Bifurcations and chaos 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 is first studied in this paper. The switching matrixes of system are obtained at the switching boundaries, and the period-doubling bifurcation and Neimark-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 establishing the Poincare mapping on the collision plane. When the rotating frequency is increased to reach the critical bifurcation point, a pair of complex conjugate Floquet multipliers is on the unit circle and others into a unit circle, and the Neimark-Sacker bifurcation appears. When the rotating frequency is decreased to another critical bifurcation point, one of Floquet multipliers of the system equals to 1 and others into a unit circle, and the period-doubling bifurcation appears. With the variation of rotating frequency, the system also experiences the complex dynamical behaviors of Nermark-Sacker bifurcation of period 3 solution 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.