Advanced Motion Parameter Sensors Based on Standing Wave Inertia

Miniaturization and increased accuracy of orientation and navigation systems for controlling mobile objects are a pressing task for the aviation, space, transport, and oil and gas industries. A promising solution to this problem is the application of wave solid-state gyroscopes (WSG), which detect object rotations by utilizing the phenomenon of standing wave inertia, excited in ring or bulk resonators. It is shown that WSGs can have various resonator configurations (ring, cylindrical, conical, hemispherical) and be made of various structural materials. Examples of ring silicon resonators are given. It is shown that WSG resonators made of metal alloys (ring, cylindrical or conical) allow creating sensors of the middle accuracy class. Navigationclass WSG are implemented on the basis of quartz cylindrical or hemispherical resonators, the time constant of which can reach up to 1000 s or more. It is shown that on the basis of WSG it is possible to create two types of sensors: angular displacement meters and angular velocity sensors. The mathematical model of the WSG, identical to the equations of the classical Foucault pendulum, is presented. It is applicable for describing sensors of both types. The efficiency of using equations for the envelopes of oscillation amplitudes in describing the dynamic characteristics of the WSG is demonstrated. It is found that for the WSG of direct measurement, operating in the angular velocity sensor mode, an increase in the resonator quality factor increases its sensitivity to the angular velocity, but reduces the response time. Based on the vector diagram, the processes occurring in the WSG with the Coriolis acceleration compensation circuit are explained. A generalized mathematical model of the compensation-type WSG is presented, taking into account the processes of demodulation, modulation and the proportional-integral law of standing wave control. It is shown that the time constant of the compensation-type WSG is determined by the coefficient of the integral part of the controller.

1. Maslov AA, Maslov DA, Ninalalov IG, Merkur'yev IV. Wave solid-state gyroscopes: review of publications. Gyroscopy and navigation. 2023;31;1(120):3-25. (In Russ.).

2. Peshekhonov VG. Prospects for the Development of Gyroscopy. Gyroscopy and Navigation. 2020;28;2 (109):3-10. (In Russ.). DOI: 10.17285/0869-7035.0028

3. Rozelle DM. The hemispherical resonator gyro: From wineglass to the planets. In Proceedings of the 19th AAS/AIAA Space Flight Mechanics Meeting, Savannah, GA, USA, 8–12 February, 2009;1157-1178 pp.

4. Klimov DM. Quartz hemispherical resonator (solid-state wave gyroscope. Moscow: Kim L. A., 2017.193 p.

5. Volchikhin IA, Volchikhin AI, Malyutin DM, Matveyev VV, Raspopov VYa, Telukhin SV, Shvedov AP. Wave solid-state gyroscopes (analytical review). Bulletin of Tula State University. Technical sciences. 2017;(9):59-78.

6. Raspopov VYa, Ladonkin AV, Likhosherst V V. Competitive wave solid-state gyroscope with a metal resonator. Mechatronics, automation, control. 2018;19(12):777-787. (In Russ.). DOI: 10.17587/mau.19.777-787

7. Vavilov VD, Timoshenkov SP, Timoshenkov AS. Microsystem sensors of physical quantities: monograph. Moscow: TEKHNOSFERA, 2018. 550 p.

8. Ivanov SYu. Development of a digital electronic subsystem of a micromechanical gyroscope with a ring resonator. Transactions of the Moscow Institute of Physics and Technology (National Research University). 2016;8;2(30):142-152.

9. Jia J, Ding X, Qin Z, Ruan Z, Li W, Liu X, Li H. Overview and analysis of MEMS Coriolis vibratory ring gyroscope. Measurement. 202;182:109704 p. DOI: 10.1016/j.measurement.2021.109704

10. Zhou X, Wu Y, Wu X, Zhang Y, Zheng Y. A novel ring vibrating gyroscope based on side piezo-electrodes. Journal of Central South University. 2016;(23):555-561. DOI: 10.1007/s11771-016-3102-4

11. Guo X, Cui R, Yan S, Cai Qi, Wei W, Shen C, Cao H. Design and Experiment for N = 3 Wineglass Mode Metal Cylindrical Resonator Gyroscope Closed-Loop System. Electronics. 2023;12(1):131. DOI: 10.3390/electronics12010131

12. Lin Z, Fu M, Zhihong D, Liu N, Liu H. Frequency Split Elimination Method for a Solid-State Vibratory Angular Rate Gyro with an Imperfect Axisymmetric-Shell Resonator. Sensors. 2015;(15):3204-3223. DOI: 10.3390/s150203204

13. Matveev VA, Basarab MA, Lunin BS, Chumankin EA, Yurin AV. Development of the theory of creating wave solid-state gyroscopes with a metal resonator. Bulletin of the Russian Foundation for Basic Research. 2015;87(3):84-96. (In Russ.).

14. Likhosherst VV, Kalikanov AV, Streltsov DS. Roll angle sensor based on a wave solid-state gyroscope]. Bulletin of the Russian Academy of Rocket and Artillery Sciences. 2023;127(2):71-75. (In Russ.). DOI: 10.53816/20753608_2023_2_71.

15. Qiu Z, Tianliang Q, Yao P, Yonglei J, Zhenfang F, Kaiyong Y, Jie Y, Hui L. Optical and Electrical Method Characterizing the Dynamic Behavior of the Fused Silica Cylindrical Resonator. Sensors. 2019;19(13): 2928. DOI: 10.3390/s19132928

16. Delhaye F. HRG by Safran The game-changing technology. 2018,3 р. DOI: 10.1109/ISISS.2018.8358163

17. Lynch DD. Vibratory gyro analysis by the method of averaging / In: Proceedings of the 2nd St. Petersburg conference on gyroscopic technology and navigation. St. Petersburg. 1995. pp. 26–34.

18. Perelyaev SE. Fundamental issues of the theory of combined free gyroscopes operating in two working modes. Bulletin of the Russian Academy of Sciences. Solid State Mechanics. 2021;(4):64–76. DOI: 10.31857/S0572329921040115

19. Shishakov KV, Khvorenkov VV. Solid-state wave gyroscopes: wave processes, control, system integration. Izhevsk, Izhevskiy gosudarstvennyy tekhnicheskiy universitet imeni M.T. Kalashnikova. 2018, 264 p.

20. Wei Z, Yi G, Huo Y, Qi Z, Xu Z. The Synthesis Model of Flat-Electrode Hemispherical Resonator Gyro. Sensors. 2019;19(7):1690. DOI: 10.3390/s19071690

21. Matveev VV, Likhosherst VV, Kalikanov AV, Pogorelov MG, Kirsanov MD, Telukhin SV. Ensuring the operating modes of Coriolis vibratory gyroscopes with lowQ resonators. Scientific and Technical Bulletin of Information Technologies, Mechanics and Optics. 2024;24(1):133143. DOI: 10.17586/2226-1494-2024-24-1-133-143