航空发动机叶片长期在复杂激励的恶劣环境中工作, 极易造成损伤产生裂纹, 导致叶片-轮盘耦合系统的模态特性发生改变, 偏离初始设计状态。以旋转裂纹叶片-弹性轮盘系统为研究对象, 基于Kirchhoff板理论和Timoshenko梁理论模拟弹性轮盘和旋转叶片, 基于释放应变能和Castigliano原理将叶片裂纹等效为旋转刚度, 建立了裂纹叶片-弹性轮盘耦合系统连续体动力学模型；通过模态实验和有限元方法验证了提出方法的正确性；并分析了裂纹深度、裂纹位置、轮盘厚度和转速对裂纹叶片-弹性轮盘耦合系统固有特性的影响。研究结果表明：叶片裂纹导致初始正交的叶片-轮盘耦合模态振型破坏, 出现模态局部化现象, 且随着裂纹深度增大, 相应的频率减小；裂纹位置靠近叶尖, 模态局部化现象消失, 形成两阶正交模态；随着轮盘厚度的增加, 发生频率转向现象, 叶片弯曲模态与多个轮盘振型相关；随着转速的增加, 发生频率转向现象, 以及在高转速下叶片弯曲模态与其余阶次叶片弯曲模态相关。
Being exposed to severe environments with complex excitation for a long time, aero-engine blades can easily cause damage and cracks, which will change the modal characteristics of the blade-disk coupling system and deviate from the initial design state. Taking the rotating cracked-blade-flexible-disk coupling system as the research object, a dynamic model is established, in which the flexible disk and rotating blades are investigated based on Kirchhoff plate and Timoshenko beam theories; the blade crack is equivalent to the rotational stiffness based on the released strain energy and Castigliano's theorem. The proposed method is verified by modal test and finite element method. In addition, the effects of crack length, crack position, disk thickness and rotating speed on the inherent characteristics of the coupling system are investigated. The research results show that: the crack leads to the destruction of the initial orthogonal blade-disk coupling modal and the phenomenon of modal localization, and the corresponding frequencies decrease with the increase of the crack length; the closer the crack position is to the blade tip, the modes localization disappears, and two-order orthogonal modes are formed; with the increase of the disk thickness, the frequency veering phenomenon occurs, and the blade-bending mode is related to multi-order modes of the disk; with the increase of speed, the frequency veering phenomenon occurs, and the blade-bending mode is related to the rest blade-bending modes at the high rotational speed.
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