7. RotorDynamics and Active Detection of Faults in Rotating Bodies

Rotor Dynamics andActive Detection of Faultsin Rotating BodiesIzhak Bucher

Rotating Machinery vs. non-rotatingDynamicsVibrationIdentificationsignal processingSpeed/Time dependentWhirl vs. vibrateAsymmetry & rotationMany response frequenciesI. Bucher

Disk dynamicsDifferences & similaritiesForward/backward traveling modes (waves)Different wavelength travel at different speedsMost modes (n>1) are de-coupled from shaftmust measure on disk directlyCannot excite from shaft (n>1)Need more sensors (or a scanning laser)I. Bucher

Effect of rotationRotating disc Frequency modulationmodal forceresonanceI. Bucher

RotationStationary excitation & responseMode waveforward backward standingresonanceI. Bucher

Disc vibration - SummaryForce frequencySpeed of rotationResponse frequencies , ±2nResonance frequencies , ±nResponse spectrumForce spectrumfrequencyfrequencyI. Bucher

Transient signal&signal processingI. Bucher

Double sided Spectrumfor a shaftI. Bucher

Forward & backward whirlseparationI. Bucher

Swept sine (runup)• PsdI. Bucher

Time-frequency• SpectrogramI. Bucher

Campbell diagramand time-frequency distributionFrequencySlidingwindowsignalSpeedtimeI. Bucher

Campbell diagram - measuredfrequencyOne sidedDouble sidedtime (speed)time (speed)I. Bucher

disk dynamics (cont.)I. Bucher

Complete test-rigI. Bucher

spectrogram n=2in disc coordinatesunbalancefwdbackwardsI. Bucher

Test Rig - OverviewLaserMeasurement &control systemSensorsActuatorsI. Bucher

Existing test rig @I. Bucher

Using laserDisksMeasurement systemI. Bucher

Active fault detection inrotating partsI. Bucher

21Actuator &sensorActuator &sensorI. Bucher33Technion, ISRAEL

Standard fault diagnosticsFaults can cause high harmonics and modulation in thenormal vibrationsspeed responseConventional fault diagnosticsUse measurements during operationSignal processing, neural networks and statisticsIn practice,Small defects produce small changes in the signalsUnbalance dominant responselow SNR for detection of faultsConsequently: Faults are only detected when theyexceed dangerous levelsI. Bucher

Whirl in presence of a crack0 O0 Oforward 50.4 [Hz]Stress - constant180 O180 O 0 O360 OStatic StressbackwardsStress-50.1 [Hz]1x0 OStress 2x90 O0 O180 O180 O0 O 360 ODynamic Stress

Gasch (1976) - “Breathing Crack Model”General non-linear EOMWeight dominance assumptionLinear Periodic Time VariantM q + (C + G) q + (K 0+ K(t)) q = f (t) Kq 0In papers crack depths are taken at 40% -75% !!!Gasch, R., "A Survey of the Dynamic Behaviorof a Simple Rotating Shaft with a TransverseCrack", Journal of Sound and Vibration, Vol.160(2), pp. 313-332, 1993.

First forward critical speed :62.9 Hz2nd forward critical speed:208 HzI. Bucher

Notch onlyNotch & CrackLog scaleLog scaleFeature is several orders of mag. Smaller than normal dynamicresponse!!!Bucher, I., Seibold, S., "Using combined Temporal and SpatialInformation in Multi-hypothesis Damage Detection", Proc. Of theXV int. Modal Analysis Conf. Orlando, Florida, 1996. 24I. Bucher

Kirson Y. Problems relating to balancing ofasymmetrical rotors, M.Sc. Thesis, Facultyof Mechanical engineering, Technion, Israel,1969.Deviatory inertiaMean inertiaAsymmetry RatiosmallI. Bucher

Body-fix cords.Rotation matrixResponse in inertial C.S. & Taylor expansion O( J2)Single frequencyNo isolationHigh sensitivity near critical speed29I. Bucher

Shaft anisotropyDeviatory stiffnessMean stiffnessResponse in inertial C.S. & Taylor expansion O( J2)3341

34I. Bucher

sensorHarmonic balance & Taylor expansion O( J2)I. Bucher

=94 [Hz] =52 [Hz] 2 - =136 [Hz]ExcitationFreq.UnbalanceresponsesimulationModulatedFreq. 2 - =136 [Hz]Asymmetry -indicator47I. Bucher

53I. Bucher

I. Bucher

asymmetric rotor with and without active probingexperiment5747

Top speed 2250RPM20 RPM/Sec= 101.5Hzfrequencyspeed58I. Bucher

frequencyspeed59I. Bucher

Waterfall diagram of speed-frequency mapssymmetricasymmetricI. Bucher 61

I. Bucher

63I. Bucher

Thank youI. Bucher

Math. backgroundFloquet, G.1883Lyapunov, A.M., 1892Yakubovich,Dynamic investigationCrandall, S.H.,Brosens, P.J.,1961Yamamoto, T.,Ota, H., 1963Tondl, A., 1991Fault detectionIwatsubo, Ariiand Oks 1992Seibold, S., andWeinert, K.,1996Isermann, R.,19972554

Angular unbalanceAsymmetric discDoF - Angular deflectionse1e3e2Angular velocity in rotating C.S.EoM in rotating C.S. for unbalance (synchronous) excitation28I. Bucher

Perfectly balanced sys.External momente1e3e2EoM – body-fixed C.S.Solution – body fix C.S.30I. Bucher

Perfectly balancedSymmetric disce3Anisotropic rotating stiffnesse1e2EoM – body-fixed C.S.32I. Bucher

Classical Rotor Dynamics Modelling3-D model : current practices for axial machinery• Complete model using twolevels of super-elements• Expensivehuge modelmust ignore many effects to analyseThis document is the property of SAMTECH S.A.Norbert KillExeter,September 10th 2008, Page

Classical Rotor Dynamics Modelling3-D model : current practices for axial machineryOne sector wheresome stages areidealized :Several blades per stage in orderto obtain cyclic symmetry:smaller modelignore more effects to analyseThis document is the property of SAMTECH S.A.Norbert KillExeter,September 10th 2008, Page

Structural Dynamics Toolbox• Structural Dynamics Toolbox offers :– 3D Finite Element Modeling– Experimental Modal Analysis– Test / Analysis correlation– Modular approach• MATLAB environmentCADMeshingFEMSimulation• OpenFEM : Core FE software Tests• FEMLink : Import / export industrial modulesRuntime SDTSDT, Visco, Rotor, …OpenFEM FEMlinkMATLAB• Custom extensions (Rotor, Visco, Runtime)• SDT Rotor extends capabilities in rotordynamics– 1 D beam/mass (critical speed, Campbell, forced response)– 3 D cyclic symmetry and full rotor super-element– Time domain (rotor/stator interaction)NASTRANPERMASSAMCEFANSYSUFF / IDEASABAQUSAdamsSimulinkIDEAS TestExcel

SDT Rotor1 D beam/mass (critical speed, Campbell,forced response)3 D models– Cyclic symmetry (mono and multi-stage)– Sector super-element (mono and multi-stage),mistuning, rogue blade, sector model, full andpartial restitution, test/analysis correlation, …– Campbell diagram (body fixed model)– Inertial, thermal and pressure loads,temperature dependent materialsTime domain (rotor/stator interaction)– Shaft superelement in body fixed framee y NL– Non-linear bearing models (currently only NLstiffness and damping)simulation resultreally hard to understandCurrently beta, stable release 2009Images A. Sternchuss, funded by SNECMALocalization due to mistuning, full shaft mode/diameter analysis,Campbell diagram for mistuned disk, time simulation of an engine withgyroscopic effects (funded PSA)

Inertial C.S.Body-Fixed C.S.I. Bucher

Inertial C.S.General formSeries Solution (FLT)37I. Bucher

65I. Bucher

Engine order domain+forwardtime (speed)-backwardI. Bucher

Top speed 2250 RPM, acceleration 20 RPM/sec .60I. Bucher

26I. Bucher

Non-synchronous excitationNatural dynamic responseDetection stageFeature isolationSensitivitySpectral separationAt early stagesUnique, fault dependentfeature signal.High sensitivity to smallchangesTuneable frequency, applicablefor any speed of rotationWhen the fault is severeNo isolation. AdditionalPhenomena may appear near orat the same freq - maskingLow sensitivityNo control over frequencySignal amplificationSignal to noise ratioAdditional S.P.By wisely choosing theexcitation freq.High S.N.R, adjustableUsually not requiredOnly when near critical speedUsually low, unless near criticalspeedMay require sophisticatedalgorithms for enhancement62I. Bucher

I. Bucher

Externally appliedmomentInertia asymmetrysensitive responseSpectral separationAdjustable, high sensitivityNon-hazardous working point3170