Визначення параметрів первинної моди твердотільного гіроскопу камертонного типу

Abstract

The use of a tuning fork resonator as sensitive element of a gyroscopic sensor has some advantages in comparison with other types of the resonators. For instance, it allows to compensate lateral accelerations in the direction perpendicular to the axis of rotation. At the same time, the task of accurate determination of the carrying frequency of the primary mode of a non-moving tuning fork is of great importance. Thus, in [1] the analysis of vibrations of a gyroscope is built on the evaluation of the first frequency of flexure vibrations of Timoshenko's beam with one rigidly fixed end [2]. As a result, the sensing frequencies of the Bryan's splitting pair [3] of the fork lie below the frequency of Timoshenko's beam, and the resonant frequency of the non-moving tuning fork remained uncertain. The purpose of a present paper is to establish this frequency. In the statement of a problem, concerning real geometric dimensions of the tuning fork elements, we assume that the length of the tuning fork rods l is much more then the radius of the base r: r/l << 1. Then, frequencies of the flexure vibrations of the half-ring lie much higher than the frequencies of the bending vibrations of the rods. It allows us to give a solution for the base in a quasi-static approximation, and to take into account the dynamics of the tuning fork in the solution for bimorph piezoceramic rods. Conditions of coupling between the rods and the half-ring are reduced to the conditions of elastic fixing of the rods, which take into account the geometric parameters r and l.