The Full Journal Bearing

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Abstract
The basic mathematics of the full journal bearing have been known since 1904 when Sommerfeld‡ 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 θ = 0 and p = ∂ p/∂θ = 0 at θ = π + α is shown to follow for the infinite 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 Southwell's 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 Nücker'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.