考虑边缘效应的扭转微镜的动力响应分析

ANALYSIS ON DYNAMIC CHARACTERISTICS OF TORSIONAL MICROMIRROR MODEL WITH CONSIDERATION OF EDGE EFFECTS

目前对扭转微镜力学特性方面的研究主要围绕静态特性展开,对于其动态特性的分析,已经给出了非耦合与耦合两种模型,但模型中的静电驱动力与驱动扭矩都是建立在无穷大板电容的基础上。而实际应用中的扭转微镜是有限尺度的,即在边缘处电力线会发生泄漏和弯曲,从而产生边缘效应。引入有限板电容的静电力修正公式,计及边缘效应对扭转微镜动态响应的影响。由于在计及边缘效应后,系统方程的驱动力项比较复杂,不能导出其解析表达式,故采用了数值积分方法进行相关处理,并采用迭代修正齐次扩容精细积分法求解非线性动力方程,得到了稳定、精确的数值解。计算结果显示,动态响应幅值在计及边缘效应后比未计及时要大,且扭转微镜的尺寸参数对边缘效应的影响有很大的关联性。

In oder to be in keeping with the real condition of torsional micromirror, the improved formulas for electrostatic force in finite scale parallel plate capacitor are introduced and the edge effects are taken into account. Owing to the edge effects, the electro-driving force and the torsional deformation of torsional micromirror system become very complicated and their analytical expressions would be very difficult to be obtained. Therefore, the numerical integration procedure and an iterative refinement homogeneous capacity high precision integration method (IRHCHPIM) are employed to solve the non-linear dynamic equations, which can achieve a stable and high precise numerical solution. The calculated results show that the dynamic responses will increase when the edge effects are considered, and the scale parameters of the torsional micromirror are in close relation to edge effects.