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A multibody-based dynamic simulation method for electrostatic actuators

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Abstract

A numerical simulation method is developed to analyze the dynamic responses of electrostatic actuators, which are electromechanically-coupled systems. The developed method can be used to determine the dynamic responses of cantilever-type switches, which are an example of typical MEMS (Micro-Electro-Mechanical System) devices driven by an electrostatic force. We propose the approach that adopts a point charge to deal with electric field effects between electrodes. This approach may be considered as a lumped parameter model for the electrostatic interactions. An advantage of this model may be the easy incorporation of the electrostatic effects between electrodes into a multibody dynamics analysis algorithm. The resulting equations contain the variables for position, velocity, and electric charge to describe the motion of the masses and the charges on the electrodes in a system. By solving these equations simultaneously, the dynamic response of an electrostatically-driven system can be correctly simulated. In order to realize this approach, we implement the procedures into RecurDyn, the multibody dynamics software developed by the authors. The developed numerical simulation tool was evaluated by applying it to cantilever-type electrostatic switches in many different driving conditions. The results suggest that the developed tool may be useful for predicting behaviors of electrostatic actuators in testing as well as in design.

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Abbreviations

Y :

Velocity vector in absolute coordinates

B :

Velocity transformation matrix

Φ :

Constraint equation for cut-joint

Φ q :

Jacobian of in relative coordinates

λ :

Lagrange multiplier

ε 0 :

Permittivity of free space

V :

Driving voltage

d :

Normal distance between two electrodes

d 0 :

Initial normal distance between two electrodes

L :

Length of a beam

b :

Width of a beam

A :

Cross sectional area of a beam

E :

Young’s modulus

ρ :

Mass density

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Authors and Affiliations

  1. Department of Mechanical Engineering, Pohang University of Science and Technology, Hyoja-dong San 31, Pohang, 790-784, South Korea

    Sangkyu Lee, Jinam Kim & Wonkyu Moon

  2. Department of Mechanical Engineering, Kyunghee University, Suhchun 1 lee, Yongin, Kyunggi-do, 449-701, South Korea

    Jinhwan Choi

  3. School of Electrical and Computer Engineering, Sungkyunkwan University, 300 Chunchun-dong, Suwon, Kyunggi-do, 440-746, South Korea

    Ilhan Park

  4. Department of Mechanical Engineering, College of Engineering, Hanyang University, Ansan, Kyungkido, 425-791, South Korea

    Daesung Bae

Authors
  1. Sangkyu Lee
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  2. Jinam Kim
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  3. Wonkyu Moon
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  4. Jinhwan Choi
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  5. Ilhan Park
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  6. Daesung Bae
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Correspondence to Wonkyu Moon.

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Lee, S., Kim, J., Moon, W. et al. A multibody-based dynamic simulation method for electrostatic actuators. Nonlinear Dyn 54, 53–68 (2008). https://doi.org/10.1007/s11071-007-9268-4

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