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      Modeling and analysis of a MEMS vibrating ring gyroscope subject to imperfections

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      Author(s)
      Hosseini-Pishrobat, Mehran
      Tatar, Erdinç
      Date
      2022-05-06
      Source Title
      Journal of Microelectromechanical Systems
      Print ISSN
      1057-7157
      Electronic ISSN
      1941-0158
      Publisher
      Institute of Electrical and Electronics Engineers
      Volume
      31
      Issue
      4
      Pages
      546 - 560
      Language
      English
      Type
      Article
      Item Usage Stats
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      Abstract
      We present a new mathematical model for a vibrating ring gyroscope (VRG) in the presence of imperfections, namely, structural defects and material anisotropy. As a novelty, we calculate the mode shapes of the internal suspension structure to enable a more accurate and modular analysis of the VRG’s mass and stiffness distributions. Solving the associated eigenvalue problem shows that imperfections result in the frequency split between the gyroscope’s operating mode shapes, rotating their orientation with respect to the nominal drive and sense axes. We then use perturbation analysis to solve the VRG’s equations of motion and analyze the quadrature error that arises from frequency/damping mismatch between the mode shapes. We use our model to detail the various effects of the etching-related undercuts, structural uncertainties, and Young’s modulus anisotropy–in the form of suitable space-dependent functions–on the mode shapes and the quadrature error for the first time. The results reveal that rings are robust against imperfection, while the straight beams used in the suspension system are most likely responsible for the frequency split and quadrature error. For example, 50 nm (0.5%) width variation in a beam that connects the VRG’s suspension to an anchored internal structure leads to 4700°/s quadrature error. To validate our modeling, using the experimental data from a fabricated 59 kHz VRG, we provide rigorous, comparative simulations against the finite element method (FEM).
      Keywords
      Frequency split
      Imperfections
      Vibrating ring
      MEMS gyroscope
      Quadrature error
      Permalink
      http://hdl.handle.net/11693/111896
      Published Version (Please cite this version)
      https://doi.org/10.1109/JMEMS.2022.3170121
      Collections
      • Department of Electrical and Electronics Engineering 4011
      • Institute of Materials Science and Nanotechnology (UNAM) 2256
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