Analytical and experimental study of stress effects in a MEMS ring gyroscope

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buir.contributor.authorHosseini-Pishrobat, Mehran
buir.contributor.authorErkan, Derin
buir.contributor.authorTatar, Erdinç
buir.contributor.orcidHosseini-Pishrobat, Mehran|0000-0002-5866-5131
buir.contributor.orcidErkan, Derin|0000-0002-7907-8788
buir.contributor.orcidTatar, Erdinc|0000-0002-6093-4994
dc.citation.epage15en_US
dc.citation.spage1
dc.citation.volumeNumber362
dc.contributor.authorHosseini-Pishrobat, Mehran
dc.contributor.authorErkan, Derin
dc.contributor.authorTatar, Erdinc
dc.date.accessioned2024-03-12T12:44:49Z
dc.date.available2024-03-12T12:44:49Z
dc.date.issued2023-09-09
dc.departmentDepartment of Electrical and Electronics Engineering
dc.departmentInstitute of Materials Science and Nanotechnology (UNAM)
dc.description.abstractExternal 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.
dc.embargo.release2025-09-09
dc.identifier.doi10.1016/j.sna.2023.114639
dc.identifier.eissn1873-3069
dc.identifier.issn0924-4247
dc.identifier.urihttps://hdl.handle.net/11693/114608
dc.language.isoen
dc.publisherElsevier
dc.relation.isversionofhttps://dx.doi.org/10.1016/j.sna.2023.114639
dc.rightsCC BY-NC-ND 4.0 DEED (Attribution-NonCommercial-NoDerivs 4.0 International)
dc.rights.urihttps://creativecommons.org/licenses/by-nc-nd/4.0/
dc.source.titleSensors and Actuators A: Physical
dc.subjectExtensible ring
dc.subjectRing gyroscope
dc.subjectStress sensing
dc.subjectQuadrature error
dc.subjectIn-phase error
dc.titleAnalytical and experimental study of stress effects in a MEMS ring gyroscope
dc.typeArticle

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Department of Electrical and Electronics Engineering
Institute of Materials Science and Nanotechnology (UNAM)