Mathematical Models for Nonideal Resonator Digital Twins of Solid-State Wave Gyroscopes

Abstract

Various variants of mathematical models for digital twins of solid-state wave gyroscope resonators with mechanical defects is given. The obtained results are designated for gyroscope manufacturing cycle maintenance to improve the quality of the output products. A general model of resonator in a resonant variable was chosen as the basic one. To take into account small residual errors of resonant manufacturing functions of space non-homogeneous distribution of shell thickness were introduced into it together with density and viscosity of material. The obtained full analytical model of wide-range gyroscope resonator employs expansion of its strained shape by the resonant form spectrum oscillations. For the considered resonators with small residual defects comparable to errors of finite-element schemes of modelling programs, resonant modes of their digital twins are to be calculated numerically for axially symmetrical resonator models. And residual errors of the manufactured shape are considered integrally in analytical models by introduction of different frequency and Q-values small parameters. Later, a working model of narrow-range gyroscope dynamics is extracted from the full model, that is presented in different forms depending on the convenience of stated problem solutions. For that purpose, fixed coordinate system axes (resonator stiffness axes, measurement instrument axes and others) were used along with moving axes following the wave process. A transition from model initial notation via fast variables into slow variable models was done, so as to avoid the effect of scheme viscosity in numerical integration programs,. The presented mathematical relations and models is possible may possibly be applied for improvement of in-process control methods and defect diagnosis of resonators to be produced.