【作者】 黑棣；

【导师】 吕延军； 陈祖安；

【作者基本信息】 西安理工大学 ， 机械电子工程， 2009， 硕士

【摘要】 大型旋转机械是国家基础设施和基础工业中关键的设备之一,随着旋转机械向着高速、高效、高可靠性发展,对旋转机械的稳定性提出了更高的要求,同时轴承-转子动力系统的研究也越来越受到重视。本文针对轴承-转子系统的非线性动力学行为进行分析。论文的具体工作包括以下几方面：1、首先,通过油膜力数据库方法对比了现有的非线性油膜力解析模型,讨论了现有非线性油膜力解析模型的适用范围和近似程度。接着对具有Reynolds边界条件的滑动轴承流体润滑的Reynolds原理进行了修正,在此基础上,采用8节点等参有限元方法,按照油膜的物理特性,形成修正的Reynolds方程的变分形式及其扰动方程,在不增加计算量的情况下,同时求得非线性油膜力和及其Jacobi矩阵。2、分析了Newmark法在计算时间步长内的计算扰动,并且对其进行补偿,形成了一种有效的求解非线性动力系统行为的方法——结合扰动补偿的Newmark法。该方法由于考虑了计算扰动效应,使得计算结果在各个离散时刻既满足运动约束条件,又基本满足动力平衡方程。3、基于Wilson-θ法,并将其改进,同时引入预估-校正机理,形成了一种有效的求解非线性动力行为的方法。该方法在迭代求解前对迭代的初值进行预估,使得迭代的初值尽可能接近真值,之后以预估值作为初值,运用Newton-Raphson方法对其进行校正,这样提高了计算效率,节约了计算时间。4、最后,运用提出的方法并结合Floquet稳定性分岔理论和Poincare映射,针对动压轴承支承的转子系统,分析了其周期解的稳定性和分岔规律。通过数值仿真,揭示了轴承-转子系统的周期解、倍周期解、准周期解、跳跃和混沌等复杂丰富的非线性动力学行为。论文得到的结果可为轴承-转子系统运动稳定性分析及产品的动力学设计提供理论参考,具有积极的指导意义。更多还原

【Abstract】 Large rotating machinery is one of the equipments in national basic facilities and industries. A lot of high requirements for stability and dynamic characteristics of rotating machinery have been made along with the development of speed, efficiency and reliability, so research on the bearing-rotor system is increasingly emphasized. Nonlinear dynamic behaviors of bearing-rotor system are analyzed in the paper.The main contents are as follow:1. The applicable range and approximate extent of the current analytical model of nonlinear oil film force are discussed by comparing data base method with the current analytical method of nonlinear oil film force. The variational approch is revised in fluid lubrication of journal bearing with Reynolds boundary. According to the physical characteristics of oil film, a revised variational form of Reynolds equation and its disturbed equation are formulated by isoparametric finite element method with 8 nodes. So the nonlinear oil film force and its Jacobian matrix are obtained simultaneously without increase of computational costs.2. The computational disturbances of Newmark method are analyzed at each time step. The computational disturbances of Newmark method are compensated, and then an effective numerical method, i.e. Newmark method with disturbance compensation, is presented to analyze dynamic behaviors of nonlinear dynamics system. Because the disturbance compensation is made in the presented method, the results obtained by the method can satisfy the movement constraints and dynamic balance equation simultaneously.3. Based on Wilson-θmethod, an effective method is presented to analyze the dynamic behaviors of nonlinear dynamic system by improving Wilson-θmethod and combining with predictor-corrector mechanism. For solving the nonlinear equations by the method, initial values of iteration are predicted to approximate the values of the nonlinear equations. Furthermore obtained values are corrected by Newton-Raphson method. The presented method can improve calculation efficiency and save calculation time.4 The nonlinear dynamic responses, stability of periodic solution and bifurcation of the bearing-rotor system are analyzed by the presented methods combining with Floquet theory and Poincare map. The numerical results reveal periodic, period-doubling, quasi-periodic, jump, chaos of rich and complex nonlinear behaviors of the bearing-rotor system.The presented methods and numerical results can direct the design of practical bearing-rotor system, and provide references for practical application of bearing-rotor system.更多还原