Response and stability of nonlinear rotor bearing systems

Nonlinear response and stability of rotor bearing systems under unbalance and self excitation are investigated using a shooting and pseudo-arc length continuation procedure developed for this study. This procedure is used to calculate the unbalance response, its stability, and bifurcations of two example nonlinear rotor systems, rigid rotors supported on squeeze-film dampers and plain journal bearings. In the case of squeeze-film damper supported rotor, fluid inertia and external cross-coupled stiffness effects on the nonlinear response of the damper are studied. It is shown that fluid-inertia can mitigate nonlinear responses such as 'jump' etc. while cross-coupled stiffness forces can enhance the bistable operation range. In the case of a plain journal bearing, the study shows that a bearing can go unstable through a period-doubling bifurcation. It is shown that increase of speed beyond the threshold speed can result in a series of such period-doubling bifurcations resulting in chaos through the well known Feigenbaum's route.; A new approach for treating large-order systems with local nonlinearities is present. Here, a finite-element formulation is used to derive system mass, damping, and stiffness matrices and then the total number of degrees of freedom of the system is reduced using a real modes fixed-interface component mode synthesis procedure (CMS) model. The resulting low order system is investigated for its unbalance response, stability, and bifurcations using the shooting and continuation scheme. A 24-dof rotor supported on journal bearings is analyzed to illustrate the efficiency of the method. The advantages of the real modes CMS employed here over complex modes CMS procedure are discussed through numerical examples.; Hopf bifurcation theory is used to calculate sub/supercritical bifurcation regimes for a finite-length bearing. It is shown that when the bearing operates at certain eccentricity positions, subcritical Hopf bifurcation can occur and the journal can go unstable at speeds below the threshold speed when given a sufficient perturbation. Such bearing instabilities cannot be determined using the usual linear analysis.