Browsing by Subject "Stress sensing"

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Embargo
Analytical and experimental study of stress effects in a MEMS ring gyroscope
(Elsevier, 2023-09-09) Hosseini-Pishrobat, Mehran; Erkan, Derin; Tatar, Erdinc
External stress affects the stiffness distribution of a MEMS gyroscope and, along with temperature, is affiliated with long-term drift. Although the detrimental effects of stress on MEMS gyroscopes are well-documented, modeling of such effects is still lacking in the literature. For the first time, we present an analytical model that mathematically describes the stress effects in a ring gyroscope. Our model revolves around the key observation that stress-induced anchor displacements result in variations of electrostatic gaps and nonhomogeneous boundary conditions at the interface between the gyroscope’s suspension system and the anchored internal structure. Our gyroscope is equipped with 16 capacitive stress sensors distributed with 45° symmetry on the inside and outside of the main ring. We use these stress sensors’ measurements to interpolate the strain field across the substrate and deduce the anchor displacements. To capture the stress effects, we show that two fundamental assumptions in the existing literature should be amended: (1) Linearity: the linear engineering strain should be upgraded to the nonlinear Green–Lagrange strain to reveal the stress-induced stiffness through geometric nonlinearity; (2) Inextensibility: for a ring, this stress stiffness is determined by the extensional stress arising from centerline extensibility. We analyze variations of frequencies and mode shapes’ orientation along with the resultant quadrature and in-phase errors. Moreover, we present a fairly general formulation incorporating fabrication-induced imperfections and elastic anisotropy. We validate our model experimentally using extensive bending tests performed on our 59 kHz, 3.2 mm diameter gyroscope.
Open Access
Modeling stress effects on frequencies of a MEMS ring gyroscope
(IEEE, 2023-03-01) Hosseini-Pishrobat, Mehran; Uzunoğlu, Baha Erim; Tatar, Erdinç
We present, for the first time, an analytical model for the external stress effects on the frequencies of a vibrating ring gyroscope (VRG). The stress-induced anchor displacements cause gap changes in the electrodes and nonhomogeneous boundary conditions in the VRG’s suspension structure. Stress stiffness arising from the geometric nonlinearity in the suspension is the principal mechanism affecting VRG’s frequencies as it dominates variations of the electrostatic softening. We validate our model using external stress tests performed on a 57kHz VRG equipped with 16 symmetrically distributed, on-chip capacitive stress sensors, which provide anchor displacement measurements.