【作者】 丁千；

【导师】 陈予恕；

【作者基本信息】 天津大学 ， 一般力学， 1997， 博士

【摘要】 转子系统存在大量非线性因素，高速运行时，会导致系统出现许多复杂的动力学现象，影响了运行的稳定性。自激激励因素的作用，更是直接危及转子系统的安全。大量事实表明，旋转机械重大事故多半是由于低频(亚谐)振动的失稳发展引起的，因此对各种非线性激励因素作用下转子低频(亚谐)自激振动的机理和失稳控制方法的研究成为转子动力学研究中的当务之急。 本文应用非线性动力学理论和方法，研究材料内阻尼和密封力两种非线性因素作用下转子运动的失稳机理，并数值分析了碰摩转子动力学行为的演化。论文工作包含以下几部分： 一、对转子非线性动力学的研究现状作了较全面的综述，同时也阐明了该领域当前和今后一段时间内的研究方向。 二、研究了材料内阻尼激励因素对转子振动特性的影响。应用Hamilton原理和Galerkin法导出了具有内阻尼和刚度非线性的转轴运动方程；应用非线性动力学方法，分析了各阶主共振时的稳定性，正常运动和自激振动响应的局部分岔，非共振和1／3亚谐共振情况下低频自激振动失稳的机理等。结果表明，转子超临界运行时，横向干扰(冲击)可能会引起转子正常运动失稳，产生低频自激振动，而增大外阻尼和做好动平衡是控制这种失稳的有效方法。 三、简单介绍了密封动特性的研究概况。采用Muszynska密封力模型，研究了单圆盘转子——密封系统的低频自激振动。内容包括： 1、应用稳定性理论求得平衡转子的线性化失稳转速。根据Hopf分岔理论，平衡点的失稳导致Hopf分岔。经过Poore代数判据的计算确定，产生Hopf分岔后，平衡转子进入稳定的周期涡动状态。 2、为研究转子质量不平衡对失稳运动的影响，即1／2和1／3亚谐共振状态下的自激振动性态，利用中心流形定理和平均方法得到了分岔点附近的自激振动的分岔方程，通过稳定性和分岔分析表明，转子自激振动的形式与不平衡量大小有关：平衡较好时，为概周期运动；平衡较差时，为倍周期运动，即更多还原

【Abstract】 Rotor systems involve many types of nonlinearities, which may lead to a lotof complex dynamic behavior, and cause problems of stability in high speed rotating Rotors. The self—excited destabilizing forces contribute more directly to the destabilization of the rotor system. Numerous cases in actual machinery have shown that more than half of serious failure happened in rotating machinery arising from the instability growth of low—frequency ( or subharmonic ) vibrations. So it is badly in need of the study on the mechanism of low—frequency (subharmonic) vibration of rotor excited by various types of nonlinear destabilizing forces and techniques of instability controlling.The theory and techniques of nonlinear dynamics are used in the thesis, to study the mechanism of instability of rotors’ whirling motion affected by the nonlinear destabilizing forces, such as internal damping of material and seal fluid forces. In addition, the transient evolution of rotor—easing rub events is analyzed by numerical method. Several parts included in the thesis are as follow:1. The study on the nonlinear dynamics of rotor at broad and.home is summarized in an all—round way. Besides, the direction for further study in this field, in these days and days to come, is indicated.2. The vibrational characteristics affected by the destabilizing forces of internal damping of material is studied. The Hamilton principle and the Galerkin’s method are applied in deducing the equations of motion of the shaft with nonlinearity of internal damping of material and rigid of bending. The studies by using methods of nonlinear dynamics include the following aspects: the stability of the rotor in any modes of primary resonances, the local bifurcations of the normal motion as well as the self—excited whirling motion, and the mechanism of instability of low—frequency self—excited vibrations, in cases of non—resonance and 1 / 3—order subharmonic resonance, etc. The study shows that an unfavouvable impact can cause rotor instable when it operates at supercritical speed, then the self-excited vibration occurring through Hopf bifurcation. The effective methods of controlling this type of self—excited whirling motion are enhancing of external damping and well balanced of the rotor.3. The study on the dynamical characteristics of seal is summarized briefly. The更多还原