Period-doubling bifurcation of a rolling bearing system with inner race fault

A piecewise non-smooth model with 3-DOF for a rolling bearing system with inner race fault was established. The period-doubling bifurcation and chaos of the bearing system were studied here. After the switch matrixes of the system were solved,the period-doubling bifurcation condition of the non-smooth bearing system was analyzed by combining the switching matrixes with Floquet theory for smooth systems. The numerical method was used to further reveal the period-doubling bifurcation and chaos of the bearing system through estabilshing Poincare mapping in the collision plane. The results showed that when the rotating frequency is close to the critical bifurcation point,one of Floquet multipliers of the system is close to-1,and its period-doubling bifurcation appears; with increase in rotating frequency,the system experiences Nermark-Sacker bifurcation of the period 2 solution,and then experiences more complex nonlinear behaviors,such as,multi-periodic solutions and chaos. Studying bifurcation and chaos of fault bearing systems provided a reliable basis for their design and fault diagnosis and provided theoretical guidance and technical support for their actual design in safe and stable operation of large high-speed rotating machineries.