Abstract—The paper addresses a hemispherical resonator gyroscope (HRG) with flat electrodes applied in the vehicle control and navigation. In order to enhance the gyro accuracy, we formulate the problem of constructing a new mathematical model describing the nonlinearities of the electromechanical system controlling the hemispherical resonator oscillations. The mathematical model of the resonator dynamics is based on Lagrange−Maxwell differential equations. The obtained nonlinear model is studied with the asymptotic Krylov−Bogolyubov averaging method. The reference voltage on flat control electrodes is shown to arouse systematic drift and changes in the resonance frequency. The provided example demonstrates the influence of reference voltage on the gyro drift and reduction in the resonator oscillation frequency.
Notes
HRG is also referred to as wave solid-state gyroscope (WSG) in Russian publications.
REFERENCES
Peshekhonov, V.G., The outlook for gyroscopy, Gyroscopy and Navigation, 2020, vol. 11, no. 3, pp. 193–197. https://doi.org/10.1134/S2075108720030062
Maslov, A.A., Maslov, D.A., Ninalalov, I.G., and Merkuryev, I. V., Hemispherical resonator gyros (An overview of publications), Gyroscopy and Navigation, 2023, vol. 14, no. 1. https://doi.org/10.1134/S2075108723010054
Perelyaev, S.E., Current state and scientific and technical forecast of the perspective application of foreign hemispherical resonator gyros (Analytical review of foreign materials), Novosti navigatsii, 2020, no. 3, pp. 14–28.
Perelyaev, S.E., Current status of wave solid-state gyroscopes. development prospects in applied gyroscopy, Anniversary 30th International Conference on Integrated Navigation Systems, St. Petersburg, 2023.
Matveev, V.A., Lunin, B.S., and Basarab, M.A., Navigatsionnye sistemy na volnovykh tverdotel’nykh giroskopakh (Navigation Systems on Wave Solid-State Gyros), Moscow: Fizmatlit, 2008.
Bodunov, B.P., Bodunov, S.B., Lopatin, V.M., and Chuprov, V.P., Development and tests of a wave solid-state gyro applied in inclinometric system, Giroskopiya i navigatsiya, 2001, no. 3, pp. 74–82.
Delhaye, F., SpaceNaute® the HRG Based Inertial Reference System of Ariane 6 European space launcher, Gyroscopy and Navigation, 2019, vol. 10, no. 1, pp. 1–6. https://doi.org/10.1134/S2075108719010036
Jeanroy, A., Bouvet, A., and Remillieux, G., HRG and marine applications, Gyroscopy and Navigation, 2014, vol. 5, no. 2, pp. 67–74. https://doi.org/10.1134/S2075108714020047
Raspopov, V.Ya. and Likhosherst, V.V., HRG with a metal resonator, Gyroscopy and Navigation, 2023, vol. 14, no. 1. https://doi.org/10.1134/S2075108723010066
Lunin, B.S., Matveev, V.A., and Basarab, M.A., Volnovoi tverdotel’nyi giroskop. Teoriya i tekhnologiya (Wave Solid-State Gyroscope. Theory and Technology), Moscow: Radiotekhnika, 2014.
Klimov, D.M., Zhuravlev, V.F., and Zhbanov, Yu.K., Kvartsevyi polusfericheskii resonator (volnovoi tverdotel’nyi giroskop) (Quartz Hemispherical Resonator of a HRG), Moscow: Kim L.A., 2017.
Zhurvalev, V.F. and Lynch, D.D., Electrical model of a hemispherical resonator gyroscope, Izvestiya RAN. Mekhanika tverdogo tela, 1995, no. 5, pp. 12–24.
Wei, Z., Yi, G., Huo, Y., Qi, Z., and Xu, Z., The synthesis model of flat-electrode hemispherical resonator gyro, Sensors, 2019, vol. 19, no. 7, 1690. https://doi.org/10.3390/s19071690
Maslov, A.A., Maslov, D.A., and Merkuryev, I.V., Nonlinear effects in dynamics of cylindrical resonator of wave solid-state gyro with electrostatic control system, Gyroscopy and Navigation, 2015, vol. 6, no. 3, pp. 224–229. https://doi.org/10.1134/S2075108715030104
Maslov, D.A. and Merkuryev, I.V., Impact of nonlinear properties of electrostatic control sensors on the dynamics of a cylindrical resonator of a wave solid-state gyroscope, Mechanics of Solids, 2021, vol. 56, no. 6, pp. 960–979. https://doi.org/10.3103/S002565442106011X
Maslov, A.A., Maslov, D.A., Merkuryev, I.V., and Podalkov, V.V., Methods to eliminate nonlinearity of electrostatic control sensors of the wave solid-state gyroscope, Anniversary 25th International Conference on Integrated Navigation Systems, St. Petersburg, 2018.
Denisov, R.A., Maslov, A.A., Maslov, D.A., Merkuryev, I.V., and Podalkov, V.V., How the reference voltage of electromagnetic control sensors affects the drift of wave solid-state gyroscopes, Gyroscopy and Navigation, 2016, vol. 7, no. 3, pp. 231–238. https://doi.org/10.1134/S2075108716030032
Maslov, A.A., Maslov, D.A., Merkuryev, I.V., and Mikhailov, D.V., On the drift of a wave solid-state gyroscope under the presence of reference voltage on the control electrodes, Vestnik MEI, 2013, no. 2, pp. 11–14.
Maslov, A.A., Maslov, D.A., and Merkuryev, I.V., The effect of the reference voltage on the drift of a wave solid-state gyroscope with flat electrodes, Anniversary 30th International Conference on Integrated Navigation Systems, St. Petersburg, 2023.
Strutt, J.W. (Lord Rayleigh), The Theory of Sound, vol. 1, Dover Publications, 1945.
Matveev, V.A., Lipatnikov, V.I., and Alekhin, A.V., Proektirovanie volnovogo tverdotel’nogo giroskopa (Designing a Wave Solid-State Gyro), Moscow: Bauman Moscow Technical University, 1997.
Filin, A.P., Elementy teorii obolochek (Elements of Shell Theory), Leningrad: Stroiizdat, 1987.
Martynenko, Yu.G., Analiticheskya dinamika elektromekhanicheskikh system (Analytical Dynamics of Electromechanical Systems), Moscow: MEI, 1984.
Tikhonov, A.N., Vasil’eva, A.B., and Sveshni-kov, A.G., Differentsial’nye uravneniya (Differential equations), Moscow: Fizmatlit, 2005.
Bogolyubov, N.N. and Mitropolskii, Yu.A, Asimptoticheskie metody v teorii nelineinykh kolebanii (Asymptotic Methods in the Theory of Nonlinear Oscillations), Moscow: Nauka, 1974.
Funding
The research has been supported by the Russian Science Foundation, grant no. 23-21-00546.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
The authors of this work declare that they have no conflicts of interest.
Additional information
Publisher’s Note.
Pleiades Publishing remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Maslov, A.A., Maslov, D.A. & Merkuryev, I.V. Nonlinear Effects in the Dynamics of HRG with Flat Electrodes. Gyroscopy Navig. 14, 320–327 (2023). https://doi.org/10.1134/S2075108724700044
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S2075108724700044