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Micro-electromechanical systems (MEMS) vibrating gyroscopes have gained a lot of attention over the last two decades because of their low power consumption, easy integration, and low fabrication cost. The usage of the gyroscope equipped with an inertial measurement unit has increased tremendously, with applications ranging from household devices to smart electronics to military equipment. However, reliability issues are still a concern when operating this inertial sensor in harsh environments, such as to control the movement and alignment of mini-satellites in space, tracking firefighters at an elevated temperature, and assisting aircraft navigation in gusty turbulent air. This review paper focuses on the key fundamentals of the MEMS vibrating gyroscopes, first discussing popular designs including the tuning fork, gimbal, vibrating ring, and multi-axis gyroscopes. It further investigates how bias stability, angle random walk, scale factor, and other performance parameters are affected in harsh environments and then discusses the reliability issues of the gyroscopes. [ABSTRACT FROM AUTHOR]

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). [2022-0035] [ABSTRACT FROM AUTHOR]

Micro-electromechanical systems (MEMS) vibrating gyroscopes have gained a lot of attention over the last two decades because of their low power consumption, easy integration, and low fabrication cost. The usage of the gyroscope equipped with an inertial measurement unit has increased tremendously, with applications ranging from household devices to smart electronics to military equipment. However, reliability issues are still a concern when operating this inertial sensor in harsh environments, such as to control the movement and alignment of mini-satellites in space, tracking firefighters at an elevated temperature, and assisting aircraft navigation in gusty turbulent air. This review paper focuses on the key fundamentals of the MEMS vibrating gyroscopes, first discussing popular designs including the tuning fork, gimbal, vibrating ring, and multi-axis gyroscopes. It further investigates how bias stability, angle random walk, scale factor, and other performance parameters are affected in harsh environments and then discusses the reliability issues of the gyroscopes.

This paper investigates laser ablation as a mechanism for fine tuning the flexural modes of vibration of a slightly imperfect suspended ring. A theoretical analysis of the effect of ablation on the natural frequencies of both in-plane and out-of-plane flexural modes is developed. Contributions made to the frequency shift from the reduced mechanical stiffness and reduced mass, as a result of ablation, are included. A specific cyclic symmetric relationship between the modes of vibration and the ablation configuration permitting multimodal tuning is developed. This relationship is expanded for the particular case of flexural modes of order 2 and 3, which are commonly used in vibrating ring gyroscope designs. For vibrating ring gyroscopes, tuning between certain flexural modes of vibration greatly increases the sensitivity of the device to applied rates of rotation. Therefore, a fine-tuning mechanism is highly desirable. An experimental examination of multimodal tuning using laser ablation is performed. In-plane modes of order 2 and out-of-plane modes of order 3 are investigated. Stiffness reduction as a possible method for modifying the natural frequencies of the out-of-plane modes of vibration is explored. [ABSTRACT FROM AUTHOR]

A novel, multi-axis rate sensor based on the vibration properties of a ring structure is presented. Vibrating ring structures have been used successfully to detect rates applied about the axis perpendicular to the plane of the ring using Coriolis coupling between in-plane displacements. The presented multi-axis sensor is capable of detecting rate applied about three mutually perpendicular axes using Coriolis coupling between in-plane and out-of-plane displacements. The steady state amplitude of the induced displacements are proportional to the applied rate. Coriolis coupling is only present for certain combinations of in-plane and out-of-plane displacement patterns, which allows a number of feasible concepts for two- and three-axis rate sensitivity. [ABSTRACT FROM AUTHOR]