Tuning Fork Gyroscope Research Articles

Free Vibrations and Energy Transfer Analysis of the Vibrating Piezoelectric Gyroscope Based on the Linear and Nonlinear Decoupling Methods

The present research is concerned with the free vibrations and energy transfer of a vibrating gyroscope, which is composed of a flexible beam with surrounded piezoelectric films in a rotating space. The governing equations involve nonlinear curvature, and rotary inertia of an in-extensional rotating piezoelectric beam is obtained by using the transformation of two Euler angles and the extended Hamilton principle. The gyroscopic effect due to the rotating angular speed is investigated in the frame of complex modes based on the invariant manifold method. The effects of angular speed, initial values, and electrical resistance to the nonlinear natural frequencies of a rotating piezoelectric beam are studied by both linear and nonlinear decoupling methods. The results reveal that the rotation causes one nonlinear frequency to bifurcate into a pair of frequencies: one forward and one backward nonlinear frequencies. The variation of the frequency with the angular speed is used to measure the angular speed. Finally, the energy transfer due to nonlinear coupling under 1:1 internal resonance condition and the energy transfer due to the linear gyroscopic decoupling are investigated.

A Decoupling Design with T-Shape Structure for the Aluminum Nitride Gyroscope.

This paper reports a novel design for the decoupling of microelectromechanical systems (MEMS) gyroscopes. The MEMS gyroscope is based on piezoelectric aluminum nitride (AlN) film, and the main structure is a mass hung by T-shape beams. A pair of parallel drive electrodes are symmetrically placed on the surface of the vertical bar for driving the oscillating mass. A serpentine sense electrode is placed on the lateral bar. When the gyroscope is oscillating in drive mode, charges with equal quantity and opposite sign will be polarized and distributed symmetrically along the lateral bar. These charges neutralize each other at the sense electrode. Therefore, no coupling signals can be detected from the sense electrode. This design can realize the decoupling between the drive mode and sense mode. In this work, the T-shape decoupled structure was designed as the key component of an AlN piezoelectric gyroscope and the whole structure was simulated by COMSOL Multiphysics 5.2a. The working principle of the decoupling is described in detail. Electrical properties were characterized by the dynamic signal analyzer. According to the test results, the drive mode and the sense mode are decoupled. The coefficient of orthogonal coupling is 1.55%.

Driving and detection system of vibrating piezoelectric gyroscope at atmospheric pressure for multi-axial inertia sensor

We developed a driving and sensing system for a multi-axial inertial sensor that operates at atmospheric pressure using vibrating piezoelectric gyroscope sensors. We developed driving circuit modules with self-oscillation and an automatic gain controller and a synchronous detection circuit for demodulation of the sensing signals. The self-oscillation function was tested using a charging amplifier and phase shifter. Self-oscillation works by detecting a displacement signal differentially, adjusting it by a phase of π/2, and sending it to the oscillation signal generator. The stop time was improved from 15 to 3 ms using an inverse driving module. The driving circuit maintained stable oscillation throughout operation of the gyroscope because the automatic gain controller was added to the self-oscillation loop. A velocity demodulation method was implemented for the sensor to demodulate the outputs of angular velocities; this is more beneficial for decoupled vibrating gyroscopes compared to displacement demodulation. The response under angular rate was 1°/s in the x- and y-directions, and the measurement sensitivity was 17.2 µV/(°/s). The measured Q of the fabricated piezoelectric gyroscope was maintained stably at 400–500 at normal pressure.

Mechanical response of outer frames in tuning fork gyroscope model with connecting diamond-shaped frame

In tuning fork micro-gyroscopes, two outer frames are connected by using the linking elements. The driving vibrations of the two outer frames are required to be exactly opposite to generate the opposite sensing modes perpendicular to driving direction. These opposite driving vibrations are provided by a mechanical structure named the diamond-shaped frame. This paper presents mechanical responses of two outer frames in a proposed model of tuning fork gyroscope when an external force with different types is applied to them. The results show that the presence of a diamond-shaped frame guarantees the absolute anti-phase mode for the driving vibrations of outer frames.

Higher-Order Overtone Thickness-Shear Vibrations of Multilayered Thin-Film Acoustic Wave Resonators and Angular Rate Sensing

We propose a new structure for piezoelectric gyroscopes. It is made from multilayered thin films of AlN or ZnO with alternating c-axes along the film thickness. It is shown theoretically that when such a film is electrically driven into higher-order overtone thickness-shear vibration in one of the two in-plane directions of the film and is rotating about the film normal, the Coriolis force due to the rotation causes a higher-order overtone thicknessshear vibration in a perpendicular direction with an electrical output that can be used to measure the angular rate of the rotation. Different from existing thickness-shear mode piezoelectric gyroscopes which are based on the fundamental or the second overtone thickness-shear mode, the proposed gyroscope operates with higher-order overtone thickness-shear modes with higher frequencies and hence potentially higher sensitivity. Because of the overtone modes, the Coriolis force acting on the gyroscope forms a self-equilibrated system and does not transmit a net force or torque to the mounting structure. This implies higher device quality factor and better performance.

Research of influence of technological admissions on characteristics of a solid-state wave gyroscope

The route of design and technique of simulation of a wave solid-state gyroscope with the ring resonator are developed. Simulation of dependences of gyroscope characteristics on design data and their optimization for the job of the necessary mode of movement, in particular, of resonance frequency of excitation of the second mode are executed. The technique of compensation of the mass defects resulting from admissions on technological operations of production of a wave solid-state gyroscope (technological defects) and leading to the shift of initial provision of nodal points is presented.

Research on Adjusting Mass Balance of Micromachined Quartz Tuning Fork Gyroscopes

To eliminate the mechanical coupling error caused between the driving fork and the picking up fork, the mass balancing method was used to decrease the mechanical coupling error by the laser etching frequency trimming technique on tuning forks. In order to get high-quality quartz tuning forks, the mechanical coupling error and frequency drift caused by machining must be resolved. The mechanical coupling error was eliminated effectively by the mass balancing method that could compensate the machining error and realize the control of the quartz tuning fork gyroscope at the best resonant frequency. Experimental results showed that, by the mass balancing method, when the symmetry of driving tuning forks and readout tuning forks was amended, the quality factor of driving forks was obviously increased, the driving voltage descended, the mechanical coupling error decreased and the impedance characteristics of quartz tuning fork was improved obviously.

Development of an algorithm for suppressing frequency splitting of an axisymmetric resonator of a wave solid-state gyroscope with optical detection

Development of an algorithm for suppressing frequency splitting of an axisymmetric resonator of a wave solid-state gyroscope with optical detection

Model and experiment of scale factor acceleration sensitivity of MEMS gyroscope in high acceleration environment

With the development of MEMS gyroscope, acceleration sensitivity is becoming an important factor in application. The acceleration sensitivity would produce an obvious output error, and researchers mainly focus on bias acceleration sensitivity. Yet, in environment of high acceleration and angular rate, it is the scale factor acceleration sensitivity that influences the output most, and there is little research on it. In this paper, scale factor acceleration sensitivity of MEMS gyroscope in high acceleration environment is investigated with our established theoretical model and experimental measurement. Based on our proposed method of measuring the acceleration sensitivity in environment of high acceleration and angular rate, the MEMS tuning fork gyroscope is used for the measurement. The results show that the output error caused by acceleration can be up to − 30.1°/s and the scale factor acceleration sensitivity contributes the most. The coefficient of scale factor acceleration sensitivity is 35 ppm/g under 50g acceleration, and this coefficient increases linearly with acceleration that coincides with theoretical model. Lastly, some suggestions of decreasing scale factor acceleration sensitivity are given. This work is useful for the researchers to improve the performance of acceleration sensitivity of MEMS gyroscope.

Design, fabrication and on-the-die characterization of a MEMS tuning-fork gyroscope

In this paper, we report design, fabrication and characterization of a MEMS tuning-fork gyroscope. The main novelty of the reported work is in devising and using an experimental set-up for angular rate measurements using an open die MEMS gyroscope structure. A detailed methodology of characterization of the gyroscope is discussed. The complete experimental setup for angular rate measurement is presented. Using in-house fabrication facilities, the gyroscopes are fabricated and tested for rate measurements at different applied rotation rates from 1 $$^{\circ }/\hbox {s}$$ to $$35^{\circ }/\hbox {s}$$ . The rate sensitivity is recorded as $$60\,\upmu \hbox {V}/^{\circ }/\hbox {s}$$ with a noise floor of $$20\,\upmu \hbox {V}$$ .

Design of A New Structure Quartz MEMS Gyroscope with High Sensitivity

This paper proposes a new structure of quartz MEMS gyroscope. Compared with the traditional double-ended quartz gyroscope, the grooves are symmetrically arranged in the sense tuning forks of new gyroscope, and the two pairs of extra electrodes are added on the grooves. The extra symmetrical sense electrodes can increase the strong electric field, and the increased area of sense electrodes is beneficial to detect charge signals. The ANSYS finite element software is used to simulate the designed structure. The influence of frequency difference is analyzed by modal type, and the parameters of quartz tuning fork gyroscope are optimized to find the suitable structure, the frequency difference of the gyroscope is 203.42Hz. At the same time, the sensitivity is analyzed by harmonic type. The results show that the increasing of the area electrode is efficient, the efficiency of electric field detection is enhanced. The sensitivity of the quartz MEMS gyroscope is increased by more than 15%.

Vibration-Induced Errors in MEMS Tuning Fork Gyroscopes with Imbalance.

This paper discusses the vibration-induced error in non-ideal MEMS tuning fork gyroscopes (TFGs). Ideal TFGs which are thought to be immune to vibrations do not exist, and imbalance between two gyros of TFGs is an inevitable phenomenon. Three types of fabrication imperfections (i.e., stiffness imbalance, mass imbalance, and damping imbalance) are studied, considering different imbalance radios. We focus on the coupling types of two gyros of TFGs in both drive and sense directions, and the vibration sensitivities of four TFG designs with imbalance are simulated and compared. It is found that non-ideal TFGs with two gyros coupled both in drive and sense directions (type CC TFGs) are the most insensitive to vibrations with frequencies close to the TFG operating frequencies. However, sense-axis vibrations with in-phase resonant frequencies of a coupled gyros system result in severe error outputs to TFGs with two gyros coupled in the sense direction, which is mainly attributed to the sense capacitance nonlinearity. With increasing stiffness coupled ratio of the coupled gyros system, the sensitivity to vibrations with operating frequencies is cut down, yet sensitivity to vibrations with in-phase frequencies is amplified.

Z-axis tuning fork gyroscope having a controlled anti-phase and freestanding architecture: design and fabrication

This paper reports the design and fabrication of a z-axis tuning fork gyroscope (TFG) having anti-phase controlled and freestanding architectures. The gyroscope is designed to suppress the in-phase sensing mode by using a self-rotation ring. To improve the performance of the TFG by limiting the influence of the squeeze-film damping, the driving and sensing parts of the gyroscope were designed to oscillate in plane. Furthermore, by removing the substrate underneath the device, the slide-film damping in the gap between the proof masses and the substrate is eliminated. The proposed architecture is analysed by finite element method using ANSYS software. The simulated frequencies of the driving and sensing modes are 9.788 kHz and 9.761 kHz, respectively, which determines the sensor bandwidth of 27 Hz. The frequency difference between the driving and sensing modes and the parasitic ones is obtained to be 57.5%. The sensing displacement and driving displacement of the gyroscope at resonance are 0.104 μm and 6.034 μm, respectively. The gyroscope was fabricated based on the bulk micromachining technology. It is shown that the quality factor of the gyroscope is 111.2. The measured sensitivity of the sensor is evaluated to be 11.56 mV/°/s.

Design, Fabrication, and Modeling of a Novel Dual-Axis Control Input PZT Gyroscope.

Conventional gyroscopes are equipped with a single-axis control input, limiting their performance. Although researchers have proposed control algorithms with dual-axis control inputs to improve gyroscope performance, most have verified the control algorithms through numerical simulations because they lacked practical devices with dual-axis control inputs. The aim of this study was to design a piezoelectric gyroscope equipped with a dual-axis control input so that researchers may experimentally verify those control algorithms in future. Designing a piezoelectric gyroscope with a dual-axis control input is more difficult than designing a conventional gyroscope because the control input must be effective over a broad frequency range to compensate for imperfections, and the multiple mode shapes in flexural deformations complicate the relation between flexural deformation and the proof mass position. This study solved these problems by using a lead zirconate titanate (PZT) material, introducing additional electrodes for shielding, developing an optimal electrode pattern, and performing calibrations of undesired couplings. The results indicated that the fabricated device could be operated at to perform dual-axis actuations and position measurements. The calibration of the fabricated device was completed by system identifications of a new dynamic model including gyroscopic motions, electromechanical coupling, mechanical coupling, electrostatic coupling, and capacitive output impedance. Finally, without the assistance of control algorithms, the “open loop sensitivity” of the fabricated gyroscope was 1.82 μV/deg/s with a nonlinearity of 9.5% full-scale output. This sensitivity is comparable with those of other PZT gyroscopes with single-axis control inputs.

Study on vacuum packaging reliability of micromachined quartz tuning fork gyroscopes

Packaging technology of the micromachined quartz tuning fork gyroscopes by vacuum welding has been experimentally studied. The performance of quartz tuning fork is influenced by the encapsulation shell, encapsulation method and fixation of forks. Alloy solder thick film is widely used in the package to avoid the damage of the chip structure by the heat resistance and hot temperature, and this can improve the device performance and welding reliability. The results show that the bases and the lids plated with gold and nickel can significantly improve the airtightness and reliability of the vacuum package. Vacuum packaging is an effective method to reduce the vibration damping, improve the quality factor and further enhance the performance. The threshold can be improved nearly by 10 times.

Z-Axis Micromachined Tuning Fork Gyroscope with Low Air Damping

This paper reports on the design and fabrication of a z-axis tuning fork gyroscope which has a freestanding architecture. In order to improve the performance of the tuning fork gyroscope by eliminating the influence of the squeeze-film air damping, the driving and sensing parts of the gyroscope were designed to oscillate in-plane. Furthermore, by removing the substrate underneath the device, the slide-film air damping in the gap between the proof masses and the substrate was eliminated. The proposed architecture was analyzed by the finite element method using ANSYS software. The simulated frequencies of the driving and sensing modes were 9.788 and 9.761 kHz, respectively. The gyroscope was fabricated using bulk micromachining technology. The quality factor and sensitivity of the gyroscope operating in atmospheric conditions were measured to be 111.2 and 11.56 mV/°/s, respectively.

Линеаризация колебаний резонатора волнового твердотельного гироскопа и сил электростатических датчиков управления

Линеаризация колебаний резонатора волнового твердотельного гироскопа и сил электростатических датчиков управления

Влияние несовершенств формы на колебания кольцевого резонатора волнового твердотельного гироскопа

Влияние несовершенств формы на колебания кольцевого резонатора волнового твердотельного гироскопа

Equivalent circuit of piezoelectric resonant disk gyroscope through admittance circle method

This work aimed to construct a new equivalent circuit which is useful for the further studying of the resonator in the piezoelectric gyroscope. Measurements of the actual admittance circle are used to improve the parameters of the Van Dyke's model. Meanwhile, a parallel resistance to form the new equivalent circuit through analysis is added. The relative error of phase and impedance are 0.335 and 3.68%, respectively. Different values of parallel resistances are added to verify the rationality of the circuit. Contrast to the traditional Van Dyke's model, the new equivalent circuit is more complete in explaining the energy dissipation.

Dicing‐free SOI process based on wet release technology

A simple, low-cost and reliable dicing-free silicon-on-insulator (SOI) process is presented for solving three major challenges in manufacturing the microelectromechanical systems devices, i.e. stiction, notching and dicing damage. In this process, the cavity is used and patterned on the handle layer to solve the stiction problem, and the exposed oxide is removed in hydrofluoric acid (HF) solution before deep reactive ion etching (DRIE) on the structure layer to eliminate the notching effect's impact. The dies are attached temporally to a designed frame by the silicon dioxide. After removing the oxide using HF solution, the dies are separated from the wafer cleanly without dicing damage. The layout design rules on the front side and backside patterns are established. Furthermore, a grooved carrier wafer with specific design rules was introduced to enhance the yield rate of the process. Finally, a tuning fork gyroscope was fabricated to demonstrate the proposed fabrication process and a yield rate of over 81% was achieved. The process solves the stiction, notching and dicing damage problems only involving the apparatus associated with lithography and DRIE, offering an economic and complete SOI process solution.