弹性支承-刚性转子系统同步全周碰摩的分岔响应  

Bifurcation on the Synchronous Full Annular Rub of a Rigid-Rotor Elastic-Support System

作　　者：张华彪[1] 陈予恕[1] 李军[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7期812-827,共16页Applied Mathematics and Mechanics

摘　　要：基于航空发动机转子系统的结构特点,将航空发动机转子系统简化为一个非线性弹性支承的刚性转子系统.根据Lagrange方程建立了弹性支承-刚性不对称转子系统同步全周碰摩的运动方程;采用平均法进行求解,得到了关于系统振幅的分岔方程;根据两状态变量约束分岔理论,分别给出了系统在无碰摩和碰摩阶段参数平面的转迁集和分岔图,讨论了转子偏心、阻尼对系统分岔行为的影响;应用Liapunov稳定性理论分析了系统碰摩周期解的稳定性和失稳方式,给出了系统参数——转速平面上周期解的稳定范围;该文的研究结果对航空发动机转子系统的设计有一定的理论意义.Aero engine rotor system was simplified to be an unsymmetrical-rigid-rotor with nonlinear-elastic-support based on its characteristics. Governing equations of the rubbing sys- tem obtained from Lagrange equation were solved by averaging method to find the bifurcation e- quations. Then, according to the two-dimensional constraint bifurcation theory, transition sets and bifurcation diagrams of the system with and without rubbing were given to study the influ- ence of system＇ s eccentric and damping on the bifurcation behaviors, respectively. Finally, ac- cording to Liapunov stability theory, the stability region of steady-state rubbing solution and the boundary of static bifurcation and Hopf bifurcation were determined to discuss the influence of system parameters on the evolution of system＇ s motion. The research results may provide some references for the design of aero rotor systems.

关 键 词：弹性支承刚性转子 碰摩 两状态变量约束分岔 稳定性 

分 类 号：O322[理学—一般力学与力学基础] V235.1[理学—力学]