ROTATING MACHINERY VIBRATION

Transcription

1 SECOND EDITION ROTATING MACHINERY VIBRATION From Analysis to Troubleshooting MAURICE L. ADAMS, JR Case Western Reserve University Cleveland, Ohio W^ C\ CRC Press У Taylor &. Francis Group Boca Raton London New York CRC Press is an imprint of the Taylor & Francis Group, an inform a business

2 Contents Preface Acknowledgments Author xvii xxi xxv Part I Primer on Rotor Vibration 1 Vibration Concepts and Methods One-Degree-of-Freedom Model Assumption of Linearity Unforced System Self-Excited Dynamic-Instability Vibrations Steady-State Sinusoidally Forced Systems Damping Undamped Natural Frequency: An Accurate Approximation DOF Model as an Approximation Multi-DOF Models Two-DOF Models Matrix Bandwidth and Zeros Standard Rotor Vibration Analyses Modes, Excitation, and Stability of Multi-DOF Models Modal Decomposition Modal Damping Forced Systems Decoupled in Modal Coordinates Harmonic Excitation of Linear Multi-DOF Models Dynamic Instability: The Complex Eigenvalue Problem Summary 31 2 Lateral Rotor Vibration Analysis Models Introduction Simple Linear Models Point-Mass 2-DOF Model 37

3 viii Contents Jeffcott Rotor Model Simple Nontrivial 8-DOF Model Lagrange Approach (i) Lagrange Approach (ii) Direct F ma Approach Formulations for RDA Software Basic Rotor Finite Element Shaft Element Lumped Mass Matrix Shaft Element Distributed Mass Matrix Shaft Element Consistent Mass Matrix Shaft Element Stiffness Matrix Shaft Element Gyroscopic Matrix Addition of Nonstructural Mass and Inertia to Rotor Element Matrices for Complete Free-Free Rotor Radial-Bearing and Bearing-Support Models Bearing Coefficients Connect Rotor Directly to Ground Bearing Coefficients Connect to an Intermediate Mass Completed RDA Model Equations of Motion Insights into Linear LRVs Systems with Nonsymmetric Matrices Explanation of Gyroscopic Effect Isotropic Model Physically Consistent Models Combined Radial and Misalignment Motions Nonlinear Effects in Rotor Dynamical Systems Large Amplitude Vibration Sources that Yield Nonlinear Effects Journal-Bearing Nonlinearity with Large Rotor Unbalance Unloaded Tilting-Pad Self-Excited Vibration in Journal Bearings Journal-Bearing Hysteresis Loop Shaft-on-Bearing Impacting Chaos in Rotor Dynamical Systems Nonlinear Damping Masks Oil Whip and Steam Whirl Oil Whip Masked Steam Whirl Masked Nonlinear Bearing Dynamics Explains Compressor Bearing Failure Summary 104

4 Contents ix Bibliography 104 Textbooks 104 Selected Papers Concerning Rotor Dynamics Insights 105 Selected Papers on Nonlinear Rotor Dynamics Torsional Rotor Vibration Analysis Models Ill 3.1 Introduction Ill 3.2 Rotor-Based Spinning Reference Frames Single Uncoupled Rotor Lumped and Distributed Mass Matrices Lumped Mass Matrix Distributed Mass Matrix Stiffness Matrix Coupled Rotors Coaxial Same-Speed Coupled Rotors Unbranched Systems with Rigid and Flexible Connections Rigid Connections Flexible Connections Complete Equations of Motion Branched Systems with Rigid and Flexible Connections Rigid Connections Flexible Connections Complete Equations of Motion Semidefinite Systems Examples High-Capacity Fan for Large Altitude Wind Tunnel Four-Square Gear Tester Large Steam Turbo-Generator Sets Summary 135 Bibliography 137 Part II Rotor Dynamic Analyses 4 RDA Code for Lateral Rotor Vibration Analyses Introduction Unbalance Steady-State Response Computations Mass Rotor Model + 2 Bearings and 1 Disk Phase Angle Explanation and Direction of Rotation 149

5 X Contents Mass Rotor Model + 2 Bearings/Pedestals and 1 Disk Anisotropie Model: 3-Mass Rotor + 2 Bearings/ Pedestals and 1 Disk Elliptical Orbits Campbell Diagrams Instability Self-Excited-Vibration Threshold Computations Symmetric 3-Mass Rotor + 2 Anisotropic Bearings (Same) and Disk Symmetric 3-Mass Rotor + 2 Anisotropic Bearings (Different) and Disk Additional Sample Problems Symmetric 3-Mass Rotor + 2 Anisotropic Bearings and 2 Pedestals Nine-Stage Centrifugal Pump Model, 17-Mass Stations, 2 Bearings Unbalance Response Instability Threshold Speed Nine-Stage Centrifugal Pump Model, 5-Mass Stations, 2 Bearings Summary 180 Bibliography Bearing and Seal Rotor Dynamics Introduction Liquid-Lubricated Fluid-Film Journal Bearings Reynolds Lubrication Equation For a Single RLE Solution Point Journal Bearing Stiffness and Damping Formulations Perturbation Sizes Coordinate Transformation Properties Symmetry of Damping Array Tilting-Pad Journal Bearing Mechanics Journal Bearing Stiffness and Damping Data and Resources Tables of Dimensionless Stiffness and Damping Coefficients Journal Bearing Computer Codes Fundamental Caveat of LRV Analyses Example Experiments to Measure Dynamic Coefficients 201

6 Contents xi Mechanical Impedance Method with Harmonic Excitation Mechanical Impedance Method with Impact Excitation Instability Threshold-Based Approach Annular Seals Seal Dynamic Data and Resources Ungrooved Annular Seals for Liquids Lomakin Effect Seal Flow Analysis Models Bulk Flow Model Approach Circumferential Momentum Equation Axial Momentum Equation Comparisons between Ungrooved Annular Seals and Journal Bearings Circumferentially Grooved Annular Seals for Liquids Annular Gas Seals Steam Whirl Compared to Oil Whip Typical Configurations for Annular Gas Seals Dealing with Seal LRV-Coefficient Uncertainties Rolling Contact Bearings Squeeze-Film Dampers Dampers with Centering Springs Dampers without Centering Springs Limitations of Reynolds Equation-Based Solutions Magnetic Bearings Unique Operating Features of Active Magnetic Bearings Short Comings of Magnetic Bearings Compliance Surface Foil Gas Bearings Summary 246 Bibliography Turbo-Machinery Impeller and Blade Effects Centrifugal Pumps Static Radial Hydraulic Impeller Force Dynamic Radial Hydraulic Impeller Forces Unsteady Flow Dynamic Impeller Forces Interaction Impeller Forces 257

7 xii Contents 6.2 Centrifugal Compressors Overall Stability Criteria Utilizing Interactive Force Modeling Similarities with Pumps High-Pressure Steam Turbines and Gas Turbines Steam Whirl Blade Tip Clearance Contribution Blade Shroud Annular Seal Contribution Partial Admission in Steam Turbine Impulse Stages Combustion Gas Turbines Axial Flow Compressors Summary 272 Bibliography 272 Part III Monitoring and Diagnostics 7 Rotor Vibration Measurement and Acquisition Introduction to Monitoring and Diagnostics Measured Vibration Signals and Associated Sensors Accelerometers Velocity Transducers Displacement Transducers Background Inductance (Eddy-Current) Noncontacting Position Sensing Systems Vibration Data Acquisition Continuously Monitored Large Multibearing Machines Monitoring Several Machines at Regular Intervals Research Laboratory and Shop Test Applications Signal Conditioning Filters Amplitude Conventions Summary 295 Bibliography Vibration Severity Guidelines Introduction Casing and Bearing Cap Vibration Displacement Guidelines Standards, Guidelines, and Acceptance Criteria Shaft Displacement Criteria 301

8 Contents xiii 8.5 Summary 302 Bibliography 303 Bibliography Supplement Signal Analysis and Identification of Vibration Causes Introduction Vibration Trending and Baselines FFT Spectrum Rotor Orbit Trajectories Bode, Polar, and Spectrum Cascade Plots Wavelet Analysis Tools Chaos Analysis Tools Symptoms and Identification of Vibration Causes Rotor Mass Unbalance Vibration Self-Excited Instability Vibrations Oil Whip Steam Whirl Instability Caused by Internal Damping in the Rotor Other Instability Mechanisms Rotor-Stator Rub-Impacting Misalignment Resonance Mechanically Loose Connections Cracked Shafts Rolling-Element Bearings, Gears, and Vane/Blade-Passing Effects Summary 343 Bibliography 344 Part IV Trouble-Shooting Case Studies 10 Forced Vibration and Critical Speed Case Studies Introduction HP Steam Turbine Passage through First Critical Speed HP-IP Turbine Second Critical Speed through Power Cycling Boiler Feed Pumps: Critical Speeds at Operating Speed Boiler Feed Pump Case Study Boiler Feed Pump Case Study Boiler Feed Pump Case Study Nuclear Feed Water Pump Cyclic Thermal Rotor Bow

9 xiv Contents 10.6 Power Plant Boiler Circulating Pumps Nuclear Plant Cooling Tower Circulating Pump Resonance Generator Exciter Collector Shaft Critical Speeds Summary 369 Bibliography Self-Excited Rotor Vibration Case Studies Introduction Swirl Brakes Cure Steam Whirl in a 1300 MW Unit Bearing Unloaded by Nozzle Forces Allows Steam Whirl Misalignment Causes Oil Whip/Steam Whirl "Duet" Summary 378 Bibliography Additional Rotor Vibration Cases and Topics Introduction Vertical Rotor Machines Vector Turning from Synchronously Modulated Rubs Air Preheater Drive Structural Resonances Aircraft Auxiliary Power Unit Commutator Vibration-Caused Uneven Wear Impact Tests for Vibration Problem Diagnoses Bearing Looseness Effects MW Steam Turbine Generator BFP 4000 hp Electric Motor LP Turbine Bearing Looseness on a 750 MW Steam Turbine Generator Tilting-Pad versus Fixed-Surface Journal Bearings A Return to the Machine of Section 11.4 of Chapter 11 Case Study Base-Motion Excitations from Earthquake and Shock Parametric Excitation: Nonaxisymmetric Shaft Stiffness Rotor Balancing Static Unbalance, Dynamic Unbalance, and Rigid Rotors Flexible Rotors Influence Coefficient Method Balancing Computer Code Examples and the Importance of Modeling Case Study of 430 MW Turbine Generator 418

10 Contents xv Continuous Automatic In-Service Rotor Balancing In-Service Single-Plane Balance Shot Summary 422 Bibliography 422 Index 425