Approaches to the Calculation of Technical Characteristics of a Solid-State Wave Gyroscope

Abstract

Nowadays, strict requirements are imposed to sensitive elements of navigation systems for which implementation it is necessary to improve constantly sensors of primary information (gyroscopes, accelerometers) in such parameters as: mass-dimensional characteristics, accuracy, reliability, long working resource. These requirements stimulate development of new types of gyroscopes. The solid-state wave gyroscope belongs to one of such new types of devices. It is necessary to develop mathematical model for increase in precision parameters of a real product and reduction of terms of production preparation. Two approaches are considered. The first one is analytical, the second one is numerical. When obtaining the analytical decision, the offered mathematical model for a hemispherical sensitive element is created on the basis of the method of masses. The spatial design of the sensitive element is given to a flat ring for simplification of a task and reduction of time of calculation. Assumptions about rigid communication of a certain number of identical masses in the district direction and elastic communication in the radial direction are applied. The ideal case is considered. Analytical transformations with certain assumptions for simplification of final dependence are carried out. The second approach to creation of mathematical model is based on application of theories of Eigen fluctuations and a method of movements for volume bodies, on condition of their elastic deformation. The ideal axisymmetric body which is rigidly jammed for a resonator leg is considered. Material of the sensitive element is considered as isotropic and the preparation processing history is not considered. With the help of a full factorial experiment, the main characteristic of the sensitive element - Eigen frequency - is investigated depending on efficiency factors, which this paper is devoted to. The assumption is made for the possibility of using the results of a numerical experiment in the analytical model for approximate calculations.