以航空发动机低压（LP）转子为代表的柔性转子，通常具有两端大质量、细长轴和长跨度支承的"弱刚度"结构力学特征，这使得碰摩产生的约束作用不可忽视，其将会导致柔性转子模态特性改变，进而造成临界转速等动力学目标偏于设计状态。本文以典型航空发动机低压柔性转子为对象，结合梁单元法提出了此类复杂转子在碰摩约束下的动力学建模方法；将谐波平衡思想与频域的自由度缩减技术结合，提出了相适用的非线性模态求解方法；在此之上基于ANSYS和MATLAB平台，建立了含碰摩约束的复杂转子非线性模态分析的一般流程。将方法应用到某型柔性转子系统，成功获得其模态特性，结果表明：碰摩约束使转子模态频率增加，且随转子振幅增加而增加，尤其是对风扇碰摩较为敏感的一阶弯曲模态，正/反进动模态频率变化率可达16%和29%，但模态频率的变化始终在特定区间内；碰摩对转子模态频率的影响程度与陀螺效应、转子振型及机匣刚度密切相关，但对摩擦系数不敏感。由于接触点处摩擦力做功影响，柔性转子各阶反进动模态阻尼在碰摩严重时小于0，反进动模态能发生失稳。
The aero-engine Low Pressure (LP) rotor system, usually of large mass, thin and long shaft and long-span supports, has a feature of low stiffness. When rub-impact occurs, the constraint effect must be considered, as it will significantly change the modal characteristics and lead to deviation of dynamic targets from the design value. In this paper, a dynamic modeling method for typical LP rotor systems in aero-engines is proposed based on the beam element method. By combining the harmonic balance and condensation method of degree of freedom in the frequency domain, an effective method is built to solve the nonlinear mode of the complex rotor system. The above methods are achieved using ANSYS and MATLAB software, and successfully applied to the analysis of the modal characteristics of real LP rotors in aero-engines. Results show that the rub-impact significantly increases the modal frequencies of the rotor system. Particularly for the first order modes, the change in the forward whirl and backward whirl modal frequencies can respectively reach 16% and 29%. However, the changes in modal frequencies are always within a certain range and have interval characteristics. While closely related to gyroscopic effect, modal shapes and casing stiffness, the influence of rub-impact on modal frequency is not sensitive to the friction coefficient. Moreover, due to the friction force at the rubbing point, the modal damping of the backward whirl mode may be less than zero when the rub-impact is severe, leading to the unstable backward whirl model.
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