Browsing by Author "Tatar, Erdinç"

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Open Access
An analtical model for vibration analysis of disk resonator gyroscopes
(Institute of Electrical and Electronics Engineers, 2022-06-08) Hosseini-Pishrobat, Mehran; Uzunoğlu, Baha Erim; Erkan, Derin; Tatar, Erdinç
Disk resonator gyroscopes (DRGs) utilize the circular symmetry of a set of concentric rings to realize high-performance MEMS gyroscopes. We set forth an analytical method to calculate the mode shapes of the rings and then obtain the corresponding modal mass, Coriolis mass, and stiffness. Following the Ritz method, we minimize the total potential energy of the rings subject to the boundary conditions imposed by the spokes that connect the rings. We show the efficacy of our method using the frequency response of a fabricated DRG and comparison with the finite element method (FEM). With respect to the FEM, our modeling is more straightforward, more intuitive, and can be extended to model imperfections and ensuing effects such as quadrature error and frequency split.
Open Access
Analysis of quadrature and frequency split in a MEMS vibrating ring gyroscope with structural imperfections
(IEEE, 2021-08-06) Hosseini-Pishrobat, Mehran; Tatar, Erdinç
Structural imperfections affect the performance of MEMS vibrating ring gyroscopes (VRGs), dominantly in terms of quadrature error and frequency split. We consider a VRG with a ring subjected to width nonuniformity and supported by an imperfect suspension. This reflects the scenario of nonuniform etching, common in microfabrication processes. We show that the ring's width nonuniformity mainly results in a rotation of the mode-shapes with respect to those of a perfect ring while an imperfect suspension induces frequency split between the modes. On this basis, we calculate the quadrature error in the gyroscope's output. As an example, a 4° mode-shape rotation and 15Hz frequency split in a 60kHz VRG generate an approximate quadrature error of 1000°/s.
Open Access
Modeling and analysis of a MEMS vibrating ring gyroscope subject to imperfections
(Institute of Electrical and Electronics Engineers, 2022-05-06) Hosseini-Pishrobat, Mehran; Tatar, Erdinç
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).
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.
Open Access
A ring gyroscope with on-chip capacitive stress compensation
(Institute of Electrical and Electronics Engineers, 2022-08-18) Uzunoğlu, Baha Erim; Erkan, Derin; Tatar, Erdinç
We present long-term stress compensation results for a 3.2mm diameter ring gyroscope integrated with 16 capacitive stress sensors for the first time in this work. A bridge-type capacitive sensor is preferred due to its compact size and temperature insensitivity for on-chip stress measurements. The ring design enables a high level of integration and stress sensor-gyroscope output correlation. We first demonstrate the stress sensor operation on a stress test-bed. The drift test for sixteen days at mismatched mode and the drift test for eight days at matched mode in room temperature reveal that the stress compensation can eliminate the gyroscope drift. The stability of the stress compensated gyroscope output can reach 0.008°/h in mismatched mode and 0.003°/h in matched mode at an averaging time of two days with no signs of long-term drift. High gyroscope stability is achieved with a partial least-squares fitting algorithm; however, we believe that stress and gyroscope output relation might be linear time-variant with possible nonlinear and hysteresis effects. Analysis of the drive and sense mode frequencies shows that only temperature cannot explain the frequency variations, and the inclusion of stress can comprehensively describe the frequency changes.