Matrix Form of Reynolds Equation : Expansion of Pressure by Orthogonal Functions

This paper presents a new method for solving the Reynolds equation with a matrix form, in which the Reynolds equation is reduced analytically without approximation to infinite dimensional linear equations with unknowns related to eigen values of operator R=▽·[(h3/6η)▽]. The paper also presents applications of the method to journal bearing problems under two boundary conditions : one is the half Sommerfeld condition and the other is the quasi Reynolds condition which assures 'continuity of the bulk flow' across the boundary. It will be shown that the present method requires much less computational time than FDM for obtaining accurate predictions.