The micromechanical silicon resonant accelerometer has attracted considerable attention in the research and development of high-precision MEMS accelerometers because of its output of quasi-digital signals, high sensitivity, high resolution, wide dynamic range, anti-interference capacity and good stability. Because of the mismatching thermal expansion coefficients of silicon and glass, the micromechanical silicon resonant accelerometer based on the Silicon on Glass (SOG) technique is deeply affected by the temperature during the fabrication, packaging and use processes. The thermal stress caused by temperature changes directly affects the frequency output of the accelerometer. Based on the working principle of the micromechanical resonant accelerometer, a special accelerometer structure that reduces the temperature influence on the accelerometer is designed. The accelerometer can greatly reduce the thermal stress caused by high temperatures in the process of fabrication and packaging. Currently, the closed-loop drive circuit is devised based on a phase-locked loop. The unloaded resonant frequencies of the prototype of the micromechanical silicon resonant accelerometer are approximately 31.4 kHz and 31.5 kHz. The scale factor is 66.24003 Hz/g. The scale factor stability is 14.886 ppm, the scale factor repeatability is 23 ppm, the bias stability is 23 μg, the bias repeatability is 170 μg, and the bias temperature coefficient is 0.0734 Hz/°C.

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.

The bandwidth characteristics of a tuning fork micro-gyroscope with mechanically coupled sense mode were investigated in this paper to provide some references for mechanical bandwidth design. The concept of sense mode mechanical coupling is introduced first. Theoretical frequency response analyses were then carried out on the mechanical part of the gyroscope. Equations representing the relationships between the differential output signal and the frequency of the input angular rate were deduced in full frequency range and further simplified in low frequency range. Based on these equations, bandwidth characteristics under ideal and non-ideal conditions are discussed. Analytical results show that under ideal conditions, the bandwidth characteristics of a tuning fork micro-gyroscope are similar to those of a single mass micro-gyroscope, but under non-ideal conditions, especially when sense mass and/or stiffness are asymmetric, the bandwidth characteristics would be quite different because the in-phase mode would participate in the anti-phase vibration response. Experimental verifications were carried out on two micro-gyroscope prototypes designed in our laboratory. The deduced equations and analytical results can be used in guiding the mechanical bandwidth design of tuning fork micro-gyroscopes with mechanically coupled sense mode.

This paper presents the design and implementation of a dual-mass MEMS gyroscope with high shock resistance by improving the in-phase frequency of the gyroscope and by using a two-stage elastic stopper mechanism and proposes a Simulink shock model of the gyroscope equipped with the two-stage stopper mechanism, which is a very efficient method to evaluate the shock resistance of the gyroscope. The structural design takes into account both the mechanical sensitivity and the shock resistance. The design of the primary structure and the analysis of the stopper mechanism are first introduced. Based on the expression of the restoring force of the stopper beam, the analytical shock response model of the gyroscope is obtained. By this model, the shock response of the gyroscope is theoretically analyzed, and the appropriate structural parameters are obtained. Then, the correctness of the model is verified by finite element (FE) analysis, where the contact collision analysis is introduced in detail. The simulation results show that the application of the two-stage elastic stopper mechanism can effectively improve the shock resistance by more than 1900 g and 1500 g in the x- and y-directions, respectively. Finally, experimental verifications are carried out by using a machete hammer on the micro-gyroscope prototype fabricated by the deep dry silicon on glass (DDSOG) technology. The results show that the shock resistance of the prototype along the x-, y- and z-axes all exceed 10,000 g. Moreover, the output of the gyroscope can return to normal in about 2 s.

This paper focuses on the detailed design issues of a peculiar quadrature reduction method named system stiffness matrix diagonalization, whose key technology is the design and application of quadrature compensation patterns. For bulk silicon micro-gyroscopes, a complete design and application case was presented. The compensation principle was described first. In the mechanical design, four types of basic structure units were presented to obtain the basic compensation function. A novel layout design was proposed to eliminate the additional disturbing static forces and torques. Parameter optimization was carried out to maximize the available compensation capability in a limited layout area. Two types of voltage loading methods were presented. Their influences on the sense mode dynamics were analyzed. The proposed design was applied on a dual-mass silicon micro-gyroscope developed in our laboratory. The theoretical compensation capability of a quadrature equivalent angular rate no more than 412 °/s was designed. In experiments, an actual quadrature equivalent angular rate of 357 °/s was compensated successfully. The actual compensation voltages were a little larger than the theoretical ones. The correctness of the design and the theoretical analyses was verified. They can be commonly used in planar linear vibratory silicon micro-gyroscopes for quadrature compensation purpose.

The output of the micromachined silicon resonant accelerometer (MSRA) is prone to drift in a temperature-changing environment. Therefore, it is crucial to adopt an appropriate suppression method for temperature error to improve the performance of the accelerometer. In this study, an improved firefly algorithm-backpropagation (IFA-BP) neural network is proposed in order to realize temperature compensation. IFA can improve a BP neural network’s convergence accuracy and robustness in the training process by optimizing the initial weights and thresholds of the BP neural network. Additionally, zero-bias experiments at room temperature and full-temperature experiments were conducted on the MSRA, and the reproducible experimental data were used to train and evaluate the temperature compensation model. Compared with the firefly algorithm-backpropagation (FA-BP) neural network, it was proven that the IFA-BP neural network model has a better temperature compensation performance. The experimental results of the zero-bias experiment at room temperature indicated that the stability of the zero-bias was improved by more than an order of magnitude after compensation by the IFA-BP neural network temperature compensation model. The results of the full-temperature experiment indicated that in the temperature range of −40 °C~60 °C, the variation of the scale factor at full temperature improved by more than 70 times, and the variation of the bias at full temperature improved by around three orders of magnitude.