Bifurcations of Cylindrical Precessions of an Unbalanced Rotor

Abstract

The problem of stability loss of a direct synchronous cylindrical precession of an unbalanced rotor is investigated. The rigid rotor is considered as a mechanical system with four degrees of freedom. Rotation occurs at constant spin speed. Non-linear elastic bearings’ reactions and viscous external and internal damping are taken into account. It is shown that different types of stability loss take place. For some range of the spin speed, jump phenomena and bi-stability occur, but the steady-state motion remains to be the direct synchronous cylindrical precession. For some other values of the parameters stability loss is accompanied by inducing hyperboloidal precession due to the conical swinging of the shaft. The precession becomes hyperboloidal as the rotor’s axis traces a one-sheet hyperboloid surface. The threshold angular speed for autovibration is found. By computational modeling the limit cycles and the strange attractor are built. The results of numerical integration with slowly accelerating spin speed confirm self-centering instability under the influence of internal damping.