转子与定子碰摩的非线性动力学研究

转子与定子碰摩的动力学行为及其与系统参数关系对旋转机械设计和安全运行至关重要. 转子/定子碰摩系统是一类多参数控制的高维非光滑强非线性系统, 其动力学行为非常复杂. 本文主要从动力学与控制的角度对过去半个世纪有关转子与定子碰摩的研究成果进行归纳和总结, 其目的在于帮助读者尽可能全面系统地了解该问题的研究现状, 提炼尚待解决的问题, 以求推动转子与定子碰摩研究的进一步深入, 并为解决实际问题提供帮助. 本文将首先从碰摩局部模型和碰摩系统模型两个方面对已有的转子/定子碰摩系统的建模进行了简单的划分和归类. 其次, 以典型碰摩非线性响应为主线, 分别介绍了有关同频碰摩响应、谐波周期碰摩响应、准周期局部碰摩响应、干摩擦自激反向全周涡动响应、碰摩的全局响应行为以及碰摩响应的分岔与混沌方面的研究成果. 接下来讨论了在主被动抑制碰摩振动方面取得的结果. 最后, 给出结论并提出有待进一步研究的问题.

ADVANCES IN THE RESEARCH ON NONLINEAR PHENOMONA IN ROTOR/STATOR RUBBING SYSTEMS

The dynamical behavior and its relationship with system parameters of rotor/stator rubbing systems are of considerable significance for the design and safe operation of rotating machinery. Rotor/stator rubbing systems are a kind of high-dimensional non-smooth nonlinear dynamical systems with many system parameters and complex dynamical behavior. In this paper the literature on rotor/stator rubbing in the past half century are summarized from the point of view of dynamics and control. The goal is to provide a comprehensive overview on the research state of this problem and help find existing problems in the research direction so as to improve our understanding on this problem. First, the existing modeling on the rotor/stator rubbing is classified into two categories: the local rubbing models and the system rubbing models, which are then discussed in details. Secondly, the progress in the study of synchronous rubbing responses, suband super-harmonic rubbing responses, quasi-periodic partial rubbing, dry whirl/whip, coexistence of multi-stable rubbing responses as well as bifurcation and chaos of rubbing responses are discussed individually. Finally, the ideas and results of passive and active suppression of rubbing in the literature are also summarized.