Stability Analysis of a Flexible Spinning and Precessing Rotor with Non-symmetric Shaft

Abstract

The present work deals with stability analysis of a spinning non-symmetric shaft with a non-central disk mounted on a rotating (precessing) base, where the spin axis and the precession axis intersect at right angles. The nutation speed is zero and the spin and precession speeds are considered to be uniform. The motion of the rotor is such that it undergoes small elastic deformation superposed on rigid body rotation. The shaft-disk system is assumed to be axially and torsionally stiff. A four-degree- of-freedom model is considered for the stability analysis. A non-symmetric shaft (e.g., shaft with rectangular or elliptic cross-section, shaft with a keyway, cracked shaft etc.) of a rotor has dissimilar stiffness in two perpendicular transverse planes. The governing equations for such a rotor are expressed in the precessing but non-spinning frame. Since the governing equations of motion are found to have periodic stiffness terms, a variant of Hill’s method is adopted for stability analysis. The stability borderlines are constructed with respect to the spin speed and precession speed.