Hydrodynamic load capacity of a full porous journal bearing of finite length in the turbulent regime considering slip flow and curvature

Abstract

The hydrodynamic lubrication of a 360° finite porous metal journal bearing of arbitrary wall thickness press fitted in a solid housing and working with a turbulent film of newtonian lubricant was analysed in a closed form using a new generalized pressure equation. Bearings of undefined axial length and narrow bearings have been considered previously. For finite bearings the flow of lubricant in the axial clearance space is of the same order as in the azimuth. Therefore the governing differential equation is three dimensional and difficult to solve. However, Warner's method was used to reduce this equation to two second-order ordinary linear differential equations with analytically known variable coefficients which are simpler to solve. Analytical solutions of these were obtained as a boundary value problem in terms of the end conditions defining the start and termination of the load-supporting film. The half Sommerfeld boundary conditions were used for the azimuthal film extent since they are mathematically simpler, and the results obtained in the laminar regime were close to those obtained using the more complex (but realistic) Reynolds boundary conditions. Film curvature effects were included by using C/ R 1 in the expression for film thickness. The curvature effect of the thick porous bearing matrix, which allows it to have an arbitrary wall thickness, was taken into account by a new direct approach which makes it possible to use the separation of variables. The collocation technique was utilized to determine the hydrodynamic pressure from which the bearing characteristics were evaluated. The results are fully analytical in nature, simple and yet exact and accurate; they permit easy and economical calculation of numerical data over a very wide range of parameters.