The development of a dynamically coupled axial-torsional-lateral point transfer matrix for a whirling eccentric mass

Abstract

A point transfer matrix for a whirling eccentric mass was developed. Two right handed cartesian coordinate systems, a fixed and a rotating, were used in the derivation. The state variables and the elliptical whirl orbit were described relative to the fixed coordinate system. The rotating coordinate system was used to describe the equivalent model of the mass. The effects of both inertial forces and gravitational forces were included. The inertial forces contained the effects of; centripetal acceleration, acceleration relative to a moving reference frame, Coriolis acceleration and a disguised form of tangential acceleration.

The transfer matrix which resulted from this derivation was verified. To verify the lateral motion equations the assumption of a circular whirl orbit in the fixed reference frame was made. The axial and torsional motion equations were verified by assuming no coupling effects.

Terms were found which had harmonic forms at twice and three times running speed. Static load terms were also found as a result of the synchronous whirl analysis. These static, 2 times and 3 times terms are extended forcing functions which can be used in static, 2 times and 3 times running speed analyses, respectively.