This paper analyzes the effect of the anisotropy of single crystal silicon on the frequency split of the vibrating ring gyroscope, operated in the n = 2 wineglass mode. Firstly, the elastic properties including elastic matrices and orthotropic elasticity values of (100) and (111) silicon wafers were calculated using the direction cosines of transformed coordinate systems. The (111) wafer was found to be in-plane isotropic. Then, the frequency splits of the n = 2 mode ring gyroscopes of two wafers were simulated using the calculated elastic properties. The simulation results show that the frequency split of the (100) ring gyroscope is far larger than that of the (111) ring gyroscope. Finally, experimental verifications were carried out on the micro-gyroscopes fabricated using deep dry silicon on glass technology. The experimental results are sufficiently in agreement with those of the simulation. Although the single crystal silicon is anisotropic, all the results show that compared with the (100) ring gyroscope, the frequency split of the ring gyroscope fabricated using the (111) wafer is less affected by the crystal direction, which demonstrates that the (111) wafer is more suitable for use in silicon ring gyroscopes as it is possible to get a lower frequency split.
In order to eliminate the frequency mismatch of MEMS (Microelectromechanical Systems) gyroscopes, this paper proposes a frequency tuning technology based on a quadrature modulation signal. A sinusoidal signal having a frequency greater the gyroscope operating bandwidth is applied to the quadrature stiffness correction combs, and the modulation signal containing the frequency split information is then excited at the gyroscope output. The effects of quadrature correction combs and frequency tuning combs on the resonant frequency of gyroscope are analyzed. The tuning principle based on low frequency input excitation is analyzed, and the tuning system adopting this principle is designed and simulated. The experiments are arranged to verify the theoretical analysis. The wide temperature range test (-20∘normalC–60∘normalC) demonstrates the reliability of the tuning system with a maximum mismatch frequency of less than 0.3 Hz. The scale factor test and static test were carried out at three temperature conditions (−20 ∘C, room temperature, 60 ∘C), and the scale factor, zero-bias instability, and angle random walk are improved. Moreover, the closed-loop detection method is adopted, which improves the scale factor nonlinearity and bandwidth under the premise of maintaining the same static performances compared with the open-loop detection by tuning.
An automatic mode-matching method for MEMS (Micro-electromechanical Systems) disk resonator gyroscopes (DRGs) based on virtual Coriolis force is presented in this paper. For this mode-matching method, the additional tuning electrodes are not required to be designed, which simplifies the structure design. By using the quadratic relationship between the driving voltage and the electrostatic force, the virtual Coriolis force is obtained by applying an AC voltage whose frequency is half of the driving mode resonant frequency to the sense electrode. The phase difference between the virtual Coriolis force and the sense output signal is used for mode-matching. The structural characteristics and electrode distribution of the DRG are briefly introduced. Moreover, the mode-matching theories of the DRG are studied in detail. The scheme of the mode-matching control system is proposed. Simultaneously, the feasibility and effectiveness of the mode-matching method are verified by system simulation. The experimental results show that under the control of mode-matching at room temperature, the bias instability is reduced from 30.7575 • /h to 2.8331 • /h, and the Angle Random Walk (ARW) decreases from 1.0208 • / √ h to 0.0524 • / √ h. Compared with the mode mismatch condition, the ARW is improved by 19.48 times.Micromachines 2020, 11, 210 2 of 22 Therefore, the mode-matching technology improves the bias stability and mechanical sensitivity of MEMS gyroscopes by eliminating the frequency split between the driving mode and the sensing mode, which has attracted significant attention from researchers [19][20][21]. Furthermore, some frequency modification techniques are proposed. Laser finishing, ion beam milling, and selective deposition mass loading reduce frequency split [22,23]. However, these methods are often used to change the dynamic characteristics of the sensor permanently, and this type of tuning is inflexible and time-consuming. The tuning control is limited and can only be achieved offline.Electrostatic tuning is usually used for mode-matching, which can provide more flexibility and real-time realization [24][25][26][27][28][29]. The mode-matching process based on phase-locked loop (PLL) takes advantage of the phase delay of 90 • between the quadrature input and output of the sensing mode. This feature is used in [27] to achieve mode-matching and to adjust the tuning voltage using PLL technology. The amplitude-frequency characteristic refers to the maximum amplitude of the quadrature response signal during mode-matching [28]. However, in these methods, the signal from the Coriolis demodulation channel is used to control the frequency tuning voltage. Therefore, the angular velocity can only be measured if the tuning voltage is fixed, and the matching loop is disconnected after mode-matching. Thus, these methods cannot achieve real-time mode-matching. However, in practical applications, the frequency split of the vibratory mode changes with changes in environmental parameters [29]. Therefore, such one-time matching methods a...
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.