The one-dimensional rapid algorithm for the generalized Reynolds equation of journal bearings

A rapid algorithm of the generalized Reynolds equation considering thermal effects was presented. Based upon the variational approach, variational inequality and complementary problem, which were equivalent to the generalized Reynolds equation under Reynolds boundary condition, the film pressure distribution in the axial direction could be solved analytically and the two-dimensional variational inequality reduced to one-dimensional form by partitioning the film pressure function and minimizing the variational approach. The modified forward elimination and backward substitution algorithm was illustrated. The most important feature of this method is that no iteration process is needed to solve the pressure of nodal points and to determine the boundary of the film rupture region. The technique described here is valid for the generalized Reynolds equation with spatially varying viscosity as long as the variation in the bearing axial direction may be neglected. At the same time, the solution of the nonlinear oil-film forces for circular journal bearing can not be obtained by the presented technique. © 2010 Chinese Society for Electrical Engineering.