Nonlinear dynamics of cylindrical resonator of wave solid-state gyroscope with electromagnetic control sensors

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The article considers the nonlinear dynamics of a cylindrical resonator of a wave solid-state gyroscope with electromagnetic control sensors. A mathematical model that describes nonlinear resonator oscillations and electrical processes of the oscillation control circuit in an interconnected form is deduced. The resulting mathematical model represents a nonlinear system of differential equations, which contains singularly perturbed equations, and the equations of electrical processes are singularly perturbed. The nonlinearity caused by the finite ratio of the small deflection to the small gap of the control sensor is taken into account. The methods of constructing approximate solutions are proposed. The fundamental difference between the nonlinear terms of the equations of resonator dynamics using eight and sixteen control sensors is shown. It is shown that by using electromagnetic control sensors it is necessary to take into account a small parameter singularly included in the differential equations of electrical processes. According to the estimation of the angular drift velocity, it is concluded that the gyroscope circuit with eight electromagnetic control sensors is inapplicable due to the obtained value of the uncompensated angular drift velocity. In the case of a gyroscope with sixteen control sensors, a formula for the angular drift velocity which can be compensated is derived and a method for calculating the displacement of the resonant peak of the amplitude-frequency response is proposed.

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作者简介

D. Maslov

National Research University “Moscow Power Engineering Institute” (MPEI)

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Email: MaslovDmA@mpei.ru
俄罗斯联邦, Moscow

参考

  1. Perelyaev S.E. Review and analysis of the lines of development of strapdown inertial navigation systems on the basis of hemispherical resonator gyroscopes // Novosti Navig. 2018. № 2. P. 21–27.
  2. Perelyaev S.E. Current State of Wave Solid-State Gyroscopes. Development Prospects in Applied Gyroscopy // Proc. of 2023 30th Saint Petersburg International Conference on Integrated Navigation Systems (ICINS) (Kontsern TsNII Elektropribor, St. Petersburg, 2023). P. 500–505. https://doi.org/10.23919/ICINS51816.2023.10168310
  3. Peshekhonov V.G. The outlook for gyroscopy // Gyroscopy Navig. 2020. V. 11. № 3. P. 193–197. https://doi.org/10.1134/S2075108720030062
  4. Maslov A.A., Maslov D.A., Merkuryev I.V., Ninalalov I.G. Hemispherical Resonator Gyros (An Overview of Publications) // Gyroscopy Navig. 2023. V. 14. № 1. P. 1–13. https://doi.org/10.1134/S2075108723010054
  5. Klimov D.M., Zhuravlev V.Ph., Zbanov Yu.K. Quartz Hemispherical Resonator (Wave-Based Solid-State Gyroscope). M.: “Kim L.A., 2017 [in Russian].
  6. Zhuravlev V.Ph., Klimov D.M. Wave Solid-State Gyroscope. M.: Nauka, 1985 [in Russian].
  7. Zhuravlev V.Ph. Theoretical foundations of solid-state wave gyroscopes // Mech. Solids. 1993. V. 28. № 3. P. 3–15.
  8. Zhuravlev V.Ph., Lynch D.D. Electric model of a hemispherical resonator gyro // Mech. Solids. 1995. V. 30. № 5. P. 10–21.
  9. Zhuravlev V.Ph. Global evolution of state of the generalized Foucault pendulum // Mech. Solids. 1998. V. 33. № 6. P. 3–8.
  10. Zhuravlev V.Ph. Identification of errors of the generalized Foucault pendulum // Mech. Solids. 2000. V. 35. № 5. P. 155–160.
  11. Zhbanov Yu.K., Zhuravlev V.Ph. On the balancing of a hemispherical resonator gyro // Mech. Solids. 1998. V. 33. № 4. P. 2–13.
  12. Zhuravlev V.Ph. Drift of an imperfect hemispherical resonator gyro // Mech. Solids. 2004. V. 39. № 4. P. 15–18.
  13. Klimov D.M. On the motion of an elastic inextensible ring // Mech. Solids. 2021. V. 56. P. 930–931. https://doi.org/10.3103/S002565442106008X
  14. Maslov A.A., Maslov D.A., Merkuryev I.V. Nonlinear effects in dynamics of cylindrical resonator of wave solid-state gyro with electrostatic control system // Gyroscopy Navig. 2015. V. 6. P. 224–229. https://doi.org/10.1134/S2075108715030104
  15. Maslov D.A., Merkuryev I.V. Increase in the accuracy of the parameters identification for a vibrating ring microgyroscope operating in the forced oscillation mode with nonlinearity taken into account // Rus. J. Nonlin. Dyn. 2018. V. 14. № 3. P. 377–386. https://doi.org/10.20537/nd180308
  16. Maslov D.A., Merkuryev I.V. Impact of nonlinear properties of electrostatic control sensors on the dynamics of a cylindrical resonator of a wave solid-state gyroscope // Mech. Solids. 2021. V. 56. P. 960–979. https://doi.org/10.3103/S002565442106011X
  17. Maslov D.A. Nonlinear Dynamics of a Wave Solid-State Gyroscope Taking into Account the Electrical Resistance of an Oscillation Control Circuit // Rus. J. Nonlin. Dyn. 2023. V. 19. № 3. P. 409–435. https://doi.org/10.20537/nd230602
  18. Maslov A.A., Maslov D.A., Merkuryev I.V. Studying stationary oscillation modes of the gyro resonator in the presence of positional and parametric excitations // Gyroscopy Navig. 2014. V. 5. P. 224–228. https://doi.org/10.1134/S2075108714040099
  19. Maslov A.A., Maslov D.A., Merkuryev I.V. Accounting for Nonlinearity of Resonator Oscillations in the Identification of Parameters of Solid-State Wave Gyroscopes of Different Types // Mech. Solids. 2022. V. 57. P. 1300–1310. https://doi.org/10.3103/S0025654422060073
  20. Maslov A.A., Maslov D.A., Merkuryev I.V. How the reference voltage of electromagnetic control sensors affects the drift of wave solid-state gyroscopes // Gyroscopy Navig. 2016. V. 7. P. 231–238. https://doi.org/10.1134/S2075108716030032
  21. Roginskii V.D., Yurmanov S.Yu., Denisov R.A. The method for exciting oscillations in the HRG sensor and the device to implement it. Patent 2518632 RF, Byull. no. 16, 2014.
  22. Salaberry B. Vibrating Gyroscope with Electromagnetic Excitation and Detection. Рat. 6443009 USA, 2002.
  23. Basarab M.A., Lunin B.S., Matveev V.A. Static balancing of metal resonators of cylindrical resonator gyroscopes // Gyroscopy Navig. 2014. V. 5. P. 213–218. https://doi.org/10.1134/S2075108714040038
  24. Raspopov V.Y., Likhosherst V.V. HRG with a Metal Resonator // Gyroscopy Navig. 2023. V. 14. № 1. P. 14–26. https://doi.org/10.1134/S2075108723010066
  25. Kachalov V.I. On the holomorphic regularization of singularly perturbed systems of differential equations // Comput. Math. and Math. Phys. 2017. V. 57. № 4. P. 653–660. https://doi.org/10.1134/S0965542517040054
  26. Kachalov V.I. On One Method of Solving Singularly Perturbed Systems of Tikhonov’s Type // Russian Mathematics. 2018. V. 62. № 6. P. 21–26. https://doi.org/10.3103/S1066369X18060038
  27. Besova M.I., Kachalov V.I. Analytical Aspects of the Theory of Tikhonov Systems // Mathematics. 2022. V. 10. № 1. P. 72. https://doi.org/10.3390/math10010072
  28. Maslov D.A. The holomorphic regularization method of Tikhonov differential equations system for mathematical modelling of the wave solid-state gyroscope dynamics // Rus. J. Nonlin. Dyn. 2025. Vol. 21. № 2. P. 233–248. https://doi.org/10.20537/nd241106
  29. Filin A.P. Elements of the Theory of Shells. Leningrad: Stroyizdat, 1975 [in Russian].
  30. Vlasov V.Z. Selected Works, V. 1: The General Theory of Shells. M.: AN SSSR, 1962 [in Russian].
  31. Egarmin N.E. On precession of standing waves of vibrations of a rotating axisymmetric shell // Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela. 1986. № 1. P. 142–148.
  32. Tikhonov A.N., Vasilyeva A.B., Sveshnikov A.G. Differential Equations. M.: Fizmatlit, 2005 [in Russian].
  33. Zhuravlev V.Ph., Klimov D.M. Applied Methods in Vibration Theory. M.: Nauka, 1988 [in Russian].
  34. Merkuryev I.V., Podalkov V.V. Dynamics of Micromechanical and Wave Solid-State Gyroscopes. M.: Fizmatlit, 2009 [in Russian].

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2. Fig. 1. Calculation scheme of a wave solid-state gyroscope.

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3. Fig. 2. Graphs of the difference DY1(0) = y1* – Y1[0] – solid line, DY1(1) = y1* – (Y1[0] + eY1[1]) – dotted line.

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