A New Mathematical Method for the Solution of Film Lubrication Problems

Abstract

The paper applies the technique of the “relaxation” method to the problem of fluid-film lubrication. It is found that a solution to Osborne Reynolds's governing equation can be obtained by this means in all cases of practical importance. The method also renders possible a new treatment of the difficulty presented by the occurrence of divergent films in journal bearings.The problem is shown to be tractable even when viscosity is correctly treated as a function of both temperature and pressure; moreover, as a part of this treatment, means of estimating the temperature distribution over the bearing surface are provided.A numerical example is used to illustrate the modifications in the solution resulting from viscosity variation.