Study on Solution Algorithm of Reynolds Equation of Self-acting Gas Journal Bearings Based on Finite Difference Method

It is very crucial to solve Reynolds equation quickly and accurately using the numerical methods in the research field of fluid lubrication. For the static Reynolds equation of self-acting gas journal bearings, the typical solution algorithm of the finite difference method is put forward and a new solution algorithm of the finite difference method is proposed. The typical solution algorithm discretizes the transformed Reynolds equation directly and the quadratic equation in one variable of the pressure can be obtained. Different from the typical solution algorithm, the both sides of the transformed Reynolds equation are firstly divided by the term of PH3 and then discretized in the new solution algorithm, thus the linear equation about the pressure can be obtained. Secondly, the Reynolds equation is solved numerically with the same parameters and the pressure distribution of gas bearings is obtained. Finally, the numerical solution from the new solution algorithm can be obtained with less number of iterations and the less computing time under the different computational grids and bearing numbers. Therefore, the new solution algorithm of the finite difference method is superior to the typical solution algorithm of the finite difference method.