Self-excited oscillation induced by the internal frictions of spline joints is a major cause of rotor system instability. In this study, the dynamic equations of spline-connected multi-span rotor systems have been derived by finite element and lumped mass hybrid modelling methods. In this model, the mathematical models of spline joints and rubber sealing rings were deduced in detail. Newmark numerical algorithm was applied to solve differential equations of the coupling system. On this basis, the amplitude–frequency response characteristics of systems without rubber sealing ring as well as the effects of several important parameters, including friction coefficient, transmission torque and unbalance value, on the self-excited vibration of the system were discussed. Then, in the case of rubber sealing ring assembled next to spline joint, the effects of rubber sealing ring on amplitude–frequency response characteristics and self-excited vibrations of the system were analyzed. The obtained results showed that self-excited oscillation occurred in supercritical state when the friction coefficient of spline joint was high enough; however, it merely occurred within a specific speed range. By the increase of friction coefficient or transmission torque, the speed range corresponding to self-excited oscillation became closer to the natural frequency of the system. However, as the unbalance value was increased, the phenomenon of self-excited vibration showed the opposite trend. Rubber sealing ring not only reduced vibration near spline joint, but also suppressed the self-excited vibration of the system induced by internal friction, thus improving system stability. This paper provides a theoretical basis for studying the mechanism and suppression of self-excited oscillation of rotor systems.

中文翻译：

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花键连接多跨转子系统建模与动力学分析

花键接头内摩擦引起的自激振荡是转子系统不稳定的主要原因。在这项研究中，花键连接的多跨转子系统的动力学方程已经通过有限元和集中质量混合建模方法推导出来。在该模型中，详细推导了花键接头和橡胶密封圈的数学模型。应用Newmark数值算法求解耦合系统的微分方程。在此基础上，讨论了无橡胶密封圈系统的幅频响应特性以及摩擦系数、传递扭矩和不平衡值等几个重要参数对系统自激振动的影响。然后，在花键接头旁边组装橡胶密封圈的情况下，分析了橡胶密封圈对系统幅频响应特性和自激振动的影响。结果表明，当花键接头摩擦系数足够高时，超临界状态下会发生自激振荡；然而，它只发生在特定的速度范围内。通过增加摩擦系数或传递扭矩，自激振荡对应的速度范围变得更接近系统的固有频率。但随着不平衡量的增加，自激振动现象呈现出相反的趋势。橡胶密封圈不仅减少了花键接头附近的振动，而且抑制了系统内摩擦引起的自激振动，从而提高了系统的稳定性。