旋转圆盘行波振动分析及静止态谐响应计算

发布时间：2018-05-03 12:37

本文选题：旋转圆盘 + 变分　；参考：《东北大学》2012年硕士论文

【摘要】：圆盘部件是被广泛应用于航空、航天、造船、土建和机械等工业领域的基本结构单元。随着材料科学的迅速发展,新型材料的应用日益广泛,圆盘类部件的在满足使用强度的要求下厚度逐渐减小,以节省材料减轻重量。转子转盘是圆盘类部件的典型代表,现代燃气轮机中带叶转子,由于技术水平的进步,更薄的转盘、更高的转动速度使得转子的横向振动以及几何非线性振动显得更加突出。对于圆盘类部件的研究,一个重要方向就是圆盘的行波振动问题：另一个是振动响应问题。本文针对中心固支旋转圆盘行波振动特性进行研究,给出了旋转圆盘行波振动的解析方法、有限元数值仿真解法以及实验分析方法。针对静止态中心固支圆盘,给出了强迫振动方程,应用Galerkin截断法求解了单点谐波激励、定点响应问题。采用模态实验理论,对本文采用的解析方法、有限元仿真进行对比验证。本文的主要研究内容大致可以归为以下几个方面： (1)根据弹性力学外力功及应变能基本理论,建立考虑薄膜应力影响的旋转圆盘动能—势能方程,应用拉格朗日方程建立旋转圆盘横向振动控制方程,利用Galerkin截断法对运动方程离散,求解圆盘固有频率随转动速度的变化规律,绘制Campbell曲线； (2)应用有限元软件ANSYS对旋转圆盘振动特性进行数值仿真。包括：单元类型的选取、材料参数的输入、固有频率、模态振型的求解方法。绘制了旋转圆盘的Campbell曲线,与解析方法进行对比,验证两种方法的吻合度。 (3)对中心固支圆盘进行单点谐响应分析,基于Kirchhoff薄板理论由一点的应力状态推导弹性薄板的动力学方程,通过坐标变化计算出弹性圆板的自由振动方程。应用振型叠加法,将中心固支圆盘的振型函数用悬臂梁模型近似替代,将圆盘振动方程转化为多个单自由度无阻尼系统振动的叠加。采用单点谐响应分析理论,计算了圆盘定点对激励的响应位移,并绘制频谱图： (4)介绍了实验模态的理论基础和实验模态分析的基本过程。对中心固支圆盘,进行静止态实验模态分析与旋转态振动测量。得到了静止态中心固支圆盘固有频率、模态振型及旋转态圆盘振动时域曲线,频响曲线。应用激光测振仪,测量了旋转圆盘的响应,绘制了瀑布图,确定了转动圆盘的固有频率,验证了离心刚化效应的存在。
[Abstract]:Disc components are widely used in aviation, aerospace, shipbuilding, civil engineering and machinery and other industrial areas of the basic structural units. With the rapid development of material science, the application of new materials is becoming more and more extensive, and the thickness of disc components decreases gradually under the requirement of strength, so as to reduce the weight of materials. Rotor turntable is a typical representative of disc components. Due to the advancement of technology, thinner rotating disk and higher rotation speed, the transverse vibration and geometric nonlinear vibration of the rotor become more prominent. One important direction of the research on disk components is the traveling wave vibration of the disk and the other is the vibration response problem. In this paper, the vibration characteristics of rotating disk with fixed center are studied, and the analytical method, finite element numerical simulation method and experimental analysis method are given. In this paper, the forced vibration equation is given for the fixed disk in the center of static state. The problem of single point harmonic excitation and fixed point response is solved by using Galerkin truncation method. The modal experiment theory is used to verify the analytical method and finite element simulation. The main contents of this paper can be classified into the following aspects: 1) according to the basic theory of external force work and strain energy of elastic mechanics, the kinetic energy potential energy equation of rotating disk considering the effect of film stress is established, and the governing equation of lateral vibration of rotating disk is established by using Lagrange equation. The equation of motion is discretized by Galerkin truncation method, and the Campbell curve is drawn by solving the law of the change of the natural frequency of the disk with the rotational velocity. 2) the vibration characteristics of rotating disk are simulated by finite element software ANSYS. It includes the selection of element type, the input of material parameters, the natural frequency and the solution of modal mode. The Campbell curve of the rotating disk is drawn and compared with the analytical method to verify the coincidence of the two methods. The dynamic equations of elastic thin plates are derived from the stress state of one point based on Kirchhoff thin plate theory, and the free vibration equations of elastic circular plates are calculated by coordinate change. By using the mode superposition method, the mode shape function of the center-clamped disk is approximately replaced by the cantilever beam model, and the vibration equation of the disk is transformed into the superposition of the vibration of several single-degree-of-freedom undamped systems. Based on the theory of single point harmonic response, the response displacement of disk fixed point to excitation is calculated, and the spectrum diagram is plotted. The theoretical basis of experimental mode and the basic process of experimental modal analysis are introduced. The static experimental modal analysis and rotational vibration measurement were carried out for the central clamped disc. The time domain and frequency response curves of the fixed disk in the static state are obtained, including the natural frequency, the mode mode and the vibration time domain of the rotating disk. The response of the rotating disk was measured by using the laser vibration measuring instrument, the waterfall diagram was drawn, the natural frequency of the rotating disc was determined, and the existence of the centrifugal stiffening effect was verified.
【学位授予单位】：东北大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：TH113.1

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