Cylindrical Precessions of an Unbalanced Jeffcott Rotor with four Degrees of Freedom in Non-linear Elastic Supports

Abstract

To study forward synchronous whirling motion (precession) of a Jeffcott rotor with 4 degrees of freedom, a new approach has been suggested. The rotor is considered to be statically and dynamically unbalanced. It is attached to a massless linear elastic shaft and supported in non-linear elastic bearings. Depending on the surface traced by undeformed axis of revolution in 3D space one can differentiate three types of precession – cylindrical, conic and hyperboloidal. In the last case this surface is one-sheet hyperboloid.

For a statically unbalanced rotor supported in isotropic bearings with Hertzian contact, a cylindrical precession has been studied in assumption that rotation occurs at constant spin speed. External and internal damping have been taken into account. Two non-linear resonances have been found and dynamic response has been built. The problem of stability loss of a forward synchronous cylindrical precession has been investigated for a full range of angular velocities. It has been shown that different types of stability loss take place. Within some range jump phenomena and bi-stability occur, but the steady-state motion remains to be the forward synchronous cylindrical precession. For some other values of the angular velocity stability loss is accompanied by inducing a hyperboloidal precession. The threshold angular velocity for autovibration has been found. By computational modeling the limit cycles and the strange attractor are determined. The results of numerical integration reveal transition ”chaos to chaos” in the process of rotation.