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Thermoelastic Damping Based Design, Sensitivity Study and Demonstration of a Functional Hybrid Gyroscope Resonator for High Quality Factor

Abstract

The most critical element of Hemispherical Resonator Gyroscope (HRG) is the high quality factor (Q-factor) mechanical resonator. This paper discusses the role of thermoelastic damping (TED) on effective Q-factor. Finite element method (FEM) is used to solve this highly coupled field problem involving vibration, solid mechanics, heat transfer and thermodynamics. The major contribution of this paper is the sensitivity analysis of the effect of material property, operating temperature and dimensions to arrive at macro scale resonator configuration. Hybrid hemispherical-cylindrical configuration is proposed by studying the performance parameters such as effective mass and angular gain. The uniqueness of the present work is the sensitivity study of ultra thin film coating (volume fraction of 0.01%), coating variations and different coating configurations. The coating can reduce the Q-factor by a few orders compared to uncoated shell. It has been found that coating material selection and coating configuration are very important factors. Another significance of the present work is the realization and detailed characterization of the hybrid fused silica resonator. Thin film gold coating is done on the 3D surfaces of the realized precision resonator. Detailed coating characterization is carried out using sophisticated instruments. Very fine balancing to the order of a few mHz is achieved after coating. Q-factor measurement of the coated resonator is carried out using LDV and achieved a few millions in the final functional hybrid resonator.

About the Authors

G.N. Sharma
ISRO Inertial Systems Unit, Thiruvananthapuram, Kerala, India
India

Sharma, G.N. 



T. Sundararajan
Vikram Sarabhai Space Centre, Thiruvananthapuram, Kerala, India
India

Sundararajan T. 



G.S. Singh
Indian Institute of Technology, Guwahati, India
India

Singh, G.S. 



References

1. Xu, W., Wenqi, W., Bing, L., and Yun, L., The modelling of hemispherical gyro and its space applications, Proceedings of 7th International Symposium on Precision Engineering Measurements and Instrumentation, 2011, 8321(1), 4–9.

2. Choudhary, V. and Iniewski, K., MEMS: Fundamental technology and applications, CRC Press, 2013.

3. Joshi, S., Hung, S., and Vengallatore, S., Design strategies for controlling damping in micromechanical and nanomechanical resonators, EPJ Techniques and Instrumentation, 2014, 1(5), 1–14.

4. Imboden, M. and Mohanty, P., Dissipation in nanoelectromechanical systems, Physics Reports, 2014, 534(3), 89–146.

5. Zener, C., Internal friction in solids. I. Theory of internal friction in reeds, Physical Review, 1937, 52(3), 230–235.

6. Roszhart, T.V., The effect of thermoelastic internal friction on the Q of micromachined silicon resonators, IEEE 4th Technical Digest on Solid-State Sensor and Actuator Conference, 1990, 13–16, S.C., U.S.A.

7. Yasumura, K.Y., Stowe, T.D., Chow, E.M., Pfafman, T., Kenny, T.W., Stipe, B.C., and Rugar, D., Quality factor in micron and submicron thick cantilevers, Journal of Microelectromechanical Systems, 2000, 9(1), 117–125.

8. Lifshitz, R. and Roukes, M.L., Thermoelastic damping in micro and nano mechanical systems, Physical Review B, 2000, 61(8), 5600–5609.

9. De, S.K. and Aluru, N.R., Theory of thermoelastic damping in electrostatically actuated microstructures, Physical review B, 2006, 74(14), 144305_1–13.

10. Sun, Y., Fang, D., and Soh, A.K., Thermoelastic Damping in micro-beam resonators, International Journal of Solids and Structures, 2006, 43(10), 3213–3229.

11. Wong, S.J., Fox, C.H.J., McWilliam, S., Fell, C.P., and Eley, R., A preliminary investigation of thermoelastic damping in silicon rings, Journal of Micromechanics and Microengineering, 2004, 14(9), S108–S113.

12. Sorenson, L., Shao, P., and Ayazi, F., Bulk and surface thermoelastic dissipation in micro hemispherical shell resonators, Journal of Microelectromechanical Systems, 2015, 24(2), 486–502.

13. Sandberg, R., Molhave, K., Boisen, A., and Svendsen, W., Effect of gold coating on the Q factor of a resonant cantilever, Journal of Micromechanics and Microengineering, 2005, 15(12), 2249–2253.

14. Darvishian, A., Shiari, B., Cho, J.Y., Nagourney, T., and Najafi, K., Investigation of thermoelastic loss mechanism in shell resonators, Proceedings of ASME International Mechanical Engineering Congress and Exposition, 2014, 39331–39336, Canada.

15. Darvishian, A., Nagourney, T., Cho, J.Y., Shiari, B., and Najafi, K., Thermoelastic dissipation in micromachined birdbath shell resonators, Journal of Microelectromechanical Systems, 2017, 26(4), 758–772.

16. Abdolvand, R., Johari, H., Ho, G.K., Erbil, A., and Ayazi, F., Quality factor in trench-refilled polysilicon beam resonators, Journal of Microelectromechanical Systems, 2006, 15(3), 471–478.

17. ComsolMultiphysicsver 5.3, COMSOL Inc., Massachusetts, U.S.A.

18. Sharma, N.G., George, A., Pandian, S.P., Sundararajan T., and Gautam S.S., Design of inertial class gyroscope resonator with ultra high quality factor for interplanetary space missions, Advances in Mechanical Engineering, Lecture notes in mechanical engineering, 2020, Springer, 1071–1084.

19. Wong, S.J., Fox, C.H.J., and McWilliam, S., Thermo elastic damping of the in-plane vibration of thin silicon rings, Journal of Sound and Vibration, 2006, 293(1–2), 266–285.

20. Lunin, B.S., Basarab, M.A., Matveev, V.A., Yurin, A.V., Resonator materials for Coriolis vibratory gyroscopes, 22nd Saint Petersburg International Conference on Integrated Navigation Systems proceedings, 2015, 383–386.

21. Penn, S.D., Harry, G.M., Gretarsson, A.M., Kittelberger, S.E., Saulson, P.R., Schiller, J.J., Smith, J.R., and Swords, S.O., High quality factor measured in fused silica, Review of Scientific Instruments, 2001, 72(9), 3670–3673.

22. Ageev, A., Palmer, B.C., Felice, A.D., Penn, S.D., and Saulson, P.R., Very high quality factor measured in annealed fused silica, Classical and Quantum Gravity, 2004, 21(16), 3887–3892.

23. Guzman, L., Miotello, A., Checchetto, R., and Adami, M., Ion beam induced enhanced adhesion of gold films deposited on glass, Surface and Coatings Technology, 2002, 158, 558–562.

24. Nagourney, T., Cho, J.Y., Darvishian, A., Shiari, B., and Najafi, K., Effect of metal annealing on the Q factor of metal coated fused silica micro shell resonators, Proceedings of IEEE International Symposium on Inertial Sensors and Systems, 2015, 1–5, Hapuna, U.S.A.

25. Li, T.J., and Bellon, L., Dissipation of micro-cantilevers as a function of air pressure and metallic coating, Europhysics Letters, 2011, 98(1), 14004_1–4.

26. Hwang, J.J., Chou, C.S., and Chang, C., Precession of vibrational modes of a rotating hemispherical shell, ASME Journal of Vibration and Acoustics, 1997, 119(4), 612–617.

27. Sharma, N.G., Sundararajan T., and Gautam S.S., Effect of geometric imperfections on anchor loss and characterization of a gyroscope resonator with high quality factor, Gyroscopy and Navigation, 2020, 11(3), 206–213.

28. Martin, P.J., Ion enhanced adhesion of thin gold films. Gold bulletin, 1986, 19(4), 102–116.

29. Nazemian, M. and Chamani, M., Experimental investigation and finite element simulation of the effect of surface roughness on nanoscratch testing, Journal of Mechanical Science and Technology, 2019, 33(5), 2331–2338.

30. Jeanroy, A., Bouvet, A., and Remillieux, G., HRG and marine applications, Gyroscopy and Navigation, 2014, 5(2), 67–74.


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For citations:


Sharma G., Sundararajan T., Singh G. Thermoelastic Damping Based Design, Sensitivity Study and Demonstration of a Functional Hybrid Gyroscope Resonator for High Quality Factor. Gyroscopy and Navigation. 2021;29(1):70-96. (In Russ.)

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ISSN 0869-7035 (Print)
ISSN 2075-0927 (Online)