针对轴承内圈破损故障，建立轴承三自由度分段非光滑的故障模型，研究内圈故障滚动轴承系统周期运动的倍化分岔现象和混沌行为；求出系统的切换矩阵后，将得到的切换矩阵结合光滑系统的 Floquet 理论来分析轴承非光滑系统周期运动发生倍化分岔的条件。通过在碰撞面处建立 Poincaré映射，用数值方法进一步揭示轴承系统的周期运动经倍化分岔通向混沌的现象；结果表明，当旋转频率接近临界分岔点时，系统有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，系统经历了周期二解的 Nermark-Sacker 分岔，随后又经历了多周期、混沌等复杂的非线性行为。对该故障轴承系统分岔和混沌的研究，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，也为实际设计时提供理论指导和技术支持。%A piecewise non-smooth model with 3-DOF for a rolling bearing system with inner race fault was established.The period-doubling bifurcation and chaos of the bearing system were studied here.After the switch matrixes of the system were solved,the period-doubling bifurcation condition of the non-smooth bearing system was analyzed by combining the switching matrixes with Floquet theory for smooth systems.The numerical method was used to further reveal the period-doubling bifurcation and chaos of the bearing system through estabilshing Poincare mapping in the collision plane.The results showed that when the rotating frequency is close to the critical bifurcation point,one of Floquet multipliers of the system is close to -1,and its period-doubling bifurcation appears;with increase in rotating frequency, the system experiences Nermark-Sacker bifurcation of the period 2 solution,and then experiences more complex nonlinear behaviors,such as,multi-periodic solutions and chaos.Studying bifurcation and chaos of fault bearing systems provided a reliable basis for their design and fault diagnosis and provided theoretical guidance and technical support for their actual design in safe and stable operation of large high-speed rotating machineries.
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