全转速系数矩阵降维重构的燃机不平衡量逆推方法

整机动平衡可大幅提高燃气涡轮发动机动平衡效率，但由于全转速范围内整机系统动力特性复杂，且结构的特殊性仅能够在机匣外表面测振，传统动平衡方法难以实现整机动平衡。为此，考虑全转速区间整机系统结构振动特性及分布式不平衡量的影响，通过仿真或试验获得全转速范围内各测点振动响应与各叶盘不平衡量间的响应系数矩阵，建立等效不平衡量逆推方程组。依据不平衡位置-转速-测点振动间的敏感性关系对全转速系数矩阵进行降维重构，获得优选配平位置、测点及转速的重构方程组，求得转子配平位置的等效不平衡量。典型双转子燃气涡轮发动机整机系统数值仿真结果验证了该方法的有效性。研究结果对实现燃气涡轮发动机整机动平衡具有一定的参考应用价值。

A backstepping method of gas turbine unbalance vector based on dimension reduction and reconstruction of full speed coefficient matrix

Whole machine dynamic balance can greatly improve the efficiency of unbalanced vibration control for gas turbine engine. However, because of the particularity in structure, the unbalanced response of the rotor cannot be directly measured, making the whole machine balance difficult. Therefore, considering the structural vibration characteristics of the whole machine system overall the full speed range and the influence of distributed unbalance vector, the response coefficient matrix between vibration response of each measuring point and unbalance vector on each blisk is obtained through simulation or test, and the equivalent unbalance vector backstepping equations are established. According to the sensitivity relationship between the unbalance vector position, rotational speed, and the measuring point, the full speed range response coefficient matrix goes through dimension reduction and reconstruction. The equivalent unbalance vector of the rotor is obtained via choosing optimal balancing positions and measuring points and rotational speeds. The effectiveness of the proposed method is verified by numerical simulation analysis of a typical dual-rotor gas turbine engine. This method is valuable for gas turbine engine rotor balance.