Browsing by Subject "In-phase error"

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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 temperature effects in a MEMS ring gyroscope: toward physics-aware drift compensation
(Institute of Electrical and Electronics Engineers, 2025-01-15) Hosseini-Pishrobat, Mehran; Tatar, Erdinç
Temperature plays an indispensable role in the long-term performance of MEMS gyroscopes, and despite extensive studies in the literature, analytical treatment of temperature effects is still an open problem. This paper, to the best of our knowledge, is the first attempt to address this gap for ring gyroscopes. We start with a superposition principle that disentangles thermal displacement fields from the gyroscope's nominal vibration. We set forth a geometrically nonlinear variational formulation to obtain the temperature-induced stiffness matrix. We conduct temperature tests on our 3.2 mm-diameter, 58 kHz ring gyroscopes equipped with 16 capacitive stress sensors. The experimental data validate our analytical modeling in the following key aspects: 1) The model accounts for not only changes in material properties but also a less explored factor, thermal stresses. Thanks to a strain interpolation module that leverages the measured stresses, the model predicts frequency variations consistently and captures hysteresis loops arising from residual stresses. Notably, we accurately estimate the deviation of the temperature coefficient of frequency (TCF) from the expected value -30 ppm/C-degrees (based on the widely known -60 ppm/C-degrees dependency of Young's modulus of silicon). 2) The model is able to capture stiffness couplings in the orders of less than 0.1 N/m (in a 7 kN/m device) and closely predicts the quadrature error and its leakage into the in-phase channel. Additionally, the model incorporates temperature variations of mechanical scale factor, drive mode's amplitude, damping coupling, and sense mode's phase in terms of their contribution to the in-phase error. Based on these merits, our model serves as a building block toward drift compensation algorithms encompassing the underlying physics of the temperature effects.