A novel method to predict the pull-in voltage in a closed form for micro-plates actuated by a distributed electrostatic force
A novel method to predict the pull-in voltage in a closed form for micro-plates actuated by a distributed electrostatic force
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DOI：
10.1088/0960-1317/16/5/016
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发表时间：
2006-05-01
影响因子：
2.3
通讯作者：
Tsai, C-Y
中科院分区：
文献类型：
--
作者：
Chao, Paul C-P;Chiu, C-W;Tsai, C-Y
本研究致力于寻找由两个平行带电板形成的微器件的精确吸合电压/位置。拉入是一种现象，其中由施加在器件的两个板上的电压引起的静电力超过由变形的板施加的弹性恢复力，导致两个板之间的接触。为了准确预测吸合过程，基于板的弹性、残余应力和分布静电力之间的平衡关系，建立了偏微分方程（PDE）形式的吸合动力学模型。采用Galerkin方法将所建立的偏微分方程分解为离散的模态方程。通过考虑低阶模式并求解它们，可以根据所施加的偏置电压来预测板的偏转。通过五阶级数和全阶数值积分近似求解挠度，成功地近似了吸合位置和电压。在变形板的中心偏转方面的拉入位置被发现是板之间的空气间隙的48%，这提出了一个更好的估计比通常使用的三分之一的差距来自所有过去的研究的基础上，一个不太现实的一维块模型。一个封闭的形式的吸合电压的推导提供设计指南的设备之前，生产。最后通过实验室设计和制作的平行带电微板MEMS器件的有限元和实验研究验证了上述理论研究结果。
This study is devoted to finding the precise pull-in voltage/position of a micro-device formed by two parallel charged plates. Pull-in is a phenomenon where the electrostatic force induced by the applied voltage across two plates of the device exceeds the elastic, restoring force exerted by the deformed plates, leading to a contact between the two plates. To offer a precise prediction of the pull-in, a dynamic model in the form of a partial differential equation (PDE) is established based on the equilibrium among plate flexibility, residual stress and distributed electrostatic forces. The Galerkin method is employed to decompose the established PDE into discrete modal equations. By considering lower order modes and solving them, one arrives at a prediction of plate deflection in terms of the applied bias voltage. Approximating the solved deflection by a fifth-order series and full-order numerical integration, the pull-in position and voltage are successfully approximated. The pull-in position in terms of center deflection of the deformed plate is found to be 48% of the air gap between the plates, which presents a better estimation than the commonly used one-third of the gap derived by all past studies based on a less realistic one-dimensional lump model. A closed form of the pull-in voltage is derived to offer design guidelines for the device prior to production. The aforementioned theoretical findings are finally validated by finite element and experimental studies on a MEMS device of parallel charged micro-plates designed and fabricated in the laboratory.