星型齿轮传动非线性动力学建模与动载荷研究

本文建立了星型齿轮传动的弯扭耦合非线性动力学计算模型,模型中考虑了原动机和负载惯性,齿轮副的啮合综合误差,齿轮的偏心误差,时变啮合刚度以及齿轮的啮合间隙。采用适当的广义坐标变换,将线性恢复力和非线性恢复力共存的动力学方程组统一成矩阵形式,用数值解法获得了在有间隙非线性的情况下受强参数激励和多频激励的系统的动态响应和动载荷历程。最后给出了一个算例,讨论了间隙、齿频误差和偏心误差对齿轮系统的响应、动载荷以及各星轮的载荷分配均匀性的影响。并研究了刚度和误差激励和间隙的相互耦合关系,得出了对星型齿轮传动设计和制造有意义的结论。 

Nonlinear Dynamic Modeling and Dynamic Tooth Loads Analysis of Star Gearing System

A torsional and translational nonlinear vibration mathematical model was established to predict the dynamic characteristics of the star gearing system.The time-varying mesh stiffness,gear composite errors,run-out errors and gear backlashes were considered.A numerical method was applied to solving the large parametrically excited nonlinear multi-DOF dynamic system.A numerical example was also presented.From the results,the influences of the time-varying meshing stiffness,run-out errors and backlashes on the dynamic responses and dynamic gear tooth loads were investigated respectively.The dynamic load equalizations among star gears were also analyzed under the existence of gear run-out errors.In comparison with some calculated results from the literature ,the numerical results presented show a good agreement.