Fast methods to numerically integrate the Reynolds equation for gas fluid films

The alternating direction implicit (ADI) method is adopted, modified, and applied to the Reynolds equation for thin, gas fluid films. An efficient code is developed to predict both the steady-state and dynamic performance of an aerodynamic journal bearing. An alternative approach is shown for hybrid journal gas bearings by using Liebmann's iterative solution (LIS) for elliptic partial differential equations. The results are compared with known design criteria from experimental data. The developed methods show good accuracy and very short computer running time in comparison with methods based on an inverting of a matrix. The computer codes need a small amount of memory and can be run on either personal computers or on mainframe systems

Wave Journal Bearing. Part 1: Analysis

A wave journal bearing concept features a waved inner bearing diameter of the non-rotating bearing side and it is an alternative to the plain journal bearing. The wave journal bearing has a significantly increased load capacity in comparison to the plain journal bearing operating at the same eccentricity. It also offers greater stability than the plain circular bearing under all operating conditions. The wave bearing's design is relatively simple and allows the shaft to rotate in either direction. Three wave bearings are sensitive to the direction of an applied stationary side load. Increasing the number of waves reduces the wave bearing's sensitivity to the direction of the applied load relative to the wave. However, the range in which the bearing performance can be varied decreases as the number of waves increases. Therefore, both the number and the amplitude of the waves must be properly selected to optimize the wave bearing design for a specific application. It is concluded that the stiffness of an air journal bearing, due to hydrodynamic effect, could be doubled and made to run stably by using a six or eight wave geometry with a wave amplitude approximately half of the bearing radial clearance

A waved journal bearing concept with improved steady-state and dynamic performance

Analysis of the waved journal bearing concept featuring a waved inner bearing diameter for use with a compressible lubricant (gas) is presented. A three wave, waved journal bearing geometry is used to show the geometry of this concept. The performance of generic waved bearings having either three, four, six, or eight waves is predicted for air lubricated bearings. Steady-state performance is discussed in terms of bearing load capacity, while the dynamic performance is discussed in terms of dynamic coefficients and fluid film stability. It was found that the bearing wave amplitude has an important influence on both steady-state and dynamic performance of the waved journal bearing. For a fixed eccentricity ratio, the bearing steady-state load capacity and direct dynamic stiffness coefficient increase as the wave amplitude increases. Also, the waved bearing becomes more stable as the wave amplitude increases. In addition, increasing the number of waves reduces the waved bearing's sensitivity to the direction of the applied load relative to the wave. However, the range in which the bearing performance can be varied decreases as the number of waves increases. Therefore, both the number and the amplitude of the waves must be properly selected to optimize the waved bearing design for a specific application. It is concluded that the stiffness of an air bearing, due to the hydrodynamic effect, could be doubled and made to run stably by using a six or eight wave geometry with a wave amplitude approximately half of the bearing radial clearance

Active-Controlled Fluid Film Based on Wave-Bearing Technology

It has been known since 1967 that the steady-state and dynamic performance, including the stability of a wave bearing, are highly dependent on the wave amplitude. A wave-bearing profile can be readily obtained by elastically distorting the stationary bearing sleeve surface. The force that distorts the elastic sleeve surface could be an applied force or pressure. The magnitude and response of the distorting force would be defined by the relation between the bearing surface stiffness and the bearing pressure, or load, in a feedback loop controller. Using such devices as piezoelectric or other electromechanical elements, one could step control or fully control the bearing. The selection between these systems depends on the manner in which the distortion forces are applied, the running speed, and the reaction time of the feedback loop. With these techniques, both liquid- (oil-) or gas- (air-) lubricated wave bearings could be controlled. This report gives some examples of the dependency of the bearing's performance on the wave amplitude. The analysis also was proven experimentally

Gas Wave Bearings: A Stable Alternative to Journal Bearings for High-Speed Oil-Free Machines

To run both smoothly and efficiently, high-speed machines need stable, low-friction bearings to support their rotors. In addition, an oil-free bearing system is a common requirement in today's designs. Therefore, self-acting gas film bearings are becoming the bearing of choice in high-performance rotating machinery, including that used in the machine tool industry. Although plain journal bearings carry more load and have superior lift and land characteristics, they suffer from instability problems. Since 1992, a new type of fluid film bearing, the wave bearing, has been under development at the NASA Lewis Research Center in Cleveland, Ohio, by Dr. Florin Dimofte, a Senior Research Associate of the University of Toledo. One unique characteristic of the waved journal bearing that gives it improved capabilities over conventional journal bearings is the low-amplitude waves of its inner diameter surface. The radial clearance is on the order of one thousandth of the shaft radius, and the wave amplitude is nominally up to one-half the clearance. This bearing concept offers a load capacity which is very close to that of a plain journal bearing, but it runs more stably at nominal speeds

Stability of the Wave Bearing on an Elastic Support

Numerical computation predicts that an elastic support can substantially improve the stability of the wave bearing if the dynamic stiffness and damping of this support are in a specific range of values. To experimentally validate this prediction, the housing of a gas bearing was mounted on elastic O-rings and the threshold of sub-synchronous whirl motion was experimentally observed when the bearing runs unloaded with a rotating speed up to 30,000 RPM. The O-ring system was also dynamically characterized by measuring its stiffness and damping at various frequencies up to 500 Hz. Good correlation exists between the experimental data and numerical prediction

Pressure measurements of a three wave journal air bearing

In order to validate theoretical predictions of a wave journal bearing concept, a bench test rig was assembled at NASA Lewis Research Center to measure the steady-state performance of a journal air bearing. The tester can run up to 30,000 RPM and the spindle has a run out of less than 1 micron. A three wave journal bearing (50 mm diameter and 58 mm length) has been machined at NASA Lewis. The pressures at 16 ports along the bearing circumference at the middle of the bearing length were measured and compared to the theoretical prediction. The bearing ran at speeds up to 15,000 RPM and certain loads. Good agreement was found between the measured and calculated pressures

Hydrodynamic Analyses and Evaluation of New Fluid Film Bearing Concepts

Over the past several years, numerical and experimental investigations have been performed on a waved journal bearing. The research work was undertaken by Dr. Florin Dimofte, a Senior Research Associate in the Mechanical Engineering Department at the University of Toledo. Dr. Theo Keith, Distinguished University Professor in the Mechanical Engineering Department was the Technical Coordinator of the project. The wave journal bearing is a bearing with a slight but precise variation in its circular profile such that a waved profile is circumscribed on the inner bearing diameter. The profile has a wave amplitude that is equal to a fraction of the bearing clearance. Prior to this period of research on the wave bearing, computer codes were written and an experimental facility was established. During this period of research considerable effort was directed towards the study of the bearing's stability. The previously developed computer codes and the experimental facility were of critical importance in performing this stability research. A collection of papers and reports were written to describe the results of this work. The attached captures that effort and represents the research output during the grant period

Free Body Dynamics of a Spinning Cylinder with Planar Restraint-(a.k.a. Barrel of Fun)

The dynamic motion of a cylinder is analyzed based on rotation about its center of mass and is restrained by a plane normal to the axis passing through its center of mass at an angle. The first part of this work presented an analysis of the stability of the motion. In the current report, the governing equations are numerically integrated in time and the steady state is obtained as a limit of the transient numerical solution. The calculated data are compared with observed behaviors