Yulie Wu

A Study of the Temperature Characteristics of Vibration Mode Axes for Vibratory Cylinder Gyroscopes

The zero bias stability, which is an important performance parameter for vibratory cylinder gyroscopes, is high sensitive to temperature change. It is considered that the varying temperature makes the vibration mode axes unstable, which has significant influence on the zero bias stability. This paper will investigate this problem in detail. First, the relationships between the angular positions of vibration mode axes and the zero bias are analyzed. Secondly, the thermal-modal model of the cylinder resonator with several defects such as mass imbalance, frequency split (FS), and geometry errors are developed by ANSYS. Simulation results show that with the increase of temperature, angular positions of the vibration mode axes obviously change, which leads to a dramatic zero bias drift. Finally, several major influence factors on the angular position stability of vibration mode axes, including frequency split, geometry errors, thermal elastic modulus coefficient (TEMC) and thermal expansion coefficient (TEC) are analyzed in detail. Simulation results in this paper will be helpful for deep understanding of the drift principle of zero bias induced by temperature for vibratory cylinder gyroscopes and also be helpful for further temperature compensation or control.

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.

Structural-Acoustic Coupling Effects on the Non-Vacuum Packaging Vibratory Cylinder Gyroscope

The resonant shells of vibratory cylinder gyroscopes are commonly packaged in metallic caps. In order to lower the production cost, a portion of vibratory cylinder gyroscopes do not employ vacuum packaging. However, under non-vacuum packaging conditions there can be internal acoustic noise leading to considerable acoustic pressure which is exerted on the resonant shell. Based on the theory of the structural-acoustic coupling, the dynamical behavior of the resonant shell under acoustic pressure is presented in this paper. A finite element (FE) model is introduced to quantitatively analyze the effect of the structural-acoustic coupling. Several main factors, such as sealing cap sizes and degree of vacuum which directly affect the vibration of the resonant shell, are studied. The results indicate that the vibration amplitude and the operating frequency of the resonant shell will be changed when the effect of structural-acoustic coupling is taken into account. In addition, an experiment was set up to study the effect of structural-acoustic coupling on the sensitivity of the gyroscope. A 32.4 mV/°/s increase of the scale factor and a 6.2 Hz variation of the operating frequency were observed when the radial gap size between the resonant shell and the sealing cap was changed from 0.5 mm to 20 mm.

A Novel Vibration Mode Testing Method for Cylindrical Resonators Based on Microphones

Non-contact testing is an important method for the study of the vibrating characteristic of cylindrical resonators. For the vibratory cylinder gyroscope excited by piezo-electric electrodes, mode testing of the cylindrical resonator is difficult. In this paper, a novel vibration testing method for cylindrical resonators is proposed. This method uses a MEMS microphone, which has the characteristics of small size and accurate directivity, to measure the vibration of the cylindrical resonator. A testing system was established, then the system was used to measure the vibration mode of the resonator. The experimental results show that the orientation resolution of the node of the vibration mode is better than 0.1°. This method also has the advantages of low cost and easy operation. It can be used in vibration testing and provide accurate results, which is important for the study of the vibration mode and thermal stability of vibratory cylindrical gyroscopes.

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.

Modeling and analysis of mechanical Quality factor of the resonator for cylinder vibratory gyroscope

Mechanical Quality factor(Q factor) of the resonator is an important parameter for the cylinder vibratory gyroscope(CVG). Traditional analytical methods mainly focus on a partial energy loss during the vibration process of the CVG resonator, thus are not accurate for the mechanical Q factor prediction. Therefore an integrated model including air damping loss, surface defect loss, support loss, thermoelastic damping loss and internal friction loss is proposed to obtain the mechanical Q factor of the CVG resonator. Based on structural dynamics and energy dissipation analysis, the contribution of each energy loss to the total mechanical Q factor is quantificationally analyzed. For the resonator with radius ranging from 10 mm to 20 mm, its mechanical Q factor is mainly related to the support loss, thermoelastic damping loss and internal friction loss, which are fundamentally determined by the geometric sizes and material properties of the resonator. In addition, resonators made of alloy 3J53 (Ni42CrTiAl), with different sizes, were experimentally fabricated to test the mechanical Q factor. The theoretical model is well verified by the experimental data, thus provides an effective theoretical method to design and predict the mechanical Q factor of the CVG resonator.

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.

A Simple Acoustic Method for Modal Parameter Measurement of the Resonator for Vibratory Shell Gyroscope

In this paper, an acoustic method measuring the frequency split, quality factor and modal deflection of the resonator for vibratory shell gyroscope (VSG) is presented. This method is based on the superposition and decomposition of acoustic waves generated by standing wave eigenmodes of the resonator. The acoustic signals from an imperfect resonator comprise two standing waves of different frequencies and orientations. Theoretical study shows that the oscillating period and trough-peak ratio of the composite acoustic wave are strongly related to the modal parameters of the resonator. Therefore, the modal parameters of the resonator can be obtained via parameter fitting of the acoustic signal. The measurement error due to vibration drift is also analyzed in the theoretical study. The proposed method could be a simple and fast way to measure the main modal parameters of the VSG resonators without using sophisticated or costly equipments. Experiments were implemented to identify the modal parameters of a typical cylindrical resonator using the acoustic method. For the sake of comparison, traditional electrical and optical methods were also employed to measure the modal parameters. The experimental results show that the modal parameters measured by the acoustic method are close to those obtained from the traditional methods.

Influences of the Structure Parameters on Sensitivity and Brownian Noise of the Disk Resonator Gyroscope

This paper presents a comprehensive investigation of the influences of the structure parameters on the sensitivity and Brownian noise of the disk resonator gyroscope (DRG). The mechanical sensitivity, transducer sensitivity, Brownian displacement, and Brownian noise floor of the DRG with varying structural parameters (including ring number, resonator diameter, structure height, and anchor size) are calculated based on the finite-element method (COMSOL Multiphysics). Each parameter is studied independently. Meanwhile, useful comparison between the DRG and the ring vibratory gyroscope is made, which indicates that the DRG has great advantages over the transducer sensitivity and Brownian noise. Last but not least, a multi-objective optimization method is used to design the ring thickness distribution of the DRG and an instructive ring thickness distribution designing rule is obtained. The preceding study can give an explicit guideline for designing all kinds of DRG and may also provide useful information for designing other micro gyroscopes. The multi-objective optimization method could be expanded to include other objectives, constraints, or variables relevant to all kinds of gyroscopes or other microelectromechanical systems devices. [2016-0136]