The Full Journal Bearing

Abstract

The basic mathematics of the full journal bearing have been known since 1904 when SommerfeldS made the complete solution, for the infinite journal, of Reynolds theory of 1886. The detailed application of the theory has not been possible owing to the uncertainty in the choice of boundary conditions. In this paper the Reynolds condition that p = 0 at 0 = 0 and p = ap/a0 = 0 at 0 = a+ a is shown to follow for the iniinite bearing from a consideration of continuity of flow and, equally important, from the shaft stability condition, first put forward by Swift in 1933. It is claimed that this is the final answer to the question of correct boundary conditions. The Reynolds equation for the infinitely wide bearing was solved using these conditions. Assuming the viscosity is constant all round the bearing, the coefficient of friction-load criterion curve has the same slope as experimentally determined curves.The Mathematics Division, N.P.L., computed, by SouthwelPs relaxation methods (1946), the figures for finite bearings of diameter length ratios of 4, 2, and 1. The theoretical figures for eccentricity ratio-load criterion are satisfactorily compared with some of Nucker's experimental results, and the coefficient of friction, load criterion, figures explain the apparent intercept found by McKee and McKee.A diagram is given allowing the eccentricity ratio c, to be obtained from the load criterion for any bearing of diameter/length ratio from 0 to 4, and this enables the minimum film thickness, which equals (1 -c) x radial clearance, to be calculated.

On the solution of large, structured linear complementarity problems: The tridiagonal case

“…His proposal used a "hand rel/txation" method for solving the difference equations. Computational results based on this method were published by Cameron and Wood [2] [24] and by Gnanadoss and Osborne [16]. The former team solved the difference equations by the Liebmann (alias Gauss-Seidel) method, the latter by successive overrelaxation (SOR).…”

To Investigate the Effect of Oil Film Thickness at the Entrance of the Infinitely Long Slider Bearing Using CFD Analysis

“…Reynolds O, simplified the complex Navier Stokes equation, to solve thin films in the field of fluid film lubrication [11]. Cameron, solved the numerical solutions in hydrodynamic lubrication by considering isoviscous and isothermal [6]. Hiromu Hashimoto and Sanae Wada, were derived the analytical solutions for three different pressure boundary conditions at inlet edge of turbulent thrust bearings [8].…”

Lubrication of Narrow Porous Bearings With Arbitrary Wall Thickness

“…The coefficient of friction fj, can be found from the formula derived by Cameron and Wood[19] for a solid bearing and shown to be valid for a porous bearing also.…”