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针对新型广义复合传动机构-机电集成超环面传动系统,其中蜗杆、行星轮间电磁啮合刚度的非线性变化,首先推导出了系统弱非线性摄动形式的运动微分方程,其次在将其转化为小参数形式的基础上,利用Linstedt-Poincare法求出了该系统频率和位移响应的近似解析形式.最后讨论了算例系统中电磁啮合力的非线性变化对系统振动频率及振幅的影响,得出了随小参数ε次幂数增大,传动系统各方向振动的振幅几乎不受影响,而各阶振动频率却变化明显的结果.
Aiming at the nonlinear change of the electromagnetic meshing stiffness between the worm gear and the planetary gear of the new generalized compound transmission mechanism-electromechanical integrated toroidal drive system, the differential equations of motion for the system with weakly nonlinear perturbation are deduced firstly. Secondly, Based on the small parameter form, the approximate analytic form of frequency and displacement response of the system was obtained by Linstedt-Poincare method.Finally, the influence of the nonlinear change of electromagnetic meshing force on the system vibration frequency and amplitude was discussed, The results show that with the increase of small power parameter ε, the amplitude of vibration in each direction of the transmission system is almost unaffected, while the vibration frequency of each step has obvious changes.