A New Mathematical Method for the Solution of Film Lubrication Problems

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.