Numerical Solution of a Fully Thermally Coupled Generalized Universal Reynolds Equation (GURE) and Its Application. Part 1: Conical Bearings

Abstract

Hannon, et al. (1), have previously presented a theoretical expansion of Dowson's equation to a generalized spherical coordinates system that allows the treatment of the bearing geometry without unwrapping the bearing. This single differential equation, coupled with the energy equations for the fluid, the rotor, and the stator allows the calculation of all classes of self-acting bearings from spherical, to conical, to cylindrical, and flat-plate thrust bearings. Turbulence is implemented through the Hirs turbulence model. The variable properties along and across the compressible air film are accounted for through a polytropic transformation equation. Part 1 of this paper focuses on the numerical presentation of the discretized form of GURE as it is applied to a conical bearing where the frustum angle varies from 10 to 45 to 80 degrees. The effects of pressure, temperature, density, and viscosity variations, as well as turbulence, are investigated numerically as a function of eccentricity and angular velocity (in addition to various frustum angles). The results are presented and discussed in a parametric fashion.