Stability of stationary vibrations of cylindrical gyro resonator with electromagnetic control system
Authors: Maslov D.A.
Published in issue: #5(53)/2016
DOI: 10.18698/2308-6033-2016-5-1493
Category: Mechanics | Chapter: Dynamics, Strength of Machines, Instruments, and Equipment
The article considers dynamics of a cylindrical resonator of the wave solid-state gyro with an electromagnetic control system allowing reducing the instrument readiness time for operation comparing to electrostatic control system. The mathematical model describing the resonator vibrations and the electromagnetic processes in the vibration excitation system in the coherent manner is created. It is shown that when the positional excitation is used attendant parametric excitation of vibrations appears. The case is considered when the simultaneous action of forced position excitation and attendant parametric excitation results in combined vibration. Using a method of splitting the non-autonomous systems of differential equations with periodic matrices and Lienard - Shepherd criterion of stability the condition of asymptotic stability of stationary vibrations of gyro resonator is obtained. The regions of asymptotic stability of stationary vibrations of gyroscope resonator in the space of system parameters are constructed.
References
[1] Peshekhonov V.G. Giroskopiya i naigatsiya - Gyroscopy and Navigation, 2011, no. 1, pp. 3-17.
[2] Basarab M.A., Lunin B.S., Matveev V.A., Fomichev A.V., Chumankin E.A., Yurin A.V. Vestnik MGTU im. N.E. Baumana. Seria Priborostroyeniye - Herald of the Bauman Moscow State Technical University. Series: Instrument Engineering, 2014, no. 4, pp. 80-96.
[3] Dzhandzhgava G.I., Bakhonin K.A., Vinogradov G.M., Trebukhov A.V. Giroskopiya i naigatsiya - Gyroscopy and Navigation, 2008, no. 1, pp. 22-33.
[4] Zhuravlev V.F., Klimov D.M. Volnovoy tverdotelnyy giroskop [The Wave Solid-State Gyro]. Moscow, Nauka Publ., 1985, 125 p.
[5] Matveev V.A., Lunin B.S., Basarab M.A., Chumankin E.A. Nauka i obrazovanie: electronnoe nauchnoe izdanie - Science and Education: Electronic Scientific Journal, 2013, no. 6. DOI http://dx.doi.org/10.7463/0613.0579179
[6] Basarab M.A., Matveev V.A., Lunin B.S., Chumankin E.A. Gyroscopy and Navigation, 2014, vol. 5, no. 4, pp. 213-218.
[7] Basarab M.A., Matveev V.A., Lunin B.S., Chumankin E.A. Algorithms and Technologies for Surface Balancing of Hemispherical and Cylindrical Resonator Gyroscopes. Proceedings of the 22nd International Conference on Integrated Navigation Systems. ICINS 2015 -22. Saint Petersburg, 2015, pp. 383-386.
[8] Maslov A.A., Maslov D.A., Merkuryev I.V. Pribory i sistemy, Upravlenie, control, diagnostika - Devices and Systems. Control, monitoring, diagnostics, 2014, no. 5, pp. 24-29.
[9] Maslov A.A., Maslov D.A., Merkuryev I.V. Gyroscopy and Navigation, 2014, vol. 5, no. 4, pp. 224-228.
[10] Maslov A.A., Maslov D.A., Merkuryev I.V. Gyroscopy and Navigation, 2015, vol. 6, no. 3, pp. 224-229.
[11] Roginskiy V.D., Yurmanov S.Yu., Denisov R.A. Sposob vozbuzhdeniya kolebaniy v chuvstvitelnom elemente tverdotelnogo volnovogo giroskopa i ustroystvo dlya ego osushchestvleniya [The Method of Vibration Excitation in the Sensor of Wave Solid-State Gyroscopes and a Device for Its Implementation]. Patent RF, no. 2518632, 2014, bull. 16.
[12] Menno G. Koning. Vibrating cylinder gyroscope and method. Fatent USA, no. 4793195, 1988.
[13] Bernard De Salaberry. Vibrating Gyroscope with Electromagnetic Excitation and Detection. Fatent USA, no. 6443009, 2002.
[14] Konyaev Yu.A. Matematicheskiy sbornik - Mathematical collection, 2001, vol. 192, no. 3, pp. 65-82.
[15] Konyaev Y.A., Mikhailov D.V., Romanova E.Y. Differential Equations, 2013, vol. 49, no. 6, pp. 760-764.
[16] Merkuryev I.V., Podalkov V.V. Dinamika mikromekhanicheskogo i volnovogo tberdotelnogo giroskopov [Dynamics of Micromechanical and Wave Solid-State Gyroscopes]. Moscow, Fismatlit Publ., 2009, 228 p.
[17] Martynenko Yu.G. Analiticheskaya dinamika elektromekhanicheskikh system [Analytical Dynamics of Electromechanical Systems]. Moscow, MEI Publ., 1984, 64 p.