Grazing bifurcation analysis of a relative rotation system with backlash non-smooth characteristic**Project supported by the National Natural Science Foundation of China (Grant No. 61104040), the Natural Science Foundation of Hebei Province, China (Grant No. E2012203090), and the University Innovation Team of Hebei Province Leading Talent Cultivation Project, China (Grant No. LJRC013).

Abstract

Grazing bifurcation of a relative rotation system with backlash non-smooth characteristic is studied along with the change of the external excitation in this paper. Considering the oil film, backlash, time-varying stiffness and time-varying error, the dynamical equation of a relative rotation system with a backlash non-smooth characteristic is deduced by applying the elastic hydrodynamic lubrication (EHL) and the Grubin theories. In the process of relative rotation, the occurrence of backlash will lead to the change of dynamic behaviors of the system, and the system will transform from the meshing state to the impact state. Thus, the zero-time discontinuous mapping (ZDM) and the Poincare mapping are deduced to analyze the local dynamic characteristics of the system before as well as after the moment that the backlash appears (i.e., the grazing state). Meanwhile, the grazing bifurcation mechanism is analyzed theoretically by applying the impact and Floquet theories. Numerical simulations are also given, which confirm the analytical results.