An Interior Collocation Method for Static and Dynamic Analysis of Finite Length Gas Journal Bearings

The general Reynolds equation for self-acting, finite length gas-lubricated journal bearings is solved using an interior collocation method. The method assumes an approximate solution to the governing differential equation in the form of a series of trial functions, w_n, with n unknown coefficients. The coefficients are evaluated by substituting the assumed solution in the governing differential equation, and forcing the residual (error) at n collocation points in the computational domain to be zero. The effectiveness of the collocation method is demonstrated by using the technique for the static and dynamic analysis of a journal supported by a plane gas bearing. The results from the collocation method agree very well with those obtained from a finite difference technique. Periodic orbit plots for a single journal in a finite bearing are presented for various journal unbalances and speeds. The collocation method is shown to be an order of magnitude computationally faster than the finite difference method. The method can be extended to other bearing types such as slider, hydrostatic and tilting pad bearings.