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Research Papers

Modeling of Contact and Stiction in Electrostatic Microcantilever Actuators

[+] Author and Article Information
C. P. Vyasarayani1 n2

Systems Design Engineering,  University of Waterloo, Waterloo, ON, N2L 3G1, Canadacpvyasar@engmail.uwaterloo.ca

Eihab M. Abdel-Rahman, John McPhee

Systems Design Engineering,  University of Waterloo, Waterloo, ON, N2L 3G1, Canada

1

Corresponding author.

2

Present address: Indian Institute of Technology Hyderabad, Ordnance Factory Estate, Yeddumailaram 502205, Andhra Pradesh, India.

J. Nanotechnol. Eng. Med 3(1), 011003 (Aug 10, 2012) (8 pages) doi:10.1115/1.4006618 History: Received January 25, 2012; Revised April 02, 2012; Published August 10, 2012; Online August 10, 2012

A dynamic model of a microcantilever actuator is developed to simulate the events of contact, impact, stiction, and pull-off from the substrate. The model accounts for geometric, electrostatic, adhesive, and contact nonlinearities. The model is validated by comparison to experimental data and other analytical model predictions. We find that microcantilever electrostatic microelectromechanical (MEMS) actuators can exhibit bistable and tristable equilibrium configurations. We also find that the transients subsequent to pull-in play an important role in determining whether or not stiction will occur.

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Copyright © 2012 by American Society of Mechanical Engineers
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References

Figures

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Figure 7

The (a) normalized natural frequency and (b) the contact length (lc ) of the beam during a backward voltage sweep for six levels of adhesion energy

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Figure 8

The (a) normalized natural frequency and (b) the contact length (lc ) of the beam during a forward voltage sweep for six levels of adhesion energy

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Figure 9

The (a) normalized natural frequency and (b) the contact length (lc ) of the beam subsequent to pull-in during a backward sweep of adhesion energy and 0 V drop

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Figure 10

The cantilever tip height above the substrate for the waveforms ν(t) = 1.2[H(t) − H(t − 2)] V and ν(t) = 1.8[H(t) − H(t − 2)] V and adhesion energy of 6 μJ/m2

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Figure 6

The beam deflection in the presence of surface adhesion (a) obtained analytically, Eq. 21, and numerically, Eq. 13, and (b) the difference between the analytical and numerical solutions

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Figure 5

The three stable static deflections of the beam in the tristable region at Vdc  = 36 V

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Figure 4

The (a) normalized natural frequency of the beam and (b) the dimensionless contact length (lc ) of the beam as functions of voltage

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Figure 3

Comparison of tip deflection at different voltages. The parameters [28] of the microbeam are E = 155 GPa, ρ = 2333 kg/m3 , L = 20 mm, b = 5 mm, h = 52 μm, d2  = 92 μm, a1  = 0, a2  = L, ɛ=8.85×10-12F/m.

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Figure 2

Stress–displacement curve at the interface of beam and the substrate due to adhesive and contact forces. A schematic of the cross section of the beam and the substrate are also shown for different values of the gap.

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Figure 1

Cantilever MEMS beam along with the foundation model for the substrate

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