phone +7 (3412) 91 60 92

Archive of Issues

Russia Izhevsk
Section Mechanics
Title Model of the hemispherical resonator gyroscope construction damping
Author(-s) Trutnev G.A.a
Affiliations Udmurt State Universitya
Abstract This article is concerned with the hemispherical resonator gyroscope, a device for measurement of the projection of the angular speed to a device axis. The basic element of the device is a resonator in which the effect of inertness of standing waves is implemented. Various defects of materials and manufacturing techniques lead to an interaction between the main working fluctuations and collateral deformations in the location of fastening, resulting in construction damping and hence in the drift of a standing wave. Problems of constructional damping in the hemispherical resonator gyroscope and emergence of drift of a wave by means of modeling in the form of a mechanical system are investigated. A mathematical model is derived using Lagrange's approach. A mechanical system is described in Cartesian coordinates in general form for the $N+1$ mass. In the mechanical system, the central weight models a fixing leg of the resonator. A more convenient coordinate system for the description of the mechanical system is chosen. Calculations for obtaining a mathematical model in the form of a system of differential equations are carried out. The resulting mathematical model is analyzed. Avenues of further research on a construction damping and drift are described.
Keywords hemispherical resonator gyroscope, resonator, constructional damping, unbalanced mass of the resonator, drift of a wave, resonator model, mechanical systems, Lagrange's equation
UDC 531.383, 534.08, 517.934
MSC 70H03
DOI 10.20537/vm190108
Received 14 January 2019
Language Russian
Citation Trutnev G.A. Model of the hemispherical resonator gyroscope construction damping, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2019, vol. 29, issue 1, pp. 84-91.
  1. Zhuravlev V.F. Wave solid-state gyroscope: present state, some aspects, Aktual'nye Problemy Aviatsionnykh i Aerokosmicheskikh Sistem: Protsessy, Modeli, Eksperiment, 2011, vol. 16, no. 2 (33), pp. 118-123 (in Russian).
  2. Matveev V.A., Lipatnikov V.I., Alekhin A.V. Proektirovanie volnovogo tverdotel'nogo giroskopa (Designing a wave solid-state gyroscope), Moscow: Bauman Moscow State Technical University, 1998, 167 p.
  3. Trutnev G.A., Nazarov S.B., Perevozchikov K.K., Shchenyatskii A.V. Measurement calculation system “Solid-state resonator gyroscope”, Intellektual'nye Sistemy v Proizvodstve, 2017, vol. 15, no. 3, pp. 62-72 (in Russian).
  4. Bryan G.H. On the beats in the vibrations of a revolving cylinder or bell, Proceedings of the Cambridge Philosophical Society, 1890, vol. 7, pt. 3, pp. 101-111.
  5. Qiu B., Wang J., Li P. Full digital control of hemispherical resonator gyro under force-to-rebalance mode, IEEE Sensors Journal, 2015, vol. 15, issue 1, pp. 71-75.
  6. Negri C., Labarre E., Lignon C., Brunstein E., Salaún E. A new generation of IRS with innovative architecture based on HRG for satellite launch vehicles, Gyroskopiya i Navigatsiya, 2016, vol. 24, no. 1 (92), pp. 49-59 (in Russian).
  7. Meyer D., Rozelle D. Milli-HRG inertial navigation system, Gyroscopy and Navigation, 2012, vol. 3, no. 4, pp. 227-234.
  8. Lunin B.S. Fiziko-khimicheskie osnovy razrabotki polusfericheskikh rezonatorov volnovykh tverdotel'nykh giroskopov (Physical and chemical bases of the development of semispherical resonators of wave solid-state giroscopes), Moscow: Moscow Aviation Institute, 2005, 224 p.
  9. Basarab M.A., Matveev V.A., Lunin B.S., Fetisov S.V. Influence of nonuniform thickness of the hemispherical resonator gyro shell on its unbalance parameters, Giroskopiya i Navigatsiya, 2016, vol. 24, no. 4 (95), pp. 14-24 (in Russian).
  10. Yi G., Xie Y., Qi Z., Xi B. Modeling of acceleration influence on hemispherical resonator gyro forsing system, Mathematical Problems in Engineering, 2015, vol. 2015, Article ID 104041.
  11. Seregin S.V. The influence of shape imperfections on the vibrations of a ring resonator of a wave solid-state gyroscope, Russian Journal of Nonlinear Dynamics, 2017, vol. 13, no. 3, pp. 423-431 (in Russian).
  12. Wang X., Wu W., Fang Z., Luo B., Li Y., Jiang Q. Temperature drift compensation for hemispherical resonator gyro based on natural frequency, Sensors, 2012, vol. 12, issue 5, pp. 6434-6446.
  13. Zhbanov Yu.K., Kalenova N.V. Surface unbalance of a hemispherical resonator gyro, Izv. Ross. Akad. Nauk. Mekh. Tv. Tela, 2001, no. 3, pp. 11-18 (in Russian)
  14. Matveev V., Lunin B., Basarab M., Chumankin E. Balancing of metallic resonators of cylindrical vibratory gyroscopes for low and medium accuracy applications, Science and Education of the Bauman MSTU, 2013, vol. 13, no. 6, pp. 251-266 (in Russian).
  15. Klimov D.M., Zhuravlev V.F., Zhbanov Yu.K. Kvartsevyi polusfericheskii rezonator (Volnovoi tverdotel'nyi giroskop) (Quartz hemispherical resonator (Wave solid-state giroscope)), Moscow: Kim L.A., 2017. 193 p.
  16. Vakhlyarskiy D., Guskov A., Basarab M., Matveev V. Numerical study of differently shaped HRG resonators with various defects, Science and Education of the Bauman MSTU, 2016, vol. 16, no. 10, pp. 1-22 (in Russian).
  17. Trutnev G.A. The model of hemispherical resonator gyroscope in terms of slow variables, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuterniye Nauki, 2015, vol. 25, issue 3, pp. 421-429 (in Russian).
  18. Arslanova M.L., Trutnev G.A. Basics of simulation solid-state wave gyroscope resonator, Intellekt. Sist. Proizv., 2017, vol. 15, no. 3, pp. 4-17 (in Russian).
  19. Zhbanov Yu.K., Zhuravlev V.Ph. Effect of movability of the resonator center on the operation of a hemispherical resonator gyro, Mechanics of Solids, 2007, vol. 42, no. 6, pp. 851-859.
  20. Kalenova N.V. Influence of the resonator angular displacements in a hemispherical resonator gyro on the coupling between the working and beam-type vibrations, Mechanics of Solids, 2009, vol. 44, no. 5, pp. 686-690.
  21. Panovko Ya.G. Vnutrennee trenie pri kolebaniyakh uprugikh sistem (Internal friction during vibrations of elastic systems), Moscow: Fizmatlit, 1960, 193 p.
  22. Samarskii A.A., Mikhailov A.P. Matematicheskoe modelirovanie: Idei. Metody. Primery (Mathematical modeling: Ideas. Methods. Examples), Moscow: Fizmatlit, 2005, 320 p.
  23. Trutnev G.A. Sixteen points' model of hemispherical wave gyroscope, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2011, issue 2, pp. 135-146 (in Russian).
  24. Drong V., Dubinin V., Il'in M., Kolesnikov K., Kosmodem'yanskii V., Nazarenko B., Pankratov A., Rusanov P., Saratov Yu., Stepanchuk Yu., Tusheva G., Shkapov P. Kurs teoreticheskoi mekhaniki (The course of theoretical mechanics), Moscow: Bauman Moscow State Technical University, 2017, 584 p.
  25. Verzhbitskii V.M. Osnovy chislennykh metodov (Fundamentals of numerical methods), Moscow: Vysshaya shkola, 2009.
Full text
<< Previous article
Next article >>