内平动齿轮副啮合综合刚度与系统的分岔特性

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

用机构反转法将内平动齿轮副转化为定轴齿轮副,然后用有限元方法分析了该内啮合定轴齿轮副的啮合综合刚度,并使用FFT变换得到其频谱特性,进而得到了内平动齿轮副的啮合综合刚度的频谱特性,在此基础上,考虑了齿侧间隙的非线性因素,进一步得到存在多齿接触的时变啮合刚度下内平动齿轮副的运动微分方程。然后,用经典的显式四阶Rouge-Kutta法对系统的各个参数进行了数值计算,得到系统的参数分岔图,并分析了各参数对系统动力学行为的影响。为内平动齿轮副的设计参数选择提供理论依据。

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.