittlebookIhaveendeavoredtoletinductivemethodcheckateverystepthemathematicalorgraphicaldeductionoftheresultsAwideexperiencewithmonoandpolyphasealternatingcurrentinductionmotors,gainedattheOerlikonEngineeringWorks,Switzerland,hasenabledmetodosoThusthecarefulreaderwhoiswillingtoprofitbytheexperienceofothers,willfindmanyvaluablehintsandresultswhichhecanturntoaccountinhispracticeManyinductionmotorshavebeendesignedontheprincipleslaiddowninthislittletreatise,andinnocasehasthetheoryfailedtoanswerthequestionssuggestedbyobservationThewritingofthisbookhasbeenmainlyalaborofloveThosewhoknowofthetroubles,caresandlaborinvolvedinwritingabookandbringingitthroughthepress,nottomentionthesacrificeofpersonalexperiencebypublication,willdoubtlessbeabletoappreciatethisthoroughlyIwishtothanktheeditorsoftheELECTRICALWORLDANDENGINEERforthepainstheyhavetakenwiththepublicationofthisbook,andImustspeciallythankMrWDWeaverfortheencouragementhehasalwaysgiventomeToMrTRTaltavall,AssociateEditorofELECTRICALWORLDANDENGINEER,whohastakenendlesspainswiththeproofsofthisbook,IfeelverymuchindebtedThesubstanceofthisvolumewasdeliveredinJanuary,intheformoflecturesattheUniversityofWisconsin,Madison,Wis,andIwishtothankProfJohnButlerJohnson,DeanoftheCollegeofMechanicsandEngineering,fortheinvitationasnonresidentlecturerwhichheextendedtomeTohimandtoProfDCJacksonIamgreatlyindebtedforthehospitalityconferreduponthestrangerwithintheirgatesCONTENTSPARACHAPTERPACEGRAPHITheGeneralAlternatingCurrentTransformeriIIATheCharacteroftheMagneticFieldinthePolyphaseMotoriiBTheFormulafortheThreePhaseCurentMotorIIITheShortCircuitCurrentandtheLeakageFactorIVTheLeakageFactorVDesignofaThreePhaseCurrentMotorforHorsePowerVITheSinglePhaseMotoroVIICalculationofaSinglePhaseCurrentMotorVIIIThePolarDiagramsoftheGeneralAlternatingCurrentTransformerAppendixAppendixIIAppendixIIITHEINDUCTIONMOTORCHAPTERITheGeneralAlternatingCurrentTransformerTheproblemofproblems,inthesolutionofwhichtheelectricalengineerisdeeplyinterested,andwhichunderliesallothers,issetbeforeusintheformofthealternatingcurrenttransformerpossessingconsiderableleakageandarelativelylargemagnetizingcurrentAtransformerwithanopensecondarytakesfromtheprimarymainsjustsomuchcurrentasisnecessarytoproduceamagneticfieldwhichcanbalancetheprimaryvoltageThiscurrentneglectingforthemomenthysteresisandeddycurrentslagsbehindtheprimaryvoltagebyaquarterofaphasehencetheworkdonebythiscurrentiszero,andthemagnetizingcurrentisthereforea"wattless"currentThisconsiderationistrueonlyforatransformerwithoutleakageThemagnetizingcurrentneednotbeawattlesscurrentinthesenseinwhichthistermisgenerallyusedWeshalllearnmoreaboutthisinChapterVIIIIfyouthrowanoninductiveloaduponthesecondary,thatistosay,ifthesecondaryofthetransformerbeclosedthrougharesistance,thentheimpedancerepresentedbytheactionandreactionoftheprimaryandthesecondarysystemofthetransformer,isdiminished,permittingalargercurrenttoflowIf,fordidacticpurposes,wemaketheassumptionthatthewholemagneticfluxoftheprimaryistransmittedwithoutlossintothesecondary,andviceversa,thenthevectoroftheprimarycurrentmustbecomposedoftwovectors,theonerepresentingthemagnetizingorwattlesscurrent,laggingbehindtheterminalvoltsbyaquarterofaphase,andtheotherrepresentingthewattirrentandbeinginphasewiththeteriTHEINDUCTIONMOTORminalvoltsThusthevectoroftheprimarycurrentforanyexternalresistanceisdeterminedbythelocusofthepointA,Figi,whichisthestraightlineADparallelwiththevectoroftheimpressedemfTheenergyconsumedbythetransformerisgivenbytheequation(i)=eicosfiTheintroductionofleakageintothetransformerchangesthediagramasfollows:Thetotalnumberoflinesofinductionpassingthroughtheprimarycoilmustremainconstantaslongastheterminalvoltageremainsconstant,neglectingforthemomenttheohmicresistanceofthecoilThemagnetomotiveforceofthemaincurrentproducesastrayfieldproportionaltothedrivingcurrentthisfieldaddedvectoriallytothemainmagneticfield,generatestheconstantmagneticfieldincludedbytheprimarycoilTheresultoftheseactionsandreactionsisthatAdoesnolongermoveinastraightline,butinasemicircledescribedupontheprolongationofODC)*AhistoricalremarkmaynotbeoutofplacehereThepresentwriterworkedoutthetheoryheregiveninthesummerof,andsentthepapertotheElektrotechnischeZeitschrift,Berlin,whereitwaspublishedinFebruary,MeanwhileMrAHeyland,insomeletterstotheabovenamedpaper,usedthesamediagramwithout,however,givinganyproofWhenMrHeyland'sletterswerepublishedIinsertedanoteinmyMSreferringtothemIhavesince,wheneverIhadanopportunity,givenMrHeylandamplecreditforhispriority,andIhavedoneitwithsatisfaction,asIreallyadmiredsomeofhislaterpapersverymuchMrSteinmetzinformedmesometimeagothathehadfoundthisrelationasearlyas,butthatcommercialreasonspreventedhimfrompublishingGENERALALTERNATINGCURRENTTRANSFORMER'ItisofextremeimportanceforustoclearlyunderstandtheserelationsastheyformthebasisforallfurtherreasoningInFigOAisthevectorofthemagnetomotiveforceoftheprimary,or,inotherwords,thetotalnumberoflinesofforce(notinduction)producedbytheprimarycurrent,andcorrespondingtothenumberofampereturnsNotallthelinesofinductionwhichtheprimarycurrentgeneratescanreachthesecondaryofthetransformerFIGhiiLetusassumethattheamountAAislost,OA*beingequaltoViOA,VibeingafactorsmallerthanoneandmeasuringthelossoflinesfromtheprimarytothesecondaryLetOBrepresentthevectorofthetotalnumberoflinesofinductionofthesecondary,andOB=vtOBthenumberoflinesthatextendintotheprimary,vtbeingagainacoefficientsmallerthanone,thenweseeatoncethatthevectorsumofAandOBmustbeequaltothevectorofthemagnetoTHEINDUCTIONMOTORmotiveforcewhichsetsupthemagnetizingcurrentThevectorofthismagnetomotiveforceisrepresentedbythelineOCThelinesofforcewhicharecommontobothprimaryandsecondary,aretheeffectofthetwomagnetizingforcesOAandBwhilethelinesofinductionwhichpassthroughthesecondaryonly,canbefoundastheresultantofOAandOBlThisresultant,OG,mustbeperpendiculartoOB,asOBisproducedthroughtheoscillationsofOGThefollowinglistwillhelptomakethediagrammoreclearlyunderstood:OA=XiisthemagnetizingforceoftheprimaryOB=XisthemagnetizingforceofthesecondaryOAOA=~B=ODisthefieldbalancingtheterminalvoltage,Itwillreadilybeseenthat,ifthedropcausedbytheohmicresistanceoftheprimarymaybeneglectedwithouttoomuchinaccuracy,ODisconstantiftheterminalvoltageissoWehave,Fig,ZHAD=ZHOG=ZOKOK~C~KX(ivj)*(=')C~GO~DVlGENERALALTERNATINGCURRENTTRANSFORMERHence,fX,sin=^ODjr)=**(*rTnvv*Inwords,thismeansthatXimayberepresentedasachordinasemicircledescribeduponLDasbasis,andhavingadiameterITD=O~D(AZ!VtIfwewanttotakefromthediagramXidirectlywithouthavingtoFIGmultiplybyv,wehavetojoinAandKbyacircleForamoredetailedtreatmentofallthesepointsIreferthereadertoChapterVIIIWecallthequotienttheleakagefactoraofthetransformer,LDandhavetherefore(),ITheleakagecoefficientaisthemostimportantfactorinthetheoryTHEINDUCTIONMOTORofthealternatingcurrenttransformer,andasuccessfuldesignmustendeavortokeepaassmallaspossibleThedeterminationofawillbetreatedofinachapterdevotedentirelytotheleakagefactorThefollowingtablecontainstheresultsofaseriesofmeasurementsasacorroborationofthetheoryThedataweretakenfromathreephasecurrentmotor,thearmatureofwhichwasstandingstillthewholeapparatuswasthusactingasatransformerwithconsiderableleakageThefieldcontainedclosedslots,conductorsineachslotresistanceofeachphaseohmsThearmaturecontainedroundholes,conductorsineachholeresistanceateachphaseohmsNumberofpoles,Frequency,PRIMARYCIRCUITGENERALALTERNATINGCURRENTTRANSFORMERWeshouldmakeagreatmistakewerewetoassumethatthisvaluewouldgiveusaleakagefactoratruetoreality,sinceinourcase,wheretheslotsinarmatureandfieldareclosed,vdependsgreatlyuponthesaturationofthethinironbridgesclosingtheslotsThesaturationofthesebridgesisdependentupontheintensityoftheFIGcurrentbeyondacertainintensityv,andthereforeaispracticallyconstantAssumingzjtobeequaltovt,weshouldgetfora=i=,insteadof'$=,asfollowsfromthediagramItmaybeadvisabletoemphasizethatinthederivationofthediagramtheohmicresistanceoftheprimaryhasnotbeentakenintoaccountAsthispointisofextremetheoreticalandpracticalimportance,wehavetodwellonitatsomelengthTHEINFLUENCEOFTHERESISTANCEOFTHEPRIMARYUPONTHEDIAGRAMThesemicircleLi''''D,Fig,representsthelocusofthecurrentforaconstantterminalvoltageOE,upontheassumptionthattheprimaryresistancebenegligible'ThearcIisthelocusofTHEINDUCTIONMOTORthecurrentifweassumethatthedropthroughohmicresistanceintheprimaryamountsforpoint'toofOEFinallytheordinatesofthecurvei*"""representtheamountofwattcomponentofthecurrentthatisavailableinthesecondarycircuitItwouldbesuperfluousheretosayanythingaboutthemannerinwhichthesecurveshavebeenplotted,aseveryonefamiliarwithpolardiagramswillreadilyunderstanditfromthelinesinthefigureItisofimportancetonotethat,thoughtheprimaryresistancewasassumedtohaveavaluewhichexceedsaboutfivetimestherealvalueinpractice,yetthecurvesLi''''DandI'deviatecomparativelylittlefromeachotherIfODwerezero,thentheywouldnotdeviateatallInreality,ODLDisalmostalwaysconsiderablysmallerthanitisinourfigureIf,however,ODislargeincomparisonwithLD,andiftheprimaryresistanceisconsiderable,wehavetodrawadiagramlikeFigThiswillbetheexceptionandnottheruleThuswehavelearnedthattheinfluenceoftheohrnicresistanceuponthelocusofthecurrentis,inmostpracticalcases,negligiblebuttheenergydissipatedintheresistance,isinallcasestobetakenintoaccountthiscanbedonebydeductingthewattcomponentcorrespondingtotheohmiclossfromtheordinatesofthesemicircleLDWethusarriveatacurvesimilartoi""""GENERALCONCLUSIONSANDSUMMARYWearenowenabled,withthehelpofthediagram,tosolveanyquestionpertainingtothealternatingcurrenttransformerWeshall,inalaterchapter,discussindetailforaconcretecasethemanyproblemsofinterestwhichthisdiagrampermitsustosolvehereweshallmerelysummarizethemainconclusionsatwhichwehavearrivedInFigOArepresentstheprimarycurrentti,ODthemagnetizingcurrentto,andADisequaltovlz'inwhichHIandn*arethejnumberofturnsintheprimaryandthesecondary,respectivelyGENERALALTERNATINGCURRENTTRANSFORMERThesmallestlag<PisdeterminedbytheintersectionofthesemicircleLDwiththesemicircleHAO,ascanbeseenataglanceThecosineofthisanglecanbeexpressedasfollowsItisHA=HD=^>,cos<t>=HAHOOO=(TII()ThisequationenablesustopredictthemaximumpowerfactoriftheleakagecoefficientaisknownIwillherepremisethatthestartingcurrentfurnishesavalueforthedeterminationofthediameterofFIGthesemicircle,whilethemagnetizingcurrentcanalwayseasilybemeasuredThismethodofdeterminingthemaximumpowerfactorTHEINDUCTIONMOTORattainable,thusrecommendsitselfnotonlytothedesigner,but,onaccountofitssimplicityandaccuracy,alsotothecustomerThefullcurveofhigherorderinFig,whichcaneasilybeconstructed,representsthepowerfactorasafunctionofthepowerinputthedottedlineshowsthepowerfactorforatransformerwithoutanyleakageCHAPTERIIATheCharacteroftheMagneticFieldinthePolyphaseMotorThemagneticfieldinathreephasecurrentmotorisproducedbythreewindings,I,II,andIII,FigIfthecurrentinIIIIFIGIllisamaximum,andifthecurrentsvaryacordingtoasimplesinecurve,thenthecurrentsinIandIIareeachequaltohalfthecurIITHEINDUCTIONMOTORrentinIIIThemagnetomotiveforcesofeachphasearerepresentedbytheordinatesofthecurvesI,II,andIIIrespectivelyEachordinatemeasuresthemagnetomotiveforceproducedinthatplaceofthecircumferenceinwhichitisdrawnTheaddingupofthethreecurvesyieldsthethicklinecurvedrawnbelowIfthemagneticreluctanceisthesameateverypointofthecircumference,inotherwords,ifthereluctanceoftheironisnegligible,thentheflux,producedbythemagnetomotiveforcerepresentedbythethicklinecurve,isproportionaltothatmagnetomotiveforceHencethethicklinecurvemaybetakenas"arepresentationofthefluxWecallthetotalnumberoflinesofinduction$,andweasIIFIGFIGQsumethatthisfluxvariesaccordingtoasimplesinelawWeshallnowproceedtocalculatetheemfinducedbythisfielduponeachphaseWehavetacitlyassumedthatthecoilsI,II,andIIIaredistributedinapracticallyinfinitenumberofslotsThoughthiscannotbethecase,yetthisassumptionmaysafelybemadeforourpresentpurposeItisobviousthat,iftheconvolutionsofeachphasewerealjconcentratedinoneslot,theeffectoftheoscillationorthetravelingofTHEMAGNETICFIELDINTHEPOLYPHASEMOTORthefieldwouldbetosetupanemfequalto~z<j>,"*voltshowever,throughthedistributionofthewinding,onlythepartsofthefluxnotcoveredwithhrtchingscanproduceanemfexpressedbythisformula,whilethehatchedpartsofthefieldwillhaveaconsiderablysmallereffectTheinducedemfcanbecalculatedasfollows:ThewidthofthecoilisbthereareconductorsinthecoilspreadoverbPerunitlengththereare,therefore,conductors,hencetheelementdxcontainsdxconductorsThenumberofblinesofinductionthreadingtheconductorsintheelementdxtequalto**representedbythehatchedareaWehave,therefore,de=~dx**voltsb*,=<BlaJr^~=Hencenr^de=~IioibL($,x*(txIJJLjV^B^lffII,^LobJn,oJe=~"ifiioWehave*=,therefore()<r=Thisisinwords,Theemfinducedbythefield*uponacoilofthewidthbistwothirdsaslargeastheemfwhichwouldbeinTHEINDUCTIONMOTORducedbythesamefielduponacoilwhichisnotdistributed,butlodgedinonlyonegrooveThelatter,caseisrepresentedinFigItmaynotbeamisstocallattentiontothefactthatacoillikethatinFigwouldproducearectangularmagneticfieldtwiceaslargeasthatshowninthefigureHencetheinductanceoftheflatcoilisonethirdaslargeastheinductanceofthecoillodgedinoneslotTheemfgeneratedbythefieldinFigcannoweasilybecalculatedThenumberoflinesofinductionrepresentedbythewhiteareainFigisequaltoTheemfproducedbythisfluxis<,=~z(tb(io*VThehatchedareasrepresentafluxequalto*""**Theemfproducedbyt

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