航空发动机双转子系统模态正交性和不平衡响应

Modal orthogonality and unbalance response of aeroengine dual-rotor system

双转子系统具有低压转子激励和高压转子激励的两组振动模态,而这两组模态的正交性是双转子系统动力学特性的核心要素。因此建立了带有中介轴承和分叉结构的航空发动机双转子动力学模型,用以分析双转子系统模态的正交性。采用复模态法分析了双转子系统在不同激励下的模态正交性,推导出正交性的条件集合。发现当双转子系统的速比不变时,双转子系统在各自激励方式下的模态关于刚度矩阵与惯量矩阵是正交的。但在不同激励方式下的模态之间不存在正交性。另外基于模态正交性经过模态分解,得到双转子系统不平衡响应的统一表达式。最后以某型航空发动机双转子系统为例用以验证之前的结论。采用离散有限元和状态向量相结合的方法计算了转速比恒定或非恒定时不同激励下的模态,并构建了模态正交性数值用以评估模态的正交性。评估结果与推导的正交性条件集吻合。

Dual-rotor system has two sets of vibration modes excited by low-pressure rotor and high-pressure rotor,and the orthogonality of these two sets of modes is the core element of dynamic characteristics of dual-rotor system.Here,the dual-rotor dynamic model of aeroengine with intermediate bearing and bifurcation structure was established to analyze its modal orthogonality.The complex modal method was used to analyze modal orthogonality of dual-rotor system under different excitations,and the condition set of orthogonality was derived.It was shown that when the rotating speed ratio of dual-rotor system is constant,modes of dual-rotor system under their respective excitation ways are orthogonal with respect to stiffness matrix and inertia matrix;no orthogonality exists between modes under different excitation ways;based on modal orthogonality,after modal decomposition,the unified expression of unbalance response of dual-rotor system was obtained.Finally,a certain type aeroengine dual-rotor system was taken as an example to verify the above conclusions.The method combining discrete finite element and state vector was used to calculate modes under different excitations with constant or non-constant rotating speed ratio,and the modal orthogonality numerical value set was constructed to evaluate the orthogonality of modes.It was shown that the evaluation results are consistent with the derived orthogonality condition set.