齿轮传动双转子弯扭振动研究

发布时间：2018-05-08 03:06

本文选题：齿轮传动转子 + 弯扭振动　；参考：《浙江大学》2012年硕士论文

【摘要】：现代工业的进步,使旋转机械向着高转速、大功率的方向发展,转子的振动问题变得越来越重要。齿轮传动是旋转机械中应用最广泛的传动机构,因此,必须对齿轮传动转子系统动力学特性进行深入研究。本文利用有限元法,应用MATLAB软件,考虑弯扭5自由度,推导了轴单元、圆盘单元和轴承单元的运动微分方程,同时分析了单转子系统的整体质量、刚度、阻尼矩阵的形成法则,得到了单转子系统的5自由度的整体运动微分方程；通过对单转子系统齐次运动微分方程的分析和降阶,求得特征值和特征向量,并从中提取出相应的临界转速和振型；计算了单转子系统的弯振不平衡响应、扭振不平衡响应；根据力与力矩平衡,经简化分析,建立了齿轮副单元弯扭5自由度有限元模型,并给出了齿轮啮合刚度与啮合阻尼的计算公式,通过坐标变换,得到了广义坐标下齿轮副单元的运动微分方程；分析了两齿轮节点号相邻和不相邻时,不同的矩阵叠加法则；然后组合未耦合齿轮-转子的运动微分方程和齿轮副单元的运动微分方程,得到了耦合的齿轮-转子的运动微分方程；分别计算了未耦合和耦合的齿轮-转子系统的临界转速、振型、弯振不平衡响应和扭振不平衡响应；研究了齿轮啮合刚度、齿轮传动比和轴承刚度对齿轮-转子系统固有频率的影响。
[Abstract]:With the development of modern industry, the rotor vibration becomes more and more important. Gear transmission is the most widely used transmission mechanism in rotating machinery. Therefore, the dynamic characteristics of gear transmission rotor system must be deeply studied. In this paper, the differential equations of motion of shaft element, disk element and bearing element are derived by using finite element method and MATLAB software, considering 5 degrees of freedom of bending and torsion. At the same time, the rules of forming integral mass, stiffness and damping matrix of single rotor system are analyzed. The global differential equations of motion of a single rotor system with 5 degrees of freedom are obtained, and the eigenvalues and eigenvectors are obtained by analyzing and reducing the homogeneous differential equations of motion of a single rotor system, and the corresponding critical speed and mode shapes are extracted from them. The unbalance response of bending vibration and torsional vibration of a single rotor system is calculated, and according to the balance of force and moment, a finite element model of five degrees of freedom for gear pair element is established by simplified analysis. The calculation formulas of gear meshing stiffness and meshing damping are given, the differential equations of motion of gear pair elements in generalized coordinates are obtained by coordinate transformation, and the different matrix superposition rules are analyzed when the two gear nodes are adjacent and non-adjacent. Then the differential equations of motion of the uncoupled gear rotor and the gear pair element are combined to obtain the coupled differential equations of motion of the gear rotor, and the critical speeds of the uncoupled and coupled gear rotor systems are calculated, respectively. The effects of gear meshing stiffness gear transmission ratio and bearing stiffness on the natural frequency of gear rotor system are studied.
【学位授予单位】：浙江大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：TH132.41

【引证文献】