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.

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 www.rotordynamics.org.

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 SpringMass 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 CoefficientsA 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 Lo...