多模态转子系统碰摩非光滑诱导的模态耦合动力学机制及复杂行为研究

Nonlinearity may induce the modal coupling in multi-modes vibration systems, by which the input energy into the systems will be re-distributed among the modes and will affect both the vibrational manner and strength of the systems. This project will focus on multi-modes rotor and stator systems with the aim to understand the the inherent mechanisms of nonsmooth induced modal coupling during rubbing,and its effects on rubbing responses. The main objectives of the project are as followings: First, setting up multi-degree-of-freedom nonsmmoth rotor/stator models that are derived from mode decretization but coupled through contact forces; Secondly, developing semi-analytic methods, constructing the nonlinear normal modes of the coupled rotor/stator rubbing systems,exploring the possible relationship between the nonlinear normal modes and the modal coupling; Thirdly, exploring the forms and the conditions of non-smmoth induced modal coupling under different excitation frequency bands,differet ways of rubbing and different rubbing responses, in order to elucidate the inherent mechanism and the effects of modal coupling on rubbing reponses; Fouthly, determining self-excited dry friction backward whirl motions of multi-mode rotor/stator systems, revealing the characteristics and the mechanisms of modal coupling induced by the super-synchronous responses; Finally, setting up a rotor/stator rubbing test rig with flexible ring stator and flexible rotor in order to verfy the corresponding results. The research of this project is devoted to investigate the inherent mechanisms of dynamical phenomena and belong to the frontier basis research for the application of nonlinear dynamical theory to the engineering problems. The works of this project may provide some valuable knowledge for reference in the design of real engineering rotor systems, and have important scientific meanings and potential values for engineering applications.

非线性可诱发多模态振动系统的模态耦合，使得输入系统的能量在不同模态间重新分配，并影响系统响应的方式和效果。本项目拟以多模态的定子和转子系统为研究对象，旨在认识碰摩非光滑性诱导的模态耦合的发生机制及对碰摩响应的影响。为此，将建立模态离散且由碰摩力耦合的多自由度转子/定子模型；发展半解析求解方法，构造多模态转子/定子碰摩耦合系统的非线性模态，探索非线性模态与碰摩模态耦合间的可能联系；研究不同激励频段、碰摩方式以及碰摩响应情形下，模态耦合的发生形式和条件，阐明其影响碰摩响应的机制和效果；求解多模态转子/定子碰摩的干摩擦自激反向涡动响应，揭示该高频非协调响应诱发模态耦合的特征和机制；搭建具有柔性转子和柔性环形定子的碰摩实验台架，验证上述分析结果。本项目研究力求认识动力学行为的本质和机理，属于面向工程应用的基础性前沿研究，也可为实际工程转子系统的设计提供理论参考，具有重要的科学意义和潜在的应用价值。

本项目以多模态非光滑转子和定子碰摩系统为研究对象，旨在通过发展高维非光滑系统的非线性模态构造方法，以及动力学全局分析数值方法，阐明非线性模态与多频碰摩响应的内在联系，揭示模态共振与模态耦合对典型碰摩响应的影响机制。其主要结果如下：.针对高维非光滑非线性系统，建立了胞和子域两个尺度异构并行的高效全局分析数值方法，发展了谐波平衡法与弗洛凯指数的希尔方法相结合的高效准确非线性模态构造和延拓方法；求解了几种典型转子/定子碰摩系统模型的非线性模态，确定了存在的参数范围及稳定性；对于存在和不存在非线性模态两种情形，阐明了准周期局部碰摩响应特征的差异，揭示了其产生与消失上动力学机制；对于自激干摩擦反向涡动响应，提出了一种基于滞滑振动特性确定解析临界条件的方法，给出了响应的近似解析解，揭示了响应的滞滑振动特征：既会出现不同的单一滑动运动模式，也会出现组合滑动运动模式，其中非线性模态耦合会造成复杂的组合滑动运动模式；发展了基于非线性模态稳定流形的转子/定子碰摩系统降阶模型的构建方法,实验验证了转子/定子碰摩系统不同响应类型的理论边界条件及滞滑振动特性分析的有效性；另外，建立数据驱动的胞映射方法，可基于测量数据对系统进行全局分析，提出了弱噪声作用下非光滑转子/定子碰摩系统的随机敏感度函数以及高维置信椭球的表示方法。发表国际期刊论文19篇。