Vladimir M. Bogolyubov, Lyalya U. Bakhtieva, Oleg V. Tsyganov

Kazan National Research Technical University named after A.N. Tupolev (KNITU-KAI)

A mathematical model of a micromechanical gyroscope (MMG) of a hybrid type is constructed, in which, in order to eliminate the "zero displacement", the principle of modulation of primary information in a mechanical circuit and its removal in a rotating coordinate system, well-established in rotary vibrating gyroscopes, is used. In addition, a mode of parametric excitation of the sensitive element has provided, which allows expanding the measuring capabilities of the device without interfering with its mechanical circuit and increasing the accuracy of the MMG. The simulation of the model has carried out in the Matlab-Simulink environment, which makes it possible to solve the differential equations of the model in an interactive mode with various input parameters. Based on the results obtained, the conditions for the implementation of parametric excitation of the MMG by modulating its angular velocity of rotation (dynamic rigidity) have formulated. The possibility of a significant increase in the accuracy of measuring the angular velocity by changing the level of parametric "pumping" of the device, as well as the ability of the device to determine the third component of the angular velocity, which coincides in direction with the gyroscope angular momentum vector, has shown. The constructed simulation model makes it possible to design an absolute angular velocity sensor capable of solving inertial navigation problems with the required accuracy.

mathematical model, gyroscope, micromechanical system