Inelastic Processes in Internal Permanent Joints of Mechanical Resonators of the Wave Solid-State Gyroscopes
| Authors: Lunin B.S. , Basarab M.A. | Published: 21.01.2026 |
| Published in issue: #4(153)/2025 | |
| DOI: | |
| Category: Instrument Engineering, Metrology, Information-Measuring Instruments and Systems | Chapter: Navigation Instruments | |
| Keywords: wave solid-state gyroscope, dissipation, internal friction | |
Abstract
The article discusses the dissipative processes occurring in typical internal permanent (adhesive and soldered) connections of wave solid-state gyroscopes, implemented when assembling a resonator with a base and installing piezoelectric elements on its surface. Part of the resonator oscillation energy is dissipated due to volumetric and thermoelastic inelastic processes in the material of the connecting layers, which significantly worsens the characteristics of the device. This effect can be reduced by balancing the resonator, increasing the area of the connection, decreasing the thickness of the connecting layer, and selecting a layer material with low volumetric internal friction. The axial asymmetry of such a connection leads to the dependence of the insertion losses on the circumferential angle. In another type of connections, piezoelectric element-resonator, in addition to the volumetric internal friction, thermoelastic losses arising during bending vibrations should also be taken into account. Calculations show that the use of soldered connections of this type is preferable compared to adhesive ones with a layer thickness of less than ~ 20 µm. In addition, the thixotropic properties of adhesives lead to hysteresis of their inelastic properties during heating and cooling, and, accordingly, to errors in wave solid-state gyroscopes operating in a wide temperature range. The influence of the configuration of internal permanent connections and the properties of the material of the connecting layer on the dissipation of oscillation energy is analyzed
Please cite this article in English as:
Lunin B.S., Basarab M.A. Inelastic processes in internal permanent joints of mechanical resonators of the wave solid-state gyroscopes. Herald of the Bauman Moscow State Technical University, Series Instrument Engineering, 2025, no. 4 (153), pp. 30--45 (in Russ.). EDN: MADNSW
References
[1] Zhbanov Yu.K., Kalenova N.V. Surface imbalance of a wave solid-state gyroscope. Izvestiya RAN. MTT, 2001, no. 3, pp. 11--18 (in Russ.).
[2] Zhbanov Yu.K., Zhuravev V.F. On balancing a wave solid-state gyroscope. Izvestiya RAN. MTT, 1998, no. 4, pp. 4--16 (in Russ.).
[3] Basarab M.A., Matveev V.A., Lunin B.S., et al. Influence of nonuniform thickness of hemispherical resonator gyro shell on its unbalance parameters. Gyroscopy Navig., 2017, vol. 8, no. 2, pp. 97--103. DOI: https://doi.org/10.1134/S207510871702002X
[4] Sharma N.G., Sundararadzhan T., Singkh G.S. Effect of geometric imperfections on anchor loss and characterisation of a gyroscope resonator with high quality factor. Gyroscopy Navig., 2020, vol. 11, no. 3, pp. 206--213. DOI: https://doi.org/10.1134/S2075108720030074
[5] Gerrard D.D., Ng E.J., Ahn C.H., et al. Modeling the effect of anchor geometry on the quality factor of bulk mode resonators. 18th TRANSDUCERS, 2015, pp. 1997--2000. DOI: https://doi.org/10.1109/TRANSDUCERS.2015.7181346
[6] Egarmin N.E., Yurin V.E. Introduction to theory of vibratory gyroscopes. Moscow, Binom, 1993.
[7] Raspopov V.Ya., Likhosherst V.V. HRG with a metal resonator. Gyroscopy Navig., 2023, vol. 14, no. 1, pp. 14--26. DOI: https://doi.org/10.1134/S2075108723010066
[8] Lunin B.S., Basarab M.A. The influence of dissipative properties of piezoceramic sensors on the characteristics of wave solid-state gyroscopes. Pribory i sistemy. Upravlenie, kontrol, diagnostika [Instruments and Systems: Monitoring, Control, and Diagnostics], 2025, no. 3, pp. 31--35 (in Russ.). DOI: https://doi.org/10.25791/pribor.3.2025.1565
[9] Ventsel E., Krauthammer T. Thin plates and shells. New York, CRC Press, 2001.
[10] Negm S.E.A., Modhny A.S.A., Ahmad S.I. Investigation of thermal and mechanical properties of Sn--Zn and Sn--Zn--Bi near-eutectic solder alloys. Results Mater., 2022, vol. 15, art. 100316.DOI: https://doi.org/10.1016/j.rinma.2022.100316
[11] Blanter M.S., Golovin I.S., Neuhauser H., et al. Internal friction in metallic materials. A handbook. Heidelberg, Springer, 2007.
[12] Postnikov V.S. Vnutrennee trenie v metallakh [Internal friction in metals]. Moscow, Metallurgiya Publ., 1974.
[13] Sapozhnikov K.V., Golyandin S.N., Kustov S.B. Temperature dependence of the internal friction of polycrystalline indium. Phys. Solid State, 2010, vol. 52, no. 12, pp. 2501--2509. DOI: https://doi.org/10.1134/S1063783410120103
[14] Fujii Y., Ono T. Temperature dependence of Young’s modulus and internal friction in Sn--Zn--Al lead-free solder. J. Solid Mech. Mater. Eng., 2008, vol. 2, no. 8, pp. 981--986. DOI: https://doi.org/10.1299/jmmp.2.981
[15] Chang S.H., Wu S.K. Low-frequency damping properties of eutectic Sn--Bi and In--Sn solders. Scrip. Mater., 2011, vol. 64, no. 8, pp. 757--760. DOI: https://doi.org/10.1016/j.scriptamat.2010.12.035
[16] Chang S.H., Wu S.K., Kuo C. Effect of reinforced multiwall carbon nanotubes on the damping characteristics of Sn--Ag--Сu lead-free solder. Mater. Lett., 2020, vol. 276, art. 128196. DOI: https://doi.org/10.1016/j.matlet.2020.128196
[17] Qiao L., Eastel A.J., Bolt C.J., et al. Thermomechanical analysis and performance tests of some EPI wood adhesives. Pigm. Resin. Technol., 2000, vol. 29, no. 4, pр. 229--237. DOI: https://doi.org/10.1108/03699420010339371
[18] Lunin B.S., Basarab M.A. Dissipation of vibration energy in a piezoceramic-substrate connection. Pribory i sistemy. Upravlenie, kontrol, diagnostika [Instruments and Systems: Monitoring,Control, and Diagnostics], 2024, no. 5, pp. 1--7 (in Russ.). EDN: QAQDRH
[19] Zener C. Internal friction in solids II. General theory of thermoelastic internal friction. Phys. Rev., 1938, vol. 53, no. 1, рp. 90--99. DOI: https://doi.org/10.1103/PhysRev.53.90
[20] Malkin A.I., Isayev A.I. Rheology: concepts, methods and applications. Toronto, ChemTec Publishing, 2006.
