Prof. Dr. rer. nat. Erwin Krämer (auth.) - Dynamics of Rotors and Foundations-Springer-Verlag Berlin Heidelberg (1993).pdf
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ErwinKramerDynamicsofRotorsandFoundationsWith304FiguresSpringer-VerlagBerlinHeidelbergGmbHProf.Dr.rer;nat.ErwinKrii.merIsselstraJ3e1264297Dannstadt-EberstadtGennanyISBN978-3-662-02800-1ISBN978-3-662-02798-1（eBook）DOI10.1007/978-3-662-02798-1Thisworkissubjecttocopyright.AIIrightsarereserved,wetherthewholeorpartofthematerialisconcemed,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation,broadcasting,reproductiononmicrofilmorinanyotherway,andstorageindatabanks.DuplicationofthispublicationorpartsthereofispermittedonlyundertheprovisionsoftheGermanCopyrightLawofSeptember9,1965,initscurrentversion,andpermissionforusemustalwaysbeobtainedfromSpringer-VerlagBerlinHeidelbergGmbH.ViolationsareliableforprosecutionundertheGermanCopyrightlaw.Springer-VerlagBerlinHeidelberg1993OriginallypublishedbySpringer-VerlagBerlinHeidelbergNewYorkin1993SoftcoverreprintofthehardcoverIstedition1993Theuseofgeneraldescriptivenames,registerednames,trademarks,etc.inthispublicationdoesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevantprotectivelawsandregulationsandthereforefrecforgeneraluse.Typesetting:
Carnera-readybyauthor;6113020543210Printedonacid-frecpaperForewordMyacquaintancewiththeAuthorbegansome30yearsagowhilehewaswithBrownBoveriinMannheim.Sincethenwehavebecomeclosecolleaguesanditwasanaturalconsequencetocooperateinwritingabookonrotordynamics-heasanexpertwithawealthofindustrialexperienceandIastranslatorfromGermanintoEnglish,withabackgroundinindustryandinuniversityteachingandresearchintothevibrationofrotatingsystems.TheoutcomeisabookwithatraditionallyGermanemphasisonawideanddetailedcoverageofthedynamicsofrotorsandfoundations.Thebibliographyisextensiveandtheauthorisnotcontenttosimplyrefertothis,buttogivehisownverylucidexplanationsofthephenomenainvolved.Thisisbackedupbydetailedcalculationsandgraphswhichgivetheengineerathoroughappreciationofthedifferentfactorsaffectingtherotordynamicperformanceofmachines.Inaddition,toolsofthetradesuchasfiniteelementmodellingandstabilityanalysisarecoveredindetailandtheresultisabookwhichIamsurewillberegardedasanessentialvolumeonthebookshelfofanystudentorengineerwhohasaneedtoconsidermachinevibration.Southampton,EnglandRoyHolmesPrefaceInthelastdecadesrotordynamicshasdevelopedintoawideareaofspeciality.Numerousinvestigationshaveappearedintheliteratureandevenforthespe-cialistitisdifficulttoappreciatethewholepicture.Achoiceoftheessentialresultsandtheircorrelationinasunderstandableaformaspossibleisthereforeaprimerequirement.Itishopedthatthiswillbeaccomplishedinthisbookthroughtheknowledgeandexperiencegainedtheauthor,overhisworkinglife.Thebookiswrittenforanyonewhoisconcernedwithrotordynamics,whetherbychoiceornecessity.Itisrecommendedforlecturersandstudentsandforthemanufacturersandusersofrotatingmachinesandtheirfounda-tions.Ontheonehandthemechanicsandmathematicalderivationsaredealtwithindetailand,ontheother,anattemptismadetosimplifytheunder-standingoftheresultsbypresentingnumerousfiguresandcorrespondingtextforreaderswithlittleexpertknowledge.ThecontentsofthisbookaredescribedindetailinChapt.1.Theyconsistofthebackgroundliterature,workinthespecialistareaofmachinedynamicsintheTechnicalUniversityofDarmstadtandoftheauthorsownpersonalexperiencesinindustry,atuniversityandasaspecialistinthefield.Thecitedliteraturehasbeenchosenfrompersonalknowledgeandjudgementandthereadersindulgenceisaskedifthechoiceinsomecasesappearsinadequate.TheobjectofwritingthisbookinEnglishcouldonlyberealizedbecauseProfessorR.Holmes,awell-knownresearcherinrotordynamics,offeredtotranslatetheGermanmanuscript.IwouldliketothankProfessorHolmesespe-ciallyforhisunselfishreadiness,forhiscriticalappraisalandtranslationofthemanuscript,aswellasformanyusefulpiecesofadvice.Dr.Ing.H.D.Klementhasalsocontributedextensivelytothecontentsofthisbook.HeconveyedtotheauthorinmanydiscussionshisknowledgeandexperienceonthesubjectofwritingandusingcomputerprogramMADYN,describedinChapt.25.Forthisandforthecalculationofmostoftheexamples,theauthorwouldliketothankDr.Klementmostwarmly.Furthermore,thanksaredueeveryonewhoreadpartsofthemanuscriptandgaveadvice,especiallyDr.Ing.L.Eckert,Prof.H.Freund,Prof.J.Glienicke,Prof.H.J.ThomasandDr.Ing.J.Schmied.ManyquestionsandacknowledgementsoriginatefromtheauthorsearlieremploymentatBBC,nowABBZurich,andfromdiscussionswithexpertsofthiscompany.TheauthorwishestothankformercolleaguesfortheirassistanceandABBforinformationonsomeofthegivenexamplesandforauthorizationtopublishtheresults.VIIIGratitudeisexpressedtoMrs.M.Mayerforthecarefultypingofthebook,toDipl.Ing.D.GlaserfordrawingthefiguresandtoMrs.Dipl.Ing.E.Grunauforfinalreviewingofthemanuscript.Finally,theauthorwouldliketothanktherepresentativesofSpringer-Verlagfortheirpleasantandefficientcooperation.Darmstadt,GermanyErwinKramerTableofContentsIFundamentals11Introduction.32TheoneDegreeofFreedomSystem72.1EquationofMotion.72.2NaturalVibration.82.3HarmonicExcitation112.4RandomExcitation.173ShaftwithCentralDisc193.1ShaftwithRigidBearings,JeffcottRotor.193.2Startup,RunDown.243.3JeffcottRotorwithFlexibleBearings293.4JeffcottRotorwithBearingDamping334ShaftwithNonCentralDisc374.1EquationsofMotion374.2NaturalVibrations.414.3UnbalanceVibrations.524.4HarmonicExcitationinoneDirection.564.5ShaftwithFlexibleBearings595TheShortandtheLongRotor655.1UnbalanceMoment.665.2NaturalFrequencies.685.3UnbalanceVibrations.716Oil-FilmBearings.776.1HydrodynamicBearingTheory776.2ShortBearingTheory.836.3StaticandDynamicProperties897RotorswithOil-filmBearings977.1EquationsofMotion.97XTableofContents7.2Stability.7.2.1RigidRotor.7.2.2TheJeffcottRotor7.3UnbalanceVibrations.7.4Summary8VerticalRotors8.1Tilt-padBearings.8.2Vibrations.9Rolling-elementBearings9.1DeformationoftheRolling-element9.2StiffnessofRolling-elementBearings9.3LateralStiffness,CriticalSpeeds.9.4ConsequencesofElementRotation.9.5DampingofRolling-elementBearings.10ShaftSeals.10.1RestoringForce.10.2JeffcottRotorwithSeals10.3SmoothSeals.10.4LabyrinthSeals.10.5FloatingRingSeals.11SteamWhirl.11.1TheSteamWhirlForce.11.2JeffcottRotorwithSteamWhirl.12InternalDamping.12.1JeffcottRotorwithInternalViscousDamping12.2DampingduetotheShaftMaterial.12.3DampingfromAssemblyComponents.12.4ConclusionandanExample13Non-circularShafts.13.1Non-circularJeffcottRotor13.2SupplementaryComments.IIRotorswithSeveralBearings14ComputerModel.15InfluenceCoefficients9999104108113115115123129130132135138140143144146152156157161161164169169174177184191192199201205207TableofContentsXI16EquationofMotion21116.1Statics.21116.2Dynamics.21716.2.1lligidMasses21716.2.2BeamElement.22116.2.3FlexibleCouplings22416.2.4BearingSupports.22716.2.5ShaftSeals,SteamWhirl.22816.3ReductionintheNumberofCoordinates22816.4DiscussionoftheEquationofMotion23017Results.23317.1GeneralDiscussionofNaturalVibrations.23317.2RotorswithtwoBearings.23617.3RotorswithSeveralBearings.24718StaticBearingLoads.255IIIRotor-foundationCoupling19Foundation.19.1Calculations.19.1.1GroundDynamics.19.1.2lligidFoundationBlock19.1.3FlexibleFoundation.19.2Results.19.2.1lligidFoundation.19.2.2FrameFoundation19.2.3TableFoundation.19.2.4SpringFoundation19.2.5ReinforcedConcreteandSteel.20RotorandFoundation20.1Calculations.20.2Results.20.2.1SmallMachineSetswithFrameFoundations20.2.2LargeTurbineSets20.2.3Conclusion.IVFurtherFeatures21RoughCalculations.21.1NaturalFrequenciesandCriticalSpeeds257261262262266269277277283283287287293294296298305311315317317XIITableofContents21.2ResonanceAmplitudes22BendingStressesinRotors23CrackedRotors.23.1VibrationsofaRotorwithaTransverseCrack.23.1.1JeffcottRotor.23.1.2GeneralRotor.23.1.3Results.23.2CaseStudies.23.3Summary.24SolutionoftheEquationofMotion24.1HomogeneousEquation,NaturalFrequencies.24.2HarmonicExcitation.24.3GeneralExcitation.24.4ModalMethodofCalculation24.4.1SymmetricMatrices.24.4.2HarmonicExcitation.24.4.3ReducedModalCalculation24.4.4TransferFunction.24.4.5UnsymmetricMatrices24.5RayleighQuotient.25ProgramMADYN.25.1Review.25.2BuildingtheModel25.3EigenvalueAlgorithm.ReferencesIndex.322325329329329334335342345349349353353353354356358360360362365365367368371381PartIFundamentals1IntroductionRotorsofmachineshave,whileinoperation,agreatdealofrotationalenergy,andasmallamountofvibrationalenergy.Thepurposeofrotordynamicsasasubjectistoascertainhowthislattercanbekeptassmallaspossible.Itssignificancecanbeunderlinedbythefollowingexample.Therotationalenergyofarotorturningwithangularvelocitynisthesameasthekineticenergyofanon-rotatingrotorwithtranslationalmotionofvelocityv=nipwhereipisitsradiusofgyration.Forexample,forarotorwithradiusofgyration200mmand3000rpm,thevelocityvis63m/sor226km/h.Thetypicalveloci
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