Bifurcations of the precessional motion of an unbalanced rotor

The loss of stability of the cylindrical and conical precession of a rigid unbalanced rotor in non-linear elastic bearings with dissipation accompanying a change in the angular velocity of rotation of the rotor is investigated. It is assumed that the rotor has four degrees of freedom. It is established, using equations of the first degree of approximation, that the loss of stability of cylindrical and conical precessions on passing through a zero root can be accompanied by the excitation of a direct synchronous precession of the hyperboloidal type. Moreover, the equation of the boundary for the onset of self-excited oscillations is obtained and it is shown by means of numerical modelling that supercritical Hopf bifurcation and a strange attractor can occur.