Taking a typical single degree of freedom gear torsional vibration system as research object

study on non-smooth dynamics characteristic of the system is carried out.The contact surface and zero phase plane ψ0 are defined as Poincaré section

the bifurcation diagram

top Lyapunov spectrum and domains of attraction of the system on ψ0 section is calculated

the variation law of system Global and local response in the process of multiple attractors coexisting phenomenon produce and disappear is obtained.The bifurcat ion diagram of section is calculated

the periodicity of gear mesh-dismesh is obtained.T he waterfall spectrum diagram is calculated

the motion frequency response characteristic of gear mesh-dismesh is obtained.By comparing

it is found that gear system has abundant dynamics behavior on different Poincaré section.