Dynamic Characteristics of a Supercritical Helicopter Tail Transmission System with Self-Excited Vibration and Rubbing Impact

This study presented a novel analytical method to investigate the coupled dynamic behavior of a supercritical helicopter tail transmission system, taking into account the friction-induced self-excitation of the floating spline, the rubbing between the limiting ring device and the shaft, and the time-varying meshing excitation experienced by multiple spiral bevel gear pairs. The tail transmission shaft was first modeled using Timoshenko beam elements in local coordinates. Subsequently, the centralized parameter method was employed to build dynamic models of critical components such as the floating spline, limiting ring devices, and multiple spiral bevel gear pairs. Finally, the system's dynamic equations were derived utilizing the interface coordination principle and spatial coordinate transformation. Numerical analyses were conducted to examine the dynamic behavior of the system, including the coupled vibration properties and the impact laws of the limiting ring device and floating spline on the system's response. The findings indicated that the limiting ring device resulted in a cross-critical vibration reduction in the tail horizontal shaft, achieved through the mechanisms of dry friction and rubbing impact. However, as a consequence, the natural and rubbing frequencies of the other shafts were generated. The self-excited vibration of the system, brought about by the friction of the spline tooth surface, had a significant impact on the shaft that was directly connected. The emergence of the self-excited vibration occurred when the speed surpassed the first-order natural speed of the directly connected shaft, with the corresponding self-excited frequency being the first-order natural frequency of said shaft. With the increase in the tooth surface friction coefficient of the spline, it even caused continuous rubbing between the shaft and the limiting ring device under a supercritical condition. The proposed dynamic analysis approach holds promise in offering theoretical guidance for the reduction of vibration and noise generated in supercritical tail transmission systems.