Hopf bifurcation in rotors supported in gas bearings

摘要

In this paper we describe a problem of control of the Hopf bifurcation. We illustrate the problem by three examples of a rotor system supported in two gas bearings. The bearing bushes are connected to the casing by means of additional air rings. In the case when parameters of the air ring are improperly chosen, at a sufficiently high rotational velocity the rotor undergoes the Hopf bifurcation and the bearing may be damaged by the growing amplitude of self-excited vibrations. We may avoid this danger by a proper selection of stiffness and damping coefficients of the air ring or, in the worst case, by a temporary change of the stiffness or damping coefficients of the air ring. Our method then guarantees a safe passage through the unstable zone between the Hopf and reversed Hopf bifurcation points.