Bifurcation and chaos of a flexible rotor supported by turbulent journal bearings with non-linear suspension

Abstract

This study presents a dynamic analysis of a rotor supported by two turbulent model journal bearings with non-linear suspension. The dynamics of the rotor centre and bearing centre are studied. The analysis of the rotor-bearing system is investigated under the assumptions of turbulent lubricant flow and a short bearing approximation. The spatial displacements in the horizontal and vertical directions are considered for various non-dimensional speed ratios. The dynamic equations are solved using the fourth-order Runge-Kutta method. The analysis methods employed in this study is inclusive of the dynamic trajectories of the rotor centre and bearing centre, power spectra, Poincaré maps, and bifurcation diagrams. The maximum Lyapunov exponent analysis is also used to identify the onset of chaotic motion. The numerical results show that the stability of the system varies with the non-dimensional speed ratios. Specifically, it is found that the dynamic behaviours of the system include 3 T-periodic, jump phenomena, and chaotic motions. The modelling results thus obtained by using the method proposed in this paper can be employed to predict the stability of the rotor-bearing system and the undesirable behaviour of the rotor and bearing centre can be avoided.