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.

A rotor supported by hydrodynamic bearings may undergo unstable motion and may exhibit several nonlinear phenomena in the vicinity of the critical stability speed. This paper presents a stability analysis of a flexible rotor supported by journal bearings using a nonlinear dynamic model and a short bearing approximation. Numerical continuation is applied to determine the boundaries of stability and the bifurcations of the limit cycles. Nonlinear phenomena such as jumping motion and bi-stability domain are predicted. An extended stability chart has also been determined including the domains of stable oscillatory motion. The investigation also includes the effect of rotor flexibility and bearing characteristics on the stability boundaries and on the safe operating speed range. For a selected range of bearing parameters, two Hopf bifurcation regions are found for high rotor stiffness, three regions for low stiffness and four bifurcation regions in transition between high and low stiffness. It has also been found that the stable operating speed range decreases with rotor flexibility and bearing parameter.

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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. Poincaré 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.

This paper presents a nonlinear stability analysis of an unbalanced rotor-bearing system using the numerical continuation method and the numerical integration method. In this study, the effect of unbalance on journal motion is highlighted and a relationship is established between the bifurcation diagram of a balanced rotor and that of an unbalanced rotor. The results show that the stable operating speed range, the shaft motion type, the whirl speed and the chaotic motion occurrence depend on the unbalance level, the bearing geometry, the oil viscosity, and the speed range of unstable limit cycles existence.