Gyroscopic Devices Research Articles

Fundamental properties of the gyroscope oscillation

Despite partial solutions by famous scientists during the early Industrial Revolution, gyroscope problems remained unsolvable until the beginning of the twentieth century when several fundamental physical laws were finally formulated to describe them. Today, the principles of classical mechanics enable the formulation and description of the physical processes involved in the rotation of any object. Gyroscopic devices are objects that rotate and exhibit oscillation, which has been a challenging problem in engineering mechanics. The oscillation of a gyroscope is caused by the interaction between external and inertial torques. This is different from other examples of oscillation, such as pendulums and springs, which have been well documented. The main difference in the physics of gyroscopic oscillation is that the spinning rotors of the gyroscopic devices are supported on one side, with their axes perpendicular to the axis of oscillation. The oscillation of gyroscopic devices is interrelated with the potential and kinetic energy of their components. However, the physics of oscillation of such objects has not been fully described in publications until recently. The theory of gyroscopic effects for rotating objects has now been published and provides a solution to this problem. According to this theory, gyroscopic inertial torques represent the potential energy of the external torque and kinetic energy of the spinning rotor. This paper demonstrates the distribution of inertial torques about the axes of Cartesian coordinates, which enables the computation of gyroscope motion and oscillation.

Vibrational and Dissipative Characteristic Measurement of Solid-state Wave Gyroscope Resonators: Algorithms Based on the Identification of Free Oscillation Equations

The article describes the methodological basis for constructing computational circuits of different complexity degrees and different purposes for solving a wide range of industrial and laboratory problems to measure angular irregularity of vibrational-dissipative resonatorcharacteristics of integrating solid-state wave gyroscopes. The main method to solve such problems is the identification of the coefficients of the differential equations of quartz hemispherical resonator state in the mode of its free oscillations. The resonator oscillation equations both in the fixed measuring axes and in the moving axes of standing waves were chosen as the equations of state. After reduction to slow variables, only slowly changing amplitudeequations are left for identification problems. In all the described circuits, it is assumed that the information signals for the solved identification tasks are formed in a measuring device similar to the standard gyroscope device. These algorithms make it possible to measure the vibrational and dissipative characteristics of resonators with different degrees of completeness and directionality for different standard initial requirements to themeasurement accuracy and experimental modes, which makes it possible to reduce the measurement time and labor intensity of the established set of production control operations. Among the tasks to be solved for the free run-down mode of the resonator wave pattern are the following: angular irregularity measurement of the gyroscope resonator dissipative properties under conditions of low and significant residual frequency difference; angular non-uniformity measurement of gyroscope resonator vibrational properties (its different frequency); simultaneous measurement of resonator oscillatory and dissipative characteristics for fixed and special rotating gyroscope modes. The detailed processing of the computational schemes for the implementation of these algorithms is focused on their practical application for various tasks of production operational control. At the same time, the choice of the most suitable computational algorithm from the considered options depends on the conditions, requirements and specifics of measurements.

Dynamic response of the micro-perforated crab beam used in MEMS vibratory gyroscope device

This paper presents a study on the dynamic response of the micro-beams with the crab shape and cut-out holes on the whole operating faces of the beam to create the micro-perforated beam by using FEM simulation software. The obtained results show that the size and shape form of the cut-out holes affect the mechanical responses of the beam on which the holes distribute. The equivalent stiffness of perforated micro-beams decreases significantly with the increasing size of the holes on the beam operating face. And thence the major frequencies of the MEMS vibratory gyroscope system that consist of these micro-beams also decrease. The results of the study are basic for being used for optimizing the structure in subsequent research.

An investigation of an athlete injury likelihood monitoring system using the random forest algorithm and DWT.

The main goal of sports science is to monitor sports injuries. Nevertheless, the existing sports injury monitoring projects have many expensive instruments and excessively extended monitoring periods, which makes it difficult to expand sports injury monitoring on a large scale. The advancement of machine learning algorithms opens up new avenues for the tracking of sports injuries. A training set of sports injuries was created using the Discrete Wavelet Transform (DWT) and Random Forest algorithms. Next, a basic analytic framework was created based on the lower-body movement of runners, and an athlete's injury likelihood monitoring system was established. First off, the wearable gyroscope device can efficiently plot the motion displacement curve and monitor the three-dimensional mechanics of the athlete's hips, thighs, and calves. Secondly, the system has a higher computational efficiency and an advantage over other classifier-based systems in terms of testing and training times. The suggested system framework identifies athletes' injury propensity, providing preventive recommendations based on displacement curves, and offering a low total cost and high testing accuracy, making it easy to implement and cost-effective. All things considered, the sports injury monitoring device is very accurate and reasonably priced, making it appropriate for widespread use.

Inertial Forces and Torques Acting on a Spinning Annulus

The many publications related to the gyroscope theory consider the action of the inertial torques on the spinning disc. All of them have simplified expressions for the inertial torques and mathematical models of the gyroscope motions do not validate by practice. Recent research in the theory of the gyroscopic effects for rotating objects solved problems with mathematical models for interrelated inertial torques generated by the spinning disc, bar, and ring and their motions. Practitioners of engineering designed gyroscopic devices with spinning rotors whose geometry can be an annulus or similar designs. Such spinning annulus generates inertial torques whose expressions differ from the disc bar and ring and hence another mathematical model describes the motions of the gyroscopic devices. The value of gyroscopic effects of the devices with spinning annulus is bigger than for the disc-type rotor. This manuscript presents mathematical models for the inertial torques generated by the spinning annulus and the interrelated angular velocities of the gyroscopic devices about axes of rotation.

Automated Method of Monitoring the Quality Surface of Glass And Mirrors by Means of Machine Vision Algorithms for Gyroscopic Devices

The paper analyzes the existing devices for surface quality control of products. A variant of machine vision system application in terms of products using glass surfaces with high requirements to the quality of manufacturing are considered. Ready-made solutions are considered and analyzed, their characteristics, advantages and disadvantages are described. The layout of a workstation for obtaining images of the product surface for subsequent software processing was developed. An example of automatic acquisition of surface images for products with complex geometrry is implemented. An algorithm and tool for detecting surface defects and classifying them, by image processing, using specially developed software, is described. The described method of surface assessment is also capable of detecting defects in various surfaces requiring high quality production of these products, and the main limitation is the optical method of obtaining a picture of the surface to be examined. The algorithm is able to work with images of medium and high quality, which allows to use this method of surface assessment with already existing systems that do not have an algorithm for surface assessment, which simplifies the possibility of implementing this system. Combination with other methods of nondestructive testing of products, that allow to obtain surface images, internal area and hidden cavities, it will make possible to analyze the quality of products in a complex way. The ue of machine vision is relevant due to its features, such as: speed of surface quality control, as well as evaluation accuracy. A machine vision system can reject parts much faster and more reliably than a human and can be used as a tool production automation.

Quadrupolar interaction induced frequency shift of nuclear spins on the surface of silicon

The combination of micro-machined technology with atomic spin gyroscope (ASG) devices can be used to fabricate a chip-scale atomic spin gyroscope (CASG). The core of the gyroscope is a micromachined vapour cell, which contains alkali metal and isotope-enriched noble gases, such as and . The quadrupolar frequency shift of is a key parameter that can affect the drift of the ASG and is related to the material of the cell in which they are contained. In micromachining technology, the utilised material is silicon. In this study, we investigated the electric quadrupolar frequency shift of atoms with the silicon wall of a micro-machined vapour cell. A cylindrical micromachined vapour cell was utilised in the experiment, and a large part of the inner cell surface comprised silicon material. We studied the temperature dependence of the spin relaxation and frequency shifts to evaluate the interaction of the nuclear spin with the container wall and alkali metal atoms. The results show that the average twisted angle of the nuclear spins as they collided with the silicon wall was measured as rad. The desorption energy required for the nuclear spin to escape from the silicon surface was . This study could help improve the bias stability of the CASG, which is a key parameter for the gyroscope, and may help to develop a method to study the surface properties of various materials.

Corrected Inertial Torques of Gyroscopic Effects

The published manuscripts in the area of gyroscope theory were presented mainly by the simplified approaches in which mathematical models contain many uncertainties. New research in machine dynamics opened breakthrough directions in gyroscopic effects of rotating objects that give the correct solutions. The pioneering work meets many problems when solving the scientific innovations that are accompanied by successes and omissions. New mathematical models for the gyroscopic inertial torques were derived with incorrect processing of the integral equations that give distorted results. The gyroscopic devices in engineering manifest gyroscopic effects as the action of the inertial torques which computing is crucial for mathematical describing of their motions. The corrected mathematical processing of the equations for the inertial torques acting in a gyroscope is presented in this manuscript.

A Handheld Gyroscopic Device for Haptics and Hand Rehabilitation.

We propose a novel, gyroscopic device for haptics and hand rehabilitation, named Gymball. It consists of a fully actuated rotor-gimbal assembly encased in an easy-to-grip appealing design. When held, the device generates a gyroscopic torque which causes the user's hand to move about the wrist. Interviews with occupational therapists, simulations, and proof-of-concept models helped determine the design specifications of Gymball. Compared to the existing gyroscopic devices, Gymball has the following advantages. (i) A smaller form-factor with better user appeal while achieving 0.5 Nm torque. (ii) A wire entanglement-free design allowing complete rotations of the rotor-gimbal assembly. (iii) Negligible rotary imbalances owing to a symmetrical design, resulting in haptic signals with minimal vibratory noise. In this paper, we detail the design and analysis of the device. A feasibility study was conducted to validate prospect of using the device for haptic feedback or therapy. Specifically, the study focused on (i) whether the gyroscopic torque generated by the device can passively move the user's hand about the wrist and (ii) whether the produced hand motion can be controlled. The results show that Gymball can successfully generate about 7° of hand oscillations. The amplitude and frequency of the hand oscillations can be controlled using the speed of rotor and gimbal.

Study of Lapping and Polishing Performance on Lithium Niobate Single Crystals.

Recently, the range of crystal materials used in industrial microelectronics has significantly increased. Lithium niobate single crystals are most often used in integrated optics, due to the high values of optical and electro-optical coefficients. An integral-optical circuit based on a lithium niobate single crystal is a key element in the production of local high-precision fiber-optic gyroscopic devices used in civil and military aviation and marine technologies. In the process of production of an integral-optical circuit, the most labor-intensive operations are mechanical processing, such as lapping and polishing. Technological problems that arise while performing these operations are due to the physical and mechanical properties of the material, as well as target surface finish. This work shows the possibility to achieve the required surface quality of lithium niobate single crystal plates by mechanization of lapping and polishing process in this article.

COMPACT ROTARY PLATFORM AS A UNIVERSAL LABORATORY STAND

A single axis rotary platform is distinguished among the laboratory equipment for testing gyroscopic devices and systems and their sensitive elements. An overview of the design principles of industrially developed stands for the study of static and dynamic characteristics of gyroscopic devices and systems is provided. The scheme of design of the universal laboratory stand is suggested as the compact rotary platform for research of static and dynamic characteristics of micromechanical gyroscopes and accelerometers as sensors of angular speed. The physical components of such a stand and technical and technological problems of its practical implementation are reviewed. The proposed laboratory stand is considered as a cyberphysical system where computing components play a crucial role in determining the parameters of the system and the studied micromechanical sensors. For this purpose, in addition to the physical control loop of the electric drive to ensure the stability of the angular velocity of the platform, an independent measuring loop is considered for analytical determination of system parameters, including the studied micromechanical sensors. The versatility of the stand is ensured by solving the inverse problems, namely determining in the process of testing static and dynamic characteristics of the electric drive and measuring sensors that work on various physical principles. It is assumed that, in addition to solving practical problems of micromechanical sensors in the development of the appropriate information interface of the virtual device, a compact laboratory stand can be effectively used in the educational process during laboratory work in relevant disciplines of instrument making direction.

The 3D motion of a charged solid body using the asymptotic technique of KBM

This paper attempts to explore the general rotatory 3D motion of a magnetic heavy solid body around one fixed point under the impact of a gyrostatic moment when the body awarded initially high angular velocity about one of its inertia principal axes. The asymptotic technique of Krylov-Bogoliubov-Mitropolski and its adjustment are applied to achieve new asymptotic periodic solutions of the controlling equations of motion. Discussion of these solutions is presented taking into consideration their graphs representations. The graphical depictions of such solutions and their corresponding phase planes are plotted to give an induction about its behaviour during the interval time of motion and to reveal the good effect of the different applied forces and moments on the body's motion. The application of the achieved results of the present work can be widely found in gyroscopic devices especially that used inertia reference systems like in satellites, airplanes, and missiles. Moreover, for devices that are responsible for the stability of motion for these applications.

Preface

13th MULTICONFERENCE ON CONTROL PROBLEMS (13 MCCP-2020) 6–8 October 2020 The 13th Multiconference on Control Problems, organized by the State Research Center of the Russian Federation - Concern CSRI Elektropribor (St. Petersburg, Russia) was held on October 6–8, 2020.Concern CSRI Elektropribor has held the multiconferences together with some research institutions and universities since 2006. The idea of holding the multiconference consists in uniting several local conferences, intimately related by the topics of scientific problems being considered. The Saint Petersburg Group of Russian National Committee on Automatic Control has become the initiator of such cooperation. The content of the Multiconference slightly changes from year to year, but the Conference in Memory of the Prominent Designer of Gyroscopic Devices N.N. Ostryakov, which has been held by CSRI Elektropribor every two years since 1956, remains a permanent part of the program. Traditionally, every even-numbered year the Multiconference is held at Concern CSRI Elektropribor, JSC (St. Petersburg), and every odd-numbered year — in Divnomorskoe town (Gelendzhik, Russia), where the A.V. Kalayev Research Institute of Multi-processor Computation Systems, Southern Federal University, is the main organizer.

A Mathematical Model for a Conceptual Design and Analyses of UAV Stabilization Systems

This article considers the principle of constructing mathematical models of functionally complex multidimensional multiloop continuous–discrete UAV stabilization systems. This is based on the proposal for constructing a mathematical model based on the class of the considered complexity of the stabilization system-multidimensionality, multi-rating, and elasticity. Multiloop (multidimensional) UAV stabilization systems are often characterized by the control of several interconnected state elements and the existence of several channels for the propagation of signals and mutual connections between individual objects. This is due to the need not only to take into account the numerous disturbing factors (for example, wind) acting on the control object as well as the need to use several points of application of control actions. Additionally, an important point is the possible separation of the mutual influence of the roll and yaw channels of the UAV on its synthesis and analysis. For this purpose, a mathematical model has been constructed using a description in the form of transfer functions, and therefore, in the form of structural diagrams. The principle of obtaining transfer functions is shown to demonstrate additional dynamic constraints introduced by elastic deformations into the stabilization loop through gyroscopic devices and accelerometers. This will make it possible to formulate a methodology for analyzing the influence of aeroelastic constraints on the stabilization loop, which will allow developing approaches to formulate requirements for the effective placement of gyroscopes and accelerometers on the UAV. The proposed approach allows creating a complete system of analysis and synthesis tools for complex multidimensional continuous–discrete UAV stabilization systems.

A Calibration Scheme With Combination of the Optical Shaft Encoder and Laser Triangulation Sensor for Low-Frequency Angular Acceleration Rotary Table

A low-frequency angular acceleration rotary table (LFAART) is capable of sinusoidal motion around a fixed position and essential to verify dynamic characteristics of a gyroscope device. The table’s performance at different swinging frequencies and amplitudes needs to be calibrated to realize traceability. However, there has been little research on the LFAART calibration. Besides, the existing measurement methods of sinusoidal angular motion parameters are not adequate for the needs of the LFAART calibration in terms of measurement range, precision, and feasibility. This article presents a calibration scheme combining an optical shaft encoder and a laser triangulation sensor. When the rotation amplitude covers sufficient slots of the scale grating, the optical shaft encoder is applied, while the laser triangulation sensor is used for a tiny amplitude motion. An algorithm is proposed to accurately calculate the angular acceleration amplitude and frequency of the rotation utilizing sinusoidal phase-modulated signals of the optical shaft encoder output. Singular zero-crossings of the series are discarded, and intervals of reversing moments are recognized according to the signal derivative’s sign at remaining zero-crossings. Then intervals are divided into subintervals to obtain accurate reversing moments. Finally, angular displacements between two adjacent reversing moments are estimated based on the fringe counting method, and the amplitude and frequency are calculated. The measurement uncertainty analysis and experiment demonstrate that the calibration scheme, including the algorithm, possesses high accuracy and resolution, wide range, and good operability, which perfectly solves the rotation’s angular acceleration amplitude and frequency.

Choice of configuration and parameters of the vibration protection system for gyroscopic angular velocity meters

The rationale for the choice of a technical solution to the issue of vibration protection of gyroscopic angular velocity meters, built on the basis of dynamically tuned gyroscopes (DTG) is presented. The proposed vibration protection system consists of shock absorbers with high elasticity and dynamic vibration dampers (DVD) with nonlinear elastic and damping characteristics. The main factors that determine the peculiarities of choosing a vibration protection system for precision gyroscopic devices are indicated. Keywords dynamically tuned gyroscope (DTG); dynamic vibration damper (DVD); vibration protection system; gyroscopic angular velocity meter

Nanophotonic optical gyroscope with sensitivity enhancement around “mirrored” exceptional points

Unavoidable thermal fluctuation and fabrication error severely compromise the sensing performance of nanophotonic optical gyroscope devices in practice. In this paper, we theoretically propose a doubly-coupled-ring gyroscope system that not only takes advantage of exceptional point enhanced rotation sensitivity but also improves the robustness against thermal fluctuation and fabrication error. In the doubly-coupled-ring gyroscope with gains, two mirrored exceptional point supermodes experience opposite responses to rotation but same response to thermal fluctuation and fabrication error. Thus, differential readout of the frequency splitting from the two mirrored exceptional point supermodes results in a nearly 100% common-mode noise rejection and remarkably enhances the measurement precision and sensitivity of the photonic optical gyroscope. The proposed doubly-coupled-ring system is a promising platform for not only the novel photonic optical gyroscope but also the next-generation exceptional point sensor in general.

Chattering-Free Adaptive Finite-Time Sliding Mode Control for Trajectory Tracking of MEMS Gyroscope

One of the inevitable problems with real-time control systems is the presence of the uncertainties and external disturbances. The existence of these uncertainties in the fabrication processes of the MEMS Gyroscope devices can deeply impact the performance of the devices. In this paper, five adaptive finite time robust control methods are employed based on SMC method for a Micro-Electro-Mechanical System (MEMS) Gyroscope with mismatched uncertainties and external disturbances to achieve trajectory tracking goal. A new Stepping SMC method is proposed in this study to improve some deficiencies of conventional and existing methods including Simple SMC, Classical SMC, Cubic SMC, and Hexagonal SMC. The upper bound of mismatched uncertainties is estimated in finite time and their estimation is utilized in the control inputs for all five control methods. The elimination of chattering phenomenon is considered in this paper. The system finite time stability proof is obtained using Lyapunov stability theory. The numerical simulation is performed in Simulink/MATLAB for the MEMS gyroscope system to demonstrate the effectiveness of our proposed control method, Stepping SMC, compared with four other methods. To make an extensive comparison among results, the performance criterion, Integral of the square value (ISV), is used.

Inertial torques acting on a spinning paraboloid

Numerous gyroscopic devices consist of rotating components that manifest gyroscopic effects, i.e., the action of unexplainable inertial torques. The rotating objects in engineering can be designed as a disk, cylinder, rotor, circular cone, sphere, paraboloid, etc. Known theories express gyroscopic effects by a simplified mathematical model based only on the principle of the change in the angular momentum for the spinning disk. New research in the area of the gyroscope theory has shown that the physics of inertial torques is more complex than that presented in known publications. Spinning objects generate a system of interrelated inertial torques based on the action of centrifugal, common inertial, and Coriolis forces, as well as the change in the angular momentum. The action of inertial torques manifests resistance and precession torques, which is known as gyroscopic effects. These inertial torques constitute the fundamental principles of the gyroscope theory. The rotating objects of complex designs demonstrate the action of inertial torques, in which mathematical models are different from the models of the spinning disk. The novelty of the work is analytical solutions for the inertial torques generated by the rotating mass of the spinning paraboloid that is new in the dynamics of rotating objects.

Stoichiometric composition of thin-film surface structures and its influence on the functional characteristics as regards gyroscopic devices

This article considers the research results of the effect of stoichiometry on the properties of titanium nitride thin-film coatings of the float and electrostatic gyroscopes. It presents the results of tests of such mechanical and optical characteristics of titanium nitride thin-film structures as microhardness, resistance to wear and friction, and image contrast determined by the reflection coefficients of a titanium nitride base surface and a raster pattern formed by local laser oxidation. When making a rotor of a cryogenic gyroscope, the prospects of use and technological methods for the formation of functional surface structures of niobium carbide and nitride are considered. It is shown that during the formation of coatings of the required composition, the most important is the thermodynamic estimation of possible interactions. These interactions allow us to accomplish the structural-phase modification of the material, which is determined by the complex of possible topochemical reactions leading to the formation of compounds, including non-stoichiometric composition.