, DYNAMICS AND ACCURACY OF A MICROMECHANICAL GYROSCOPE WITH PROVISION FOR THE DISPLACEMENT OF INERTIAL MASS // BSU bulletin. Mathematics, Informatics. - 2020. №3. . - С. 49-62.

DYNAMICS AND ACCURACY OF A MICROMECHANICAL GYROSCOPE WITH PROVISION FOR THE DISPLACEMENT OF INERTIAL MASS

We consider a micromechanical gyroscope (MMG), used in navigation and motion control systems for moving objects. In order to improve the accuracy of the gyroscope in the integrating mode of operation on a rocking base, we have studied the dynamics and accuracy of the gyroscope, taking into account the small instrumental

errors in creation of the sensitive element of the gyroscope – unequal rigidity of the elastic support elements, small shifts of the gyroscope center of mass relative to the geometric center of the assembly. The method for increasing the accuracy of the gyroscope is based on the construction of a new mathematical model of its dynamics and errors using the general theorems of dynamics and Krylov–Bogolyubov averaging

methods. The new mathematical model of oscillations of the sensitive element of a weight-size prototype makes it possible to estimate the errors of the gyroscope in the integrating mode of operation in form of dependence of the precession angle on the parameters of the differences in Q factor, frequency and shifts of the inertial mass on a

rocking base of the device. The article presents a comparative analysis of the constructed model with experimental data obtained for the case of free oscillations of the

sensitive element of the gyroscope on a fixed base. Based on the results of analysis, we

have confirmed the adequacy of the constructed mathematical model of a weight-size

prototype. We propose to use the methods of parameter identification for matching the

experimental data with the simulation results. It is shown that the shifts of the inertial

mass leads to a change in the natural frequencies of the gyroscope oscillations and the

additional different frequencies. The results of the work can be used to improve the

accuracy of the device using the algorithm for analytical compensation of the gyro

error.

errors in creation of the sensitive element of the gyroscope – unequal rigidity of the elastic support elements, small shifts of the gyroscope center of mass relative to the geometric center of the assembly. The method for increasing the accuracy of the gyroscope is based on the construction of a new mathematical model of its dynamics and errors using the general theorems of dynamics and Krylov–Bogolyubov averaging

methods. The new mathematical model of oscillations of the sensitive element of a weight-size prototype makes it possible to estimate the errors of the gyroscope in the integrating mode of operation in form of dependence of the precession angle on the parameters of the differences in Q factor, frequency and shifts of the inertial mass on a

rocking base of the device. The article presents a comparative analysis of the constructed model with experimental data obtained for the case of free oscillations of the

sensitive element of the gyroscope on a fixed base. Based on the results of analysis, we

have confirmed the adequacy of the constructed mathematical model of a weight-size

prototype. We propose to use the methods of parameter identification for matching the

experimental data with the simulation results. It is shown that the shifts of the inertial

mass leads to a change in the natural frequencies of the gyroscope oscillations and the

additional different frequencies. The results of the work can be used to improve the

accuracy of the device using the algorithm for analytical compensation of the gyro

error.

RR-type gyroscope; gyroscopic precession; gyroscope error estimation; micromechanical gyroscope; free oscillations.

Peshekhonov V. G. Sovremennoe sostoyanie perspektivy razvitiya giroskopicheskikh sistem [Сurrent State of the Prospects for the Development of Gyroscopic Systems]. Gyroscopy and Navigation. 2011. No. 1. Pp. 3–16.

2. Zhuravlev V. F. Upravlyaemyi mayatnik Fuko kak model odnogo klassa svobodnykh giroskopov [Controlled Foucault Pendulum as a Model of One class of Free Gyroscopes]. Mechanics of Solids. 1997. No. 6. Pp. 27–35.

3. Raspopov V. Ya. Mikromekhanicheskie pribory [Micromechanical Devices]. Moscow: Mashinostroyeniye Publ., 2007. 400 p.

4. Basarab M. A., Kravchenko V. F., Matveev V. A. Metody modelirovaniya i tsifrovaya obrabotka signalov v giroskopii [Simulation Methods and Digital Signal Processing in Gyroscopy]. Moscow: Fizmatlit Publ., 2008. 248 p.

5. Merkuryev I. V., Podalkov V. V. Dinamika mikromekhanicheskogo i volnovogo tverdotelnogo giroskopov [Dynamics of Micromechanical and Wave Solid-State Gyroscopes]. Moscow: Fizmatlit Publ., 2009. 228 p.

6. Merkuryev I. V., Podalkov V. V. Nelineinye effekty v dinamike mikromekhanicheskogo giroskopa [Nonlinear Effects in the Dynamics of a Micromechanical Gyroscope]. Vestnik MEI. 2004. No. 2. Pp. 5–10.

7. Basarab M., Lunin B., Vakhlyarskiy D., Chumankin E. Investigation of Nonlinear High-Intensity Dynamic Processes in a Non-Ideal Solid-State Wave Gyroscope Resonator. 27th Saint Petersburg International Conference on Integrated Navigation Systems, ICINS 2020 Proceedings. No. 9133943.

8. Basarab M. A., Matveev V. A., Lunin B. S., Fetisov S. V. Influence of Nonuniform Thickness of Hemispherical Resonator Gyro Shell on its Unbalance Parameters. Gyroscopy and Navigation. 2018. No.8 (2). Pp. 97–103.

9. Apostolyuk V. Theory and Design of Micromechanical Vibratory Gyroscopes. MEMS/NEMS Handbook. 2006. No. 1(6). Pp. 173–195.

10. Askari S., Asadian M. H., Shkel A. M. High Quality Factor MEMS Gyroscope with Whole Angle Mode of Operation. 2018 IEEE Int. Symposium on Inertial Sensors and Systems (INERTIAL). Moltrasio, Italy, 2018. Pp. 1–4.

11. Markeyev A. P. Teoreticheskaya mekhanika [Theoretical Mechanics]. Moscow; Izhevsk: Regulyarnaya i khaoticheskaya mekhanika Publ., 2007. 592 p.

12. Bogolyubov N. N., Mitropolskiy Yu. A. Asimptoticheskie metody v teorii nelineinykh kolebanii [Asymptotic Methods in the Theory of Nonlinear Oscillations]. Moscow: Nauka Publ., 1974. 503 p.

2. Zhuravlev V. F. Upravlyaemyi mayatnik Fuko kak model odnogo klassa svobodnykh giroskopov [Controlled Foucault Pendulum as a Model of One class of Free Gyroscopes]. Mechanics of Solids. 1997. No. 6. Pp. 27–35.

3. Raspopov V. Ya. Mikromekhanicheskie pribory [Micromechanical Devices]. Moscow: Mashinostroyeniye Publ., 2007. 400 p.

4. Basarab M. A., Kravchenko V. F., Matveev V. A. Metody modelirovaniya i tsifrovaya obrabotka signalov v giroskopii [Simulation Methods and Digital Signal Processing in Gyroscopy]. Moscow: Fizmatlit Publ., 2008. 248 p.

5. Merkuryev I. V., Podalkov V. V. Dinamika mikromekhanicheskogo i volnovogo tverdotelnogo giroskopov [Dynamics of Micromechanical and Wave Solid-State Gyroscopes]. Moscow: Fizmatlit Publ., 2009. 228 p.

6. Merkuryev I. V., Podalkov V. V. Nelineinye effekty v dinamike mikromekhanicheskogo giroskopa [Nonlinear Effects in the Dynamics of a Micromechanical Gyroscope]. Vestnik MEI. 2004. No. 2. Pp. 5–10.

7. Basarab M., Lunin B., Vakhlyarskiy D., Chumankin E. Investigation of Nonlinear High-Intensity Dynamic Processes in a Non-Ideal Solid-State Wave Gyroscope Resonator. 27th Saint Petersburg International Conference on Integrated Navigation Systems, ICINS 2020 Proceedings. No. 9133943.

8. Basarab M. A., Matveev V. A., Lunin B. S., Fetisov S. V. Influence of Nonuniform Thickness of Hemispherical Resonator Gyro Shell on its Unbalance Parameters. Gyroscopy and Navigation. 2018. No.8 (2). Pp. 97–103.

9. Apostolyuk V. Theory and Design of Micromechanical Vibratory Gyroscopes. MEMS/NEMS Handbook. 2006. No. 1(6). Pp. 173–195.

10. Askari S., Asadian M. H., Shkel A. M. High Quality Factor MEMS Gyroscope with Whole Angle Mode of Operation. 2018 IEEE Int. Symposium on Inertial Sensors and Systems (INERTIAL). Moltrasio, Italy, 2018. Pp. 1–4.

11. Markeyev A. P. Teoreticheskaya mekhanika [Theoretical Mechanics]. Moscow; Izhevsk: Regulyarnaya i khaoticheskaya mekhanika Publ., 2007. 592 p.

12. Bogolyubov N. N., Mitropolskiy Yu. A. Asimptoticheskie metody v teorii nelineinykh kolebanii [Asymptotic Methods in the Theory of Nonlinear Oscillations]. Moscow: Nauka Publ., 1974. 503 p.