Dynamics and accuracy of a micromechanical gyroscope with provision for the displacement of inertial mass

We consider a micromechanical gyroscope (MMG), used in navigation and motion control systems for moving objects. In order to improve the accuracy of the gyroscope in the integrating mode of operation on a rocking base, we have studied the dynamics and accuracy of the gyroscope, taking into account the small instrumental errors in creation of the sensitive element of the gyroscope - unequal rigidity of the elastic support elements, small shifts of the gyroscope center of mass relative to the geometric center of the assembly. The method for increasing the accuracy of the gyroscope is based on the construction of a new mathematical model of its dynamics and errors using the general theorems of dynamics and Krylov-Bogolyubov averaging methods. The new mathematical model of oscillations of the sensitive element of a weight-size prototype makes it possible to estimate the errors of the gyroscope in the integrating mode of operation in form of dependence of the precession angle on the parameters of the differences in Q factor, frequency and shifts of the inertial mass on a rocking base of the device. The article presents a comparative analysis of the constructed model with experimental data obtained for the case of free oscillations of the sensitive element of the gyroscope on a fixed base. Based on the results of analysis, we have confirmed the adequacy of the constructed mathematical model of a weight-size prototype. We propose to use the methods of parameter identification for matching the experimental data with the simulation results. It is shown that the shifts of the inertial mass leads to a change in the natural frequencies of the gyroscope oscillations and the additional different frequencies. The results of the work can be used to improve the accuracy of the device using the algorithm for analytical compensation of the gyro error.