Rotating Machinery Vibration: From Analysis to Troubleshooting, Second Edition

478 Pages·2009·7.87 MB·English

by  Maurice L. Adams

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Library of Congress Cataloging-in-Publication Data
Adams, Maurice L.
Rotating machinery vibration : from analysis to troubleshooting / author, Maurice
L. Adams.
p. cm.
“A CRC title.”
Includes bibliographical references and index.
ISBN 978-1-4398-0717-0 (hardcover : alk. paper)
1. Turbomachines--Vibration. 2. Rotors--Vibration. I. Title.
TJ266.A33 2010
621.406--dc22 2009041606
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Contents
Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvii
Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxi
Author . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxv
PartI PrimeronRotorVibration
1 VibrationConceptsandMethods . . . . . . . . . . . . . . . . . . . . . . 3
1.1 One-Degree-of-FreedomModel . . . . . . . . . . . . . . . . . . . . . 3
1.1.1 AssumptionofLinearity . . . . . . . . . . . . . . . . . . . . . . 3
1.1.2 UnforcedSystem . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.1.3 Self-ExcitedDynamic-InstabilityVibrations. . . . . . . . 6
1.1.4 Steady-StateSinusoidallyForcedSystems . . . . . . . . . 7
1.1.5 Damping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.1.6 UndampedNaturalFrequency:AnAccurate
Approximation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.1.7 1-DOFModelasanApproximation. . . . . . . . . . . . . . 11
1.2 Multi-DOFModels. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.2.1 Two-DOFModels . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.2.2 MatrixBandwidthandZeros . . . . . . . . . . . . . . . . . . 16
1.2.3 StandardRotorVibrationAnalyses . . . . . . . . . . . . . . 18
1.3 Modes,Excitation,andStabilityofMulti-DOF
Models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
1.3.1 ModalDecomposition . . . . . . . . . . . . . . . . . . . . . . . 19
1.3.2 ModalDamping . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
1.3.3 ForcedSystemsDecoupledinModal
Coordinates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
1.3.4 HarmonicExcitationofLinearMulti-DOF
Models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
1.3.5 DynamicInstability:TheComplex
EigenvalueProblem . . . . . . . . . . . . . . . . . . . . . . . . . 28
1.4 Summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
2 LateralRotorVibrationAnalysisModels. . . . . . . . . . . . . . . . . 35
2.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.2 SimpleLinearModels . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2.2.1 Point–Mass2-DOFModel. . . . . . . . . . . . . . . . . . . . . 37
vii
viii Contents
2.2.2 JeffcottRotorModel . . . . . . . . . . . . . . . . . . . . . . . . . 39
2.2.3 SimpleNontrivial8-DOFModel . . . . . . . . . . . . . . . . 41
2.2.3.1 LagrangeApproach(i). . . . . . . . . . . . . . . . . . 44
2.2.3.2 LagrangeApproach(ii) . . . . . . . . . . . . . . . . . 49
2.2.3.3 DirectF=maApproach . . . . . . . . . . . . . . . . 52
2.3 FormulationsforRDASoftware . . . . . . . . . . . . . . . . . . . . . 55
2.3.1 BasicRotorFiniteElement . . . . . . . . . . . . . . . . . . . 55
2.3.2 ShaftElementLumpedMassMatrix . . . . . . . . . . . . 57
2.3.3 ShaftElementDistributedMassMatrix . . . . . . . . . . 58
2.3.4 ShaftElementConsistentMassMatrix. . . . . . . . . . . 59
2.3.5 ShaftElementStiffnessMatrix. . . . . . . . . . . . . . . . . 61
2.3.6 ShaftElementGyroscopicMatrix . . . . . . . . . . . . . . 62
2.3.7 AdditionofNonstructuralMassandInertiato
RotorElement . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
2.3.8 MatricesforCompleteFree–FreeRotor . . . . . . . . . . 63
2.3.9 Radial-BearingandBearing-SupportModels . . . . . . 64
2.3.9.1 BearingCoefficientsConnectRotor
DirectlytoGround . . . . . . . . . . . . . . . . . . . 67
2.3.9.2 BearingCoefficientsConnecttoan
IntermediateMass. . . . . . . . . . . . . . . . . . . . 68
2.3.10 CompletedRDAModelEquationsofMotion. . . . . . 70
2.4 InsightsintoLinearLRVs . . . . . . . . . . . . . . . . . . . . . . . . . . 70
2.4.1 SystemswithNonsymmetricMatrices . . . . . . . . . . . 71
2.4.2 ExplanationofGyroscopicEffect. . . . . . . . . . . . . . . . 77
2.4.3 IsotropicModel . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
2.4.4 PhysicallyConsistentModels . . . . . . . . . . . . . . . . . . 82
2.4.5 CombinedRadialandMisalignmentMotions . . . . . . 82
2.5 NonlinearEffectsinRotorDynamicalSystems . . . . . . . . . . 83
2.5.1 LargeAmplitudeVibrationSourcesthatYield
NonlinearEffects . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
2.5.2 Journal-BearingNonlinearitywithLargeRotor
Unbalance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
2.5.3 UnloadedTilting-PadSelf-ExcitedVibrationin
JournalBearings . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
2.5.4 Journal-BearingHysteresisLoop. . . . . . . . . . . . . . . . 96
2.5.5 Shaft-on-BearingImpacting . . . . . . . . . . . . . . . . . . . 97
2.5.6 ChaosinRotorDynamicalSystems. . . . . . . . . . . . . . 99
2.5.7 NonlinearDampingMasksOilWhipand
SteamWhirl . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
2.5.7.1 OilWhipMasked . . . . . . . . . . . . . . . . . . . . . 100
2.5.7.2 SteamWhirlMasked . . . . . . . . . . . . . . . . . . . 101
2.5.8 NonlinearBearingDynamicsExplains
CompressorBearingFailure . . . . . . . . . . . . . . . . . . . 101
2.6 Summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
Contents ix
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
Textbooks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
SelectedPapersConcerningRotorDynamicsInsights . . . . . . . . 105
SelectedPapersonNonlinearRotorDynamics . . . . . . . . . . . . . 105
3 TorsionalRotorVibrationAnalysisModels. . . . . . . . . . . . . . . 111
3.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
3.2 Rotor-BasedSpinningReferenceFrames . . . . . . . . . . . . . . . 113
3.3 SingleUncoupledRotor . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
3.3.1 LumpedandDistributedMassMatrices . . . . . . . . . . 115
3.3.1.1 LumpedMassMatrix . . . . . . . . . . . . . . . . . . 115
3.3.1.2 DistributedMassMatrix . . . . . . . . . . . . . . . . 116
3.3.2 StiffnessMatrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
3.4 CoupledRotors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
3.4.1 CoaxialSame-SpeedCoupledRotors . . . . . . . . . . . . 120
3.4.2 UnbranchedSystemswithRigidandFlexible
Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
3.4.2.1 RigidConnections. . . . . . . . . . . . . . . . . . . . . 122
3.4.2.2 FlexibleConnections . . . . . . . . . . . . . . . . . . . 124
3.4.2.3 CompleteEquationsofMotion . . . . . . . . . . . 124
3.4.3 BranchedSystemswithRigidandFlexible
Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
3.4.3.1 RigidConnections. . . . . . . . . . . . . . . . . . . . . 127
3.4.3.2 FlexibleConnections . . . . . . . . . . . . . . . . . . . 129
3.4.3.3 CompleteEquationsofMotion . . . . . . . . . . . 129
3.5 SemidefiniteSystems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
3.6 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
3.6.1 High-CapacityFanforLargeAltitude
WindTunnel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
3.6.2 Four-SquareGearTester . . . . . . . . . . . . . . . . . . . . . . 132
3.6.3 LargeSteamTurbo-GeneratorSets . . . . . . . . . . . . . . 134
3.7 Summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
PartII RotorDynamicAnalyses
4 RDACodeforLateralRotorVibrationAnalyses . . . . . . . . . . . 141
4.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
4.2 UnbalanceSteady-StateResponseComputations . . . . . . . . 142
4.2.1 3-MassRotorModel+2Bearingsand1Disk . . . . . . 145
4.2.2 PhaseAngleExplanationandDirection
ofRotation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149