An in-depth analysis of machine vibration in rotating machinery Whether it's a compressor on an offshore platform, a turbocharger in a truck or automobile, or a turbine in a jet airplane, rotating machinery is the driving force behind almost anything that produces or uses energy. Counted on daily to perform any number of vital societal tasks, turbomachinery uses high rotational speeds to produce amazing amounts of power efficiently. The key to increasing its longevity, efficiency, and reliability lies in the examination of rotor vibration and bearing dynamics, a field called rotordynamics. A valuable textbook for beginners as well as a handy reference for experts, Machinery Vibration and Rotordynamics is teeming with rich technical detail and real-world examples geared toward the study of machine vibration. A logical progression of information covers essential fundamentals, in-depth case studies, and the latest analytical tools used for predicting and preventing damage in rotating machinery. Machinery Vibration and Rotordynamics: Combines rotordynamics with the applications of machinery vibration in a single volume Includes case studies of vibration problems in several different types of machines as well as computer simulation models used in industry Contains fundamental physical phenomena, mathematical and computational aspects, practical hardware considerations, troubleshooting, and instrumentation and measurement techniques For students interested in entering this highly specialized field of study, as well as professionals seeking to expand their knowledge base, Machinery Vibration and Rotordynamics will serve as the one book they will come to rely upon consistently.

Table of Contents:
Preface xiii 1 Fundamentals of Machine Vibration and Classical Solutions 1 The Main Sources of Vibration in Machinery 1 The Single Degree of Freedom (SDOF) Model 4 Using Simple Models for Analysis and Diagnostics 6 Six Techniques for Solving Vibration Problems with Forced Excitation 13 Some Examples with Forced Excitation 15 Illustrative Example 1 15 Illustrative Example 2 17 Illustrative Example 3 20 Illustrative Example 4 24 Some Observations about Modeling 27 Unstable Vibration 28 References 30 Exercises 30 2 Torsional Vibration 35 Torsional Vibration Indicators 36 Objectives of Torsional Vibration Analysis 37 Simplified Models 38 Computer Models 45 Kinetic Energy Expression 46 Potential Energy 46 Torsional Vibration Measurement 51 French’s Comparison Experiments 53 Strain Gages 53 Carrier Signal Transducers 54 Frequency-modulated Systems 55 Amplitude-modulated Systems 56 Frequency Analysis and the Sideband System 57 French’s Test Procedure and Results 59 A Special Tape for Optical Transducers 61 Time-interval Measurement Systems 62 Results from Toram’s Method 65 Results from the Barrios/Darlow Method 67 References 68 Exercises 69 3 Introduction to Rotordynamics Analysis 71 Objectives of Rotordynamics Analysis 72 The Spring–Mass Model 74 Synchronous and Nonsynchronous Whirl 77 Analysis of the Jeffcott Rotor 78 Polar Coordinates 79 Cartesian Coordinates 80 Physical Significance of the Solutions 81 Three Ways to Reduce Synchronous Whirl Amplitudes 82 Some Damping Definitions 83 The “Gravity Critical” 83 Critical Speed Definitions 84 Effect of Flexible (Soft) Supports 84 Rotordynamic Effects of the Force Coefficients—A Summary 90 The Direct Coefficients 90 The Cross-coupled Coefficients 91 Rotordynamic Instability 91 Effect of Cross-Coupled Stiffness on Unbalance Response 99 Added Complexities 100 Gyroscopic Effects 101 Effect of Support Asymmetry on Synchronous Whirl 107 False Instabilities 110 References 112 Exercises 114 4 Computer Simulations of Rotordynamics 119 Different Types of Models 119 Bearing and Seal Matrices 126 Torsional and Axial Models 127 Different Types of Analyses 128 Eigenanalysis 129 Linear Forced Response (LFR) 133 Transient Response 134 Shaft Modeling Recommendations 135 How Many Elements 135 45-Degree Rule 137 Interference Fits 138 Laminations 139 Trunnions 140 Impeller Inertias via CAD Software 140 Stations for Added Weights 142 Rap Test Verification of Models 143 Stations for Bearings and Seals 143 Flexible Couplings 144 Example Simulations 146 Damped Natural Frequency Map (NDF) 147 Modal Damping Map 149 Root Locus Map 151 Undamped Critical Speed Map 151 Mode Shapes 157 Bode/Polar Response Plot 160 Orbit Response Plot 163 Bearing Load Response Plot 164 Operating Deflected Shape (ODS) 165 Housing Vibration (ips and g’s) 168 References 168 5 Bearings and Their Effect on Rotordynamics 171 Fluid Film Bearings 171 Fixed-geometry Sleeve Bearings 174 Variable-geometry Tilting Pad Bearings 185 Fluid Film Bearing Dynamic Coefficients and Methods of Obtaining Them 190 Load Between Pivots Versus Load on Pivot 195 Influence of Preload on the Dynamic Coefficients in Tilt Pad Bearings 201 Influence of the Bearing Length or Pad Length 203 Influence of the Pivot Offset 204 Influence of the Number of Pads 205 Ball and Rolling Element Bearings 208 Case Study: Bearing Support Design for a Rocket Engine Turbopump 209 Ball Bearing Stiffness Measurements 213 Wire Mesh Damper Experiments and Computer Simulations 214 Squeeze Film Dampers 216 Squeeze Film Damper without a Centering Spring 217 O-ring Supported Dampers 220 Squirrel Cage Supported Dampers 223 Integral Squeeze Film Dampers 224 Squeeze Film Damper Rotordynamic Force Coefficients 225 Applications of Squeeze Film Dampers 226 Optimization for Improving Stability in a Centrifugal Process Compressor 226 Using Dampers to Improve the Synchronous Response 232 Using the Damper to Shift a Critical Speed or a Resonance 236 Insights into the Rotor–Bearing Dynamic Interaction with Soft/Stiff Bearing Supports 238 Influence on Natural Frequencies with Soft/Stiff Bearing Supports 240 Effects of Mass Distribution on the Critical Speeds with Soft/Stiff Bearing Supports 243 Influence of Overhung Mass on Natural Frequencies with Soft/Stiff Supports 252 Influence of Gyroscopic Moments on Natural Frequencies with Soft/Stiff Bearing Supports 255 References 264 Exercises 267 Appendix: Shaft With No Added Weight 269 6 Fluid Seals and Their Effect on Rotordynamics 271 Function and Classification of Seals 271 Plain Smooth Seals 274 Floating Ring Seals 276 Conventional Gas Labyrinth Seals 277 Pocket Damper Seals 283 Honeycomb Seals 285 Hole-pattern Seals 287 Brush Seals 289 Understanding and Modeling Damper Seal Force Coefficients 291 Alford’s Hypothesis of Labyrinth Seal Damping 292 Cross-coupled Stiffness Measurements 295 Invention of the Pocket Damper Seal 295 Pocket Damper Seal Theory 299 Rotordynamic Testing of Pocket Damper Seals 300 Impedance Measurements of Pocket Damper Seal Force Coefficients (Stiffness and Damping) and Leakage at Low Pressures 301 The Fully Partitioned PDS Design 304 Effects of Negative Stiffness 310 Frequency Dependence of Damper Seals 313 Laboratory Measurements of Stiffness and Damping from Pocket Damper Seals at High Pressures 317 The Conventional Design 317 The Fully Partitioned Design 319 Field Experience with Pocket Damper Seals 325 Two Back-to-Back Compressor Applications 325 Case 1 325 Case 2 328 A Fully Partitioned Application 332 Designing for Desired Force Coefficient Characteristics 336 The Conventional PDS Design 337 The Fully Partitioned Pocket Damper Seal 340 Leakage Considerations 343 Some Comparisons of Different Types of Annular Gas Seals 347 References 348 7 History of Machinery Rotordynamics 353 The Foundation Years, 1869–1941 354 Shaft Dynamics 355 Bearings 360 Refining and Expanding the Rotordynamic Model, 1942–1963 363 Multistage Compressors and Turbines, Rocket Engine Turbopumps, and Damper Seals, 1964–Present 368 Stability Problems with Multistage Centrifugal Compressors 370 Kaybob, 1971–72 370 Ekofisk, 1974–75 373 Subsequent Developments 381 New Frontiers of Speed and Power Density with Rocket Engine Turbopumps 382 The Space Shuttle Main Engine (SSME) High-pressure Fuel Turbopump (HPFTP) Rotordynamic Instability Problem 382 Noncontacting Damper Seals 385 Shaft Differential Heating (The Morton Effect) 386 References 388 Index 393