Whirling Vibrations of a Rotating Shaft with Load Torque : Instability due to Load Torque

Abstract

When a shaft rotates resisting a certain load, the rotating shaft must undergo bending and torsion simultaneously. The driving torque on such a rotating shaft influences the whirling motion of the shaft. This paper presents an analytical study of the effect of the load torque on the whirling vibration of the rotating shaft. Equations of motion are derived with an accuracy of the second order for the deflection and the torsion, and are analyzed by using the. asymptotic method. The analyses produced the following results. The effective damping coefficient for the whirling vibration can become negative when the viscous damping coefficient of the torsional vibration is larger than that of the lateral-reciprocal vibration. In this case, the whirling vibration of the rotating shaft assumes an unstable state. The damping coefficient for whirling vibration of the shaft in an accelerated rotation differs from that in a decelerated rotation.