Mechanical Analysis and Design of Vibratory Micromachined Gyroscopes

Vibratory micromachined gyroscopes typically exhibit certain undesirable behaviors that impede the angular rate measurement, such as nonlinearity, cross-axis sensitivity, scale factor offset, and quadrature error. These errors have sources in both the mechanical and electrical components of a gyroscope. This dissertation presents an extensive analysis of the mechanics of vibratory rate gyroscopes which identifies many mechanical error sources. The results enable gyroscope designers to predict error sources limiting the achievable performance prior to fabrication of the device.
Linear, lumped-parameter models are derived for two classes of vibratory rate gyroscopes, one based on translations of a proof mass and one based on rotations. The models include terms that are often omitted in the published literature. These terms are shown to produce cross-axis sensitivity. Scaling laws for evaluating the significance of the terms producing these errors are discussed. 
The contributions of the suspension beams to spurious mechanical behavior is examined extensively. A nonlinear rod theory, which models flexure (including shearing deformations), torsion, and axial extension/compression, is applied to the suspension of a micromachined gyroscope based on proof mass rotations. A linearized version of the theory is used to derive a continuum model of the suspension beams. Approximations to the nonlinear theory provide formulas for the coefficients of cubic stiffening, which enable predictions of spring-hardening behavior, as demonstrated by a comparison with experimental data. Suspension designs which minimize nonlinearity and design rules for the maximum achievable linear displacement for common microsystem suspension designs are discussed. A model for nonlinear elastic coupling between the drive and sense modes of a gyroscope is derived, and is used to show how the suspension can generate scale factor offset and quadrature error even in the absence of manufacturing defects. However, such defects also contribute to spurious dynamics, and so a linear model for a gyroscope with non-identical suspension beams is presented.
Two new designs for dual-axis gyroscopes based on proof mass rotations are proposed. The comparisons of experimental data from these devices with the analytical resuIts of this work is suggested as a future research direction.
Publication date: 
January 31, 2001
Publication type: 
Ph.D. Dissertation
Davis, W. O. (2001). Mechanical Analysis and Design of Vibratory Micromachined Gyroscopes. United States: University of California, Berkeley.

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