Period-Doubling Bifurcation of Rolling Bearing System with Fault in Inner Ring
WANG Qiang1,LIU Yong-bao1,XU Hui-dong2,HE Xing1,LIU Shu-yong1
1. Naval University of Engineering, College of Power Engineering ,Wuhan 430033, China,
2. Hunan University, College of Mechanical and Vehicle Engineering, Changsha,410082
Abstract： Piecewise non-smooth model of three-degree-of-freedom rolling bearing system with fault in inner Ring is established. The period-doubling bifurcation and chaos of bearing system is studied in this paper. After the switch matrixes of system are obtained, the period-doubling bifurcation condition of non-smooth bearing 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 estabilshing 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 appears. With the increase of rotating frequency, the system has experienced the Nermark-Sacker bifurcation of period 2 solution, and then experienced more complex nonlinear behaviors such as multi-period solutions and chaos. The study of bifurcation and chaos of the fault bearing system provides reliable basis for the design and fault diagnosis and provides theoretical guidance and technical support for the actual design in the safe and stable operation of large high-speed rotating machinery.
王强 1，刘永葆 1,2，徐慧东 3，贺星 1，刘树勇 1. 内圈故障滚动轴承系统周期运动的倍化分岔[J]. 振动与冲击, 2015, 34(23): 136-142.
WANG Qiang1,LIU Yong-bao1,XU Hui-dong2,HE Xing1,LIU Shu-yong1. Period-Doubling Bifurcation of Rolling Bearing System with Fault in Inner Ring. JOURNAL OF VIBRATION AND SHOCK, 2015, 34(23): 136-142.
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