A MEMS diamond hemispherical resonator

Bernstein, J.; Bancu, Mirela G.; Cook, Eugene H.; Chaparala, M.; Teynor, William A; Weinberg, Marc S.

doi:10.1088/0960-1317/23/12/125007

Cited by 48 publications

(22 citation statements)

References 13 publications

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“…MEMS Coriolis vibratory gyroscopes (CVGs) with circular micro-resonators, such as ring [1,2,3,4], disk [5,6], hemispherical [7,8], birdbath shell [9,10], and wineglass [11], exhibit extraordinary performances by their structural symmetry and, consequently, have drawn tremendous interest in both the academic and the industrial fields. The most significant benefit of the CVGs with circular micro-resonators is the ability of angular rate-integrating under the whole-angle operation [12,13,14], which has advantages in direct angle output, wide measurement range, fast response, and extensive dynamic range over the force re-balance operation of CVGs.…”

Section: Introductionmentioning

confidence: 99%

A Lumped Mass Model for Circular Micro-Resonators in Coriolis Vibratory Gyroscopes

et al. 2019

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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.

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Section: Introductionmentioning

confidence: 99%

A Lumped Mass Model for Circular Micro-Resonators in Coriolis Vibratory Gyroscopes

et al. 2019

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“…Small fabrication errors, however, cause the modal frequencies to detune, thereby reducing the signal-to-noise ratio that can be achieved with the associated CVG (see [1] for the analysis of a disk resonator). With the successful development of modematched micro-scale disk resonators [2], [3], [4], quadruple mass resonators [5], hemispherical [6], [7], [8], [9], [10], [11], [12], and hemitoroidal [13], [14] resonators, it has become imperative to create post-fabrication corrective procedures so that the pairs of modal frequencies can be brought back to degeneracy. This paper reports the development and application of a wafer-level targeted SiDRIE process for eliminating the modal frequency differences in a planar axisymmetric silicon resonator.…”

Section: Introductionmentioning

confidence: 99%

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

Behbahani

Kim

Stupar

et al. 2017

J. Microelectromech. Syst.

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Abstract-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 waferlevel 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.

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“…Examples in which the experimental reduction of the modal frequency differences have been achieved are given in [14,15]. In the latter reference, the Rayleigh-Ritz analysis from [5] was adapted to create an iterative frequency trimming procedure that employs mass deposition on a planar microscale resonator consisting of multiple nested rings.…”

Section: Introductionmentioning

confidence: 99%

Frequency analysis of a uniform ring perturbed by point masses and springs

Behbahani

M’Closkey

2017

Journal of Sound and Vibration

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Perturbation expansions of solutions for a uniform, thin, linear elastic ring perturbed by point masses and radial massless springs are developed. The perturbation locations divide the ring into uniform segments so a variational formulation is used to determine the boundary conditions that must be satisfied between adjoining segments. The motion of each segment can be represented as a weighted sum of the eigenfunctions for the uniform thin ring so when the boundary conditions are enforced, the resulting algebraic relations are expanded as a function of the perturbation parameter (the perturbation mass normalized by the ring mass). A series of algebraic problems are sequentially solved to yield perturbation expansions for the modal frequencies and eigenmodes.Single-mass, dual-mass, and mass-spring case studies are considered. The perturbation results show excellent agreement with finite element analysis of a thin ring for mass perturbations up to 15% of the nominal ring mass. The results are also compared to Rayleigh-Ritz analysis.

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A MEMS diamond hemispherical resonator

Cited by 48 publications

References 13 publications

A Lumped Mass Model for Circular Micro-Resonators in Coriolis Vibratory Gyroscopes

A Lumped Mass Model for Circular Micro-Resonators in Coriolis Vibratory Gyroscopes

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

Frequency analysis of a uniform ring perturbed by point masses and springs

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