内圈故障滚动轴承系统周期运动的倍化分岔

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振动与冲击 ›› 2015, Vol. 34 ›› Issue (23) : 136-142.

论文

内圈故障滚动轴承系统周期运动的倍化分岔

王强 1，刘永葆 1,2，徐慧东 3，贺星 1，刘树勇 1

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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

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摘要

本文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。

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.

导出引用

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[J]. Journal of Vibration and Shock, 2015, 34(23): 136-142

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