Prediction of the nonlinear hysteresis loop for fluid-film bearings by numerical continuation

A nonlinear dynamic model of a short journal bearing is used to predict the steady-state motion of the journal and its successive bifurcations in the neighbourhood of the stability critical speed. Numerical continuation is applied to determine the branch of equilibrium point and its bifurcation into stable or unstable limit cycles. It has been found that the unstable limit cycles undergo a single limit point bifurcation whereas the stable limit cycles undergo two successive limit point bifurcations. Thus, the bi-stability domain, the potential jumping from small to large motion and the hysteresis loop motion are predicted.