水轮机转轮叶片系统动力分析(Ⅰ)——力学模型与方程列式

Dynamic analysis of hydraulic turbine runner and blade system(Ⅰ) —Mechanics model and formulation

根据水轮机转轮具有旋转周期性的特点，引入复约束的概念，对水轮机结构进行简化，可以显著缩减动力分析问题的计算规模。同时，为了考虑水对水轮机转轮的影响，假设水是不可压，无粘和无旋的，从而将水对水轮机的作用通过附加质量的方式引入到结构振动方程中。在结构动力方程求解过程中，注意到方程的系数矩阵中和子结构内部自由度相应的主要部分保持为实数矩阵，求解时利用此特点，可以大大节省计算的工作量。

A method for the dynamic analysis of hydraulic turbine runner is presented. The method is based on the dynamics of rotationally periodic structure and the theory of added mass. In accordance to the rotationally periodic characteristic of the runner, the concept of complex constraint is intoduced to simplify the structure. It reduces significantly the dimension of structural dynamic analysis. In order to consider the influence of the water on the dynamic response of the runner, the water has been assumed to be incompressible, irrotational and inviscid, and is induced into the governing equation for the vibration of the runner as the hydrodynamic added mass. In the coefficient matrix of dynamic equation, the main part corresponding to the inner degrees of freedom of the substructure is real matrix. Using this characteristic in calculation, the computer time can be saved to a great extent.