Tuning Fork Gyroscope Research Articles

Bridging piezoelectric and electrostatic effects: a novel piezo-MEMS pitch/roll gyroscope with sub 10°/h bias instability

This paper proposes a novel piezo-MEMS pitch/roll gyroscope that co-integrates piezoelectric and electrostatic effects, for the first time achieves electrostatic mode-matching operation for piezoelectric gyroscopes. Movement of operated out-of-plane (OOP) mode (n = 3) and in-plane (IP) mode (n = 2) are orthogonal, ensuring that the OOP amplitude is not significantly limited by parallel plates set at nodes of IP mode. Therefore, a large OOP driving amplitude actuated by piezoelectric and frequency tuning in the IP sense mode trimmed by electrostatic can be achieved together with a low risk of pull-in, hence releases the trade-off between the tuning range and the linear actuation range. At a tuning voltage of 66 V, the frequency split decreased from 171 Hz to 0.1 Hz, resulting in a 167x times improvement in sensitivity. The mode-matched gyroscope exhibits an angle random walk (ARW) of 0.41°/√h and a bias instability (BI) of 8.85°/h on a test board within a customized vacuum chamber, marking enhancements of 68x and 301x, respectively, compared to its performance under mode-mismatch conditions. The BI performance of the presented pitch/roll gyroscope is comparable to that of the highest-performing mechanically trimmed piezo-MEMS yaw gyroscopes known to date, while offering the unique advantage of lower cost, better mode-matching resolution, and the flexibility of real-time frequency control.

UV laser formation of complex topologies for sensitive elements of navigation sensors based on surface acoustic waves

A method utilizing a UV laser to form complex electrode structures on the surface of the sensitive element prototype for a solid-state gyroscope (SSG) based on surface acoustic waves (SAW) was tested. The prospects of using the method are demonstrated in terms of the flexibility of changing the topology, the speed of navigation sensors prototypes manufacturing, and reducing the cost. Methods for forming surface structures on piezoelectric materials using an IR and UV laser are compared. The parameters of laser formation of a surface pattern for configuring the topology of a sensitive element by evaporation of a thin-film coating 5000 nm and 200 nm thick deposited on lithium niobate substrates are determined. The amplitude-frequency characteristics of the manufactured samples of SAW-based SSG sensing elements are obtained. Additionally a finite-element modeling was performed to obtain theoretical prediction of dependencies of the sensing element characteristics on the thickness of the metallization forming the electrodes. It was found that when using a fiber UV laser with a wavelength of 355 nm, it is necessary to impose more stringent requirements on the quality of metallization and on the calculation of laser radiation regimes for processing coatings with a thickness of 200 nm. It is shown that when using a UV laser, it is possible to manufacture more compact sensitive elements of navigation sensors on surface acoustic waves than when using IR lasers.

Virtual Coriolis-Force-Based Mode-Matching Micromachine-Optimized Tuning Fork Gyroscope without a Quadrature-Nulling Loop.

A VCF-based mode-matching micromachine-optimized tuning fork gyroscope is proposed to not only maximize the scale factor of the device, but also avoid use of an additional quadrature-nulling loop to prevent structure complexity, pick-up electrode occupation, and coupling with a mode-matching loop. In detail, a mode-matching, closed-loop system without a quadrature-nulling loop is established, and the corresponding convergence and matching error are quantitatively analyzed. The optimal straight beam of the gyro structure is then modeled to significantly reduce the quadrature coupling. The test results show that the frequency split is narrowed from 20 Hz to 0.014 Hz. The scale factor is improved 20.6 times and the bias instability (BI) is suppressed 3.28 times. The observed matching accuracy demonstrates that a mode matching system without a quadrature suppression loop is feasible and that the proposed device represents a competitive design for a mode-matching gyroscope.

A tuning fork gyroscope with drive-sense orthogonal thin-walled holes for high sensitivity

A tuning fork gyroscope (TFG) with orthogonal thin-walled round holes in the driving and sensing directions is proposed to improve sensitivity. The thin walls formed by through holes produce stress concentration, transforming the small displacement of tuning fork vibration into a large concentrated strain. When piezoelectric excitation or detection is carried out here, the driving vibration displacement and detection output voltage can be increased, thereby improving sensitivity. Besides, quadrature coupling can be suppressed because the orthogonal holes make the optimal excitation and detection positions in different planes. The finite element method is used to verify the benefits of the holes, and the parameters are optimized for better performance. The experimental results show that the sensitivity of the prototype gyroscope with a driving frequency of 890.68 Hz is 100.32 mV/(°/s) under open-loop driving and detection, and the rotation rate can be resolved at least 0.016 (°/s)/Hz, which is about 6.7 times better than that of the conventional TFG. In addition, the quadrature error is reduced by 2.7 times. The gyroscope has a simple structure, high reliability, and effectively improves sensitivity, which is helpful to guide the optimization of piezoelectric gyroscopes and derived MEMS gyroscopes.

Design and analysis of MEMS tuning fork gyroscope with dual mode ordering

AbstractThis paper reports a MEMS tuning fork gyroscope which can effectively reduce the acceleration output in both drive and sense directions. The structure adjusts the order of mechanical vibration modes through the design of internal and external lever coupling mechanism, moves the spurious in‐phase mode frequency above the antiphase operating frequency, and provides a large frequency separation between the two modes. It provides true mechanical rejection of external shocks and accelerations. Two comparative tuning fork gyroscopes (TFG) structures are designed, which have traditional coupling in the drive direction and sense direction respectively. Through modal simulation, the internal lever‐coupling brings the antiphase drive mode before the in‐phase drive mode and the external lever‐coupling brings the antiphase sense mode before the in‐phase sense mode. The harmonic response simulation of three stiffness unbalanced TFGs verifies that the mode ordering of two directions can effectively suppress the acceleration output. The results show that the new TFG structure can suppress the acceleration output by more than 80%, and the finite element simulation results are consistent with the theoretical calculation.

Nonlinear Dynamics of a Wave Solid-State Gyroscope Taking into Account the Electrical Resistance of an Oscillation Control Circuit

This article is concerned with investigating the nonlinear dynamics of the cylindrical resonator of a wave solid-state gyroscope. The nonlinearity of oscillations caused by the nonlinear properties of electrostatic control sensors is considered. This nonlinearity is derived by taking into account the finite ratio of resonator flexure to the small gap of electrostatic control sensors. The equations of the electromechanical system that in interconnected form describe the nonlinear mechanical oscillations of the gyroscope resonator and electrical oscillations in the control circuit are derived. The resulting differential equations belong to the class of Tikhonov systems, since the equation of electrical processes in the control circuit is singularly perturbed. By taking into account the low electrical resistance of the oscillation control circuit, which determines a small parameter at the derivative in the singularly perturbed equation of electrical processes, the nonlinear oscillations of the wave solid-state gyroscope resonator are studied. The small parameter method is used to obtain a mathematical model of the resonator dynamics, which jointly takes into account the nonlinearity of the resonator oscillations and the electrical resistance of the oscillation control circuit. A special method is proposed to reduce the nonlinear equations of the resonator dynamics to the standard form of the system of differential equations for averaging and the equations of the dynamics of the wave solid-state gyroscope resonator are averaged. It is shown that, in the case of nonlinear oscillations, consideration of the electrical resistance of the oscillation control circuit does not affect the angular velocity of the gyroscope drift, but causes slight dissipation of the oscillations, which also leads to an insignificant correction of the resonant frequency.

A dual-mass fully decoupled MEMS gyroscope with optimized structural design for minimizing mechanical quadrature coupling

Mechanical quadrature coupling is one of the main sources of zero-rate output in microelectromechanical system (MEMS) gyroscope, which limits the further improvement of gyroscope performance. This paper reports a dual-mass MEMS tuning fork gyroscope based on fully decoupled structure. The theoretical analysis and finite element method (FEM) simulation are performed to identify the sources of the mechanical quadrature error in detail and to find ways to optimize the structural design of MEMS gyroscope. The results show that reducing the quadrature coupling stiffness of local sensing components is a key factor in minimizing the overall gyroscope quadrature error. By deliberately optimization of the geometry of the sensing components including sense frame and the drive springs closed to the sense frame, the quadrature induced deformation of sense electrode can be reduced from 160 nm to 5.1 nm with a driving displacement of 1 μm based on FEM simulation. The equivalent angular rate output caused by quadrature coupling of each sense electrode can be reduced from 3960 °/s to 60 °/s. The optimized gyroscope operates in split-mode with open-loop readout. The measured scale factor of gyroscope is 90.46 LSB/(°/s) with a non-linearity of 810 ppm in the full scale range of ±300 °/s. The measurement result shows a bias instability of 8.9 °/h and an angular random walk (ARW) of 0.74°/h at room temperature, respectively. The proposed approach of structural improvements can be used to reduce the quadrature error of the gyroscope in processing tolerances.

Algorithms for Increasing the Accuracy of Solid-State Wave Gyroscopes

Introduction. Wave solid-state gyroscopes (SWG) are promising sensors of inertial information used in the navigation systems of air- and spacecrafts. Over the past decade, much attention has been paid to the problem of improving the accuracy of SWGs. The accuracy of measurements performed by inertial navigation instruments can be increased by developing effective algorithms, which fact determines the relevance of the present study. Research works conducted at the JSC Research Institute of Command Instruments are aimed at developing a compensationtype angular velocity sensor (AVS) based on an SWG with a cylindrical metal resonator, an electrostatic system for excitation of oscillations and information readout, with a digital feedback.Aim. To develop methods for increasing the accuracy of SWGs based on the connection between the measurement and excitation channels, as well as accounting for the uncompensated component.Materials and methods. To obtain information about the output signal of the sensing element (SE), the fast Fourier transform (FFT) method was used. A PID controller was used to control the effect on the sensitive element.Results. Methods for increasing the accuracy of an SWG-based AVS by means of compensating the output signal errors were proposed, whose correctness was confirmed experimentally. The use of the developed algorithm for reducing the instability of the zero-velocity signal allowed its root-mean-square deviation at startup to be decreased by 76.4 %. The application of the developed method for increasing the accuracy using the uncompensated component led to a decrease in the standard deviation by 69.52 %.Conclusion. The obtained experimental results demonstrate the possibility of improving SWG characteristics significantly by using various mathematical algorithms for processing information.

Investigation of the Functioning of the Electronics Unit and the Resonator of a Wave Solid-State Gyroscope in the Mode Angular Velocity Sensor

The principles of operation of a wave solid-state gyroscope are described using the example of a cylindrical metal resonator design, in which oscillations are created and a signal is picked up by means of piezoelectric elements located on the base of the resonator. The mode of positional excitation of primary oscillations and the formation of a feedback signal to ensure the operation of the resonator in the mode of an angular velocity sensor are considered. A block diagram of the conversion sequence of the signal taken from the piezoelectric elements of the axes of nodes and antinodes for the organization of feedbacks is given. Approaches to the construction of control loops for the amplitude and phase of oscillations to create primary oscillations and compensate for the amplitude of oscillations of the node axis are considered. The presence of these circuits makes it possible to ensure the operation of a wave solid-state gyroscope in the mode of an angular velocity sensor. For all areas of signal conversion, a mathematical description of computational processes has been compiled, based on the condition for the implementation of computational procedures by a digital computer. Mathematical dependences necessary for correcting the output signal — ensuring its linearity and stability in the range of operating temperatures and the range of measured angular velocities are compiled. The results of tests confirming the operability of a wave solid-state gyroscope in the mode of an angular velocity sensor are presented. An approach to constructing a resonator model based on the finite element method is considered. An approach to the verification of a finite element model is shown by comparing the results of an experimental study of the characteristics of the resonator with the simulation results.

Design and Optimization of a Novel MEMS Tuning Fork Gyroscope Microstructure.

This paper presents the design and optimization of a novel MEMS tuning fork gyroscope microstructure. In order to improve the mechanical sensitivity of the gyroscope, much research has been carried out in areas such as mode matching, improving the quality factor, etc. This paper focuses on the analysis of mode shape, and effectively optimizes the decoupling structure and size of the gyroscope. In terms of structural design, the vibration performance of the proposed structure was compared with other typical structures. It was found that slotting in the middle of the base improved the transmission efficiency of Coriolis vibration, and opening arc slots between the tines reduced the working modal order and frequency. In terms of size optimization, the Taguchi method was used to optimize the relevant feature sizes of the gyroscope. Compared with the initial structure, the transmission efficiency of Coriolis vibration of the optimized gyroscope was improved by about 18%, and the working modal frequency was reduced by about 2.7 kHz. Improvement of these two indicators will further improve the mechanical sensitivity of the gyroscope.

An Electrostatic MEMS Roll-Pitch Rotation Rate Sensor with In-Plane Drive Mode.

In this paper, we presented a novel electrostatic Roll/Pitch MEMS gyroscope with in-plane drive mode and out-of-plane sense mode. The proposed structure is developed based on a tuning fork gyroscope with decoupled sense mass on each tine that control the sense out-of-plane frequency. A multi-height deep reactive ion etching (DRIE) fabrication process was utilized to achieve and enhance decoupling between the drive and sense modes. We presented our design methodology followed by an analytical and finite element (FEM) model. Our experimental results showed a good match between the analytical model and those obtained experimentally, from the drive and sense oscillation frequencies. Our characterization setup used a custom made application specific integrated circuit (ASIC) for characterization and was able to achieve ARW of 0.2 deg/rt-h, a bias instability 5.5 deg/h, and scale factor non-linearity (SFNL) 156 ppm FS.

ZRO Drift Reduction of MEMS Gyroscopes via Internal and Packaging Stress Release

Zero-rate output (ZRO) drift induces deteriorated micro-electromechanical system (MEMS) gyroscope performances, severely limiting its practical applications. Hence, it is vital to explore an effective method toward ZRO drift reduction. In this work, we conduct an elaborate investigation on the impacts of the internal and packaging stresses on the ZRO drift at the thermal start-up stage and propose a temperature-induced stress release method to reduce the duration and magnitude of ZRO drift. Self-developed high-Q dual-mass tuning fork gyroscopes (TFGs) are adopted to study the correlations between temperature, frequency, and ZRO drift. Furthermore, a rigorous finite element simulation model is built based on the actual device and packaging structure, revealing the temperature and stresses distribution inside TFGs. Meanwhile, the relationship between temperature and stresses are deeply explored. Moreover, we introduce a temperature-induced stress release process to generate thermal stresses and reduce the temperature-related device sensitivity. By this way, the ZRO drift duration is drastically reduced from ~2000 s to ~890 s, and the drift magnitude decreases from ~0.4 °/s to ~0.23 °/s. The optimized device achieves a small bias instability (BI) of 7.903 °/h and a low angle random walk (ARW) of 0.792 °/√ h, and its long-term bias performance is significantly improved.

Wave Solid-State Gyroscopes of Russian Design for Aircraft Onboard Systems

Wave Solid-State Gyroscopes of Russian Design for Aircraft Onboard Systems

Analytical Solution of the Dynamics Equations for a Wave Solid-State Gyroscope Using the Angular Rate Linear Approximation

The exact solution is provided of the dynamics equation for an elastic inextensible ring being the basic model of a wave solid-state gyroscope with the linear law of the base angular rotation rate alteration. This solution is presented in terms of the parabolic cylinder functions (Weber function). Asymptotic approximations are used in the device certain operating modes. On the basis of the solution obtained, the analytical solution to the equation of the ring dynamics in case of piecewise linear approximation of the angular rate arbitrary profile on a time grid is derived. This significantly expands the class of angular rate dependences, for which the solution could be written down analytically. Earlier, in addition to the simplest case of constant angular rate, solutions were obtained for angular rate varying according to the square root law with time (Airy function), as well as according to the harmonic law (Mathieu function). Error dependence of such approximation on the discretization step in time is estimated numerically. Results obtained make it possible to reduce the number of operations, when it is necessary to study long-term evolutions of the dynamic system oscillations, as well as to quantitatively and qualitatively control convergence of finite-difference schemes in solving dynamics equations for a wave solid-state gyroscope with the ring resonator

A Novel High-Q Dual-Mass MEMS Tuning Fork Gyroscope Based on 3D Wafer-Level Packaging.

Tuning fork gyroscopes (TFGs) are promising for potential high-precision applications. This work proposes and experimentally demonstrates a novel high-Q dual-mass tuning fork microelectromechanical system (MEMS) gyroscope utilizing three-dimensional (3D) packaging techniques. Except for two symmetrically decoupled proof masses (PM) with synchronization structures, a symmetrically decoupled lever structure is designed to force the antiparallel, antiphase drive mode motion and eliminate low frequency spurious modes. Thermoelastic damping (TED) and anchor loss are greatly reduced by the linearly coupled, momentum- and torque-balanced antiphase sense mode. Moreover, a novel 3D packaging technique is used to realize high Q-factors. A composite substrate encapsulation cap, fabricated by through-silicon-via (TSV) and glass-in-silicon (GIS) reflow processes, is anodically bonded to the wafer-scale sensing structures. A self-developed control circuit is adopted to realize loop control and characterize gyroscope performances. It is shown that a high-reliability electrical connection, together with a high air impermeability package, can be fulfilled with this 3D packaging technique. Furthermore, the Q-factors of the drive and sense modes reach up to 51,947 and 49,249, respectively. This TFG realizes a wide measurement range of ±1800 °/s and a high resolution of 0.1°/s with a scale factor nonlinearity of 720 ppm after automatic mode matching. In addition, long-term zero-rate output (ZRO) drift can be effectively suppressed by temperature compensation, inducing a small angle random walk (ARW) of 0.923°/√h and a low bias instability (BI) of 9.270°/h.

Development of an effective method to reduce mechanical coupling error in a micro quartz tuning fork gyroscope

To overcome the performance limitations of quartz microelectromechanical system (QMEMS) gyroscopes, which are extensively employed in various applications, a method was developed in this study to effectively reduce the zero-output error, which is primarily caused by the anisotropy of the quartz crystal. The proposed method increases the gold counterweights at the end of the tuning fork beam and trims them to reduce the zero-output error. First, the vibrations were determined by conducting a theoretical analysis of ideal and non-ideal gyroscopes. A finite element analysis and simulation were then performed on gyroscope models with five structures, and the influences of different crystal edge positions and counterweight trimming methods on the vibrations and outputs of the gyroscopes were simulated. Thereafter, by analyzing the simulation and experimental results, we verified that the addition of counterweights and an error-eliminating method can reduce the zero-output error of QMEMS gyroscopes, and that specific alternative methods can achieve similar results.

Structural Solutions that Increase the Dynamic Accuracy of a Wave Solid-State Gyroscope

The development of wave solid-state gyroscopes (VTG) is one of the promising areas of development of gyroscopic angular velocity sensors. VTG from the standpoint of manufacturing technology, tuning and control systems, as well as accuracy characteristics, has a number of advantages compared to other types of gyroscopes. When developing VTG, they strive to reduce the gyroscope's own care, zero signal bias, and the non-linearity of the scale factor in the operating temperature range However, when creating the device, due attention is often not paid to the existing opportunities to improve the dynamic accuracy of the gyroscope by developing promising structural solutions for building control circuits and information processing. The solution to this problem was the goal of the work.Using the methods of the theory of automatic control, the dynamics of a wave solid-state gyroscope with a metal resonator and piezoelectric elements in the closed-loop mode of Сoriolis acceleration compensation are studied. Piezoelectric elements perform the functions of displacement and force sensors.Two promising structural solutions for constructing VTG control and information processing circuits are proposed and considered. Relations are established for selecting the parameters of the links of these contours, which provide an increase in the dynamic accuracy of the gyroscope. In the first case, the proposed structure for constructing the VTG allows us to significantly reduce the dynamic errors caused by the difference in the scale coefficient of the VTG at different frequencies of the measured angular velocity in the bandwidth. Such a structure for constructing a VTG can be recommended when solving a measurement problem in which it is necessary to accurately measure the angular velocity, and the phase lag of the output signal in relation to the measured angular velocity is of secondary importance. In the second case, the proposed structure of the VTG construction corresponds to the transfer function of the relative measurement error with secondorder astatism, and the absolute measurement error in the frequency band of 10 Hz does not exceed 0.1 %.

Drone controlled real live flight simulator

Flight simulator has been used to train pilots for more than 80 years, whether to fly military aircrafts, passenger aircrafts, or even private aircrafts. A flight simulator is a flying cockpit installed on the ground to help training pilots in flying real aircrafts in a low risk and cost-effective way. Nevertheless, all the previous simulators are dependent on a program being installed in combination with special hardware. Therefore, the purpose of this paper is to design a ground-based flight training simulator. This simulator depends on a drone to transfer the flying environment in real-time to the trainee. A prototype of the project has been implemented based on a small drone equipped with a MPU6050 piezoelectric gyroscope, laptop, and Arduino since the building of the final shape of the simulator is relatively expensive. Satisfying results are gained and the prototype can transfer the drone movement to the ground simulator giving the trainee the feeling as in a real aircraft, improving the trainee’s capabilities of having real-time decisions over the flying environment. The main contribution of this study is the improvement of the current flight simulators by cloning the real environmental effects to the highest possible levels especially for the training purpose of the new pilots or the rehabilitation of pilots with long out-of-service periods.

Constructing and characterizing a novel MEMS-based Tuning Fork Gyroscope using PolyMUMPs

Constructing and characterizing a novel MEMS-based Tuning Fork Gyroscope using PolyMUMPs

Automated Control System of Physical and Accuracy Parameters of Sensitive Elements of Solid-State Wave Gyroscopes

The paper describes the first comprehensive version of the developed software and hardware stand of automation of end-to-end production control of physical parameters of sensitive elements of solid-state wave gyroscopes to enhance the accuracy characteristics of their output signals. The general characteristic of the system of control of physical and accuracy parameters of sensitive elements in production is given. To do this, the process of making a sensitive element is summarized and procedures for determining its physical and accuracy parameters are given. The focus is on creating "hrgCheck" software for the system of automated physical and accuracy parameters monitoring. For this purpose, a diagram of the state of the system, program algorithms, data collection, calculation of physical parameters, calculation of accuracy parameters, software and measurement control structures as well as the program's user interface are given. As a demonstration example of the performance of the software, a trial test of the effectiveness of use in the control of physical and accuracy parameters of sensitive elements of solid-state wave gyroscopes was carried out. For one of the sensors, 37 standing wave runs were measured, which took 2 hours and 15 minutes. The dependence of identification results on the initial measurement conditions is shown, which requires an excessive series of experiments. The resulting data on the physical and precise parameters of sensitive elements show the feasibility of introducing the developed software into the production cycle of end-to-end control of the gyroscopes produced. This will reduce the labor and cost of manufacturing, improve product accuracy and reduce the possibility of production faults. The inherent opportunities for improvement, development and expansion allow us to consider it in the general trend of updating the technologies of production processes for the manufacture of high-precision solid-state wave gyroscopes.