Nonlinear Dynamics of a Multi-shaft Gear System in Parameter-state Space

A nonlinear dynamic model of a 12-degree-of-freedom multi-shaft gear system is established, which includes nonlinear factors such as gear backlash, bearing clearance and time-varying mesh stiffness. The bifurcation diagrams and the maximum dynamic load coefficient diagrams that describe the dynamics of the gear transmission system are simulated by using the Runge-Kutta method, combined with three Poincaré mapping. The mutual transition of the adjacent period one motion through the grazing bifurcation and saddle-node bifurcation form a hysteresis zone where two types of impact motion coexist. The correlation between the dynamic response and the gear backlash under the parameter-state space is investigated, and it is verified that the extreme parameter conditions lead to abnormal vibration phenomena such as jumping, mesh-apart and chaotic motion. The results show that, near the critical value of ω = 0.7164 for grazing bifurcation, the meshing gear pair undergoes a jump in relative micro-displacement and dynamic load, increasing system impact vibration and a decrease in transmission efficiency, which is an undesirable parameter interval. In the initial stage of dynamic designing, the backlashes can be selected through the internal characteristics and transition mechanism of periodic motions