三维叶盘失谐模态分析的摄动降阶方法  

A Perturbed Order-Reduction Method for Modal Analysis of 3-D Blade Disk with Mistuning

作　　者：周子宣 徐自力[1,2] ZHOU Zixuan;XU Zili(State Key Laboratory for Strength and Vibration of Mechanical Structures,Xi’an Jiaotong University,Xi’an 710049,China;School of Aerospace Engineering,Xi’an Jiaotong University,Xi’an 710049,China)

机构地区：[1]西安交通大学机械结构强度与振动国家重点实验室,西安710049 [2]西安交通大学航天航空学院,西安710049

出　　处：《西安交通大学学报》2019年第9期42-48,共7页Journal of Xi'an Jiaotong University

基　　金：国家自然科学基金资助项目(51675406)

摘　　要：针对失谐叶盘结构振动局部化引起的叶盘高周疲劳会对叶片安全性产生不利影响,真实叶盘结构的细节较多、网格划分后的节点数目庞大、模态计算的效率较低等问题,提出了一种摄动降阶方法。将叶盘刚度阵和质量阵分为谐调部分与失谐部分,利用固定界面模态综合法中的坐标降阶转换关系,将已知的原始结构中的失谐部分转换为降阶结构中对应的改变量。通过摄动方法,循环利用谐调模态信息,将失谐叶盘模态的求解转化为失谐矩阵与谐调矩阵的乘积形式,快速计算对应失谐分布下的叶盘固有频率与振型。对Rotor#67压气机叶盘进行计算,结果表明:相对于完整求解方法,摄动降阶算法的频率计算误差低于0.3%,模态位移计算误差小于0.25%;摄动降阶法的模态计算时间最高为常规降阶法的30%,说明在满足工程计算精度的要求下,所提方法能大幅提高失谐叶盘模态的计算效率。The high-cycle fatigue of mistuned blade disks caused by vibration localization has adverse effects on safety of the blades. A real blisk structure contains many details, so if FEM is used, the number of nodes in the mesh is so large that the modal computation efficiency is low. In order to solve this problem, a perturbed order-reduction method is proposed in this paper. Firstly, the blade disk’s stiffness and mass matrixes are divided into two components: the tuned component and the mistuned component. Then, the mistuned component of the original structure is transformed into the corresponding change in the order-reduced structure by using coordinate order-reduction transformation relationship in the fixed interface modal synthesis method. The coordinated modal information is repeatedly used by the perturbation method. The solution of mistuned blade disk modal is transformed into the product of tuning matrix and mistuning matrix, and the natural frequencies and modals of blade disk under mistuned distribution are calculated efficiently. A Rotor 67 compressor blade disk is taken as the calculating example, and the computation results show that the frequency calculation error of the perturbed order-reduction method is less than 0.3% and the modal displacement calculation error is less than 0.25%. The modal calculation time of the perturbed order-reduction method is 30% that of the conventional order-reduction method. It is concluded that this method can greatly improve the efficiency of modal calculation of mistuned blade disk under the requirement of engineering calculation accuracy.

关 键 词：失谐叶盘 模态分析 摄动降阶 

分 类 号：TK05[动力工程及工程热物理]