The subject of this monograph is the fluid dynamics of liquid turbomachines, particularly pumps. Rather than attempt a general treatise on turbomachines, we shall focus attention on those special problems and design issues associated with the flow of liquid through a rotating machine. There are two characteristics of a liquid that lead to these special problems, and cause a significantly different set of concerns than would occur in, say, a gas turbine. These are the potential for cavitation and the high density of liquids that enhances the possibility of damaging unsteady flows and forces.

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Hydrodynamics of Pumps

Part I: Primer on Rotor Vibration Vibration Concepts and Methods One-Degree-of-Freedom Model Multi-DOF Models Modes, Excitation, and Stability of Multi-DOF Models Lateral Rotor Vibration Analysis Models Simple Linear Models Formulations for RDA Software Insights into Linear LRVs Nonlinear Effects in Rotor Dynamical Systems Torsional Rotor Vibration Analysis Models Rotor-Based Spinning Reference Frames Single Uncoupled Rotor Coupled Rotors Semidefinite Systems Part II: Rotor Dynamic Analyses RDA Code for Lateral Rotor Vibration Analyses Unbalance Steady-State Response Computations Instability Self-Excited-Vibration Threshold Computations Additional Sample Problems Bearing and Seal Rotor Dynamics Liquid-Lubricated Fluid-Film Journal Bearings Experiments to Measure Dynamic Coefficients Annular Seals Rolling Contact Bearings Squeeze-Film Dampers Magnetic Bearings Compliance Surface Foil Gas Bearings Turbo-Machinery Impeller and Blade Effects Centrifugal Pumps Centrifugal Compressors High-Pressure Steam Turbines and Gas Turbines Axial Flow Compressors Part III Monitoring and Diagnostics Rotor Vibration Measurement and Acquisition Introduction to Monitoring and Diagnostics Measured Vibration Signals and Associated Sensors Vibration Data Acquisition Signal Conditioning Vibration Severity Guidelines Casing and Bearing Cap Vibration Displacement Guidelines Standards, Guidelines, and Acceptance Criteria Shaft Displacement Criteria Signal Analysis and Identification of Vibration Causes Vibration Trending and Baselines FFT Spectrum Rotor Orbit Trajectories Bode, Polar, and Spectrum Cascade Plots Wavelet Analysis Tools Chaos Analysis Tools Symptoms and Identification of Vibration Causes Part IV Trouble-Shooting Case Studies Forced Vibration and Critical Speed Case Studies HP Steam Turbine Passage through First Critical Speed HP-IP Turbine Second Critical Speed through Power Cycling Boiler Feed Pumps: Critical Speeds at Operating Speed Nuclear Feed Water Pump Cyclic Thermal Rotor Bow Power Plant Boiler Circulating Pumps Nuclear Plant Cooling Tower Circulating Pump Resonance Generator Exciter Collector Shaft Critical Speeds Self-Excited Rotor Vibration Case Studies Swirl Brakes Cure Steam Whirl in a 1300 MW Unit Bearing Unloaded by Nozzle Forces Allows Steam Whirl Misalignment Causes Oil Whip/Steam Whirl "Duet" Additional Rotor Vibration Cases and Topics Vertical Rotor Machines Vector Turning from Synchronously Modulated Rubs Air Preheater Drive Structural Resonances Aircraft Auxiliary Power Unit Commutator Vibration-Caused Uneven Wear Impact Tests for Vibration Problem Diagnoses Bearing Looseness Effects Tilting-Pad versus Fixed-Surface Journal Bearings Base-Motion Excitations from Earthquake and Shock Parametric Excitation: Nonaxisymmetric Shaft Stiffness Rotor Balancing Index

Rotating Machinery Vibration: From Analysis to Troubleshooting

Mechanical model development of rolling bearing-rotor systems: A review

Clearance control is of paramount importance to turbomachinery designers and is required to meet today's aggressive power output, efficiency, and operational life goals. Excessive clearances lead to losses in cycle efficiency, flow instabilities, and hot gas ingestion into disk cavities. Insufficient clearances limit coolant flows and cause interface rubbing, overheating downstream components and damaging interfaces, thus limiting component life. Designers have put renewed attention on clearance control, as it is often the most cost effective method to enhance system performance. Advanced concepts and proper material selection continue to play important roles in maintaining interface clearances to enable the system to meet design goals. This work presents an overview of turbomachinery sealing to control clearances. Areas covered include: characteristics of gas and steam turbine sealing applications and environments, benefits of sealing, types of standard static and dynamics seals, advanced seal designs, as well as life and limitations issues.

Sealing in Turbomachinery

Modelling and Vibration Analysis of Misaligned Rotor-Ball Bearing Systems

Introduction. Rotordynamic Considerations in Turbomachinery Design. Torsional Vibration Analysis. Critical Speeds and Response to Imbalance. Rotor Balancing in Turbomachinery. Bearings and Seals. Rotordynamic Instability in Turbomachinery. Measurements.

Rotordynamics of Turbomachinery

PREFACE. 1 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. Illustrative Example 1. Illustrative Example 2. Illustrative Example 3. Illustrative Example 4. Some Observations about Modeling. Unstable Vibration. References. Exercises. 2 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. 3 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. 4 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. 5 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. 6 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. Case 1. Case 2. 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. 7 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.

Machinery Vibration and Rotordynamics

Fluid Seals and Their Effect on Rotordynamics

Bearings and Their Effect on Rotordynamics

The most common sources of vibration in machinery are related to the inertia of moving parts in the machine. Some parts have a reciprocating motion, accelerating back and forth. In such a case Newton’s laws require a force to accelerate the mass and also require that the force be reacted to the frame of the machine. The forces are usually periodic and therefore produce periodic displacements observed as vibration. For example, the piston motion in the slider-crank mechanism of Fig. 1-1 has a fundamental frequency equal to the crankshaft speed but also has higher frequencies (harmonics). The dominant harmonic is twice crankshaft speed (2nd harmonic). Figure 1-2a shows the displacement of the piston. It looks almost like a sine wave but it is slightly distorted by higher-order harmonics due to the nonlinear kinematics of the mechanism. Fig. 1-2b shows the acceleration of the piston, where the 2nd harmonic is amplified since the acceleration amplitude is frequency-squared times the displacement amplitude. Even without reciprocating parts, most machines have rotating shafts and wheels that cannot be perfectly balanced, so according to Newton’s laws, there must be a rotating force vector at the bearing supports of each

John Vance

Papers

Rotordynamics of Turbomachinery

Machinery Vibration and Rotordynamics

Fluid Seals and Their Effect on Rotordynamics

Bearings and Their Effect on Rotordynamics

Fundamentals of Machine Vibration and Classical Solutions