Dr. FOUAD Y. ZEIDAN is the President of KMC, Inc., and Bearings Plus, Inc., two companies specializing in the supply of high-performance bearings, flexible couplings, and seals. Dr. Zeidan holds nine U.S. patents for integral squeeze film dampers and high-performance journal and thrust bearings. He has published more than thirty technical papers and articles on various turbomachinery topics and has been lecturing at the Annual Machinery Vibrations and Rotordynamics short course since 1991. Dr. Zeidan holds a BS, MS, and PhD degrees in mechanical engineering from Texas A&M University.

BRIAN T. MURPHY, PhD, PE, is a senior research scientist with the Center for Electromechanics at The University of Texas at Austin. He is also president of RMA, Inc., which develops and markets the Xlrotor suite of rotordynamic analysis software used worldwide by industry and academia. Dr. Murphy is the creator of the polynomial transfer matrix method, which is the fastest known method of performing rotordynamic calculations. He has authored numerous technical papers on rotordynamics and machinery vibration, and is also caretaker of the Web site [...]

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