Abstract: Considering the characteristics of a nonlinear rotor-bearing system,the extended equation method was presented In order to obtain the system Hopf bifurcation point under conditions of determined solution accurately, the constrained equations to the rigid Jeffcott rotor system based on the long-bearing model was added and the singularity of system bifurcation was eliminated At the same time, the system was tested by means of numerical simulation The result shows that this method can determine the Hopf bifurcation point of a nonlinear rotor-bearing system effectively And the theoretical foundation of qualitative control for the stable operating state of rotors is provided

Key words: Rotor;Bearing;Nonlinear system;System stability;Extended equation;Numerical calculation

摘要： 针对非线性转子 轴承系统的具体特点 ,引入扩展方程方法 ,对采用长轴承模型的刚性Jeffcott转子系统增加约束方程 ,消除系统分叉的奇异性 ,使系统的Hopf分叉点在定解条件下得以准确求解。同时 ,为验证该方法 ,在相同条件下对该系统进行数值仿真研究。结果表明 ,扩展方程方法可以快速准确地确定转子 轴承系统的Hopf分叉点 ,分析结果为定性控制转子的稳定运行状态提供了理论依据。

关键词: 转子;轴承;非线性系统;系统稳定性;扩展方程;数值计算