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Thermoelastic Dissipation in Diamond Micro Hemispherical Shell Resonators

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Abstract

Maximizing quality factor (Q) is essential to improve the performance of micro hemispherical shell resonators (μHSRs) which can be used in microelectromechanical system (MEMS) gyroscopes to measure angular rotation. Several energy dissipation mechanisms limit Q, where thermoelastic dissipation (TED) is the major one and studied in this paper. Fully coupled thermo-mechanical equations for calculating TED are formulated, and then temperature distribution in a deformed μHSR and its quality factor related to TED (QTED) are obtained by solving the equations through a finite-element method (FEM). It has been found that different fabrication process conditions can obtain various geometrical parameters in our previous studies. In order to provide guidelines for the design and fabrication of μHSRs, the effects of their geometry on resonant frequency (f0) and QTED are studied. The change of anchor height and small enough anchor radius have no effect on both f0 and QTED, but the shell size including its radius, thickness and height has significant impact on f0 and QTED. It is found that whether a μHSR has lower f0 and higher QTED or higher f0 and higher QTED can be achieved by changing these geometrical parameters. The results presented in this paper can also be applied to other similar resonators.

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References

  1. TRUSOV A A, PHILLIPS M R, MCCAMMON G H, et al. Continuously self-calibrating CVG system using hemispherical resonator gyroscopes [C]//2015 IEEE International Symposium on Inertial Sensors and Systems (ISISS). Hapuna Beach, USA: IEEE, 2015: 15112569.

    Google Scholar 

  2. CHALLONER A D, GE H H, LIU J Y. Boeing disc resonator gyroscope [C]//2014 IEEE/ION Position, Location and Navigation Symposium. Monterey, USA: IEEE, 2014: 504–514.

    Google Scholar 

  3. DARVISHIAN A, NAGOURNEY T, CHO J Y, et al. Thermoelastic dissipation in micromachined birdbath shell resonators [J]. Journal of Microelectromechanical Systems, 2017, 26(4): 758–772.

    Article  Google Scholar 

  4. SORENSON L, SHAO P, AYAZI F. Bulk and surface thermoelastic dissipation in micro-hemispherical shell resonators [J]. Journal of Microelectromechanical Systems, 2015, 24(2): 486–502.

    Article  Google Scholar 

  5. KONG L, Research on structural mechanism and fabrication process of micro hemispherical resonator gyroscope [D]. Nanjing, China: Southeast University, 2015 (in Chinese).

    Google Scholar 

  6. BASARAB M A, MATVEEV V A, LUNIN B S, et al. Influence of nonuniform thickness of hemispherical resonator gyro shell on its unbalance parameters [J]. Gyroscopy and Navigation, 2017, 8(2): 97–103.

    Article  Google Scholar 

  7. FAN S C, LIU G Y, WANG Z J. On flexural vibration of hemispherical shell [J]. Applied Mathematics and Mechanics, 1991, 12(10): 1023–1030.

    Article  Google Scholar 

  8. BERNSTEIN J J, BANCU M G, COOK E H, et al. A MEMS diamond hemispherical resonator [J]. Journal of Micromechanics & Microengineering, 2013, 23(12): 125007.

    Article  Google Scholar 

  9. LIU Z Y, ZHANG W P, CUI F, et al. Fabrication and characterisation of microscale hemispherical shell resonator with diamond electrodes on the Si substrate [J]. Micro & Nano Letters, 2019, 14(6): 674–677.

    Article  Google Scholar 

  10. JIAO W J, SONG J, GUO F G. Thermoelastic damping of micro resonators operating in the longitudinal vibration mode: In comparison with the case of flexural vibration [J]. Mechanics Research Communications, 2014, 62: 31–36.

    Article  Google Scholar 

  11. HAO Z L. Thermoelastic damping in the contour-mode vibrations of micro- and nano-electromechanical circular thin-plate resonators [J]. Journal of Sound and Vibration, 2008, 313(1/2): 77–96.

    Article  Google Scholar 

  12. DARVISHIAN A, SHIARI B, CHO J Y, et al. Investigation of thermoelastic loss mechanism in shell resonators [C]//ASME 2014 International Mechanical Engineering Congress and Exposition. Montreal, Canada: American Society of Mechanical Engineers, 2014: 39331.

    Google Scholar 

  13. LIFSHITZ R, ROUKES M L. Thermoelastic damping in micro- and nanomechanical systems [J]. Physical Review B, 2000, 61(8): 5600–5609.

    Article  Google Scholar 

  14. WONG S J, FOX C H J, MCWILLIAM S. Thermoelastic damping of the in-plane vibration of thin silicon rings [J]. Journal of Sound and Vibration, 2006, 293(1): 266–285.

    Article  Google Scholar 

  15. PAI P, CHOWDHURY F K, POURZAND H, et al. Fabrication and testing of hemispherical MEMS wineglass resonators [C]//2013 IEEE 26th International Conference on Micro Electro Mechanical Systems (MEMS). Taipei, China: IEEE, 2013: 677–680.

    Chapter  Google Scholar 

  16. CHO J Y. High-performance micromachined vibratory rate- and rate-integrating gyroscopes [D]. Michigan, USA: The University of Michigan, 2012.

    Google Scholar 

  17. SORENSON L D, SHAO P, AYAZI F. Effect of thickness anisotropy on degenerate modes in oxide microhemispherical shell resonators [C]//2013 IEEE 26th International Conference on Micro Electro Mechanical Systems (MEMS). Taipei, China: IEEE, 2013: 169–172.

    Chapter  Google Scholar 

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Acknowledgment

The authors would like to thank the cleanroom staff at the Center for Advanced Electronic Materials and Devices (AEMD) of Shanghai Jiao Tong University for their help in the device fabrication.

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Authors and Affiliations

  1. National Key Laboratory of Science and Technology on Micro/Nano Fabrication, Shanghai Jiao Tong University, Shanghai, 200240, China

    Jun Feng  (冯军), Weiping Zhang  (张卫平), Zhaoyang Liu  (刘朝阳) & Liutao Gu  (谷留涛)

  2. Department of Micro/Nano Electronics, School of Electronic Information and Electrical Engineering, Shanghai Jiao Tong University, Shanghai, 200240, China

    Jun Feng  (冯军), Weiping Zhang  (张卫平), Zhaoyang Liu  (刘朝阳) & Liutao Gu  (谷留涛)

  3. Shanghai Aerospace Control Technology Institute, Shanghai, 200233, China

    Yuxiang Cheng  (成宇翔)

Authors
  1. Jun Feng  (冯军)
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  2. Weiping Zhang  (张卫平)
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  3. Zhaoyang Liu  (刘朝阳)
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  4. Liutao Gu  (谷留涛)
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  5. Yuxiang Cheng  (成宇翔)
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Corresponding author

Correspondence to Weiping Zhang  (张卫平).

Additional information

Foundation item: the National Natural Science Foundation of China (No. 61574093), the National Key Laboratory of Science and Technology on Nano/Micro Fabrication (No. 614280504010317), the Aerospace Science and Technology Innovation Fund (No. 16GFZJJ01- 309), the Space Advanced Technology Joint Research Innovation Fund (No. USCAST2016-5), and the Professional Technical Service Platform of Shanghai (No. 19DZ2291103)

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Feng, J., Zhang, W., Liu, Z. et al. Thermoelastic Dissipation in Diamond Micro Hemispherical Shell Resonators. J. Shanghai Jiaotong Univ. (Sci.) 25, 281–287 (2020). https://doi.org/10.1007/s12204-020-2182-3

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  • DOI: https://doi.org/10.1007/s12204-020-2182-3

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