Study on free oscillations of a micromechanical gyroscope taking into account the nonorthogonality of the torsion axes

Introduction. The paper is devoted to the study on free oscillations of the sensing element of a micromechanical R-Rtype gyroscope of frame construction developed by the Kuznetsov Research Institute of Applied Mechanics, taking into account the nonorthogonality of the torsion axes. The influence of the instrumental manufacturing error on the accuracy of a gyroscope on a movable base in the case of free oscillations is studied. The work objective was to improve the device accuracy through developing a mathematical model of an R-R type micromechanical gyroscope, taking into account the nonorthogonality of the torsion axes, and to study the influence of this error on the device accuracy. The urgency of the problem of increasing the accuracy of micromechanical gyroscopes is associated with improving the accuracy of inertial navigation systems based on micromechanical sensors.Materials and Methods. A new mathematical model that describes the gyroscope dynamics, taking into account the instrumental error of manufacturing the device, and a formula for estimating the error of a gyroscope, are proposed. The dependences of the state variables obtained from the results of modeling and on the basis of the experiment are presented. Methods of theoretical mechanics and asymptotic methods, including the Lagrange formalism and the Krylov-Bogolyubov averaging method, were used in the research.Results. A new mathematical model of the gyroscope dynamics, taking into account the nonorthogonality of the torsion axes, is developed. The solution to the equations of small oscillations of the gyroscope sensing element and the estimate of the precession angle for the case of a movable base are obtained. A comparative analysis of the developed model and the experimental data obtained in the case of free oscillations of the gyroscope sensing element with a fixed base is carried out. The analysis has confirmed the adequacy of the constructed mathematical model. Analytical expressions are formed. They demonstrate the fact that the nonorthogonality of the torsion axes causes a cross-influence of the amplitudes of the primary vibrations on the amplitudes of the secondary vibrations of the sensing element, and the appearance of an additional error in the angular velocity readings when the gyroscope is operating in free mode.Discussion and Conclusions. The results obtained can be used to improve the device accuracy using the algorithm for analytical compensation of the gyroscope error and the method for identifying the mathematical model parameters.

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.

Development and Implementation of the Robot Prototype with Inertial Navigation for Work in the Arctic

Currently, there is a very rapid development of robotics. People use robots in many areas of their activities. Especially valuable is the use of robots in hazardous conditions for humans, in particular in studies in the Arctic. In this case, there is an acute problem of navigation. The use of global navigation satellite systems (GNSS) in the Arctic is difficult due to the small number of satellites and the influence of Aurora. Therefore, we chose the inertial type of navigation for the prototype of the robot. We used LSM330DL micromechanical sensors and Atmega8-16AU microcontroller to create a navigation system. We used wireless access point Ubiquiti Bullet M2HP Titanium to connect the robot with researchers. Tests of a prototype of a robot on a wheeled platform showed that the coordinate determination error does not exceed 6%. Tests of the navigation system were carried out up to -20°C. System components allow operation up to -40°C. The proposed navigation system can be used to create robots for work in the Arctic.