Dynamic response analysis for non-smooth gear rattling system

Due to the non-smooth characteristics in the gear rattling system, a method of local map was introduced. Based on Poincare maps on impact plane, a method to calculate the Lyapunov exponents of gear rattling system was constructed. A numerical example of spur gear rattling system was given by the proposed method. Phase portraits and Lyapunov exponents were used to describe the dynamic response of the Non-smooth gear rattling system. With the increasing of exciting amplitude, the complete dynamic response was obtained. The bifurcation diagram and the spectrum of Lyapunov exponents in a large range of parameters were used to verify the method given herein.