Analytical bifurcation analysis of a rotor supported by floating ring bearings

Like with other types of fluid bearings, rotors supported by floating ring bearings may become unstable with increasing speed of rotation due to self-excited vibrations. In order to study the effects of the nonlinear bearing forces, within this contribution a perfectly balanced symmetric rotor is considered which is supported by two identical floating ring bearings. Here, the bearing forces are modeled by applying the short bearing theory for both fluid films. A linear stability analysis about the static equilibrium position of the rotor shows that for a critical revolution speed the real part of an eigenvalue pair changes its sign. By means of a center manifold reduction it is shown that this destabilization of the steady state is due to a Hopf-bifurcation. Furthermore, the type of this bifurcation is determined as well as the existence and stability of limit-cycles. Notably it is found that depending on the parameters of the floating ring bearing subcritical as well as supercritical bifurcations may occur. Additionally, the analytical results obtained from the center manifold reduction are compared to numerical results by a continuation method. In conclusion, the influences of bearing design parameters on the stability and on the limit-cycles are discussed.