12 1989 shaft stress
DESCRIPTION
12 1989 Shaft StressTRANSCRIPT
-
4BENTLYROTOR DYNAMICS
ORBIT December1989
__ ~) ShaftCenterLINESRESEARCH CORPORATION
FigureIRotatingshaftcircularsynchronous(IX)orbitingarounda neutralaxisataconstantspeed.Constantstressinshaftfibers.
By Dr.AgnesMuszynskaSeniorResearchScientist
BentlyRotorDynamicsResearchCorporation
This articlediscussesrotorlat-eral vibrations and radial
preload-related rotor dis-placementsas a source oflow andhighcyclefatigueof
rotormaterial.
The availability of vibration trans-ducersandvibrationmDnitoringsystemscreatedundisputableawarenessofvibra-tion levelsin machinery.Vibrations ofrotorsandof other machineparts,suchas blades, couplings, pedestals andcasings,occurasasideeffectof themaindynamicmode, namelyshaft rotation.Due to the existenceof severalphysicalmechanisms,part of the rotativeenergybecomestransferredinto the energyofvibration at various modes.The rotor
itself,thecarrierof therotativeenergy,ismostpronetovibrationalmotion.Vibra-tionsof othermachineelementsareusu-
ally secondaryto the rotor. They aretransmittedfrom therotor.Shaftlateral
vibrationsareamongthemostdamagingandoftendestructivevibrationalmodes.
Vibration monitoringsystems,whicharenowwidelyusedon machinery,havecreatedanoverallimpressionthatvibra-tions are unwelcome and that the
vibrationlevelon machineryshouldbekept aslow aspossible.This philosophygenerallyholds true.There is, however,onecatch.
A horrorstory"Our machineshaveverylowvibration
levels;' the maintenance technician
__ NEUTRAL AXIS
SHAFT
PRECESSION (ORBITING)
WlTH FREQUENCY w
of a chemical plant told us proudly."Since we installedthe vibration mon-
itoringsystem,wecanmonitorandcontrolvibrations.If the vibration level is too
high,wesimplypreloadtheshaftbymis-aligning it within the machine train,until vibration sufficiently decreases.
No vibration,no problem!"
COUNTERCLOCKWlSE ROTATION
'MTH FREQUENCY W
HIGH SPOT
1 ROTAllON I TIME
-
ONE ORBITING PERIOD
December1989
Twomonthslater,thistechnicianwasverysurprisedwhen,subsequently,theshaftsin twomachinesbroke,creatingamajordisasterfortheplant.Why?Therewasnobadvibrationandyettheshaftsbroke?
ShaftstressThis unfortunatetechnicianover-
looked one important aspect.Themachineshaftnotonlyvibrates;theshaftalsorotates.Thus,theshaft'sdynamicmotionhastwoimportantcomponentswhichcontributetoshaftmaterialstress.Shaftbreakageis duetoeitherstressinthematerialexceedingtheultimatelimitorduetolowcycleorhighcyclefatigue.In thenextsectionswewillexplainhowto correlateshaftvibrationand shaftmaterialstress.
Theleastdamagingmode:Shaftlateralsynchronousvibrationaroundaneutralaxis
Synchronous(IX) lateralvibrationsof rotatingshaftsare mainlydue tounbalance.Evenwell-balancedshaftsexperiencesomeresidualsynchronousvibration in two orthogonallateraldirections(e.g,horizontalandvertical),
ONE ROTATION
ORBIT
whichare perpendicularto the shaftaxis.The resultingshaftmodeis repre-sentedbythefamiliarorbiting.FigureIillustratestheinstancewheretherotat-ingshaft'sIX orbitiscircular.Thecon-ventionofthedrawingisasfollows:Theorbitis,in fact,muchsmallerthantheshaftradius.Imagine,however,thatthecirclesdonotrepresenttheentireshaftcrosssections,but just tiny portionsaroundtheshaftcenter.The stressattheshaftsurfacewillberoughlypropor-tional to the stressat the surfaceofthesetinycircles.Sincetheconsidera-tionsherearequalitative,thisconven-tionprovidessatisfactoryresults.
When the shaftvibrationmodeispurelysynchronousandtheorbitiscir-culararoundaneutral(nostress)axis,then,ata constantrotativespeed,partof the shaft fibers are constantlystretched.Another part is constantlycompressed.Themoststretchedsectionoccursattheshafthighspot.If theIXvibrationamplitudeis not large,themaximumstressremainswithin anacceptableconstantlevel.Althoughshaftvibrationis alwaysunwelcome,this synchronouscircular vibrationmodearoundthe neutralaxisis lessdamagingtotheshaft.
COUNTERCLOCKWISE ROTATION
WITI-i FREQUENCY W
ElUPTICAL 1X ORBIT
TIME
5
Preloadeffect:Periodicallyvariablestress
Assumethat the unbalancedshaft,rotatingat a constantspeed,is pre-loadedbyaconstantradialforce.Suchforcecanbegenerated,for instance,byamisalignment,bygravityonhorizontalrotorsorbyaradialpumpingsideload,suchasin asinglevolutepump.In thiscase, the shaft centerlinebecomesdeformedand thusput understress,roughlyproportionalto the preload-resultingdisplacement(Figure2).Dueto thecombinationof rotationandIXorbiting,theshaftfibersareperiodicallystretchedandcompressed.Thus, thedisplacementof theshaftneutralaxisresultsin muchmoresevereconditionsontheshaft.EvenasmallIX vibrationamplitude(asmeasuredbyaproximityprobe)andsomeshaftpreload-relateddisplacement(also measuredby theproximityprobe as the dc gap) mayresult in significantlyhigh reversal,cyclicstressin theshaft.
Thisperiodicvariablestress(withIXfrequency)leadstomaterialfatigue,tolowcyclefatiquewhenstressamplitudesare largeand to highcyclefatique~
~I
-+-
TIME
Figure2Preloadedrotatingshaft:displacedIX orbitexhibitsamoreellipticalshape.Shaftfibersareunderreversalcyclicstress.
Figure3Shaftstressduringwhipconditions.Whipfrequency=1/4rotativefrequency.Shaftstressfrequency= 3/4rotativespeedfrequency.
-
6cyclefatigueresultswhenthe ampli-tudesaresmaller.Thelowcyclefatigueoccursrelativelyquicklydue to non-linearplasticdeformations.The highcyclefatiguerequiresmanymorecyclesof reversalstress(of108to 109range)todamagetheshaftmaterial.Thenumber108seemstobeaverylarge.Calculate,however,howmanycyclesa machinemakeswhilecontinuouslyoperatingataconstantspeedof3600rpm.In only500hoursof operation,thenumberof IXfrequencyreversalstresscyclesreaches1.08X 108.Therefore,in abouttwentydaysthe highcyclefatigueconditionsmayeasilyoccur.This mayresult inshaftcrackingandbreakage.
Othercasesof shaftstress
Highor lowcyclefatigueconditionsmayresultfromeither(1) a largepre-load andsmallvibrationas discussedabove,(2)a largevibrationof thenon-synchronoustypeor (3) a largevibra-tiontogetherwithasmallpreload.
In thecaseof highpreload-resultingdisplacementof the shaftcenterline,thefrequencyof shaftreversalstressisalwaysIX for anyvibrationpatternoftheshaft,if thedisplacementis larger
ORBIT
thanthevibrationamplitude(peak).
In thecaseof largenonsynchronousvibrationsof the shaftwith no initialdisplacement,the reversalstressfre-quencycanbeestimatedastheabsolutevalueof thedifferencebetweenvibra-tion androtativefrequencieswith therelativedirectionsofrotationandorbit-ingtakenintoaccount.Thus,if therotoris in forwardwhipconditionwithsub-synchronousfrequencyl/4X, theshaftwillbecyclicallystressedwithfrequency3/4X(Figure3).If theshaftoperatesatits halt-balanceresonancespeed,andtheorbithasa IX andasignificant2Xforwardcomponent,then, the shaftstresswillhaveIX frequency(Figure4).The rub-relatedself-excitedbackwardvibrations("drywhip")withfrequency,for instance,twicehigherthanrotativespeed,result in 3X frequencyshaftreversalstress(Figure5). In thiscase,however,therubbingdamagewillmostprobablyoccurmuchearlierthananyfatiguedamage.
Theunbalance-relatedIX shaftvibra-tionsseldomresultin circularorbits.Asymmetryofstiffnessandotherparam-etersin twoorthogonaldirectionsof theshaftitself,as well as the supporting
December 1989
structure,usuallycausestheIX orbitstobeelliptical.FortheellipticalIX orbits,theshaftstresshasapulsatingcharacterwithfrequency2X (Figure6).Pulsatingstressoccursalsointheshaft,vibratinginthecircularorbitmodewithashaftcen-teronlyslightlydisplaced(Figure7).
Shaftmode
The shaft-observingproximitytrans-ducersareusuallymountedat,or nextto,bearings.At themachineoperatingspeed,theselocationsmightbe verycloseto nodalpointsat whichlateralvibrationsdo notoccur.The anticipa-tionof theactualshaftvibrations,andlocationof theanti-nodal,highampli-tudevibrationsectionsshouldbebasedonmodalconsiderations.Twomils(5011m)of shaftvibrationat the bearingmaytranslateinto50mils(127011m)atmid-spanof the rotor.On the otherhand,thesetwomilsatthebearingmaybe accompaniedbythemisalignment-relatedpreloadandhighreversalstressin theshaft.The axiallocationof thepreloadforcein considerationof thevibration mode shapessignificantlyaffectsthe shaft stressdistribution.Additionalstressconcentrationfactorsalongthe shaft,suchas press-fitted
TIME
SHAFT
ORBIT
SHAFTORBIT
Figure4Orbit, consistingof IX and a significant2Xcomponent,resultsin shaftstressfrequencyIX.
Figure5Rotor/sealbackward"drywhip"orbitwith2Xfrequencyresultsin 3Xfrequencyreversalstressontheshaft.
-
December 1989
partsor diameterdiscontinuities,mayjeopardizethe shaft conditionevenmore.
Diagnosisusingvibrationmonitoringwarnsaboutshafthigh stress
The casesdiscussedaboveindicate.thattheshaftstressconditionscanbeeasily predicted if the machine isequippedwith a vibrationmonitoringsystembasedon shaftobservingdis-placementproximitytransducers.Theadvantageof theuseof displacementtransducers,as opposedto VelocitySeismoprobesand accelerometers,consistsof theabilitytomeasureshaftstatic(zerofrequency)displacements,i.e,theshaftcenterlineposition,aroundwhichvibrationtakesplace.Changesinshaftstressconditionsdependnotablynot onlyon thevibrationlevel,tradi-tionallyconsideredas the main andoftenonlycauseof machineproblems,butalsoontheshaftcenterlineposition.The latter should be continuouslyobservedandcorrelatedwiththeshaftvibrationlevelin ordertoavoidprema-turestress-relateddamageofrotors.
ORBIT
ShaftcrackingShaftcrackinitiationmayhavevar-
iousorigins,suchascorrosion,materialirregularity,and/orinclusions,etc.Interms of mechanicalperformance,thesematerialdefectsactasstresscon-centratingfactors.Theshaftstressisthemajor reasonthat crackspropagate;thus,highstresspreventionbecomesanimportanttask to maintainmachineintegrity.The earlydetectionof shaftcrackingbyusingvibrationmonitoringequipmenthasbeendescribedin sev-eralpublications[1-4].
Closing remarksNo easilyapplicableandwidely-used
directstressmeasuringinstrumentationisavailableasitexistsforvibrationmon-itoring.Shaft stressduringmachineoperationhasbecomesomehowhiddenand forgotten;it represents,l).owever,the major sourceof potential cata-strophicfailuresof machines.Thepur-pose of this article is to swaythevibration-orientedto a shaft stress-orientedphilosophy,by showingthecorrelationbetweenshaftvibrationandstress.
7
References
1:BentlyNevadaPublicationsonShaftCrackDetection.
2.Bently,D.E., Muszynska,A.,DetectionofRotorCracks.Pro-ceedingsofTexasA&M University15thTurbomachinerySymposiumandShortCourses.CorpusChristi,Texas,November10to13,1986,pp.129-139.
3.Bently,D.E., Muszynska,A. EarlyDetectionofShaftCracksonFluid-HandlingMachines.ProceedingsofASME InternationalSymposiumonFluidMachineryTroubleShoot-ing.1986WinterAnnualMeeting,Anaheim,California,December7to12,1986,.pp.53-58.
4.Bently,D.E.,Muszynska,A.,Thomson,A. S.,VibrationMon-itoringTechniquesandShaftCrackDetectiononReactorCoolantPumpsandRecirculationPumps.EPRI WorkshoponReactorCool-antPumpRecirculation.PumpMonitoringSymposium,Toronto,Ontario,Canada,March29to31,1988.
SHAFT
ORBIT
TIME 1 ROTATION TIME
Figure6IX elliptical orbit causes shaft pulsating stress withfrequency2X.
Figure7IX circular orbit with slightlydisplacedcentercausesshaftpulsatingstresswithfrequencyIX.