SECOND EDITION ROTATING MACHINERY VIBRATION From Analysis to Troubleshooting MAURICE L. ADAMS, JR Case Western Reserve University Cleveland, Ohio C\ CRC Press W^ У Taylor &. Francis Group Boca Raton London New York CRC Press is an imprint of the Taylor & Francis Group, an inform a business
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S E C O N D E D I T I O N
ROTATING MACHINERY V I B R A T I O N
From Analysis to Troubleshooting
MAURICE L. ADAMS, JR Case Western Reserve University
Cleveland, Ohio
C\ CRC Press W ^ У Taylor &. Francis Group
Boca Raton London New York
CRC Press is an imprint of the Taylor & Francis Group, an inform a business
Contents
Preface xvii Acknowledgments xxi Author xxv
Part I Primer on Rotor Vibration
1 Vibration Concepts and Methods 3 1.1 One-Degree-of-Freedom Model 3
1.1.1 Assumption of Linearity 3 1.1.2 Unforced System 4 1.1.3 Self-Excited Dynamic-Instability Vibrations 6 1.1.4 Steady-State Sinusoidally Forced Systems 7 1.1.5 Damping 8 1.1.6 Undamped Natural Frequency: An Accurate
Approximation 10 1.1.7 1-DOF Model as an Approximation 11
1.2 Multi-DOF Models 13 1.2.1 Two-DOF Models 13 1.2.2 Matrix Bandwidth and Zeros 16 1.2.3 Standard Rotor Vibration Analyses 18
1.3 Modes, Excitation, and Stability of Multi-DOF Models 19 1.3.1 Modal Decomposition 19 1.3.2 Modal Damping 24 1.3.3 Forced Systems Decoupled in Modal
Coordinates 27 1.3.4 Harmonic Excitation of Linear Multi-DOF
2.2.2 Jeffcott Rotor Model 39 2.2.3 Simple Nontrivial 8-DOF Model 41
2.2.3.1 Lagrange Approach (i) 44 2.2.3.2 Lagrange Approach (ii) 49 2.2.3.3 Direct F — ma Approach 52
2.3 Formulations for RDA Software 55 2.3.1 Basic Rotor Finite Element 55 2.3.2 Shaft Element Lumped Mass Matrix 57 2.3.3 Shaft Element Distributed Mass Matrix 58 2.3.4 Shaft Element Consistent Mass Matrix 59 2.3.5 Shaft Element Stiffness Matrix 61 2.3.6 Shaft Element Gyroscopic Matrix 62 2.3.7 Addition of Nonstructural Mass and Inertia to
Rotor Element 62 2.3.8 Matrices for Complete Free-Free Rotor 63 2.3.9 Radial-Bearing and Bearing-Support Models 64
2.3.9.1 Bearing Coefficients Connect Rotor Directly to Ground 67
2.3.9.2 Bearing Coefficients Connect to an Intermediate Mass 68
2.3.10 Completed RDA Model Equations of Motion 70 2.4 Insights into Linear LRVs 70
2.4.1 Systems with Nonsymmetric Matrices 71 2.4.2 Explanation of Gyroscopic Effect 77 2.4.3 Isotropic Model 79 2.4.4 Physically Consistent Models 82 2.4.5 Combined Radial and Misalignment Motions 82
2.5 Nonlinear Effects in Rotor Dynamical Systems 83 2.5.1 Large Amplitude Vibration Sources that Yield
Nonlinear Effects 84 2.5.2 Journal-Bearing Nonlinearity with Large Rotor
Unbalance 85 2.5.3 Unloaded Tilting-Pad Self-Excited Vibration in
Journal Bearings 94 2.5.4 Journal-Bearing Hysteresis Loop 96 2.5.5 Shaft-on-Bearing Impacting 97 2.5.6 Chaos in Rotor Dynamical Systems 99 2.5.7 Nonlinear Damping Masks Oil Whip and