Preface | |
Fundamentals of Machine Vibration and Classical Solutions | |
The Main Sources of Vibration in Machinery | |
The Single Degree of Freedom (SDOF) Model | |
Using Simple Models for Analysis and Diagnostics | |
Six Techniques for Solving Vibration Problems with Forced Excitation | |
Some Examples with Forced Excitation | |
Some Observations about Modeling | |
Unstable Vibration | |
References | |
Exercises | |
Torsional Vibration | |
Torsional Vibration Indicators | |
Objectives of Torsional Vibration Analysis | |
Simplified Models | |
Computer Models | |
Kinetic Energy Expression | |
Potential Energy | |
Torsional Vibration Measurement | |
French's Comparison Experiments | |
Strain Gages | |
Carrier Signal Transducers | |
Frequency-modulated Systems | |
Amplitude-modulated Systems | |
Frequency Analysis and the Sideband System | |
French's Test Procedure and Results | |
A Special Tape for Optical Transducers | |
Time-interval Measurement Systems | |
Results from Toram's Method | |
Results from the Barrios/Darlow Method | |
References | |
Exercises | |
Introduction to Rotordynamics Analysis | |
Objectives of Rotordynamics Analysis | |
The Spring-Mass Model | |
Synchronous and Nonsynchronous Whirl | |
Analysis of the Jeffcott Rotor | |
Polar Coordinates | |
Cartesian Coordinates | |
Physical Significance of the Solutions | |
Three Ways to Reduce Synchronous Whirl Amplitudes | |
Some Damping Definitions | |
The "Gravity Critical" | |
Critical Speed Definitions | |
Effect of Flexible (Soft) Supports | |
Rotordynamic Effects of the Force Coefficients-A Summary | |
The Direct Coefficients | |
The Cross-coupled Coefficients | |
Rotordynamic Instability | |
Effect of Cross-Coupled Stiffness on Unbalance Response | |
Added Complexities | |
Gyroscopic Effects | |
Effect of Support Asymmetry on Synchronous Whirl | |
False Instabilities | |
References | |
Exercises | |
Computer Simulations of Rotordynamics | |
Different Types of Models | |
Bearing and Seal Matrices | |
Torsional and Axial Models | |
Different Types of Analyses | |
Eigenanalysis | |
Linear Forced Response (LFR) | |
Transient Response | |
Shaft Modeling Recommendations | |
How Many Elements | |
45-Degree Rule | |
Interference Fits | |
Laminations | |
Trunnions | |
Impeller Inertias via CAD Software | |
Stations for Added Weights | |
Rap Test Verification of Models | |
Stations for Bearings and Seals | |
Flexible Couplings | |
Example Simulations | |
Damped Natural Frequency Map (NDF) | |
Modal Damping Map | |
Root Locus Map | |
Undamped Critical Speed Map | |
Mode Shapes | |
Bode/Polar Response Plot | |
Orbit Response Plot | |
Bearing Load Response Plot | |
Operating Deflected Shape (ODS) | |
Housing Vibration (ips and g 's) | |
References | |
Bearings and Their Effect on Rotordynamics | |
Fluid Film Bearings | |
Fixed-geometry Sleeve Bearings | |
Variable-geometry Tilting Pad Bearings | |
Fluid Film Bearing Dynamic Coefficients and Methods of Obtaining Them | |
Load Between Pivots Versus Load on Pivot | |
Influence of Preload on the Dynamic Coefficients in Tilt Pad Bearings | |
Influence of the Bearing Length or Pad Length | |
Influence of the Pivot Offset | |
Influence of the Number of Pads | |
Ball and Rolling Element Bearings | |
Case Study: Bearing Support Design for a Rocket Engine Turbopump | |
Ball Bearing Stiffness Measurements | |
Wire Mesh Damper Experiments and Computer Simulations | |
Squeeze Film Dampers | |
Squeeze Film Damper without a Centering Spring | |
O-ring Supported Dampers | |
Squirrel Cage Supported Dampers | |
Integral Squeeze Film Dampers | |
Squeeze Film Damper Rotordynamic Force Coefficients | |
Applications of Squeeze Film Dampers | |
Optimization for Improving Stability in a Centrifugal Process Compressor | |
Using Dampers to Improve the Synchronous Response | |
Using the Damper to Shift a Critical Speed or a Resonance | |
Insights into the Rotor-Bearing Dynamic Interaction with Soft/Stiff Bearing Supports | |
Influence on Natural Frequencies with Soft/Stiff Bearing Supports | |
Effects of Mass Distribution on the Critical Speeds with Soft/Stiff Bearing Supports | |
Influence of Overhung Mass on Natural Frequencies with Soft/Stiff Supports | |
Influence of Gyroscopic Moments on Natural Frequencies with Soft/Stiff Bearing Supports | |
References | |
Exercises | |
Appendix: Shaft With No Added Weight | |
Fluid Seals and Their Effect on Rotordynamics | |
Function and Classification of Seals | |
Plain Smooth Seals | |
Floating Ring Seals | |
Conventional Gas Labyrinth Seals | |
Pocket Damper Seals | |
Honeycomb Seals | |
Hole-pattern Seals | |
Brush Seals | |
Understanding and Modeling Damper Seal Force Coefficients | |
Alford's Hypothesis of Labyrinth Seal Damping | |
Cross-coupled Stiffness Measurements | |
Invention of the Pocket Damper Seal | |
Pocket Damper Seal Theory | |
Rotordynamic Testing of Pocket Damper Seals | |
Impedance Measurements of Pocket Damper Seal Force Coefficients (Stiffness and Damping) and Leakage at Low Pressures | |
The Fully Partitioned PDS Design | |
Effects of Negative Stiffness | |
Frequency Dependence of Damper Seals | |
Laboratory Measurements of Stiffness and Damping from Pocket Damper Seals at High Pressures | |
The Conventional Design | |
The Fully Partitioned Design | |
Field Experience with Pocket Damper Seals | |
Two Back-to-Back Compressor Applications | |
A Fully Partitioned Application | |
Designing for Desired Force Coefficient Characteristics | |
The Conventional PDS Design | |
The Fully Partitioned Pocket Damper Seal | |
Leakage Considerations | |
Some Comparisons of Different Types of Annular Gas Seals | |
References | |
History of Machinery Rotordynamics | |
The Foundation Years, 1869-1941 | |
Shaft Dynamics | |
Bearings | |
Refining and Expanding the Rotordynamic Model, 1942-1963 | |
Multistage Compressors and Turbines, Rocket Engine Turbopumps, and Damper Seals, 1964-Present | |
Stability Problems with Multistage Centrifugal Compressors | |
Kaybob, 1971-72 | |
Ekofisk, 1974-75 | |
Subsequent Developments | |
New Frontiers of Speed and Power Density with Rocket Engine Turbopumps | |
The Space Shuttle Main Engine (SSME) | |
High-pressure Fuel Turbopump (HPFTP) | |
Rotordynamic Instability Problem | |
Noncontacting Damper Seals | |
Shaft Differential Heating (The Morton Effect) | |
References | |
Index | |
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