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.
出处
《应用数学和力学》
CSCD
北大核心
2012年第7期812-827,共16页
Applied Mathematics and Mechanics
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
unsymmetrical-rigid-rotor elastic-support system
rubbing
two dimensional con-straint bifurcation theory
stability
