基于绝对节点坐标方法的柔性转子的动力学研究

发布时间：2018-09-07 21:29

【摘要】：实际工程中常见的机器都装有旋转部件即转子,比如汽轮机、发电机以及电动机等都是典型的旋转机器,都以转子作为工作的主体。机器运转时,转子系统常常会发生振动,其害处是降低了机器的工作效率,严重的时候该振动会使元件发生断裂。因此,应用转子动力学的理念,合理设计转子横向振动的自振特性,成为了一项重要课题。绝对节点坐标方法的问世开创了多体系统动力学研究的新时代。运用绝对节点坐标方法描述的梁、板、壳等单元均为等参单元,通过绝对节点坐标方法推导并建立的多体系统动力学运动方程具有常数系统质量矩阵、不存在科氏力和离心力项,能够准确地描述出柔性系统的刚体运动,以上这些特点使得绝对节点坐标方法比之传统方法更能精确地解决多体系统动力学的问题,尤其是一些柔性大变形,大转动系统动力学问题。本文主要应用转子动力学的理念,考虑到绝对节点坐标方法的诸多优点,将其运用到转子动力学问题,探究该方法在转子动力学领域中的应用前景。首先介绍了转子动力学、运动学方程求解算法和绝对节点坐标方法的研究概况。随后运用绝对节点坐标方法,建立三维二节点圆截面绕轴自转梁模型,推导出考虑陀螺效应情况下的系统运动方程。最后通过编程进行数值仿真,对已知参数的梁模型展开模态分析,将其与传统有限元方法计算结果进行对比,分析两种方法的相对误差。并且考察在绝对节点坐标方法中,转速和长径比的大小对进动频率的影响。此外,运用广义-α方法求解梁模型系统运动方程,计算出瞬态响应,拟合梁模型的幅频响应曲线,并且考察不同转速下梁模型幅频响应曲线的变化,验证了该方法计算梁模型瞬态响应的正确性。本课题的研究验证了绝对节点坐标方法在考虑陀螺效应情况下的转子动力学问题当中应用的可行性。因此,在实际工程中对转子进行模态分析、计算瞬态响应时,绝对节点坐标方法具有良好的应用前景。
[Abstract]:The common machines in practical engineering are equipped with rotor, such as steam turbine, generator and motor, all of which are typical rotating machines and take the rotor as the main part of the work. When the machine is running, the rotor system often vibrates, and the harm is that the working efficiency of the machine is reduced, and when the vibration is serious, the element will break. Therefore, applying the concept of rotor dynamics to reasonably design the natural vibration characteristics of rotor lateral vibration has become an important subject. The advent of the absolute node coordinate method opens a new era for the study of multi-body system dynamics. The beam, plate and shell elements described by the absolute node coordinate method are isoparametric elements. The equations of motion of the multi-body system derived and established by the absolute node coordinate method have the constant mass matrix. Because there is no Coriolis force and centrifugal force, the rigid body motion of flexible system can be accurately described. These characteristics make the absolute nodal coordinate method more accurate than the traditional method in solving the problem of multi-body system dynamics. In particular, some flexible large deformation, large rotational system dynamics problems. In this paper, the concept of rotor dynamics is applied to rotor dynamics, considering the advantages of absolute node coordinate method, and the application prospect of this method in rotor dynamics is explored. Firstly, the rotor dynamics, kinematics equation solving algorithm and absolute node coordinate method are introduced. Then, by using the absolute node coordinate method, the three-dimensional two-node circular section rotation beam model is established, and the system motion equation considering the gyroscope effect is derived. Finally, the modal analysis of the beam model with known parameters is carried out by programming, and the results are compared with those of the traditional finite element method, and the relative errors of the two methods are analyzed. The effects of rotational speed and aspect ratio on precession frequency are investigated in the absolute node coordinate method. In addition, the generalized-伪 method is used to solve the equations of motion of the beam model system, the transient response is calculated, the amplitude-frequency response curve of the beam model is fitted, and the variation of the amplitude-frequency response curve of the beam model under different rotational speeds is investigated. The correctness of the method in calculating the transient response of the beam model is verified. The research in this paper verifies the feasibility of applying absolute node coordinate method to rotor dynamics problem considering gyroscope effect. Therefore, the absolute node coordinate method has a good prospect in the application of modal analysis and transient response calculation in practical engineering.
【学位授予单位】：北京理工大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：TH113

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