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

The numerical developments described in Part 1 are extended to incorporate the consideration of non-Newtonian effects, and fully coupled solutions of the thermal non-Newtonian elastohydrody...

Thermal elastohydrodynamic analysis of circular contacts Part 2: Non-Newtonian model

A theoretical basis for static and dynamic operation of tilting pad journal bearings (TPJBs)
has evolved over the last 50 years. Originally demonstrated by Lund using the pad assembly
method and a classic Reynolds equation solution, the current state of the art includes full
thermoelastohydrodynamic solutions of the generalized Reynolds equation that include fluid
convective inertia effects, pad motions; and thermal and mechanical deformations of the
pads and shaft. The development of TPJB theory is reviewed, emphasizing dynamic modeling. The paper begins with the early analyses of fixed geometry bearings and continues to
modern analyses that include pad motion and stiffness and damping effects. The development
of thermohydrodynamic, thermoelastohydrodynamic, and bulk-flow analyses is reviewed. The
theories of TPJB dynamics, including synchronous and nonsynchronous models, are reviewed.
A discussion of temporal inertia effects in tilting pad bearing is considered. Future
trends are discussed, and a path for experimental verification is proposed.

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A Review of Tilting Pad Bearing Theory

Experimental assessment of hydrostatic thrust bearing performance

Evaluation of the finite journal bearing characteristics, using the exact analytical solution of the Reynolds equation

Elastic and Damping Properties of Cylindrical Journal Bearings

Theory of Lubrication and Failure of Rolling Contacts

: The determination of the bearing fluid film forces in a rotor system under dynamical conditions is discussed. In the case of a vertical rotor operating in a gaseous medium in plain cylindrical journal bearings, the steady whirl approximation is appropriate. In the steady whirl approximation, a set of rotating coordinates is employed, and the time dependence of the Reynolds equation is eliminated. At the same time, the compressibility number, Lambda, is replaced by the quantity (1-2 alpha/omega) multiplied by lambda. This approximation applies when both whirl acceleration and the radial velocity of the shaft are small. The attitude angle of the fluid film force is strongly dependent on the whirl motion. Experimental data of synchronous whirl agrees with the theoretical calculations based on the steady whirl analysis. A perfectly balanced vertical rotor in a plain gas dynamic journal bearing is always unstable with respect to the half frequency whirl.

On the Translatory Whirl Motion of a Vertical Rotor in Plain Cylindrical Gas-Dynamic Journal Bearings

: The regions of stability for plane cylindrical journal bearings are determined analytically. The linear variational equation of motion was employed to obtain the stability regions bounded by families of load-carrying capacity and operating eccentricity curves. The results were applied to the quisi-static equilibrium case for gas lubricated cylindrical journal bearings L/D equals 2. They show that there exists a minimum in the stability curves, a prediction supported by experimental evidence. The results of this work seem to bridge together observation on stability at very small and large clearances. (Author)

B. Sternlicht

Papers

Elastic and Damping Properties of Cylindrical Journal Bearings

Theory of Lubrication and Failure of Rolling Contacts

On the Translatory Whirl Motion of a Vertical Rotor in Plain Cylindrical Gas-Dynamic Journal Bearings

On the stability of rotors in cylindrical journal bearings

Performance of Elastic, Centrally Pivoted, Sector, Thrust-Bearing Pads—Part I