Experimental-Modal-Analysis.ppt
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Experimental-Modal-Analysis.ppt
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ExperimentalModalAnalysis,Copyright2003Brel&KjrSound&VibrationMeasurementA/SAllRightsReserved,SDOFandMDOFModelsDifferentModalAnalysisTechniquesExcitingaStructureMeasuringDataCorrectlyModalAnalysisPostProcessing,SimplestFormofVibratingSystem,D,d=Dsinnt,m,k,T,Time,Displacement,Frequency,Period,Tninsec,Frequency,fn=inHz=1/sec,Displacement,k,m,n=2fn=,MassandSpring,time,m1,m,Increasingmassreducesfrequency,Mass,SpringandDamper,Increasingdampingreducestheamplitude,M=mass(force/acc.)C=damping(force/vel.)K=stiffness(force/disp.),BasicSDOFModel,SDOFModelsTimeandFrequencyDomain,H(),F(),X(),ModalMatrix,ModalModel(Freq.Domain),MDOFModel,0-90-180,m,d1+d2,d1,dF,2,1,1+2,1,2,1+2,Frequency,Frequency,Phase,Magnitude,WhyBotherwithModalModels?
PhysicalCoordinates=CHAOS,ModalSpace=Simplicity,q1,1,1,q3,1,3,DefinitionofFrequencyResponseFunction,F,X,f,f,f,H(f)isthesystemFrequencyResponseFunctionF(f)istheFourierTransformoftheInputf(t)X(f)istheFourierTransformoftheOutputx(t),F(f),H(f),X(f),BenefitsofFrequencyResponseFunction,F(f),H(f),X(f),FrequencyResponseFunctionsarepropertiesoflineardynamicsystemsTheyareindependentoftheExcitationFunctionExcitationcanbeaPeriodic,RandomorTransientfunctionoftimeThetestresultobtainedwithonetypeofexcitationcanbeusedforpredictingtheresponseofthesystemtoanyothertypeofexcitation,ComplianceDynamicstiffness(displacement/force)(force/displacement)MobilityImpedance(velocity/force)(force/velocity)InertanceorReceptanceDynamicmass(acceleration/force)(force/acceleration),DifferentFormsofanFRF,AlternativeEstimators,X(f),F(f),H(f),WhichFRFEstimatorShouldYouUse?
Definitions:
UsercanchooseH1,H2orH3aftermeasurement,Accuracy,Accuracyforsystemswith:
H1H2H3Inputnoise-Best-OutputnoiseBest-Input+outputnoise-BestPeaks(leakage)-Best-Valleys(leakage)Best-,SDOFandMDOFModelsDifferentModalAnalysisTechniquesExcitingaStructureMeasuringDataCorrectlyModalAnalysisPostProcessing,ThreeTypesofModalAnalysis,HammerTestingImpactHammertaps.serialorparallelmeasurementsExciteswidefrequencyrangequicklyMostcommonlyusedtechniqueShakerTestingModalExcitershakesproduct.serialorparallelmeasurementsManytypesofexcitationtechniquesOftenusedinmorecomplexstructuresOperationalModalAnalysisUsesnaturalexcitationofstructure.serialorparallelmeasurementsCuttingedgetechnique,DifferentTypesofModalAnalysis(Pros),HammerTestingQuickandeasyTypicallyInexpensiveCanperformpoormanmodalaswellasfullmodalShakerTestingMorerepeatablethanhammertestingManytypesofinputavailableCanbeusedforMIMOanalysisOperationalModalAnalysisNoneedforspecialboundaryconditionsMeasurein-situUsenaturalexcitationCanperformothertestswhiletakingOMAdata,DifferentTypesofModalAnalysis(Cons),HammerTestingCrestfactorsdueimpulsivemeasurementInputforcecanbedifferentfrommeasurementtomeasurement(differentoperators,difficultlocation,etc.)Calibratedelbowrequired(doublehits,etc.)TipperformanceoftenanoverlookedissueShakerTestingMoredifficulttestsetup(stingers,exciter,etc.)UsuallymoreequipmentandchannelsneededSkilledoperator(s)neededOperationalModalAnalysisUnscaledmodalmodelExcitationassumedtocoverfrequencyrangeofinterestLongtimehistoriessometimesrequiredComputationallyintensive,FrequencyResponseFunction,Input,Output,FFT,FFT,HammerTestonFree-freeBeam,Frequency,Distance,Amplitude,Beam,Rovinghammermethod:
ResponsemeasuredatonepointExcitationofthestructureatanumberofpointsbyhammerwithforcetransducer,Pressanywheretoadvanceanimation,Modesofstructureidentified,FRFsbetweenexcitationpointsandmeasurementpointcalculated,Acceleration,MeasurementofFRFMatrix(SISO),OnerowOneRovingExcitationOneFixedResponse(reference)SISO,=,X1H11H12H13.H1nF1X2H21H22H23.H2nF2X3H31H32H33.H3nF3:
XnHn1Hn2Hn3.HnnFn,MeasurementofFRFMatrix(SIMO),MorerowsOneRovingExcitationMultipleFixedResponses(references)SIMO,=,X1H11H12H13.H1nF1X2H21H22H23.H2nF2X3H31H32H33.H3nF3:
XnHn1Hn2Hn3.HnnFn,FRFsbetweenexcitationpointandmeasurementpointscalculated,Whitenoiseexcitation,ShakerTestonFree-freeBeam,Frequency,Distance,Amplitude,FirstMode,SecondMode,ThirdMode,Beam,Acceleration,Pressanywheretoadvanceanimation,Force,Shakermethod:
ExcitationofthestructureatonepointbyshakerwithforcetransducerResponsemeasuredatanumberofpoints,Modesofstructureidentified,MeasurementofFRFMatrix(ShakerSIMO),OnecolumnSingleFixedExcitation(reference)SingleRovingResponseSISOorMultiple(Roving)ResponsesSIMOMultiple-Output:
Optimizedataconsistency,X1H11H12H13.H1nF1X2H21H22H23.H2nF2X3H31H32H33.H3nF3:
XnHn1Hn2Hn3.HnnFn,=,WhyMultiple-InputandMultiple-Output?
Multiple-Input:
Forlargeand/orcomplexstructuresmoreshakersarerequiredinorderto:
gettheexcitationenergysufficientlydistributedandavoidnon-linearbehaviourMultiple-Output:
Measureoutputsatthesametimeinordertooptimizedataconsistencyi.e.MIMO,SituationsneedingMIMO,Oneroworonecolumnisnotsufficientfordeterminationofallmodesinfollowingsituations:
Moremodesatthesamefrequency(repeatedroots),e.g.symmetricalstructuresComplexstructureshavinglocalmodes,i.e.referenceDOFwithmodaldeflectionforallmodesisnotavailableInbothcasesmorecolumnsormorerowshavetobemeasured-i.e.polyreference.Solutions:
ImpactHammerexcitationwithmoreresponseDOFsOneshakermovedtodifferentreferenceDOFsMIMO,MeasurementofFRFMatrix(MIMO),=,MorecolumnsMultipleFixedExcitations(references)SingleRovingResponseMISOorMultiple(Roving)ResponsesMIMO,X1H11H12H13.H1nF1X2H21H22H23.H2nF2X3H31H32H33.H3nF3:
XnHn1Hn2Hn3.HnnFn,ModalAnalysis(classic):
FRF=Response/Excitation,Output,FFT,FFT,InverseFFT,Excitation,Response,Force,Vibration,Input,Output,H(w)=,=,=,FrequencyResponseFunction,ImpulseResponseFunction,TimeDomain,FrequencyDomain,OperationalModalAnalysis(OMA):
Responseonly!
NaturalExcitation,SDOFandMDOFModelsDifferentModalAnalysisTechniquesExcitingaStructureMeasuringDataCorrectlyModalAnalysisPostProcessing,TheEternalQuestioninModal,F1,F2,a,ToTap,or.,ToShake!
ImpactExcitation,MeasuringonerowoftheFRFmatrixbymovingimpactposition,LAN,#1,#2,#3,#4,#5,Accelerometer,ForceTransducer,ImpactExcitation,t,a(t),GAA(f),f,Magnitudeandpulsedurationdependson:
WeightofhammerHammertip(steel,plasticorrubber)DynamiccharacteristicsofsurfaceVelocityatimpactFrequencybandwidthinverselyproportionaltothepulseduration,a(t),t,1,2,1,2,WeightingFunctionsforImpactExcitation,Howtoselectshiftandlengthfortransientandexponentialwindows:
Leakageduetoexponentialtimeweightingonresponsesignaliswelldefinedandthereforecorrectionofthemeasureddampingvalueisoftenpossible,Transientweightingoftheinputsignal,Criteria,Exponentialweightingoftheoutputsignal,CompensationforExponentialWeighting,Withexponentialweightingoftheoutputsignal,themeasuredtimeconstantwillbetooshortandthecalculateddecayconstantanddampingratiothereforetoolarge,shift,Length=,Recordlength,T,Originalsignal,Weightedsignal,Windowfunction,Time,1,b(t),Correctionofdecayconstantsanddampingratioz:
Correctvalue,Measuredvalue,3lbHandSledge,Rangeofhammers,Buildingandbridges,12lbSledge,Largeshaftsandlargermachinetools,Carframedandmachinetools,1lbhammer,Components,GeneralPurpose,0.3lb,Hard-drives,circuitboards,turbineblades,MiniHammer,Application,Description,Impacthammerexcitation,Advantages:
SpeedNofixturingNovariablemassloadingPortableandhighlysuitableforfieldworkrelativelyinexpensiveDisadvantagesHighcrestfactormeanspossibilityofdrivingstructureintonon-linearbehaviorHighpeakforceneededforlargestructuresmeanspossibilityoflocaldamage!
Highlydeterministicsignalmeansnolinearapproximation,ConclusionBestsuitedforfieldworkUsefulfordeterminingshakerandsupportlocations,ShakerExcitation,MeasuringonecolumnoftheFRFmatrixbymovingresponsetransducer,#1,#2,#3,#4,#5,Accelerometer,ForceTransducer,VibrationExciter,LAN,AttachmentofTransducersandShaker,Accelerometermounting:
StudCementWax(Magnet),ForceTransducerandShaker:
StudStinger(ConnectionRod),PropertiesofStingerAxialStiffness:
HighBendingStiffness:
Low,Accelerometer,Shaker,F,a,ForceTransducer,AdvantagesofStinger:
NoMomentExcitationNoRotationalInertiaLoadingProtectionofShakerProtectionofTransducerHelpspositioningofShaker,ConnectionofExciterandStructure,Exciter,Measuredstructure,Slenderstinger,Accelerometer,ForceTransducer,Tipmass,m,Shaker/Hammermass,M,Fs,Fm,Piezoelectricmaterial,Structure,Forceandaccelerationmeasurementsunaffectedbystingercompliance,but.Minormasscorrectionrequiredtodetermineactualexcitation,ShakerReactionForce,Reactionbyexternalsupport,Reactionbyexciterinertia,Exampleofanimproperarrangement,StructureSuspension,ExciterSupport,StructureSuspension,ExciterSuspension,SineExcitation,a(t),Time,A,Crestfactor,Forstudyofnon-linearities,e.g.harmonicdistortion,Forbroadbandexcitation:
SinewavesweptslowlythroughthefrequencyrangeofinterestQuasi-stationarycondition,RMS,SweptSineExcitation,Advantages,LowCrestFactorHighSignal/NoiseratioInputforcewellcontrolledStudyofnon-linearitiespossible,Disadvantages,VeryslowNolinearapproximationofnon-linearsystem,RandomExcitation,A(f1),Freq.,Time,a(t),B(f1),GAA(f),N=1,GAA(f),N=10,RandomvariationofamplitudeandphaseAveragingwillgiveoptimumlinearestimateincaseofnon-linearities,Freq.,SystemOutput,SystemInput,RandomExcitation,Randomsignal:
Characterizedbypowerspectraldensity(GAA)andamplitudeprobabilitydensity(p(a),a(t),p(a),Time,Canbebandlimitedaccordin
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- Experimental Modal Analysis