Toward Perfection of Gyros! Modeling, Analysis, and Modification of Ring-Type Resonators

Gyroscopes are sensors that measure the rate of rotation of an object. One common type is a "Coriolis Vibratory Gyroscope" (CVG) which takes advantage of Coriolis coupling in sensing rotation. CVGs exploit two resonant modes for measuring the sensor's angular rate of rotation. The highest sensitivity to angular motion is achieved when the resonant modes have degenerate frequencies as this configuration provides the greatest signal-to-noise ratio (SNR) with respect to extrinsic (electronic) noise sources. One way to achieve degeneracy is to design an axisymmetric resonator such as the UCLA CVG. It is impossible to retain the symmetry during manufacturing process because small fabrication errors detune the modes of interest. To compensate for these fabrication errors, post-processing of the resonator to recover its optimal axisymmetric configuration is required. One process, considered here, is the perturbation of the resonator's mass distribution by removing mass from specific locations. Perturbing the stiffness of the structure is not permanent, and it requires relatively large size electronics. A technique which retains wafer-scale processing and packaging compatibility is described for customizing the dynamics of individual silicon resonators. The approach uses laser ablation of a protective conformal layer (Parylene-C) to expose silicon in regions that are targeted for mass removal by subsequent deep reactive-ion etching (DRIE). The technique is demonstrated on a planar axisymmetric resonator design whereby the frequency mismatches of a subset of the resonators are reduced to less than 100 mHz which is the mechanical bandwidth of the resonator.The model for the resonator is based on a perturbation analysis of ring dynamics which serves as a basis for the ring-type resonators. The perturbation expansion is found for the exact solution of imperfect rings for the case in which the damping is neglected. The results show excellent agreement with both Rayleigh-Ritz and finite element results. The perturbation model is refined and modified for multi-modal tuning where both n = 2 and n = 3 are considered. The search algorithm is also improved using linear programming and a branch and bound routine. The results are successfully demonstrated on a few devices.The damping mechanisms of this type of resonator are also studied. The thermoelastic damping which is the dominant damping mechanism in ring-type resonators is studied in detail for a ring structure. The equation of motion is derived and solved using strong form Galerkin method for imperfect rings. The imperfections studied are caused by the manufacturing processes (e.g., etch non-uniformities) and tuning the devices in practice. The analysis demonstrates a practical limitation in the tuning process where the damping asymmetries may not necessarily be removed even for the case that the frequencies are perfectly tuned. A general design guideline based on the geometry and material of the ring is presented. The temperature profile for the different materials is shown as well