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The squeeze-film air damping of circular and elliptical micro-torsion mirrors

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Abstract

This paper proposes an analytical solution to calculate the squeeze-film air damping of circular and elliptical micro-torsion mirrors. To derive the expressions of squeeze-film air-damping torque, the nonlinear Reynolds equation, which governs the air behavior of torsion mirror, is solved by the method of eigenfunction expansions in polar coordinate and elliptical coordinate, respectively. The series solutions are integrated and summed up to deduce the damping torque of circular and elliptical torsion mirrors. The formulas of circular mirror and elliptical mirror are deduced independently, and their results match when the eccentricity of the elliptical mirror approaches zero. Besides, the results of the formulas are consistent with numerical simulation. Both of them verifies the damping torque formulas in this paper.

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Acknowledgments

We gratefully acknowledge Dr. Hui Fang for helpful suggestions. And this research was supported by the National Natural Science Foundation of China (Grant Nos. 51375399, 51375400), the Fundamental Research Funds for the Central Universities (3102014KYJD023) and NPU Foundation for Fundamental Research (Grant No. JCY20130119).

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Authors and Affiliations

  1. Key Laboratory of Micro/Nano Systems for Aerospace, Ministry of Education, Northwestern Polytechnical University, Xi’an, 710072, China

    Changfeng Xia, Dayong Qiao, Qi Zeng & Weizheng Yuan

  2. Shaanxi Province Key Laboratory of Micro and Nano Electro-Mechanical Systems, Northwestern Polytechnical University, Xi’an, 710072, China

    Changfeng Xia, Dayong Qiao, Qi Zeng & Weizheng Yuan

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  1. Changfeng Xia
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  2. Dayong Qiao
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  3. Qi Zeng
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  4. Weizheng Yuan
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Correspondence to Dayong Qiao.

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Xia, C., Qiao, D., Zeng, Q. et al. The squeeze-film air damping of circular and elliptical micro-torsion mirrors. Microfluid Nanofluid 19, 585–593 (2015). https://doi.org/10.1007/s10404-015-1585-1

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  • DOI: https://doi.org/10.1007/s10404-015-1585-1

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