Dynamics of a rotor shaft driven by a non-ideal source through a universal joint

Abstract

A rigid rotor system which is driven through a Universal joint (U-joint) and is mounted on weakly-damped flexible supports exhibits principal and combination type parametric instabilities at certain torque-speed combinations. In this article, the transient dynamics of such a non-linear system driven by a non-ideal source (a DC motor) is studied through numerical simulation of the bond graph model of the system. It is shown that the dynamic coupling between the DC motor and the whirling rotor in the non-ideal system can stabilize the system in the speed ranges where the corresponding ideal system is unstable. This stabilization depends upon the motor characteristic constant or the torque/speed constant; i.e. if two motors with different motor characteristic constants produce the same torque at the same operating speed (where the ideal system is unstable) then the motor with higher motor characteristic constant tends to better stabilize the system. This bounded-input bounded-output stabilization is shown to occur through repeated transitions between stable and unstable speed regions. Several simulation results for the system driven by ideal and non-ideal sources at different operating speeds are presented to derive motor sizing specifications.