Axial turbines are widely used in hydropower systems. Owing to the complex hydraulic excitation force during operation, its flow-passing components, particularly the runner, are prone to severe vibrations. To further understand the vibration of the runner under different excitation forces, this study systematically investigated the modal characteristics of an axial turbine runner through numerical simulation using the example of a prototype Kaplan runner, including a shaft. The finite element method (FEM) and acoustic-structure coupling method were used to solve the natural modes of the runner in vacuum and the added mass effect of water, respectively. It was found that the modes of cantilever-blade structures without a shaft are mainly represented as vibrations of the blades, which can be classified into a series of mode families based on the single-blade modes, corresponding to a series of frequency bands with very small widths. The composition of members in each mode family depended strictly on the number of blades with a clear rule. For axial turbines, the modal vibration of the shaft and blades is prone to coupling, which leads to abnormal changes in some modes in the mode family, resulting in the scattering of the natural frequencies and greatly improving the possibility of resonance. The law of mode coupling was revealed, and the effects of the blade opening and bearing stiffness on the mode coupling and frequency bandwidth were explored. The stiffness of the bearing close to the runner significantly affected the frequency bandwidths. The greater the stiffness, the smaller are the bandwidths. This study can provide a reference for resonance cause analysis and vibration avoidance design of axial turbines and similar structures.

轴流式水轮机广泛应用于水电系统。由于运行过程中水力激振力复杂，其过流部件特别是转轮容易发生剧烈振动。为了进一步了解转轮在不同激励力下的振动，本研究以卡普兰转轮原型（包括轴）为例，通过数值模拟系统地研究了轴流式涡轮转轮的模态特性。分别采用有限元法(FEM)和声-结构耦合法求解转轮在真空中的固有模态和水的附加质量效应。结果发现，没有轴的悬臂叶片结构的模态主要表现为叶片的振动，可以根据单叶片模式划分为一系列模式族，对应一系列宽度非常小的频带。每个模式家族的成员构成严格取决于刀片的数量，有明确的规则。对于轴流式水轮机，轴与叶片的模态振动容易发生耦合，导致模态族中部分模态发生异常变化，导致固有频率的分散，大大提高了共振的可能性。揭示了模式耦合规律，探讨了叶片开度和轴承刚度对模式耦合和频率带宽的影响。靠近转轮的轴承刚度显着影响频率带宽。刚度越大，带宽越小。