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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…mehr
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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.
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Hinweis: Dieser Artikel kann nur an eine deutsche Lieferadresse ausgeliefert werden.
Produktdetails
- Produktdetails
- Verlag: John Wiley & Sons / Wiley
- Seitenzahl: 416
- Erscheinungstermin: 24. Mai 2010
- Englisch
- Abmessung: 244mm x 162mm x 29mm
- Gewicht: 690g
- ISBN-13: 9780471462132
- ISBN-10: 0471462136
- Artikelnr.: 29337630
- Herstellerkennzeichnung
- Libri GmbH
- Europaallee 1
- 36244 Bad Hersfeld
- 06621 890
- Verlag: John Wiley & Sons / Wiley
- Seitenzahl: 416
- Erscheinungstermin: 24. Mai 2010
- Englisch
- Abmessung: 244mm x 162mm x 29mm
- Gewicht: 690g
- ISBN-13: 9780471462132
- ISBN-10: 0471462136
- Artikelnr.: 29337630
- Herstellerkennzeichnung
- Libri GmbH
- Europaallee 1
- 36244 Bad Hersfeld
- 06621 890
Dr. JOHN M. VANCE was professor of mechanical engineering at Texas A&M University, retiring in 2007. He received his PhD (1967) degree from The University of Texas at Austin. His book Rotordynamics of Turbomachinery (Wiley) has sold more than 3,000 copies and is used by turbomachinery engineers around the world. He is an inventor on several patents relating to rotating machinery and vibration reduction. His patented TAMSEAL has been retrofitted to solve vibration problems in a number of high-pressure industrial compressors. He is an ASME Fellow and a registered professional engineer in the state of Texas. 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 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
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
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
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