弹性支承-刚性转子系统同步全周碰摩的分岔响应

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.

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

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 system obtained from Lagrange equation were solved by averaging method to find the bifurcation equations.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 influence of system’s eccentric and damping on the bifurcation behaviors,respectively.Finally,according 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.