中文摘要：

以混流式水轮发电机组主轴系统为研究对象，针对主轴系统存在扭振的情形，应用有限元法建立主轴系统动力学方程，利用理论力学和流体力学知识推导转轮内的水流对主轴系统所产生的作用力矩，得到水轮机转轮内水流激励向量，应用振动知识建立主轴系统的扭振频率方程，并根据扭振频率方程研究转轮内水流激励对主轴系统扭振固有频率的影响。研究表明：水轮机转轮内的水流激励不仅与水力参数有关，而且还和主轴系统的扭振有关，在水流激励的作用下，主轴系统扭振固有频率将比其未受到水流激励作用时的扭振固有频率有所降低，其中第一阶扭振固有频率降低幅度最大。最后通过实例对理论分析结果进行验证。

英文摘要：

The main shaft system of a Francis turbine-generator unit is taken as an object of study. Based on the torsional vibration of the main shaft system, the dynamic equations of the main shaft system are established by the finite element method. According to the theoretical mechanics and fluid mechanics, the torque acted on the main shaft system by the fluid in turbine runner is derived and the fluid excitation vector in turbine runner is obtained. Based on the frequency equations of torsional vibration established by vibration knowledge, the effect of the fluid excitation on the natural frequencies of the torsional vibration of system is studied. The research shows that the fluid excitation in turbine runner relates not only fluid parameters, but also the torsional vibration of the main shaft system, and the natural frequencies of torsional vibration of the main shaft system are decreased with consideration of fluid excitation, especially the first order natural frequency. Finally, an example is presented to verify the theoretical analysis.