Experimental and numerical investigations of the modal behavior of a prototype Kaplan turbine runner in air have been conducted in this paper. The widely used roving accelerometer method was used in the experimental modal analysis. A systematic approach from a single blade model to the whole runner has been used in the simulation to get a thorough understanding. The experimental results show that all the detected modes concentrate their displacements on the impacted blade. The numerical results show that the modes of the single blade form different mode families of the runner, and each mode family corresponds to a narrow frequency band. Harmonic response analysis shows that, at the response peak point, the single blade excitation can only get mode shapes with concentrations on the exciting blade due to the superposition of the close modes in each mode family, which explains the experimental results well, while the mode superposition can be avoided by the order excitation method. With the reduction of the connection stiffness between the blades and hub/control system, the frequencies of most modes change from insensitive to more and more sensitive to the connection stiffness change, which results in a sensitive area and an insensitive area. Through comparison with the experimental results, it is indicated that the natural frequencies of the runner can probably be predicted by merging the runner into a whole body.

中文翻译：

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原型卡普兰涡轮转轮动态行为的数值模型

本文对原型卡普兰涡轮在空气中的模态行为进行了实验和数值研究。实验模态分析采用了广泛使用的粗纱加速度计方法。模拟中使用了从单个叶片模型到整个转轮的系统方法，以获得透彻的理解。实验结果表明，所有检测到的模式都集中在受冲击的叶片上。数值结果表明，单个叶片的模态形成转轮的不同模态族，每个模态族对应一个较窄的频带。谐波响应分析表明，在响应峰值点，由于各模态族中近模的叠加，单叶片激励只能得到激励叶片上集中的模态形状，这很好地解释了实验结果，而阶次激励方法可以避免模态叠加。随着叶片和轮毂/控制系统之间连接刚度的降低，大多数模式的频率对连接刚度的变化从不敏感变为越来越敏感，从而产生敏感区和不敏感区。通过与实验结果的对比表明，将转轮合并为一个整体，很可能可以预测转轮的固有频率。随着叶片和轮毂/控制系统之间连接刚度的降低，大多数模式的频率对连接刚度的变化从不敏感变为越来越敏感，从而产生敏感区和不敏感区。通过与实验结果的对比表明，将转轮合并为一个整体，很可能可以预测转轮的固有频率。随着叶片与轮毂/控制系统之间连接刚度的降低，大多数模式的频率对连接刚度的变化从不敏感变为越来越敏感，从而产生敏感区和不敏感区。通过与实验结果的对比表明，将转轮合并为一个整体，很可能可以预测转轮的固有频率。