Zhanqiang Hou

Design of a Disk Resonator Gyroscope With High Mechanical Sensitivity by Optimizing the Ring Thickness Distribution

In this paper, we present the mechanical sensitivity improvement of a disk resonator gyroscope (DRG) by optimizing the thickness distribution of the nested rings. The mechanical sensitivities of the DRGs with uniform, linearly changing, and step changing rings have been simulated. The results suggest that the ring thickness distribution has great influence on the performance of the DRG. Then, the optimized ring thickness distribution was obtained by using the traditional method of moving asymptotes (MMA), which result in a 24% improvement of the mechanical sensitivity. Finally, the bio-inspired particle swarm optimization (PSO) algorithm has also been used. The optimization results of PSO coincide well with that of MMA, and the optimized result is the global optimum. Meanwhile, the optimized distribution rules can be used on the series of DRGs and the optimization methods can be widely used on other microelectromechanical systems (MEMS) devices.

Effect of Axial Force on the Performance of Micromachined Vibratory Rate Gyroscopes

It is reported in the published literature that the resonant frequency of a silicon micromachined gyroscope decreases linearly with increasing temperature. However, when the axial force is considerable, the resonant frequency might increase as the temperature increases. The axial force is mainly induced by thermal stress due to the mismatch between the thermal expansion coefficients of the structure and substrate. In this paper, two types of micromachined suspended vibratory gyroscopes with slanted beams were proposed to evaluate the effect of the axial force. One type was suspended with a clamped-free (C-F) beam and the other one was suspended with a clamped-clamped (C-C) beam. Their drive modes are the bending of the slanted beam, and their sense modes are the torsion of the slanted beam. The relationships between the resonant frequencies of the two types were developed. The prototypes were packaged by vacuum under 0.1 mbar and an analytical solution for the axial force effect on the resonant frequency was obtained. The temperature dependent performances of the operated mode responses of the micromachined gyroscopes were measured. The experimental values of the temperature coefficients of resonant frequencies (TCF) due to axial force were 101.5 ppm/°C for the drive mode and 21.6 ppm/°C for the sense mode. The axial force has a great influence on the modal frequency of the micromachined gyroscopes suspended with a C-C beam, especially for the flexure mode. The quality factors of the operated modes decreased with increasing temperature, and changed drastically when the micromachined gyroscopes worked at higher temperatures.

A novel sandwich differential capacitive accelerometer with symmetrical double-sided serpentine beam-mass structure

This paper presents a novel differential capacitive silicon micro-accelerometer with symmetrical double-sided serpentine beam-mass sensing structure and glass–silicon–glass sandwich structure. The symmetrical double-sided serpentine beam-mass sensing structure is fabricated with a novel pre-buried mask fabrication technology, which is convenient for manufacturing multi-layer sensors. The glass–silicon–glass sandwich structure is realized by a double anodic bonding process. To solve the problem of the difficulty of leading out signals from the top and bottom layer simultaneously in the sandwich sensors, a silicon pillar structure is designed that is inherently simple and low-cost. The prototype is fabricated and tested. It has low noise performance (the peak to peak value is 40 μg) and μg-level Allan deviation of bias (2.2 μg in 1 h), experimentally demonstrating the effectiveness of the design and the novel fabrication technology.

Effect of parasitic resistance on a MEMS vibratory gyroscopes due to temperature fluctuations

Parasitic resistance is one of the most prevalent error sources preventing the performance of MEMS vibratory gyroscopes. This paper reports the effect of parasitic resistance on the performance of a MEMS vibratory gyroscope which is suspended with a slanted cantilever. The parasitic resistance and capacitance of the micromachined gyroscope were analyzed. The electrical model of the overall system was built. The transfer function of the gyroscope was derived as a parallel connection of a mass-spring-damper model and a R-C network made of parasitic resistance and capacitance. The parasitic resistance affects on the performance of the frequency response was simulated. The temperature characteristic of the frequency response was tested, which is in accordance with the simulated results. The gain of the frequency response changed about 20% in dBs over the range of 30°C to 60°C.

Enhanced sensitivity in a butterfly gyroscope with a hexagonal oblique beam

A new approach to improve the performance of a butterfly gyroscope is developed. The methodology provides a simple way to improve the gyroscope’s sensitivity and stability, by reducing the resonant frequency mismatch between the drive and sense modes. This method was verified by simulations and theoretical analysis. The size of the hexagonal section oblique beam is the major factor that influences the resonant frequency mismatch. A prototype, which has the appropriately sized oblique beam, was fabricated using precise, time-controlled multilayer pre-buried masks. The performance of this prototype was compared with a non-tuned gyroscope. The scale factor of the prototype reaches 30.13 mV/ ˚/s, which is 15 times larger than that obtained from the non-tuned gyroscope. The bias stability of the prototype is 0.8 ˚/h, which is better than the 5.2 ˚/h of the non-tuned devices.

Improvement of bias stability for a micromachined gyroscope based on dynamic electrical balancing of coupling stiffness

Abstract. We present a dynamic electrical balancing of coupling stiffness for improving the bias stability of micromachined gyroscopes, which embeds the coupling stiffness in a closed-loop system to make the micromachined gyroscope possess more robust bias stability by suppressing the variation of coupling stiffness. The effect of the dynamic electrical balancing control is theoretically analyzed and implemented using a silicon micromachined gyroscope as an example case. It has been experimentally shown that, comparing with open loop detection, the proposed method increased the stability of the amplitude of the mechanical quadrature signal by 38 times, and therefore improved the bias stability by 5.2 times from 89 to 17  deg/h, and the temperature stability of scale factor by 2.7 times from 622 to 231  ppm/°C. Experimental results effectively indicated the theoretical model of dynamic electrical balancing of coupling stiffness.

Micro shell resonator with T-shape masses for improving out-of-plane electrostatic transduction efficiency

This paper presents a novel micro shell resonator (MSR) with eight circular-distributed T-shape masses based on fused silica (FS), which is fabricated by combining micro blowing-torch process with high precise mold. FS is been heated instantaneously above the softening point by micro blowing-torch and flow down into the mold. The resonator shell is shaped using a pressure difference and surface tension whose precision is determined by the precision of mold. The key process is that eight T-shape masses are defined along the rim of resonator shell. Electrostatic transduction is used to detect spatial deformation of resonators by out-of-plane electrodes, which has wineglass modes at 10.27 k and 10.70 k with quality factors of 12558 and 6964. A large capacitance enabled by T-shape masses for driving and sensing is measured as 1.31pF~1.6pF, which improves out-of-plane transduction efficiency. Besides, it is more convenient to trim the frequency by adding or removing mass on the T-shape masses.

Structural improvement in resonant silicon sensors to sub-ppm/°C temperature coefficient of resonance frequency

Abstract. This paper presents a structural improvement method for temperature coefficient of resonance frequency (TCF) in resonant silicon sensors. A silicon resonator, whose mass was suspended by a slanted flexible beam, was adopted in this study. The slanted suspension beam was formed by (1 0 0) and (1 1 1) crystal planes and fabricated by anisotropic wet etching. We propose a stress buffer structure to improve the robustness of resonance frequency against temperature variations. Theoretical considerations of the tested resonator are proposed to augment the effect of the buffer structure. The temperature dependence of the resonance frequency is experimentally characterized over the range −40°C to 60°C. The TCF of the original resonators with no stress buffer structure was linearly fitted to be 36 and 40  ppm/°C. After using an appropriate stress buffer structure, the TCF is linearly fitted to be −0.98 and 0.36  ppm/°C. The experimental results suggest that the TCF of the resonator is improved to sub-ppm/°C level by using a stress buffer structure, which has more than an order of magnitude improvement comparing to the original one. The small range of TCF is much more convenient to be compensated by electrical ways.

Stiffness-mass decoupled silicon disk resonator for high resolution gyroscopic application with long decay time constant (8.695 s)

We propose a stiffness-mass decoupling concept for designing large effective mass, low resonant frequency, small size, and high quality factor micro/nanomechanical resonators. This technique is realized by hanging lumped masses on the frame structure. An example of a stiffness-mass decoupled silicon disk resonator for gyroscopic application is demonstrated. It shows a decay time constant of 8.695 s, which is at least 5 times longer than that of the pure frame silicon disk resonator and is even comparable with that of the micromachined three-dimensional wine-glass resonators made from diamond or fused silica. The proposed design also shows a Brownian noise induced angle random walk of 0.0009°/√h, which is suitable for making an inertial grade MEMS gyroscope.

The mechanical sensitivity optimization of a disk resonator gyroscope with mutative ring thickness

In this paper, we present the mechanical sensitivity improvement of a disk resonator gyroscope (DRG) by optimizing the thickness distribution of the nested rings. The mechanical sensitivities of the DRGs with uniform, linearly changing and step changing rings have been simulated. The results suggest that the ring thickness distribution has great influence on the performance of the DRG. Then the optimized ring thickness distribution was obtained by using the bio-inspired particle swarm optimization (PSO) algorithm. The rule of the optimized ring thickness distribution is that the outer ring is thicker than the other rings (1.7-1.8 times for this DRG) whereas the other rings should be as thin as possible. Meanwhile the optimized distribution rules can be used on series of DRGs and the optimization methods can be widely used on other MEMS devices.