Continuation Analysis of Rotor Bearing Systems Through Direct Solution of Reynolds Equation Hussein SAYED a,d , Tamer A. EL-SAYED a,b,c,1 , M I. FRISWELL e a Department of Mech. Design, Faculty of Eng. Mataria, Helwan University, Egypt b CADR, School of Engineering, University of Aberdeen, Aberdeen, AB24 3UE c School of Engineering, University of Hertfordshire Hosted by GAF, Cairo, Egypt d High Institute for Engineering & Technology Al-Obour, Egypt e Faculty of Science and Engineering, Swansea University, Bay Campus, UK 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. Keywords. Reynolds equation, continuation analysis, journal bearings, rigid rotor model, Hopf bifurcation, threshold speed 1. Introduction The dynamic analysis of rotor-bearing systems has been a topic of significant interest for scientists and engineers for over a century and a half. Notably, one of the pioneering articles in this field was published by Rankine in 1869, which investigated the centrifugal force of rotating shafts [3]. Since then, numerous research studies have been conducted to investigate the dynamic behavior of such systems due to their critical importance. 1 Tamer A. EL-SAYED, Corresponding author, Department of Mechanical Design, Faculty of Engineering, Mataria, Helwan University, P.O. Box 11718, Helmeiat-Elzaton, Cairo, Egypt; E-mail: Tamer_Alsayed@m-eng.helwan.edu.eg. Advances in Machinery, Materials Science and Engineering Application IX M. Chen et al. (Eds.) © 2023 The Authors. This article is published online with Open Access by IOS Press and distributed under the terms of the Creative Commons Attribution Non-Commercial License 4.0 (CC BY-NC 4.0). doi:10.3233/ATDE230462 217