非线性套齿联接的超静定转子系统动力学特性研究

Low-pressure rotor of the modern turbofan engine has large span, quality uneven distribution three elastic supports, and statically indeterminate characteristics. The power transmission is realized by adopting the gear coupling structure which relies on the gears of small clearance and the cylindrical contact of locating surface to transfer force or moment. The structure presents nonlinear characteristics such as interval and gap. Thus, there are problems of prominent vibration, vibration fluctuation, critical speed drift and even loose coupling existing in the rotor system. .Force and moment equilibrium equations of each tooth and locating surface contact of gear coupling will be established. The dynamic model of gear coupling structure will be established and its nonlinear behavior will be revealed. The micro elastoplastic contact of tooth pair and locating surface will be studied. The effect of coupling nonlinearity will be evaluated. The deformation compatibility condition of the statically indeterminate rotor system will be constructed. Analytic model of the rotor system will be built. Dynamic characteristics of revealed..By theoretical deduction, analytical solution and experimental verification, characteristics of nonlinear vibration of gear coupling structure and its origin, and dynamic deformation coordination and nonlinear dynamic characteristics of statically indeterminate rotor system will be obtained. The dynamic theory and method of the statically indeterminate rotor system with nonlinear coupling will be formed, which can improve the vibration analysis, vibration control, and dynamic design level.

现代涡扇发动机低压转子跨度大、质量分布不均、采用三弹支结构、具有超静定特征，并采用套齿联接结构实现动力传递；联接结构依赖小间隙套齿和定位面的柱面接触传递力/力矩/弯矩，呈现区间、间隙等非线性特征，导致超静定转子系统存在振动突出、振动敏感、临界转速漂移、甚至联接松动等问题。.建立套齿联接结构各齿对和定位面接触力与力矩平衡方程，研究建立套齿联接结构动力学模型并揭示其非线性联接行为，开展齿对和定位面微观弹塑性接触研究，评估其对联接非线性的影响；构建超静定转子系统变形协调一致条件进行转子系统的解析建模，研究揭示非线性联接的超静定转子系统动力学特性。.通过理论推导、解析求解和实验检验，获得套齿联接结构非线性振动现象特征及产生根源、超静定转子系统动态变形协调规律及其非线性动力学特性；形成非线性套齿联接的超静定转子系统动力学理论与方法，提高我国航空发动机振动分析与振动控制、动力学设计水平。

【背景】现代航空涡扇发动机的低压转子跨度大、质量分配不均、转速高、采用3弹性支撑，使其具有超静定结构特征。低压转子的套齿联接结构依赖粗糙表面接触传递力、扭矩或弯矩，使得转子系统存在振动突出、振动敏感、振幅不稳，临界转速波动或漂移等问题。.【内容】从微观角度研究小间隙柱面（曲面）弹塑性接触模型，粗糙表面接触刚度模型，从而构建多柱面微观接触变形与轮齿宏观弹性变形协调方程，实现套齿联接结构的非线性联接刚度建模，研究具有超静定特征的转子系统联接、支撑与转轴的协调变形一致条件，实现转子系统的解析建模，揭示其转子系统动力学特性。.【结果】（1）提出粗糙表面之间弹塑性接触的统计模型，该模型与接触面积和接触载荷的经典模型相吻合。（2）提出基于固有频率实验和有限元分析预测接触界面的接触刚度，成果发表在机械领域最高影响因子的《Tribology International》。（3）提出基于模态应变能的接触刚度精确识别方法，成果发表在《机械工程学报》。（4）提出基于试验和薄层单元仿真的接触阻尼识别方法。（5）建立超静定转子系统及其不对中解析动力学模型，通过超静定转子系统不对中动力学仿真与实验，获得超静定转子的动力学建模方法和动力学特性。.【关键数据】获得实际航空发动机套齿连接结构的粗糙表面接触刚度模型和模态实验数据；获得实际航空发动机低压转子系统动力学模型和动力学计算结果数据，获得具有动力学相似的航空发动机低压转子模拟试验台振动实验数据。.【科学意义】由于粗糙表面接触刚度量级可达10次方数量级，导致现有的接触刚度理论难以经得起实验检验，本项目基于动力学实验和薄层单元法，提出（1）粗糙表面接触力学建模方法、（2）考虑装配次数的粗糙表面二次接触力学方法、（3）基于模态应变能的接触刚度精确识别方法，系统性建立接触刚度识别方法，并经过检验具有3%的识别精度，是本项目的理论贡献。