Finite-Element Simulation of the Eigen Frequency Spectrum of the Cylindrical Resonator with Geometrical Imperfectness

The solid-state wave gyroscope belongs to the class of the so-called Coriolis vibratory gyroscopes. They are industrially produced, as a rule, in two versions: precise solid-state wave gyroscopes with expensive fused quartz resonators, and devices of low accuracy with metal resonators. The use of metal for the manufacture of a solid-state wave gyroscope resonator for inertial systems of medium and low accuracy can significantly simplify the design of the device and reduce its cost, however, the low-quality factor of the metal resonator and the instability of its dissipative characteristics limit the accuracy characteristics of the solid-state wave gyroscope. The use of high-quality precision fused quartz glass resonators in such solid-state wave gyroscopes is unacceptable because of their high cost. The purpose of the work is to study the characteristics of inexpensive quartz resonators made from industrially produced fused quartz tubes, with the aim of creating a medium-accuracy solid-state wave gyroscope. Using the finite element method, the main types of geometric heterogeneities arising from the production of such resonators and their influence on their spectral characteristics are investigated. The experimental results allow us to draw conclusions about the most significant defects affecting the performance and accuracy of the solid-state wave gyroscopes

References

[1] Remilliex G., Delhaye F. Sagem Coriolis Vibrating Gyros: a vision realized. DGON ISS, 2014. DOI: 10.1109/InertialSensors.2014.7049409

[2] Tactical grade gyroscopes. innalabs.com: website. Available at: http://www.innalabs.com/product-category/tactical-grade-gyroscopes (accessed: 21.03.2020).

[3] Lunin B.S., Basarab M.A., Yurin A.V., et al. Fused quartz cylindrical resonators for low-cost vibration gyroscopes. 25th ICINS, 2018, pp. 291--294. DOI: https://doi.org/10.23919/ICINS.2018.8405896

[4] Lunin B., Basarab M., Chumankin A., et al. Quartz cylindrical resonators for mid-accuracy Coriolis vibratory gyroscopes. Proc. IEEE INERTIAL, 2018, pp. 34--36. DOI: https://doi.org/10.1109/ISISS.2018.8358120

[5] Basarab M.A., Lunin B.S., Chumankin E.A. Tsilindricheskiy resonator [Cylindric resonator]. Patent RF 187272. Appl. 28.11.2018, publ. 28.02.2019 (in Russ.).

[6] Novozhilov V.V. Teoriya tonkikh obolochek [Theory of thin shells]. St. Petersburg, SPBU Publ., 2010.

[7] Xu Z., Yi G., Qi Z., et al. Structural optimization research on hemispherical resonator gyro based on finite element analysis. 35th Chinese Control Conference (CCC), 2016, pp. 5737--5742.

[8] Wei Z., Yi G., Huo Y., et al. The synthesis model of flat-electrode hemispherical resonator gyro. Sensors, 2019, vol. 19, iss. 7, art. 1690. DOI: https://doi.org/10.3390/s19071690

[9] Gao S., Wu J. Theory and finite element analysis of HRG. 2007 Int. Conf. Mechatronics and Automation, 2007, pp. 2768--2772. DOI: https://doi.org/10.1109/ICMA.2007.4303997

[10] Pai P., Chowdhury F.K., Pourzand H., et al. Fabrication and testing of hemispherical MESM wineglass resonators. MEMS, 2013, pp. 677--680. DOI: https://doi.org/10.1109/MEMSYS.2013.6474333

[11] Lunin B.S., Basarab M.A., Matveev V.A., et al. Resonator materials for Coriolis vibratory gyroscopes. Proc. 22th Saint Petersburg Int. Conf. on Integrated Navigation Systems. St. Petersburg, 2015, Concern CSRI "Elektropribor", pp. 379--382 (in Russ.)

[12] Basarab M.A., Lunin B.S., Matveev V.A., et al. Miniature gyroscope based on elastic waves in solids for small spacecraft. Herald of the Bauman Moscow State Technical University, Series Instrument Engineering, 2014, no. 4 (97), pp. 80--96 (in Russ.).

[13] Matveev V.A., Basarab M.A., Lunin B.S., et al. Development of the theory of cylindrical vibratory gyroscopes with metallic resonators. Vestnik RFFI [Russian Foundation for Basic Research Journal], 2015, no. 3 (87), pp. 84--96 (in Russ.).

[14] Naraykin O.S., Sorokin F.D., Kozubnyak S.A., et al. Numerical simulation of elastic wave precession in the cylindrical resonator of a hemispherical resonator gyroscope featuring a non-homogeneous density distribution. Herald of the Bauman Moscow State Technical University, Series Mechanical Engineering, 2017, no. 5 (116), pp. 41--51 (in Russ.). DOI: https://doi.org/10.18698/0236-3941-2017-5-41-51

[15] Pan Y., Wang D., Wang Y., et al. Monolithic cylindrical fused silica resonators with high Q factors. Sensors, 2016, vol. 16, iss. 8, art. 1185. DOI: https://doi.org/10.3390/s16081185

[16] Vakhlyarskiy D.S., Guskov A.M., Basarab M.A., et al. Using a combination of FEM and perturbation method in frequency split calculation of a nearly axisymmetric shell with middle surface shape defect. Nauka i obrazovanie: nauchnoe izdanie MGTU im. N.E. Baumana [Science and Education: Scientific Publication], 2016, no. 5 (in Russ.). DOI: http://dx.doi.org/10.7463/0516.0839190

[17] Vakhlyarskiy D.S., Guskov A.M., Basarab M.A., et al. Numerical study of differently shaped HRG resonators with various defects. Nauka i obrazovanie: nauchnoe izdanie MGTU im. N.E. Baumana [Science and Education: Scientific Publication], 2016, no. 10 (in Russ.). DOI: http://dx.doi.org/10.7463/1016.0848188

[18] Lunin B.S., Yurin A.V., Basarab M.A., et al. Thermoelastic losses in structural materials of wave solid-state gyroscope resonators. Herald of the Bauman Moscow State Technical University, Series Instrument Engineering, 2015, no. 2 (101), pp. 28--39 (in Russ.). DOI: https://doi.org/10.18698/0236-3933-2015-2-28-39

[19] Mitchell A.R., Wait R. The finite element method in partial differential equations. Wiley, 1977.

[20] COMSOL Multiphysics® Modeling Software. Available at: http://www.comsol.com (accessed: 21.03.2020).

[21] Chumankin E.A., Lunin B.S., Basarab M.A. Features of balancing metal resonators of solid-state wave gyroscopes. Dinamika slozhnykh sistem --- XXI vek [Dynamics of Complex Systems --- XXI century], 2018, no. 4, pp. 85--95 (in Russ.).