中文摘要：

基于非线性理论,建立了三自由度分段弹性移动碰撞面系统模型。首先,研究了该情况下系统周期运动的倍化分岔和混沌等非线性行为,求出了系统碰撞前后的切换矩阵,并使用得到的切换矩阵结合光滑系统的Floquet理论确定了该非光滑系统周期运动发生倍化分岔的条件;然后,通过在碰撞面处建立Poincaré映射,用数值方法进一步揭示了该系统周期运动经倍化分岔通向混沌的过程。结果表明：当旋转频率接近临界分岔点时,有1个Floquet特征乘子接近-1,系统发生周期倍化分岔;随着旋转频率的增加,系统经历了多周期、混沌等复杂的非线性行为。该研究结果可为大型高速旋转机械的安全稳定运行提供可靠的设计与故障诊断依据,也为其实际设计提供了理论指导和技术支持。

英文摘要：

Based on nonlinear theory,apiecewise non-smooth model of three-degree-of-freedom system is established.The period-doubling bifurcation and chaos of bearing system are investigated.The switching matrixes of system are obtained at the switching boundaries and the period-doubling bifurcation condition of non-smooth system is analyzed by combining the switching matrixes with the Floquet theory for smooth systems.The numerical method is used to further reveal the period-doubling bifurcation and chaos of bearing system through establishing the Poincare mapping on the collision plane.The results show that when the rotating frequency is close to critical bifurcation point,one of Floquet multipliers of the system is close to-1,and the period-doubling bifurcation occurs.With the increase of rotating frequency,the system has experienced more complex nonlinear behaviors such as multiperiod solutions and chaos.The study of bifurcation and chaos of the system provides reliable basis for the design and fault diagnosis and provides the theoretical guidance and technical support for the actual design in the safe and stable operation of large high-speed rotating machinery.