Neimark-Sacker Bifurcation of Rolling Bearing System with Fault in Outer Ring

Abstract

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 Neimark-Sacker bifurcation of bearing system is first studied in this paper. The switching matrixes of system are obtained at the switching boundaries, and theNeimark-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 Neimark-Sacker bifurcation 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.The study of bifurcation 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.