The fused silica cylindrical resonator is a type of axisymmetric resonator that can be used for Coriolis vibratory gyroscopes. Although the resonant frequency, frequency mismatch, and Q factor are natural properties of the resonator, they can change with temperature. Therefore, the temperature drift severely limits the detection accuracy and bias stability of the gyroscope. In this paper, the influence of temperature variation on the vibrational characteristics of fused silica cylindrical resonators was investigated. Experiments were performed on a fused silica cylindrical resonator coated with Cr/Au films. It was shown that at the temperature range from 253.15 K to 353.15 K, the resonant frequency linearly increased with temperature, the frequency mismatch remained unchanged, and the Q factor gradually increased till about 333.15 K, when it began to decrease. Meanwhile, the change of thermoelastic damping with temperature may dominate the variation of Q factor at the temperature range from 253.15 K to 353.15 K. This phenomenon was theoretically analyzed and the variation trends of results were consistent with the theoretical analysis. This study indicates that, for the fused silica cylindrical resonator, to discover the influence of temperature variation on the resonant frequency, frequency mismatch, and Q factor, there are certain rules to follow and repeat. The relationship between temperature and frequency can be established, which provides the feasibility of using self-calibration based on temperature characteristics of the resonator for temperature drift compensations. Additionally, there is an optimum temperature that may improve the performance of the Coriolis vibratory gyroscope with the fused silica cylindrical resonator.

Damping mismatch, detection error, and actuation error are the primary sources of the output drift in rate-integrating hemispherical resonator gyroscopes (HRGs). To date, separating the three errors remains a challenge, which hinders the accurate compensation of HRGs. This article proposes a novel method to separate the damping, detection, and actuation errors of HRGs. Theoretically, a dynamics model of HRGs considering the three errors is developed, where the detection and actuation errors are modeled using Fourier analysis. The effects of these three errors on the scale factor and the bias under different operation modes are discussed in detail for the first time. It is found that the three errors can be decoupled under the decay with quadrature control (DQC) mode, a special operation mode designed in this article. In the experiments, by measuring the angle dependence of the scale factor and the bias of the energy loop, the damping, detection, and actuation errors of three HRGs are successfully identified and then comprehensively compensated. For one typical tested HRG, after compensation, the angle-dependent error of the scale factor decreases from 1.08% to 0.036% by a factor of 30, the angle-dependent variation of the static drift reduces from $5.14 \times 10^{-3} \; ^{\circ }$ /s to $2.37 \times 10^{-4} \; ^{\circ }$ /s by a factor of 22, and the fluctuation of the dynamic output at different input rates decreases 14–25 times. Our method can also be conveniently applied to other rate-integrating Coriolis vibrating gyroscopes (CVGs).

Detection signal nonlinearity, induced by nonlinear capacitive variations in electrode gaps, fundamentally limits the performance of whole-angle (WA) mode hemispherical resonator gyroscopes (HRGs). This letter proposes a rapid identification method for this nonlinearity based on the relationship between the amplitude-gap ratio and resonator vibration energy. Experimental results across 100-500 °/s input rotation velocities confirms method accuracy and operational robustness. Post-compensation HRG achieves a bias instability (BI) of 0.006 °/h and a scale factor nonlinearity (SFN) of 0.08 ppm. The achieved SFN of 0.08 ppm represents the lowest reported value for WA mode HRGs to date.

The Coriolis Vibratory Gyroscopes are a type of sensors that measure angular velocities through the Coriolis effect. The resonator is the critical component of the CVGs, the vibrational characteristics of which, including the resonant frequency, frequency mismatch, Q factor, and Q factor asymmetry, have a great influence on the performance of CVG. The frequency mismatch and Q factor of the resonator, in particular, directly determine the precision and drift characteristics of the gyroscope. Although the frequency mismatch and Q factor are natural properties of the resonator, they can change with external conditions, such as temperature, pressure, and external forces. In this paper, the influence of electrostatic forces on the vibrational characteristics of the fused silica cylindrical resonator is investigated. Experiments were performed on a fused silica cylindrical resonator coated with Cr/Au films. It was shown that the resonant frequency, frequency mismatch, and the decay time slightly decreased with electrostatic forces, while the decay time split increased. Lower capacitive gaps and larger applied voltages resulted in lower frequency mismatch and lower decay time. This phenomenon was theoretically analyzed, and the variation trends of results were consistent with the theoretical analysis. This study indicates that, for fused silica cylindrical resonator with electrostatic transduction, the electrostatic influence on the Q factor and frequency, although small, should be considered when designing the capacitive gap and choosing bias voltages.

The damping asymmetry, the phase delay and the electrode errors are crucial factors that limit the performance of hemispherical resonator gyroscopes. This paper employs mode reversal to compensate for damping asymmetry. A mathematical model is first established incorporating the stiffness asymmetry, the damping asymmetry, the phase delay and the electrode errors. The influences of the phase delay and the electrode errors on mode-reversal force-to-rebalance hemispherical resonator gyroscopes are analyzed, respectively. New methods to identify the phase delay and the electrode errors are proposed, which eliminate the influences of both the control-loop couplings and the couplings among different error sources. Experimental results demonstrate that the angle-dependent bias in the turntable-rotation mode is reduced from 3.72 °/s to 0.02 °/s after the compensation of detection electrode errors, demonstrating a decrease of 99.5%; the angle-dependent bias in the virtual-rotation mode is reduced from 0.107 °/s to 0.006 °/s after the compensation of actuation electrode errors, demonstrating a decrease of 94.4%. After compensation, the bias instability of the mode-reversal force-to-rebalance hemispherical resonator gyroscope is improved from 0.046 °/h to 0.003 °/h, demonstrating an improvement of 93.5%. The proposed methods can be widely applied to Coriolis vibratory gyroscopes with symmetric structures operating in both the force-to-rebalance mode and the whole-angle mode.

Hemispherical resonator gyroscopes (HRGs) exhibit exceptional force-to-rebalance (FTR) precision but suffer from temperature-dependent drift, limiting widespread deployment. This study presents a temperature-dependent bias drift compensation method for HRGs using a dual-HRG system configuration. The dual-HRG system compensates for temperature-dependent bias drift based on mode reversal. By implementing alternating mode-reversal control sequences between two HRGs, the dual-HRG system overcomes the limitations of single HRG mode reversal in practical applications. Furthermore, based on the calibration results of phase delay errors, electrode errors and scale factors (SFs) at different temperatures, corresponding temperature compensation modules are incorporated into the dual-HRG system. The residual temperature-dependent bias drift is further compensated by applying the multiple regression algorithm. Experimental results demonstrate that the bias stability of the dual-HRG system after mode reversal is improved by more than 98.7% and 87.7% compared to the two individual HRGs, respectively. Moreover, the temperature-dependent bias drift is further compensated by the multiple regression algorithm, and the bias stability of the dual-HRG system is improved by more than 70.5%.