A Bounded Variable Approach to the Optimum Slider Bearing

Abstract

Contemporary methods for treating inequality constraints in the calculus of variations are employed to determine the maximum load-capacity one-dimensional slider bearing using a lubricant with pressure-dependent viscosity. A lower bound on the minimum film thickness is put into equational form to facilitate the use of the Euler-Lagrange equations, the corner conditions, and the Weierstrass E-function. It is found that, for typical lubricants, the slider bearing contains only one step separting two values of the film thickness. It is shown also that there exist cases for which a solution cannot be obtained to describe a real situation.