基于接触刚度分布特性的叶片振动响应分析

根据接触刚度在锯齿形叶冠结合面上非均匀分布的特性，提出一种基于定义和有限元计算相结合的接触刚度计算方法。在此基础上，将微-宏滑动摩擦模型作为叶冠结合面处的摩擦模型，推导微滑动和宏滑动状态下摩擦力表达式。利用谐波平衡法将非线性摩擦力转化为等效刚度和等效阻尼进行振动特性分析。针对叶冠结合面相对位移幅值动态变化的特点，提出了一种迭代求解的振动响应分析方法。与文献提供的带摩擦阻尼结构悬臂梁振动响应实验数据相比，共振峰附近的振幅误差为1.99 mm，相对误差为3.9%。振幅的最大误差为5.53 mm，出现在远离共振峰的位置，验证了响应分析方法的可行性。将该方法应用于带冠叶片上，结果表明当激振力频率为812.3 Hz时，振幅为0.56 mm。

Analysis of blade vibration response based on contact stiffness distribution characteristics

According to the non-uniform distribution characteristics of contact stiffness between interfaces of the zigzag shroud, a method for calculating contact stiffness was proposed based on the combination of definition and finite element calculation. On this basis, the micro-macro-slide friction model was applied to shroud contact interfaces, and the frictional force expressions were derived in micro-slide state and the macro-slide state. The harmonic balance method was used to convert the nonlinear friction force into the equivalent stiffness and equivalent damping. Considering the dynamic change of the relative displacement amplitude between interfaces, an iterative solution method for analyzing vibration response was proposed. Compared with experimental data of vibration response of cantilever beam with frictional damping structure provided in literature, the amplitude error near the resonance peak was 1.99 mm, and the relative error rate was 3.9%. The maximum error of the amplitude was 5.53 mm, which appeared far away from the resonance peak. It was believed that the accuracy of the response analysis method was relatively high. This method was applied to the shrouded blade, and the results showed that the amplitude was 0.56 mm when the excitation force frequency was 812.3 Hz.