Numerical Continuation Applied to Nonlinear Rotor Dynamics

Besides the synchronous oscillations due to unbalance, high-speed rotors in oil film bearings are known to show whirl/whip instabilities which exhibit various types of subsynchronous oscillations. Here, the methods of numerical continuation are applied to study the subsynchronous oscillations in detail. The main scope is to analyze the stability and bifurcation behavior of the unbalanced Laval/Jeffcott rotor supported in semi-floating ring bearings. Characteristic bifurcation scenarios prove the existence of two different types of Hopf bifurcations which represent whirl/whip instabilities due to the inner or the outer oil films. Furthermore, it is shown that the critical limit cycle of non-tolerable amplitude is born at a saddle-node bifurcation. Finally, the influence of unbalance on the subsynchronous oscillations is investigated by tracing the occurring bifurcations in the parameter plane of the unbalance load and the rotor speed. The obtained bifurcation curves provide extended stability charts which illustrate the global solution behavior of the considered rotor bearing systems.