Nonlinear stability analysis of long hydrodynamic journal bearings using numerical continuation

• A nonlinear model is derived to investigate the stability of long journal bearings.
• Stability boundaries are decomposed into sub- and supercritical bifurcations.
• The size of limit cycles is determined using a numerical continuation method.
• Boundaries of bi-stability regions and hysteresis phenomenon are elucidated.

Hydrodynamic bearings are frequently used in applications involving high loads and high speeds. They may however be subjected to oil whirl instability which may cause their failure. For a successful application of fluid film bearings, it is essential to predict the stability boundaries in terms of the bearing characteristics as well as other nonlinear phenomena observed near the stability limits such as stable and unstable limit cycle motion, hysteresis and jumping phenomena.A model of a long balanced hydrodynamic journal bearing is considered in this paper. Numerical continuation is then used to predict the branch of the journal equilibrium point, the Hopf bifurcation point and the emerging stable or unstable limit cycles.Depending on the bearing characteristics, the stability threshold occurs either at a supercritical or at a subcritical Hopf bifurcation. For journal speeds above the supercritical bifurcation, the journal undergoes stable limit cycles. For the stability boundaries due to a subcritical bifurcation, a limit point of cycle bifurcation is found defining the domain of possible journal jumping from the equilibrium position to large limit cycles and hysteresis phenomenon during rotor speed variation near the stability threshold.