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.

Influences of system parameters on dynamic behavior of the vehicle shimmy system with clearance in steering linkage

“…There will be slide movement between the two components at the contact surface (Ghosh et al, 2010;Chen et al, 2012), which can be given by…”

Flexible spinning and precessing rotor–stability analysis based on different analytical and finite element models

“…Xiao et al (2005) demonstrated the effect of simultaneous dynamic softening and stiffening in a rotating beam with a tip mass. Ghosh et al (2010) analyzed a spinning and precessing rotor using a four-d.f. rotor model, where the shaft was assumed to be mass-less.…”