Vibrating Flexoelectric Micro-Beams as Angular Rate Sensors

We studied flexoelectrically excited/detected bending vibrations in perpendicular directions of a micro-beam spinning about its axis. A set of one-dimensional equations was derived and used in a theoretical analysis. It is shown that the Coriolis effect associated with the spin produces an electrical output proportional to the angular rate of the spin when it is small. Thus, the beam can be used as a gyroscope for angular rate sensing. Compared to conventional piezoelectric beam gyroscopes, the flexoelectric beam proposed and analyzed has a simpler structure.

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.

Research on the signal process of a bell-shaped vibratory angular rate gyro

A bell-shaped vibratory angular rate gyro, which is inspired by the Chinese traditional bell, is a kind of axisymmetric shell resonator gyroscope. Its sensitive element is a vibratory-like Chinese traditional bell, using a piezoelectric element on the wall of the vibrator to detect the standing wave's precession to solve the input angular rate. This work mainly studies the circuit system of a bell-shaped vibratory angular rate gyro. It discusses the process of circuit system design, analysis and experiment, in detail, providing the foundation to develop a bell-shaped vibratory angular rate gyro. Since the bell-shaped resonator's curved structure has the characteristics of large noise in the piezoelectric signal and large harmonics, this paper analyzes its working and signal detection method, then gives the whole plan of the circuit system, including the drive module, the detection module and the control loop. It also studies every part of the whole system, gives a detailed design and analysis process and proves part of the circuit system using digital simulation. At the end of the article, the test result of the circuit system shows that it can remove the disadvantages of the curved structure having large noise in the piezoelectric signal and large harmonics and is more effective at solving the input angular rate.

Characterization of the bell-shaped vibratory angular rate gyro

The bell-shaped vibratory angular rate gyro (abbreviated as BVG) is a novel shell vibratory gyroscope, which is inspired by the Chinese traditional bell. It sensitizes angular velocity through the standing wave precession effect. The bell-shaped resonator is a core component of the BVG and looks like the millimeter-grade Chinese traditional bell, such as QianLong Bell and Yongle Bell. It is made of Ni43CrTi, which is a constant modulus alloy. The exciting element, control element and detection element are uniformly distributed and attached to the resonator, respectively. This work presents the design, analysis and experimentation on the BVG. It is most important to analyze the vibratory character of the bell-shaped resonator. The strain equation, internal force and the resonator's equilibrium differential equation are derived in the orthogonal curvilinear coordinate system. When the input angular velocity is existent on the sensitive axis, an analysis of the vibratory character is performed using the theory of thin shells. On this basis, the mode shape function and the simplified second order normal vibration mode dynamical equation are obtained. The coriolis coupling relationship about the primary mode and secondary mode is established. The methods of the signal processing and control loop are presented. Analyzing the impact resistance property of the bell-shaped resonator, which is compared with other shell resonators using the Finite Element Method, demonstrates that BVG has the advantage of a better impact resistance property. A reasonable means of installation and a prototypal gyro are designed. The gyroscopic effect of the BVG is characterized through experiments. Experimental results show that the BVG has not only the advantages of low cost, low power, long work life, high sensitivity, and so on, but, also, of a simple structure and a better impact resistance property for low and medium angular velocity measurements.

Dynamic Characteristics of Vertically Coupled Structures and the Design of a Decoupled Micro Gyroscope

In a vertical type, vibratory gyroscope, the coupled motion between reference (driving) and sensing vibrations causes the zero-point output, which is the unwanted sensing vibration without angular velocity. This structural coupling leads to an inherent discrepancy between the natural frequencies of the reference and the sensing oscillations, causing curve veering in frequency loci. The coupled motion deteriorates sensing performance and dynamic stability. In this paper, the dynamic characteristics associated with the coupling phenomenon are theoretically analyzed. The effects of reference frequency and coupling factor on the rotational direction and amplitude of elliptic oscillation are determined. Based on the analytical studies on the coupling effects, we propose and fabricate a vertically decoupled vibratory gyroscope with the frequency matching.

A review of analyses related to vibrations of rotating piezoelectric bodies and gyroscopes

A review of analyses on vibrations of rotating piezoelectric structures for applications in piezoelectric angular rate sensors is presented. The operating principle and the basic behaviors of piezoelectric gyroscopes are shown by a simple example. Structural shapes and vibration modes that can be used to make gyroscopes are summarized. Analytical and numerical results from the three-dimensional equations of a rotating piezoelectric body and the corresponding one- and two-dimensional theories of piezoelectric beams, rings, plates, and shells are reviewed.

Analysis of a rotating elastic beam with piezoelectric films as an angular rate sensor

The flexural vibration of an elastic beam with surface-bonded piezoelectric films rotating about its axis is studied. One-dimensional equations governing the motion of the beam are developed, including the effects of Coriolis and centrifugal forces. The equations are used in the analysis of the flexural vibration of the beam under the excitation of an alternating electric voltage. Forced vibration solution is obtained. The beam can be used as a gyroscope for detecting the angular rate of the rotation. Voltage sensitivity and its dependence on various geometric and physical parameters are examined.