Generalized Universal Reynolds Equation for Variable Properties Fluid-Film Lubrication and Variable Geometry Self-Acting Bearings

Abstract

The present article represents a theoretical further development of Dowson's equation (1). The developments presented herein start from the fundamental Dowson concept and proceed to a final generalization, which, by using a spherical coordinate system, accounts for the previously neglected curvature effect. The generalization brought about by this system of coordinates allows the derivation of the Generalized Universal Reynolds Equation (GURE) to best suit liquid and gas film lubrication, with variable properties. This single equation can now be customized by a simple change in angle, allowing all common classes of self-acting bearings to be modeled. Dowson's development in Cartesian coordinates lends itself only to geometries of small curvatures when compared to the film thickness and thus can be unwrapped. GURE's flexibility of spherical coordinates eliminates the minimal curvature assumption for Cartesian geometries. GURE provides a single-equation approach to cylindrical journal bearings, flat-plate thrust bearings, and conical and spherical bearings.

Keywords:

• Generalized Reynolds Equation
• Variable Properties
• Spherical Coordinates
• Coupled Energy Equation
• Conical Bearing
• Cylindrical Bearing
• Thrust Bearing

ACKNOWLEDGMENT

The authors would like to thank Mr. D. Deng for his technical support in the generation of the graphics.

Presented at the STLE 58th Annual Meeting in New York City April 28-May 1, 2003

Final manuscript approved November 14, 2003

Review led by Theo G. Keith, Jr.