David P. Fleming

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

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.

Zero-Load Stability of Rotating Externally Pressurized Gas-Lubricated Journal Bearings

A small eccentricity analysis was performed for a bearing having two feeding planes, each of which is assumed to be a line source. Numerical results were obtained for a range of bearing number, pressure ratio, feeding parameter, and orifice recess volume by means of a digital computer. Steady-state load and attitude angle were obtained, as well as stability data. Stability decreased markedly with increasing recess volume; moreover, for large recess volume and low bearing number, an increase in pressure ratio decreased stability. There was no correlation between stability and steady-state attitude angle for any of the cases studied. Fair agreement was obtained with available experimental data.

Dynamic Modeling of a Dual Clearance Squeeze Film Damper—Part I: Test Rig and Dynamic Model with One Damper

This paper presents a description of a dual clearance squeeze film damper (SFD) test rig and a dynamic model of a single SFD. The purpose of a dual SFD is to provide protection at high levels of vibration, when conventional devices are no longer effective. An experimental facility was designed and built for tire study of SFD behavior within mechanically controlled orbits. It can be used for both single and dual squeeze film dampers. In Part 1 of this paper, measured and computed responses are presented while operating as a single squeeze film device. Numerical and experimental results for undamped cases are presented, i.e., when no oil film is present in the damper. Subsequently, the effects of the oil film are considered. Good agreement was obtained between experimental data and predictions. Presented at the 57th Annual Meeting in Houston, Texas May 19–23, 2002

Computation of Pressurized Gas Bearings Using CE/SE Method

A numerical scheme that has been successfully used to solve a wide variety of compressible flow problems, including flows with large and small discontinuities, entitled the space-time conservation element and solution element (CE/SE) method, is extended to compute compressible viscous flows in pressurized thin fluid films. This method is applied to calculate the pressure distribution in a hybrid gas journal bearing. The formulation of the problem is presented, including the modeling of the feeding system. The numerical results obtained are compared with experimental data. Good agreement between the computed results and the test data were obtained, and thus, validate the CE/SE method to solve such problems. Presented at the 57th Annual Meeting in Houston, Texas May 19–23, 2002

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

Experimental studies were conducted on six rotors, 1 1/2 in. dia by 12 1/4 in. long operating in ambient air to high compressibility numbers. Herringbone-groove geometries and clearances were varied to determine their effect on half-frequency whirl (HFW). All rotors were operated vertically and without any applied radial load. Results show that half-frequency-whirl onset is very sensitive to radial clearance. Limited test results indicate that a fully grooved bearing is more stable than a partially grooved one, other parameters being equal. Generally fair agreement between theory and experiment was achieved for predicting HFW onset speeds.

Unbalance Response Prediction for Rotors on Ball Bearings Using Speed- and Load-Dependent Nonlinear Bearing Stiffness

Rolling-element bearing forces vary nonlinearly with bearing deflection. Thus, an accurate rotordynamic analysis requires that bearing forces corresponding to the actual bearing deflection be utilized. For this work, bearing forces were calculated by COBRA-AHS, a recently developed rolling-element bearing analysis code. Bearing stiffness was found to be a strong function of bearing deflection, with higher deflection producing markedly higher stiffness. Curves fitted to the bearing data for a range of speeds and loads were supplied to a flexible rotor unbalance response analysis. The rotordynamic analysis showed that vibration response varied nonlinearly with the amount of rotor imbalance. Moreover, the increase in stiffness as critical speeds were approached caused a large increase in rotor and bearing vibration amplitude over part of the speed range compared to the case of constant-stiffness bearings. Regions of bistable operation were possible, in which the amplitude at a given speed was much larger during rotor acceleration than during deceleration. A moderate amount of damping will eliminate the bistable region, but this damping is not inherent in ball bearings.

Experimental load capacity and power loss of herringbone grooved gas lubricated journal bearings

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.

Transient Vibration Prediction for Rotors on Ball Bearings Using Load-Dependent Nonlinear Bearing Stiffness

Rolling-element bearing forces vary nonlinearly with bearing deflection. Thus an accurate rotordynamic transient analysis requires bearing forces to be determined at each step of the transient solution. Analyses have been carried out to show the effect of accurate bearing transient forces (accounting for nonlinear speed and load-dependent bearing stiffness) as compared to conventional use of average rolling-element bearing stiffness. Bearing forces were calculated by COBRA-AHS (Computer Optimized Ball and Roller Bearing Analysis—Advanced High Speed) and supplied to the rotordynamics code ARDS (Analysis of Rotor Dynamic Systems) for accurate simulation of rotor transient behavior. COBRA-AHS is a fast-running five degree-of-freedom computer code able to calculate high speed rolling-element bearing load-displacement data for radial and angular contact ball bearings and also for cylindrical and tapered roller bearings. Results show that use of nonlinear bearing characteristics is essential for accurate prediction of rotordynamic behavior.

Dynamic Modeling of a Dual Clearance Squeeze Film Damper. Part II

Squeeze film dampers (SFD) have been used for many years to control the vibrations of the shafts in high-speed rotating machinery. Dual squeeze film dampers are essentially a combination of two SFDs separated by a sleeve. Normal operation utilizes only one oil film, as in a conventional damper, and the sleeve is fixed in place. However, under high load conditions, the sleeve is released and both oil films become operational. An experimental facility was designed and built to study both single and dual SFD behavior within mechanically controlled orbits. The first part of this paper presents a description of this test rig and provides a dynamic model of a single SFD. In this portion of the paper, we present results obtained while the inner sleeve is released and both oil films are operational. Here the inner sleeve is not supported by any mechanical device; the anti-rotational effect is provided by the opposed actions of the inner oil film and of the outer oil film. The modeling covers the inner and the outer oil films, the elastic fixtures, the unbalanced shaft, and the sleeve. Numerical results are compared with the experimental data. Presented at the ASME/STLE Tribology Conference, in Long Beach, California October 24-27, 2004 Review led by Luis San Andres

Calculation of the Flow in High-Speed Gas Bearings Including Inertia Effects Using the CE/SE Method

In the classical Reynolds equation, inertia effects are neglected. Gas bearings working at very high speeds may encounter flow discontinuities (shock waves), which require the inclusion of inertia terms within the momentum equations. In order to solve the resulting system of equations, a numerical method capable of capturing flow discontinuities is necessary, and the space-time conservation element/solution element (CE/SE) is such a method. In addition, it does not incorporate any other assumptions or special numerical treatment. Results obtained using this method are compared with experimental data and theoretical results, as well as with results obtained by neglecting inertia effects.