机电集成超环面传动系统内共振研究

Internal resonance of an electromechanical integrated toroidal drive system

机电集成超环面传动系统为集机、电和控制于一体的新型广义复合机电耦合系统,工作中非线性电磁啮合力可能导致明显的内共振现象,影响系统的正常运行。考虑系统中行星轮与蜗杆、定子间电磁啮合非线性,建立了系统强非线性运动微分方程组,针对不存在与存在内共振两种情形,用多尺度法求出了系统时域响应的一次近似解析解,作出了系统振幅随时间的变化曲线和系统时域响应曲线;针对不存在与存在内共振两种情形,研究了系统各部件动态位移随时间的变化规律。研究结果表明:内共振使得系统能量在系统内不同零件间交互传递,导致各零件振动振幅增大,影响系统动态性能,设计时应该避免内共振的产生。

An electromechanical integrated toroidal drive is a new-style generalized composite transmission,in which drive,power and control are integrated.Nonlinear electromagnetic meshing force can lead to obvious internal resonance during operation and cause a drive system to run unusually.Considering the nonlinear electromagnetic mesh forces among planets,worm and stator,strongly nonlinear dynamic differential equations of a toroidal drive were presented.Based on two different situations of internal resonance and non-internal resonance,the first order approximate analytic solutions of time responses were obtained by multi-scale method.Time histories of vibration amplitudes and displacements of the drive system were obtained.Meanwhile,changes of time responses of different components of the drive system under the two situations of internal resonance and non-internal resonance were investigated.The results showed that internal resonance makes energy alternately transfer among different components;it leads to increase in amplitudes and affects dynamic performance of the drive system,so it should be avoided during design.