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Closed-form empirical relations to predict the static pull-in parameters of electrostatically actuated microcantilevers having linear width variation

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Abstract

We develop novel closed-form empirical relations to estimate the static pull-in parameters of electrostatically actuated tapered width microcantilever beams. A computationally efficient single degree-of-freedom model is employed in the setting of Ritz energy technique to extract the static pull-in parameters of the distributed electromechanical model that takes into account the effects of fringing field capacitance. The accuracy of this single-dof model together with the variable-width equivalent of the Palmer’s fringing model is established through a comparison with 3D finite element simulations. A unique surface fitting model is proposed to characterize the variations of both the pull-in displacement and pull-in voltage, over a realistically wide range of system parameters. Optimum coefficients of the proposed surface fitting model are obtained using nonlinear regression analysis. Empirical estimates of pull-in parameters are validated against finite element simulations, and available experimental and numerical data. An excellent agreement indicates that the proposed relationships are sufficiently accurate to be safely used for the electromechanical design of tapered microcantilever beams.

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Acknowledgments

The authors gratefully acknowledge the support extended by the Industrial Research and Consultancy Centre (IRCC), IIT Bombay, through Seed Grant no. 04IR0009. Authors are also thankful to T. Murali, IIT Bombay for his help in performing FE simulations.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Indian Institute of Technology Bombay, Mumbai, 400 076, India

    M. M. Joglekar & D. N. Pawaskar

Authors
  1. M. M. Joglekar
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  2. D. N. Pawaskar
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Corresponding author

Correspondence to D. N. Pawaskar.

Appendix

Appendix

In this section, we provide the details of the finite element models discussed earlier in the article (two cases in Table 1 and five cases in Table 4). In all models, quadratic tetrahedral elements are used to mesh both, the electrostatic and structural domain. Large deflection option is set off in order to have a consistent comparison between the present analysis and the FE simulations. For all cases, half width models are analyzed owing to the lateral symmetry of the beam’s cross-section. The pertinent details of the seven finite element models are listed in Table 5. The computation time indicates the time required to estimate the static pull-in parameters of the respective geometry on an Intel™ Core2Quad 2.4 GHz CPU.

Table 5 Details of finite element models and the corresponding computation time
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Joglekar, M.M., Pawaskar, D.N. Closed-form empirical relations to predict the static pull-in parameters of electrostatically actuated microcantilevers having linear width variation. Microsyst Technol 17, 35–45 (2011). https://doi.org/10.1007/s00542-010-1153-2

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