The Accuracy of Short Bearing Theory for Newtonian Lubricants

Abstract

The accuracy of the short bearing approximation is analyzed in this discussion. The results apply to Newtonian lubricants, and they can also be extended to non-Newtonian power-law lubricants. Reynolds’ lubrication equation is first solved by applying a regular perturbation expansion in pressure to the π film journal bearing; after this, a matched asymptotic expansion is applied to linear slider bearings. Approximate solutions are then compared with numerical solutions, to estimate the accuracy of the short bearing approximation. Finally, the accuracy of fluid film pressures predicted via short bearing theory is shown to depend upon three factors: the bearing aspect ratio, eccentricity ratio, and the partial-arc extent. Ocvirk’s short bearing series approximation—for finite bearing aspect ratio—is shown to become singular in the limit as the eccentricity ratio approaches unity. The one term π film Ocvirk solution is shown to be a nonconservative approximation to the journal bearing load capacity. A method to extend the accuracy of the short bearing approximation for partial-arcs and slider bearings is then presented.