In this paper, we present the mechanical sensitivity improvement of a disk resonator gyroscope (DRG) by optimizing the thickness distribution of the nested rings. The mechanical sensitivities of the DRGs with uniform, linearly changing, and step changing rings have been simulated. The results suggest that the ring thickness distribution has great influence on the performance of the DRG. Then, the optimized ring thickness distribution was obtained by using the traditional method of moving asymptotes (MMA), which result in a 24% improvement of the mechanical sensitivity. Finally, the bio-inspired particle swarm optimization (PSO) algorithm has also been used. The optimization results of PSO coincide well with that of MMA, and the optimized result is the global optimum. Meanwhile, the optimized distribution rules can be used on the series of DRGs and the optimization methods can be widely used on other microelectromechanical systems (MEMS) devices. [2015-0310]

Design of a Disk Resonator Gyroscope With High Mechanical Sensitivity by Optimizing the Ring Thickness Distribution

This paper introduces a utility algorithm to reduce the permanent frequency mismatch of the primary wineglass modes in a disk resonator gyroscope via stiffness perturbation. In this algorithm, each tuning electrode is regarded as two rows of radial springs with negative stiffness. On the basis of the tuning model for a ring with radial springs, we can obtain the functional relation between equivalent stiffness or voltage of each tuning electrode and the frequency split. Corresponding simulations are conducted to demonstrate the performance of the algorithm. Finally, the electrostatic tuning experiment is presented to further verify the algorithm and illustrate the use of the tuning procedure. Results of experiment show that the frequency split of resonator is decreased to smaller than 0.03 Hz from original about 15 Hz.

Frequency Tuning of a Disk Resonator Gyroscope via Stiffness Perturbation

This paper presents a study on dynamics of a dual-mass MEMS vibratory gyroscope in presence of imperfections and reports a method for precision electrostatic frequency tuning of the operational modes The presented tuning algorithm involves, first, assessing the modes mismatch using the experimental frequency responses of both proof-masses, followed by the identification of the stiffness mismatch along the two axes and anisoelasticity angles α and β, then choosing the tuning voltages for modification of the diagonal, off-diagonal, and coupling terms in the stiffness matrix Results of simulation are verified using experimental electrostatic frequency tuning of a dynamically amplified gyroscope The frequency split between the operational modes was reduced from 26 Hz down to 50 mHz, resulting in 17× increase in the gyroscope scale factor

Electrostatic compensation of structural imperfections in dynamically amplified dual-mass gyroscope

This paper reports a new design strategy of adding lumped masses to the frame structure of a disk resonator gyroscope (DRG) to mitigate its figure of merit (FOM). A greatly enhanced decaying time constant τ can lead to very small FOM, which could then greatly mitigate the DRG's bias and bias drift. Additionally, this technique could also reduce the Brownian noise floor. A comprehensive investigation of the possible ways to add the lumped masses is presented, and a detailed design guideline is provided. A DRG prototype based on this design strategy is then presented and shows a τ of 38.5 s, a quality factor Q of 358 k, and a FOM of 1.9°/s. The prototype is operated in the force-to-rebalance mode, and an angle random walk of 0.012°/√h and a bias stability of 0.08°/h are demonstrated experimentally. This design strategy is suitable for use in batch fabrication of very high precision microelectromechanical systems devices such as gyroscopes.

Decaying Time Constant Enhanced MEMS Disk Resonator for High Precision Gyroscopic Application

This paper reports a wafer-level technique for the systematic elimination of the modal frequency difference between a nominally degenerate pair of modes in an axisymmetric resonator design. A targeted etch process is developed in which masking resist and a conformal layer are ablated at specific sites on the resonator thereby exposing the underlying silicon and enabling site-specific mass removal by SiDRIE. A model of the perturbed resonator dynamics guides the selection of the ablation sites so that the subsequent timed etch reduces the modal frequency differences by a prescribed amount. This wafer-level process is demonstrated on seven resonators whose modal frequency differences are reduced below 100 mHz from initial splits as large as 15 Hz for a pair of modes with 13.5 kHz nominal frequencies. [2016-0208]

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Tailored Etch Profiles for Wafer-Level Frequency Tuning of Axisymmetric Resonators

This paper reports the permanent frequency mismatch reduction of the primary wineglass modes in a planar axisymmetric resonator by strategic mass loading. The resonator consists of a set of concentric rings that are affixed to neighboring rings by a staggered system of spokes. The outer layers of spokes are targets for mass deposition. This paper develops modified ring equations that guide the mass perturbation process, and despite the fact that the deposited mass and deposition locations are quantized, it is possible to systematically reduce the frequency difference of the wineglass modes to effective degeneracy such that two modes cannot be distinguished in a frequency response plot. Results on five resonators are reported with nominal wineglass modes near 14 kHz, quality factors of 50k, and frequency mismatches exceeding 30 Hz in some cases, but with postperturbation mismatches smaller than 80 mHz. Furthermore, it is also shown that the quality factors remain unchanged. [2014-0227]

/pdf/modal-parameter-tuning-of-an-axisymmetric-resonator-via-mass-1iajq2mvtd.pdf

Modal Parameter Tuning of an Axisymmetric Resonator via Mass Perturbation

Techniques for reducing the frequency split between the Coriolis-coupled modes in disc resonator gyroscopes (DRGs) by perturbing the mass distribution on the disc resonator based on an identified model are disclosed. A model-identification method of tuning a resonator comprises perturbing the mass and measuring a frequency response matrix of the resonator. The frequency response matrix includes a plurality of inputs and a plurality of outputs and the resonator has a plurality of coupled resonance modes. A reduced structural mechanics matrix model of the resonator in sensor and actuator coordinates is identified from the measured frequency response matrix and analyzed to determine generalized eigenvectors of the structural mechanics model and their variations due to selected mass perturbations which is then estimated to improve degeneracy of the plurality of coupled resonance modes based on the generalized eigenvectors of the mass and the stiffness.

David M. Schwartz

Papers

Modal Parameter Tuning of an Axisymmetric Resonator via Mass Perturbation

Frequency tuning of disc resonator gyroscopes via resonator mass perturbation based on an identified model