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SimulationandVibrationAnalysisofShaftCracksSpectraQuest,Inc.8201HermitageRoadRichmond,VA23228(804)261-3300www.spectraquest.comApril,2007Abstract:AShaftcrackisoneofthemostcommondefectsinarotorsystemanddetectionofsuchshaftcrackisaveryseriousmatter.Inthisstudy,shaftcracksweresimulatedandanalyzedusingSpectraQuest’srotorMachineryFaultSimulatorTM(MFS).Aseriesofexperimentswereconductedtoobservethebehavioralchangesofthecrackedshaftincriticalspeed,1Xand2Xfrequencyresponses.Theexperimentalresultswerefoundtobeconsistentwiththetheoreticalpredictionoftheshaftcrack.1.INTRODUCTIONAshaftcrackisaslowlygrowingfractureoftherotor.Ifundetectedinanoperatingmachine,asacrackgrows,thereducedcrosssectionoftherotorwillnotabletowithstandthedynamicloadsappliedtoit.Whenthishappens,therotorwillfailinafastbrittlefracturemode.Thesuddenfailurereleasesalargeamountofenergythatisstoredintherotatingsystem,andtherotorwillflyapart.Thiskindoffailuremaycauseseriousinjuryorevendeathtoanyoneunfortunatelystandingnearthemachineatthatmoment.Obviously,shaftcrackdetectionisaveryseriousmatter,andmachinesthataresuspectedofhavingacrackmustbetreatedwiththeutmostcaution.Cracksareinitiatedintheshaftinregionsofhighlocalstress.Shaftsaresubjectedtolarge-scalestressesduetobending,torsion,staticradialloads,constrainedthermalbows,thermalshock,andresidualstressesfromheattreatment,weldingandmachineoperations.Allofthesestressescombinetoproducealocalstressfieldthatchangesperiodically.Inasmall,localregionwherestressesexceedthemaximumthatthematerialcanwithstand,acrackwillforminthematerial.Ifthecyclicstressesaresufficientlyhigh,theleadingedgeofthecrackwillslowlypropagatesothattheplaneofthecrackisperpendiculartotheorientationofthetensilestressfield.Theorientationofthisstressfieldisdeterminedbythetypeofstress(bendingortorsional)andbygeometricfactors.Iftherotorissubjectedonlytosimplebendingstresses,thenthestressfieldwillbeorientedalongthelongaxisoftherotor,andthecrackwillpropagatedirectlyintoandacrosstherotorsection,formingatransversecrack.Thepuretorsionalstresswillproduceatensilestressfieldthatisorientedat45°relativetotheshaftaxis.Acrackinthisstressfieldwillpropagateintotherotorandtendtoformaspiralontheshaftsurface.Figure1showsthesetwotypesofcracks.Inmostrotorsystems,thestressfieldcontainsamixtureofbendingandtorsionalstress.Bendingstress,however,isusuallythedominantcomponent,thusthecrackwillusuallypropagatedintotherotormoreorlessasatransversecrack.Figure1.Transverseandtorsioncracks.Shaftbendingstiffnessisrelatedtotheshaftcross-sectionarea.Asacrackpropagatesacrosstheshaft,theremainingcrosssectionbecomessmaller,andthebendingstiffnessoftheshaftdecreases.Thiswillreducetheresonancefrequencyaswellasthecriticalspeedoftherotorsystem.Thereductioninshaftstiffnessalsocausestherotortobowmoreinresponsetoastaticordynamicload,suchasarotatingunbalance.Thebowislikelytochangeovertime.Asaresult,itwillchangetheeffectivelocationandmagnitudeoftheheavyspot,whichwillconsequentlychangethe1Xrotorresponse.Ifarotorwithacrackhasasteady,unidirectionalradialload,thenastrong2Xresponsemayappearwhentherotoristurningathalfofanyresonancespeed.Asabreathingcrackinvolvesboththeclosingandopeninginonerevolution,therotorwillrespondatthe2Xfrequency.Ifaresonanceexistsattwicerunningspeed,thenthe2Xvibrationwillbeamplified.Inthisstudy,aseriesoftestswerecarriedoutonaSpectraQuestMFSwithcrackedshaftstoobservetheirbehavioralchanges,includingthecriticalspeed,1Xand2Xfrequencyresponses,comparedwithanintactshaft.2.EXPERIMENTALSETUPThreeexperimentsweredesignedtoapproachtheobjectiveofthisstudy.Theywere:A.CrackedshaftsimulatedusingFlangeB.NotchedshaftwithV-shapecrack1.6”fromtheinboardbearinghousingC.NotchedshaftwithV-shapecrack1”fromtheinboardbearinghousingThechangesofcriticalspeedsfortheintactandcrackedshaftswerestudiedinexperimentsAandB.Thechangesof1Xand2XfrequencyresponsesfortheintactandcrackedshaftswereinvestigatedinexperimentsBandC.Therunningspeedswerechosentobe2000rpmand4000rpm.ThetestswereconductedontherotorMFSwhichisillustratedinFigure2.Fouraccelerometersweremountedontheinboardandoutboardbearinghousingsintheverticalandhorizontaldirection,respectively.ThesetupofexperimentAisshowninFigure3.Figure2SpectraQuest’sMachineryFaultSimulator(MFS)Figure3showstheflange-simulatedcrackedshaft.Itconsistsoftwoseparableshaftsjoinedatthematingflanges.Thefour(4)boltscompressBellevillewasherswhichcanbeloosenedortightenedinapatterntocreateanun-symmetrictimevaryingstiffnessandsimulatetheopeningandclosingofatransversecrack.Thelargediscnexttotheflangesprovidesgravityloadingandashaftbendingmoment.Testswererunwithone,twoandthreeboltsloosened.Figure3.SetupforexperimentAThesetupforexperimentsBandCuseashaftwithasimple90degree0.150”deepnotch.Asmalltappedholeinthecenterallowedasmallfillerpiecetobeclampedinthenotchtovarythestiffnesschangeduetothenotch.Testswererunwiththefillerpieceremoved,partiallyandfullytightened.3.EXPERIMENTALRESULTSANDANALYSISAllexperimentaldatahavebeencollectedandanalyzedbyusingSpectraQuest’sVibraQuestsoftwarepackage.Transient,Waterfa