Research On Nonsmooth Bifurcation Of Gear Drive System

The nonsmooth vibration phenomena occurring in gear drive system in working process will seriously influence the products’ quality and yield efficiency, even destroy the equipments, so the researches about the nonsmooth vibration of gear drive system are very practical significance. Gear drive system is the research object and the nonsmooth characteristics are the research focus in this paper. The influence of backlash on the nonsmooth dynamical behavior based on the gear drive system is discussed. Meanwhile, the influence of friction between the roller and the strip on the nonsmooth dynamical behavior based on the rolling mill driven by gear is investigated.Firstly, considering the oil film, backlash, time-varying stiffness and time-varying error and according to the Newton’s law, the dynamical equation of a relative rotation system with backlash non-smooth characteristic is deduced by applying Elastic Hydrodynamic Lubrication(EHL) and 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 single-sided 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-induced instability mechanism is analyzed theoretically by applying impact and Floquet theories. Numerical simulations are also given, which confirm the analytical results.Secondly, considering the friction between the roller and the strip, the torsional vibration of gear pair and the horizontal vibration of the roller, the dynamical equation of a horizontal-torsional coupled main drive system of rolling mill is deduced. The stability of the equilibrium point in the autonomous system is analyzed by using the Hopf bifurcation theorem. The Filippov convex method is used to extend the system. The theoretical conditions of the stick-slip motion are given, which are used to numerically predict the sliding bifurcation. The stability of periodic solutions in the non-autonomous system is analyzed by using the Floquet theory. The influences of mixed friction coefficient on the dynamic behaviors of the system under the conditions of autonomy and non-autonomy are compared. Numerical simulations are also given, which confirm the analytical results.