Bifurcation analysis of rotor/bearing system using third-order journal bearing stiffness and damping coefficients

Abstract

Hydrodynamic journal bearings are used in many applications which involve high speeds and loads. However, they are susceptible to oil whirl instability, which may cause bearing failure. In this work, a flexible Jeffcott rotor supported by two identical journal bearings is used to investigate the stability and bifurcations of rotor bearing system. Since a closed form for the finite bearing forces is not exist, nonlinear bearing stiffness and damping coefficients are used to represent the bearing forces. The bearing forces are approximated to the third order using Taylor expansion, and infinitesimal perturbation method is used to evaluate the nonlinear bearing coefficients. The mesh sensitivity on the bearing coefficients is investigated. Then, the equations of motion based on bearing coefficients are used to investigate the dynamics and stability of the rotor-bearing system. The effect of rotor stiffness ratio and applied load on the Hopf bifurcation stability and limit cycle continuation of the system are investigated. The results of this work show that evaluating the bearing forces using Taylor’s expansion up to the third-order bearing coefficients can be used to profoundly investigate the rich dynamics of rotor-bearing systems.

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

“…This approach proves particularly useful for investigating system stability and identifying points of bifurcation as parameters change. Prior literature has demonstrated the application of numerical continuation in assessing the stability of rotor-bearing systems, as evidenced by studies such as [1,[13][14][15][16]. The majority of these investigations have relied on approximations of Reynolds equation to evaluate nonlinear bearing forces.…”