Solving the Coriolis Vibratory Gyroscope Motion Equations by Means of the Angular Rate B-Spline Approximation

The exact solution of the movement equation of the Coriolis vibratory gyroscope (CVG) with a linear law of variation of the angular rate of rotation of the base is given. The solution is expressed in terms of the Weber functions (the parabolic cylinder functions) and their asymptotic representations. On the basis of the obtained solution, an analytical solution to the equation of the ring dynamics in the case of piecewise linear approximation of an arbitrary angular velocity profile on a time grid is derived. The piecewise linear solution is compared with the more rough piecewise constant solution and the dependence of the error of such approximations on the sampling step in time is estimated numerically. The results obtained make it possible to significantly reduce the number of operations when it is necessary to study long-range dynamics of oscillations of the system, as well as quantitatively and qualitatively control the convergence of finite-difference schemes for solving the movement equations of the Coriolis vibratory gyroscope.

Significance of the Asymmetry of the Haltere: A Microscale Vibratory Gyroscope

Nature has evolved a beautiful design for small-scale vibratory gyroscopes in the form of halteres located in the metathorax region of the dipteran flies that detect body rotations based on the Coriolis principle. The specific design of the haltere is in contrast to the existing MEMS vibratory gyroscope, where the elastic beams supporting the proof mass are typically designed with symmetric cross-sections so that there is a mode matching between the actuation and sensing vibrations. The mode matching provides high sensitivity and low bandwidth. Hence, the objective of the manuscript is to understand the mechanical significance of the haltere’s asymmetry. In this study, the distributed Coriolis force and the corresponding bending stress by incorporating the actual mass variations along the haltere length are estimated. In addition, it is hypothesied that sensilla sense the rate of rotation based on the differential strain (difference between the final strain (strain due to the inertial and Coriolis forces) and the reference strain (strain due to inertial force)). This differential strain always occurs either on the dorsal or ventral surface of the haltere and at a distance away from the base, where the campaniform sensilla are located. This study brings out one specific feature—the asymmetric geometry of the haltere structure—that is not found in current vibratory gyroscope designs. This finding will inspire new designs of MEMS gyroscopes that have elegance and simplicity of the haltere along with the desired performance.

Damping Asymmetry Trimming Based on the Resistance Heat Dissipation for Coriolis Vibratory Gyroscope in Whole-Angle Mode

Damping asymmetry is one of the most important factors that determines the performance of Coriolis Vibratory Gyroscope. In this paper, a novel damping tuning method for the resonator with parallel plate capacitors is presented. This damping tuning method is based on resistance heat dissipation and the tuning effect is characterized by the control force in Whole-Angle mode. As the damping tuning and stiffness tuning in the resonator with parallel plate capacitors are coupled with each other, a corresponding tuning system is designed. To verify the tuning effects, experiments are conducted on a hemispherical resonator gyroscope with Whole-Angle mode. The damping tuning theories is demonstrated by the testing results and 87% of the damping asymmetry is reduced by this tuning method with a cost of 3% decaying time. Furthermore, the angle-dependent drift in rate measurement after tuning is only 15.6% of the one without tuning and the scale factor nonlinearity decreases from 5.49 ppm to 2.66 ppm. The method can be further applied on the damping tuning in other resonators with symmetrical structure.

A low-noise readout interface for silicon MEMS vibratory gyroscope

This paper proposes a novel readout interface for a high-precision silicon MEMS vibratory gyroscope. The readout interface contains a closed-loop self-resonating driving circuit and a low-noise open-loop capacitance sensing circuit. In order to achieve an overall optimization in noise performance, the noise in driving loop of the interface is analyzed in detail. After the noise optimization, the driving frequency stability achieves 0.93 ppm, the front-end capacitance resolution achieves 0.002 [Formula: see text]. The total zero bias instability achieves [Formula: see text]/h, and angle random walk (ARW) achieves 0.014[Formula: see text]/s/[Formula: see text].

Frequency Split Analysis of a Ring Vibratory Gyroscope Based on Harmonic Transformation of Parametric Errors

Ring vibratory gyroscopes are important angular rate sensors widely used in inertial navigation systems. A highly symmetrical resonator is the core part of the ring vibratory gyroscope. Frequency split is a key parameter which denotes the level of unbalanced mass and stiffness of the resonator. Many research works focus on the precise machining of the resonator for the sake of eliminating frequency split. However, for metallic ring resonators, the decrease of frequency split is not always proportional to the promotion of geometric accuracy. This paper investigates the frequency split of the ring resonator gyroscope caused by parametric errors including geometric and material imperfection via a method of harmonic transformation. The roundness error of the ring resonator is extracted, and then decomposed to a series of orders of harmonic waves. Transformation results show that for the tested resonator, its first 20 orders of harmonic waves contain the main components of the roundness error. Then a precise FEM modeling is built for frequency split analysis. The simulation result shows that the roundness error of the resonator can cause a frequency split of 0.6 Hz, which accounts for 16.2 % of the total frequency split. Based on the metallographic observation and grouping experiment of different metallic resonators, it is deduced that the main frequency split is caused by material heterogeneity. It shows that the material homogenization is as important as precise machining for the resonator of small frequency split. The proposed research provides an instruction to manufacture high quality metallic resonators.