多转子系统振动分析的整体传递矩阵法研究

【作者】 刚宪约；

【导师】 刘迎曦； 柴山；

【作者基本信息】 大连理工大学 ， 工程力学， 2002， 硕士

【摘要】 随着旋转机械转速不断增加、性能不断提高，转子系统的振动特性越来越成为人们研究的焦点。在很多情况下，转子与转子之间通过齿轮、联轴器等连接在一起，组成一个多轴、多速、多转向的复杂转子系统。工程实践发现，要分析这样的多转子系统的振动特性，必须把它看作一个整体，综合考虑各转子的动力特性，研究其弯曲振动、扭转振动以及二者之间的耦合响应。在Prohl传递矩阵法和Riccati传递矩阵法的基础之上，本文发展了多转子振动分析的整体传递矩阵法，并建立了相应的整体传递矩阵—Riccati法。根据整体传递矩阵法理论开发的多转子系统动力分析程序(MSDAP)在大量的数值算例中表现出良好的性能。 本文第一章主要介绍转子振动问题的研究现状，以及四种典型的计算分析方法。 第二章总结了计算转子系统临界转速、振动模态和不平衡响应的传递矩阵法，并简要讨论了转子系统的扭转振动和弯扭耦合振动问题。附录中列出了各种类型单元的传递矩阵。 第三章从一个四自由度弹簧振子的振动分析问题提出耦合单元的概念，建立了多转子系统振动分析的整体传递矩阵法；在此基础上，吸收Riccati传递矩阵法的思想，研究了整体传递矩阵—Riccati法，不仅提高了计算过程的数值稳定性，而且通过把高阶稀疏矩阵的运算变换为低阶矩阵运算，大大提高了计算效率。齿轮啮合是转子之间常见的一种耦合形式，根据耦合单元的概念，推导了在全局坐标系下斜齿轮啮合的传递矩阵。 第四章介绍自行开发的多转子系统动力分析程序(MSDAP)，并利用它计算了大量数值算例。 第五章总结了在多转子系统振动分析研究过程中遇到的一些问题，并提出对进一步研究的展望。更多还原

【Abstract】 With the increase of rotational speed of rotary and the improvement of its performance, the vibration characteristic of the rotor system has been becoming a research foqus. Usually several rotors linked with some gears or couplings constitute a complex rotor system with multiple rotors, rotation speeds and rotation directions. Many engineering problem indicate a multi-rotor system should be taken as a whole to study its vibration characteristic, considering the dynamic property of each rotor, studying lateral vibration, torsional vibration and their coupling effect. Based on Prohl transfer matrix methods and Riccati transfer matrix method, a whole transfer matrix method and its Riccati method are developed to solve the vibration problem of a multi-rotor system. With these method applied, a Multi-rotor System Dynamic Analysis Program (MSDAP) is programmed, whose good performance is testified with several numerical examples.In the first part of this paper, the present research state of rotor dynamics and four types of computation method are introduced.In the second part, the transfer matrix method to calculate the critical speed, the mode and the unbalanced response, is presented. And the torsional vibration and lateral-torsional coupling vibration problem is discussed briefly. Many transfer matrices of different elements are appended in the end.In the third part, the concept of coupling element is derived from the vibration analysis of a four-degree spring-oscillator system, and a whole transfer matrix method is developed on the basis of it. With the advantages of the Riccati transfer matrix method, a Riccati method of whole transfer matrix is proposed. Besides the improvement of numeric stability, it increases the computation efficiency by transforming the high-order sparse matrix calculation into low-order matrix calculation. Since the gear engagement is a common coupling form between rotors, the transfer matrix of skew gear engagement in global coordinate system is deduced based on the concept of coupling element.In the fourth part, a self-programmed multi-rotor system dynamic analysis program and lots of numerical examples are introduced.In the last part, some problem encountered in the research is discussed, and the further study is proposed.更多还原