Coupled torsion-lateral stability of a shaft-disk system driven through a universal joint

Understanding the instability phenomena of rotor-shaft and driveline systems incorporating universal joints is becoming increasingly important because of the trend towards light-weight, high-speed supercritical designs. In this paper, a nondimensional, periodic, linear time-varying model with torsional and lateral degrees-of-freedom is developed for a rotor shaft-disk assembly supported on a flexible bearing and driven through a U-joint. The stability of this system is investigated utilizing Floquet theory. It is shown that the interaction between torsional and lateral dynamics results in new regions of parametric instability, that have not been addressed in previous investigations. The presence of load inertia and misalignment causes dynamic coupling of the torsion and lateral modes, which can result in torsion-lateral instability for shaft speeds near the sum-type combinations of the torsion and lateral natural frequencies. The effect of angular misalignment, static load-torque, load-inertia, lateral frequency split, and auxiliary damping on the stability of the system is studied over a range of shaft operating speeds. Other than avoiding the unstable operating frequencies, the effectiveness of using auxiliary lateral viscous damping as a means of stabilizing the system is investigated. Finally, a closed form technique based on perturbation expansions is derived to determine the auxiliary damping necessary to stabilize the system for the least stable case (worst case).