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Vol. 139, No. 4, April 2012, pp. 24-34

 

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Improved Modeling of the Comb Drive Levitation Effect by Using Schwartz-Christoffel Mapping

 

Fengyuan LI and Jason Vaughn CLARK

Purdue University, 1205 W. State St., West Lafayette, IN, 47906, USA

Tel.: +1-765-494-3437, fax: +1-765-494-2806

E-mail: li200@purdue.edu, jvclark@purdue.edu

 

 

Received: 7 December 2011   /Accepted: 23 April 2012   /Published: 30 April 2012

Digital Sensors and Sensor Sysstems

 

Abstract: In this paper we model the comb drive levitation effect quickly and accurately by using Schwarz-Christoffel mapping (SCM) and study the sensitivity of the levitation effect to the comb finger width and the gap between the comb fingers. The levitation effect occurs when the substrate is within close proximity to the comb fingers. Lumped comb drive models found in the literature ignore the levitation effect, which decreases their accuracy. Previously, potential theory method, finite element analysis (FEA) and boundary element analysis (BEA) were used to model the levitation effect. We show that the levitation effect can be modeled more quickly and accurately by using SCM in this paper. Our method is several times faster than FEA because it does not discretize the boundaries or subdomains into a large number of coupled equations. We find that the vertical forces on a rotor finger are in balance when the levitation is 1.239 0.001 mm for 4 mm wide, 2 mm thick comb fingers with 2 mm gap apart from each other and apart from the substrate. This result is slightly larger and more accurate than previously reported values. Our improvement in accuracy is most likely because our model includes all the electric fields around the rotor finger, captures the effect of the periodic array of comb fingers, treats the electrostatic fields at the vertices exactly, and uniquely considers reflection due to a multitude of neighboring comb drive fingers.

 

Keywords: Comb drive, Levitation, Modeling and simulation, Online tool, Schwarz-Christoffel mapping

 

 

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