Meshing stiffness of an inner parallel moving gear pair and its bifurcation characteristics

The meshing stiffness of an inner meshed gear pair with a fixed shaft and small tooth number difference was analyzed. Its frequency spectrum properties was obtained by using FFT, indirectly showed the frequency spectrum properties of the inner parallel moving gear pair. Based on that, considering the gear backlash, its dynamic equations with multi-tooth meshing were derived. Then, using the classical explicit 4-order Rouge-Kutta method, the equations with different parameters were solved and the parameter bifurcation figures were obtained, they showed effects of different parameters. These results provided a theoretic basis for designing an inner parallel gear pair.