A Variational Principle Applied to the Plane Slider Bearing

Abstract

A minimum principle from hydrodynamics is applied to the one-dimensional plane slider bearing which is provided with a self-seeking pivot mechanism. An analysis was made in which a certain integral was minimized subject to the constraint that the load, speed, and viscosity were held fixed. This analysis showed that this corresponded exactly to that combination of minimum film thickness and inclination which would minimize the power loss subject to the above-mentioned constraint. It was also found that, in order to satisfy the minimum principle, there exists a definite numerical ratio between the slider inclination and the nondimensional minimum film thickness. This, in turn, fixed the pivot location relative to the length of the slider.