doi: 10.17586/2226-1494-2016-16-3-541-549


M. I. Evstifeev, D. P. Eliseev

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For citation: Evstifeev M.I., Eliseev D.P. Mathematical model of RR-type micromechanical gyro capacitive comb-type sensors with account for vibrations. Scientific and Technical Journal of Information Technologies, Mechanics and Optics, 2016, vol. 16, no. 3, pp. 541–549. doi: 10.17586/2226-1494-2016-16-3-541-549


Subject of Research.The reasons for subharmonic resonances in RR-type micromechanical gyro output under linear vibrations are investigated. In ideal case, this type of gyro should be insensitive to this kind of impact due to primary and secondary angular oscillations. However, experimental results reveal significant increase in output signal under external vibrations in 20 Hz - 2 kHz bandwidth, though the device natural frequencies are above 3 kHz. This effect is caused by characteristicsnonlinearity of plate-type and comb-type capacitive sensors. Method. Mathematical model of the capacitive comb-type sensors is clarified. Electromechanical interactions in the sensors under external vibrations are described. Simulink modeling of specified mathematical model is carried out. External vibration modeling is doneby “oscillating frequency” method with constant accelerationamplitude in 20 Hz - 2 kHz bandwidth. Main Results.We have received good agreement of modeling and experimental results in the form of occurrence of subharmonic resonances under linear vibrations in three orthogonal directions. Obtained effects are explained by proposed mathematical models. The main reason for subharmonic resonances in RR-type micromechanical gyro output is that combs of stator and combs of proof mass jump out of mesh. Practical Relevance. The provided investigation gives the possibility to determine algorithmic and construction compensation methods of studied interactions for enhancing vibration resistance of RR-type micromechanical gyro.

Keywords: micromechanical gyro, vibration, subharmonic resonance

Acknowledgements. The authors are thankful to the staffof international scientific laboratory “Integrated orientation and navigation systems” based on Information Navigation Systems Department of ITMO University and personally to its head O.A. Stepanov for assistance in organization of research.


1. Peshekhonov V.G. Gyroscopic systems: current status and prospects. Gyroscopy and Navigation, 2011, vol. 2, no.3, pp. 111–118. doi: 10.1134/S2075108711030096
2. Lestev A.M., Popova I.V., Evstifeev M.I., Pyatyshev E.N., Lur'e M.S., Semenov A.A. Features of micromechanical gyroscopes. Mikrosistemnaya Tekhnika, 2000, no. 4, pp. 16–18. (In Russian)
3. Barbour N., Hopkins R., Kourepenis A. Inertial MEMS system applications. Advances in Navigation Sensors and Integration Technology, 2004, vol. 232, pp. 7-1–7-12.
4. Geen J. Progress in integrated gyroscopes. IEEE Aerospace and Electronic Systems Magazine, 2004, vol. 19, no. 11, pp. 12–17. doi: 10.1109/MAES.2004.1365660
5. Weinberg H. Gyro Mechanical Performance: The Most Important Parameter. Technical Article MS-2158. Analog Devices, Inc, 2011, pp. 1–5.
6. Nguyen C. The Harsh Environment Robust Micromechanical Technology (HERMiT) program: success and some unfinished business. IEEE MTT-S International Microwave Symposium Digest, 2012, art. 6259750. doi: 10.1109/MWSYM.2012.6259750
7. Evstifeev M.I., Chelpanov I.B. Providing the mechanical stability of MEMS gyros. Gyroscopy and Navigation, 2013, no. 1(80), pp. 119–133.
8. Evstifeev M.I. Problems of calculation and design for micromechanical gyroscopes. Gyroscopy and Navigation, 2004, no. 1(44), pp. 27–39.
9. Evstifeev M.I. Teoriya i Metody Rascheta Uprugikh Podvesov Inertsial'nykh Chuvstvitel'nykh Elementov Priborov Navigatsii. Dis. dokt. tekhn. nauk. St. Petersburg, 2007, 341 p.
10. Evstifeev M.I., Eliseev D.P., Kovalev А.S., Rozentsvein D.V. Results of MEMS gyro mechanical tests. Gyroscopy and Navigation, 2011, vol. 2, no. 3, pp. 119–126. doi: 10.1134/S2075108711030047
11. Evstifeev M.I., Kovalev А.S., Eliseev D.P. Electromechanical model of RR type MEMS gyro with consideration for the platform vibrations. Gyroscopy and Navigation, 2014, vol. 5, no. 3, pp. 174–180. doi: 10.1134/S2075108714030043
12. Eliseev D.P., Kovalev А.S. Investigation of the linear vibrations influence on the MMG RR type with regard to non-linearity of the capacitive sensor. Navigatsiya i Upravlenie Dvizhenie Materialy XVI Konferentsii Molodykh Uchenykh [Navigation and control. Proc. XII Conference of Young Scientists]. St. Petersburg, 2014, pp. 406–412. (In Russian)
13. Evstifeev M.I., Eliseev D.P., Chelpanov I.B. MEMS RR-type gyro with a moving electrode. Gyroscopy and Navigation, 2015, no. 4(91), pp. 67–76.
14. Evstifeev M.I., Eliseev D.P. Micromechanical Vibration Gyroscope. Patent RU2561006, 2015.
15. Bernstein J.J., Weinberg M.S. Comb Drive Micromechanical Tuning Fork Gyro. Patent US5349855. Published 27.09.1994.
16. Kovalev А.S. Upravlenie Pervichnymi i Vtorichnymi Kolebaniyami Mikromekhanicheskogo Giroskopa. Dis. kand. tekhn. nauk [Control of Primary and Secondary Oscillations of a Micromechanical Gyroscope. Dis. Eng. Sci.]. St. Petersburg, 2008, 157 p.
17. Evstifeev M.I. Eliseev D.P., Kovalev А.S., Rozentsvein D.V. Research of the MEMS gyro dynamics under the mechanical impact. Scientific and Technical Journal of Information Technologies, Mechanics and Optics, 2011, no. 4(74), pp. 72–76.
18. Kovalev A.S., Gryazin D.G., Shadrin Yu.V., Lychev D.I. Investigation of operation modes of micromechanical gyroscope with superimposed frequencies along the primary and secondary Oscillation axes. Nauchnoe Priborostroenie (Scientific Instrumentation), 2007, vol. 17, no. 1, pp. 91–97.
19. Eliseev D.P. Povyshenie Vibroustoichivosti Mikromekhanicheskogo Giroskopa RR-tipa. Dis. kand. tekhn. nauk. [Increasing Vibration Resistance of Micromechanical Gyroscope RR-type. Dis. Eng. Sci.]. St. Petersburg, 2015, 142 p.
20. Evstifeev M.I., Eliseev D.P., Chelpanov I.B. Enhancing the mechanical resistance of micromechanical gyros. Gyroscopy and Navigation, 2015, vol. 6, no. 2, pp. 115–122. doi: 10.1134/S2075108715020042

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