基于多坐标系的多转子-机匣时变系统3-D有限元建模及降维分析

Aeroengine is a complex structural system with coupling vibration of rotor and thin-walled flexible casing. It is difficult to find the exactly reason of the whole engine vibration fault. Moreover, with the adoption of integral blade disc and "bending, sweeping and twisting" fan blades, the non-axisymmetry of the rotor becomes prominent. Meanwhile, the asymmetry of thin-walled casing and its constraints makes the relative spatial position and phase of the asymmetric characteristics change with time, which inevitably leads to time-varying characteristics. The establishment of the refined model based on 3-D finite element has been paid attention to, but the key problem is that it is difficult to express the time-varying characteristics of the system and the degree of freedom of the model is too large. Therefore, a modeling method is proposed by using 3-D finite element for multi-rotor-case time-varying system based on multi-coordinate system. The rotor is modeled in rotating coordinate system and the casing is modeled in fixed coordinate system respectively. The time-varying characteristics of the system are simulated only by bearing mechanical parameters which are easy to be expressed explicitly. A 3-D finite element model reduction method in multi-coordinate system is proposed to solve the reduction problem of rotating-stationary multi-coordinate model. The proposed method is used to analyze the coupled blade-disk-shaft-casing vibration characteristics of a dual-rotor aeroengine, and the application validation is completed by measuring the typical vibration characteristics of the electric drive test rig of a vacuum-pumped aeroengine. The work will provide an effective method for 3-D finite element modeling and dimensionality analysis of aero-engine.

航空发动机整机是（多）转子、薄壁柔性机匣振动相互耦合的复杂机械系统，其振动故障定因、定位困难。整体叶盘、“弯掠扭”风扇叶片等先进结构件的采用，使转子的非轴对称性凸显，与机匣结构及其约束非对称的相对空间位置和相位不可避免产生时变特性。基于3-D有限元建立整机精细化模型已受到重视，但关键需解决系统时变特性难以显式表达及模型自由度太大的问题。为此，提出基于多坐标系的多转子-机匣时变系统3-D有限元模拟方法，转子在旋转坐标系、机匣在固定坐标系分别建模，系统时变特性仅由易于显式表达的轴承力学参数模拟；提出多坐标系下3-D有限元模型降维方法，解决旋转-固定多坐标系下转子与机匣自由度联合降维问题。利用所提方法对某双转子航空发动机叶片-盘-轴-机匣耦合振动特性进行分析，通过整机抽真空电驱试验台实测典型振动特征完成应用性验证。为航空发动机整机3-D有限元建模及降维分析提供一套有效方法。

航空发动机的发展对推重比、经济性及可靠性要求越来越高，整体叶盘、“弯掠扭”风扇叶片等先进结构件的采用，使转子的非轴对称因素凸显，对具有精细结构特征的转子-机匣时变系统动力特性分析需求也不断提高，为满足航空发动机多转子-薄壁柔性机匣系统及各部件耦合振动机理分析，以典型双转子-机匣时变系统为研究对象，开展了系统深入的研究：首先，提出了基于多坐标系多转子-机匣时变系统 3-D 有限元建模方法，从能量角度出发，解决了不同坐标系连接位置处力与位移的变换关系及其参数化模拟的关键问题，进行了基于旋转-固定多坐标系动力方程的推导与分析方法的研究，研究并完成了基于Hill无穷行列式的多坐标系时变系统模态特性分析方法和基于Floquet理论以及谐波平衡的多坐标系时变系统稳态响应分析方法；其次，采用典型实例对所提模态特性分析方法，稳态响应特性分析方法的有效性进行了验证，阐释了多坐标系求解结果的物理意义；进而，在多坐标系建模方法研究的基础上，建立某型航空发动机整机动力学模型，利用广义固定界面模态综合法生成该发动机双转子-机匣系统降维模型，通过试验与仿真分析比较，完成了发动机关键部件模型修正，分析了典型发动机整机系统稳态响应特性；最后，通过航空发动机系统试验模态分析，探索完成了典型航空发动机双转子-机匣整机装配状态下模型准确性和主要的模态特性准确性验证，开展探索并初步完成了发动机实际运行工况下典型振动特征试验验证。.本项目的研究可为航空发动机多转子-薄壁柔性机匣总体及各部件耦合振动机理分析、振动故障溯源定位诊断等提供方法基础。在本项目的支持下已发表录用论文10篇，其中SCI期刊论文2篇，EI期刊论文8篇，中国科技期刊卓越行动计划期刊论文5篇。

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