Numerical methods for theoretical analysis of foil bearing dynamics

The bearing under consideration is a self-acting, gas bearing with a flexibly supported foil. In order to conduct the theoretical analysis, three systems were identified: a rotor, a gas film and a flexible structure. Each of these elements has been mathematically analysed and analytical equations have been formulated. It was found, that the gas flow in the bearing can be described by the Reynolds equation, whereas a spring-damper model was selected for the structural analysis. The Reynolds equation is a differential equation the exact solution to which is unknown. The work describes the finite difference method in detail, where the partial derivatives in the Reynolds equation are replaced by a system of algebraic equations. In order to solve the resulting system, the Alternating Direction Implicit method (ADI) was used. Based on that and on the analysis of interactions between the three systems the equations have been computed. The accuracy of methods has been verified by means of series of numerical tests. Chosen results are described in this paper.