静电谐波微电机的非线性动力学

Nonlinear Dynamics of Electrostatic Harmonic Micromotors

介绍了一种基于静电驱动的新型谐波微电机,描述了该微电机的基本工作原理。分析了柔轮所受的非线性径向电场力,通过引入摄动小参数,得出了Fourier级数形式的径向载荷动态分量。运用Donnell壳理论,建立了非线性系统的动力学模型。在线性系统解的基础上,运用摄动法,通过比较系数和消除久期项,得到初始位移激励下弱非线性系统的近似解。对比发现,非线性系统的频率较线性系统的频率有所减小。讨论了非线性频率随系统参数的变化规律,给出了非线性系统动态响应的规律。

A novel harmonic micromotor actuated by electrostatic force was proposed,whose basic operating principle was also presented.The nonlinear radial electrostatic force was analyzed for the flexspline.By introducing the small parameter,the dynamic component of radial load was represented in Fourier series form.The nonlinear dynamic model was obtained by using the Donnell＇s shell theory.Taking into account of the corresponding linear system solution,the perturbation method was employed.By comparing the coefficients and eliminating the secular terms,the asymptotic solution was implemented for the weakly nonlinear system subjected to the initial displacement excitation.The result shows that the nonlinear frequency is less than the linear one.Finally,variation of the nonlinear frequencies with respect to system parameters was discussed.The dynamic response was summarized for the nonlinear system as well.