非线性转子-密封系统1∶2亚谐共振分岔研究  

Research on the 1∶2 Subharmonic Resonance and Bifurcation of the Nonlinear Rotor-Seal System

作　　者：李忠刚[1] 陈予恕[1] 

机构地区：[1]哈尔滨工业大学航天学院,哈尔滨150001

出　　处：《应用数学和力学》2012年第4期475-485,共11页Applied Mathematics and Mechanics

基　　金：国家自然科学基金资助项目(10632040)

摘　　要：研究了转子-密封系统在气流激振力作用下的低频振动———1∶2亚谐共振现象.利用流体计算动力学(CFD)方法对转子-密封系统进行了流场模拟计算,辨识出适用于气流流场的Muszyns-ka模型参数,并建立了转子-密封系统动力学方程.采用多尺度方法将系统进行3次截断,并得到系统响应.采用奇异性理论研究了系统的1∶2亚谐共振,进一步得到系统亚谐共振的分岔方程和转迁集,根据转迁集给出了在不同奇异性参数空间内的分岔图.同时,由分岔方程得到了亚谐共振非零解存在的条件.其分析结果对抑制转子-密封系统的亚谐振动有重要的工程意义.The 1 ： 2 subharmonic resonance of the labyrinth seals/rotor systems was investigated, which the low-frequency vibration of stream turbines could be caused by the gas exciting force in. The empirical parameters of gas exciting force of Muszynska model were obtained by using the results of Computational Fluid Dynamics （CFD）. Based on multiple scale method, the 1：2 subharmonic resonance response of the dynamic system was gained by truncating the system with three orders. The transition sets and the local bifurcations diagrams of the dynamics system were presented by employing singular theory analysis. Meanwhile, the existence conditions of subharmonic resonance non-zeros solutions of the dynamic system were obtained, which provides a new theoretical basis in recognizing and protecting the rotor from the subharmonic resonant failures in the turbine machinery.

关 键 词：密封转子 1亚谐共振 流场计算 气流激振力 奇异性 

分 类 号：O322[理学—一般力学与力学基础] TH133[理学—力学]