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

Dynamic modeling for rigid rotor bearing systems with a localized defect considering additional deformations at the sharp edges

By R. Hill Oxford: Pergamon Press. 1964. Pp. viii +191. Price 42s. This is a book which every university teacher of mechanics should possess. He should then make up his mind whether or not it is a suitable companion to his course.

Principles of Dynamics

In this paper, we present a review of the experimental identification of dynamic parameters of bearings in a rotating machine. Major emphasis is given to vibration-based identification methods and the review encompasses descriptions of experimental measurement techniques, mathematical modeling, parameter extraction algorithms and uncertainty in the estimates applied to a variety of bearings. The parameter extraction algorithms include the descriptions of governing equations of the rotor-bearing system and identification methods in both time and frequency domains. The identification techniques have been classified based on methods used to excite the system. The review includes a variety of bearings and similar components, which play an active link between the rotating and stationary parts of a machine. Based on the state of the art in bearing identification, conclusions are made and future directions are suggested.

Identification of Dynamic Bearing Parameters: A Review

Non-linear transient analysis of rotor-casing rub events

The method of component mode synthesis is developed to determine the forced response of nonlinear, multishaft, rotor-bearing systems. The formulation allows for simulation of system response due to blade loss, distributed unbalance, base shock, maneuver loads, and specified fixed frame forces. The motion of each rotating component of the system is described by superposing constraint modes associated with boundary coordinates and constrained precessional modes associated with internal coordinates. The precessional modes are truncated for each component and the reduced component equations are assembled with the nonlinear supports and interconnections to form a set of nonlinear system equations of reduced order. These equations are then numerically integrated to obtain the system response. A computer program, which is presently restricted to single shaft systems, has been written and results are presented for transient system response associated with blade loss dynamics with squeeze film dampers, and with interference rubs.

Nonlinear Analysis of Rotor-Bearing Systems Using Component Mode Synthesis

Herringbone grooved gas lubricated journal bearing stability, testing effects of geometries and clearances on onset speed for half frequency whirl

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Experimental Stability Studies of the Herringbone-Grooved Gas-Lubricated Journal Bearing

A single mass flexible rotor analysis was used to optimize the stiffness and damping of a flexible support for a symmetric five-mass rotor. The flexible support attenuates the rotor motions and forces transmitted to the support bearings when the rotor operates through and above its first bending critical speed. An oil squeeze-film damper was designed based on short bearing lubrication theory. The damper design was verified by an unbalance response computer program. Rotor amplitudes were reduced by a factor of 16 and loads reduced by a factor of 36 compared with the same rotor on rigid bearing supports.

Design of a Squeeze-Film Damper for a Multi-Mass Flexible Rotor

Load capacity, attitude angle, and power loss were determined for 1-1/2-in.-diam herringbone grooved journal bearings operating in air to speeds of 60,000 rpm. Results showed that groove-to-ridge-clearance ratios of 2.0 to 2.4 give a greater load capacity than do ratios outside this optimum range. Agreement with a small-eccentricity pressure perturbation theory was good for groove-to-ridge-clearance ratios in the optimum range. Power loss, relative to that calculated for a plain bearing of the same dimensions, did not vary widely for the range of geometric variables used. Relative power loss generally increased with speed and was generally comparable to that for a plain bearing.

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Experimental Load Capacity and Power Loss of Herringbone Grooved Gas Lubricated Journal Bearings

An oil-lubricated wave journal-thrust bearing assembly was successfully tested at conditions found in general aviation engine gearboxes. The bearing performed well at both steady state conditions and in start-stop tests. It ran stably under all loading conditions, including zero load, at all speeds up to 16 000 rpm. The bearing carried 25 percent more load than required for the gearbox application, supporting 8900 N (94 bars average pressure), and showed very good thermal stability. 450 start-stop cycles were also performed, including 350 cycles without oil supply during starting and stopping. Test results and numerical predictions were in good agreement.

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David P. Fleming

Papers

Nonlinear Analysis of Rotor-Bearing Systems Using Component Mode Synthesis

Experimental Stability Studies of the Herringbone-Grooved Gas-Lubricated Journal Bearing

Design of a Squeeze-Film Damper for a Multi-Mass Flexible Rotor

Experimental Load Capacity and Power Loss of Herringbone Grooved Gas Lubricated Journal Bearings

Wave Fluid Film Bearing Tests for an Aviation Gearbox