Bifurcation and chaos analysis of spur gear pair in two-parameter plane

A developed algorithm is designed based on the simple cell mapping method and escape time algorithm to examine every state cell and the dynamic characteristics of the multi-parameter coupling in torsion-vibration gear system. Two different types of bifurcation caused by the intersection of the period-doubling bifurcation curves are researched by analyzing the distribution map and the bifurcation diagram of system’s dynamic characteristic in the parameter plane, ω - F . The occurrence processes of periodic bubbles and saltatory periodic bifurcation are studied. The stationary solution and its phase trajectory of the fractal of the periodic motion attractor boundary are researched too. The sufficient condition of the fractal structure of the periodic attractor domain is achieved. Homoclinic or heteroclinic trajectory in phase space is found caused by the intersection of the different periodic motion trajectories in non-smooth system.