基于本征正交分解的叶片碰摩系统降阶方法

针对叶片碰摩响应求解问题，提出了采用本征正交分解进行动力学降阶的方法。通过对快照矩阵进行本征正交分解生成投影子空间，将系统动力学方程投影到子空间进行模型降阶，并结合数值积分方法进行了碰摩响应求解。基于降阶模型分析了不同转速及侵入量参数下的叶片碰摩响应，并与全阶模型进行了对比。结果表明:降阶模型的时域响应幅值偏差小于5%，计算效率了提升98.4%；通过改变叶片转速、侵入量参数验证了降阶模型的鲁棒性，并且发现随着转速、侵入量的增加，本征正交模态能量在低阶与高阶之间发生转移，并呈现出不同的传递规律，由转速引起的模态能量转移与结构的固有频率存在一定关系。该方法及结论可为叶片碰摩分析及故障诊断提供依据。 

Reduced order method of blade rubbing system based on proper orthogonal decomposition

In view of the problem of blade rubbing response，a proper orthogonal decomposition method was proposed to reduce the dynamic order of the system.The projection space was generated by the proper orthogonal decomposition of the snapshot matrix，the system dynamic equation was projected into the subspace for model reduction，and the rubbing response was solved in combination with the numerical integration method.Based on the reduced order model，the blade rub impact response under different speed and penetration parameters was analyzed and compared with the full order model.The results showed that the time-domain response deviation of the reduced order model was less than 5%，and the computational efficiency of the reduced order model was improved by 98.4%.The robustness of the reduced order model was verified by changing the blade speed and penetration.With the increase of rotational speed and penetration，it was found that the energy of the proper orthogonal modes transferred between the lower order and the higher order，and presented different transfer laws.There was a certain relationship between the modal energy transfer caused by the rotational speed and the natural frequency of the structure.The method and conclusion can provide a basis for blade rub impact analysis and fault diagnosis.