Lateral-Torsional Coupled Vibrations of a Rotating Shaft Driven by a Universal Joint : Derivation of Equations of Motion and Asymptotic Analyses

Abstract

A driven shaft system consists of a flexible shaft with circular section and a rotor. The flexible shaft is supported by a universal joint at one end and a bearing at the other end. When a drive shaft rotates with a constant angular velocity, the driven shaft is subjected to the angular velocity fluctuation governed by a joint angle between the drive shaft and the driven one. However, when the driven shaft vibrates laterally and causes bending in itself, the joint angle is slightly changed and the rotating speed deviates. This is why the lateral-torsional coupled vibrations become unstable at the same time. These unstable vibrations occur when the drive shaft rotates at a speed of nearly half the sum of the natural angular frequency for the lateral vibration and the one for the torsional vibration.