Stability Analysis of an Unbalanced Journal Bearing with Nonlinear Hydrodynamic Forces

Abstract

The research reported in this paper is based on a nonlinear two degree of freedom model of an unbalanced rigid rotor bearing system. The nonlinearity is introduced into the model through closed form expressions of the short bearing hydrodynamic forces. The model in its nondimensional form depends on three nondimensional parameters: the bearing modulus, the rotor rotating speed and unbalance. For the balanced system, numerical continuation is applied to predict the branch of equilibrium positions of the journal and its bifurcation into stable or unstable limit cycles at the linear stability threshold speed. For the unbalanced system, however, numerical integration is used to find the bifurcation diagrams using the rotor speed as a bifurcation parameter. Poincare sections are used to characterize the journal motion. The investigation is carried out for three bearing parameters covering a large domain of rotor bearing conditions. The effect of unbalance on the journal motion is investigated in each case. Compared to the balanced system, it has been found that unbalance may introduce, at different speed ranges, periodic oscillations at multiple periods of rotation, quasi-periodic oscillations and chaotic motion. The effect of unbalance on journal motion is highlighted and closely related to the bifurcation diagram of the balanced rotor.