Coriolis vibratory gyroscopes (CVGs) with circular micro-resonators, such as hemispherical, ring, and disk resonators, exhibit excellent performances and have extraordinary potential. This paper discusses a generalized lumped mass model for both 3D and planar circular micro-resonators, establishing the relationship between the modal effective mass, the modal equivalent force, and the point displacement of the resonator. The point displacement description of a continuous circular resonator's motion is defined from the view of capacitance measurement. The modal effective mass is, consequently, determined by the kinetic and the potential energy of the structure and is computed with numerical simulations. Moreover, the modal equivalent force, which can be theoretically calculated for any configuration of discrete electrodes, is deduced by using the concept of force density and the force distribution function. By utilizing the lumped mass model in this paper, the stiffness softening, the mode tuning, and the quadrature correction of the micro-resonators are investigated in detail. The theoretical model is verified by both the finite element method (FEM) and the experiments.
Keywords: circular micro-resonators; coriolis vibratory gyroscopes; electrostatic stiffness tuning; modal effective mass; modal equivalent force.