外圈故障滚动轴承周期运动Neimark-Sacker分岔研究

文章基于非线性理论,建立了三自由度非光滑系统轴承外圈故障模型,研究了该情况下,系统周期运动的Neimark-Sacker分岔现象和混沌等非线性行为。求出系统的切换矩阵,将得到的切换矩阵结合Floquet理论确定了该非光滑系统周期运动发生Neimark-Sacker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Neimark-Sacker分岔通向混沌的现象。发现当旋转频率接近临界分岔点时,系统有一对Floquet特征乘子的模接近1,其余特征乘子模都小于1,系统发生Neimark-Sacker分岔,随着旋转频率的增加,系统经历了典型的Neimark-Sacker分岔通向混沌的非线性行为。同时研究了不同的阻尼系数对系统分岔的影响,发现阻尼可以有效地延迟系统的分岔点。对该故障轴承系统分岔和混沌的研究,可为实际装备安全运行及故障诊断提供依据,同时为设计提供理论指导和技术支持。

Neimark-Sacker bifurcation of rolling bearing system with fault in outer ring

Piecewise non-smooth model of three-degree-of-freedom rolling bearing system with fault in outer ring is established by the method of the nonlinear theory. The bifurcations and chaos of bearing system are studied. The switching matrixes of system are obtained at the switching boundaries, and the Neim-ark-Sacker bifurcation 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 bifurcations and chaos of bearing system through estabilshing the Poincare mapping on the collision plane. Results show that when the rotating frequency is decreased to a critical bifurcation point, a pair of complex conjugate Flo-quet multipliers is on the unit circle and others into a unit circle, and the Neimark-Sacker bifurcation appears. With the increase of rotating frequency, the system has experienced the nonlinear dynamical be-haviors of classical Neimark-Sacker bifurcations to chaos. Also the influence of different damping coeffi-cients on the bifurcation of system is analyzed and it is found that the damping of system can effectively reduce the nonlinear behaviors of bifurcation 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.