Continuation Analysis of Rotor Bearing Systems Through Direct Solution of Reynolds Equation

Abstract

Rotor bearing systems are a crucial component in many engineering applications, with bearings are typically classified as either rolling contact or sliding contact. In this context, we focus specifically on sliding contact bearings, and more specifically on fluid film journal bearings. The fluid film between the rotor and stator in such bearings can be modeled using Reynolds equation, with the solution of this equation being important for evaluating the bearing’s nonlinear forces. In order to solve the dynamics of a rotor bearing system, Reynolds equation must be solved at each time step. However, this process can be time-consuming, leading many researchers to use approximate formulae to solve the equation more efficiently. In the present study, a continuation analysis was introduced to examine the dynamics of a rigid rotor bearing system without relying on any such approximations. Subsequently, a comparison was made between the findings of this analysis and those of two previously published models, one based on four variable polynomial regression [1] and the other based on short bearing approximation [2]. The results suggest that all three methods are effective in assessing the threshold speed. However, it was observed that the short bearing model exhibits reduced accuracy beyond the threshold speed.