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Micromachines 2016, 7(4), 53; doi:10.3390/mi7040053

A New Analytical Model to Estimate the Voltage Value and Position of the Pull-In Limit of a MEMS Cantilever

1
Department of Electrical and Electronics Engineering, Toros University, Mersin 33140, Turkey
2
Department of Electrical and Electronics Engineering, Mersin University, Mersin 33343, Turkey
*
Author to whom correspondence should be addressed.
Academic Editors: Hiroshi Toshiyoshi and Nam-Trung Nguyen
Received: 25 January 2016 / Revised: 16 March 2016 / Accepted: 18 March 2016 / Published: 24 March 2016
View Full-Text   |   Download PDF [1364 KB, uploaded 24 March 2016]   |  

Abstract

In this study, a new analytical model is developed for an electrostatic Microelectromechanical System (MEMS) cantilever actuator to establish a relation between the displacement of its tip and the applied voltage. The proposed model defines the micro-cantilever as a rigid beam supported by a hinge at the fixed-end with a spring point force balancing the structure. The approach of the model is based on calculation of the electrostatic pressure centroid on the cantilever beam to localize the equivalent electrostatic point load. Principle outcome of the model is just one formula valid for all displacements ranging from the initial to the pull-in limit position. Our model also shows that the pull-in limit position of a cantilever is approximately 44% of the initial gap. This result agrees well with both simulation results and experimental measurements reported previously. The formula has been validated by comparing the results with former empirical studies. For displacements close to the pull-in limit, the percentage errors of the formula are within 1% when compared with real measurements carried out by previous studies. The formula also gives close results (less than 4%) when compared to simulation outcomes obtained by finite element analysis. In addition, the proposed formula measures up to numerical solutions obtained from several distributed models which demand recursive solutions in structural and electrostatic domains. View Full-Text
Keywords: cantilever; electrostatic actuator; lumped model; pull-in limit; pull-in voltage; pivot model cantilever; electrostatic actuator; lumped model; pull-in limit; pull-in voltage; pivot model
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Ak, C.; Yildiz, A. A New Analytical Model to Estimate the Voltage Value and Position of the Pull-In Limit of a MEMS Cantilever. Micromachines 2016, 7, 53.

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