A Detailed Analysis of the Dynamic Behavior of a MEMS Vibrating Internal Ring Gyroscope
Abstract
:1. Introduction
2. Dynamics of MEMS Vibrating Ring Gyroscope
2.1. Reference Frames
- = the inertial reference frame (stationary);
- = the non-inertial reference frame (accelerating);
- = the position vector of non-inertial reference frame ”” with respect to the inertial frame “”;
- = the velocity of the non-inertial reference frame “” with respect to “”;
- = the acceleration of the non-inertial frame “” with respect to “”;
- = the position vector relative to the inertial reference frame;
- = the position vector relative to the non-inertial reference frame;
- = the acceleration of the inertial reference frame;
- = the acceleration of the non-inertial reference frame.
2.2. Motion Equations of Vibrating Ring Gyroscope
2.2.1. Coordinates for Vibrating Ring Gyroscope
2.2.2. Effects of Various Energies
Kinetic Energy
Elastic Strain Energy
Strain Energy of Semicircular Beams
Damping Energy
2.3. Implication of Resonance Analysis on MEMS Vibrating Ring Gyroscope Design
2.4. Mode Matching in Vibrating Ring Gyroscopes
3. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Gill, W.A.; Howard, I.; Mazhar, I.; McKee, K. A Detailed Analysis of the Dynamic Behavior of a MEMS Vibrating Internal Ring Gyroscope. Micromachines 2024, 15, 1107. https://doi.org/10.3390/mi15091107
Gill WA, Howard I, Mazhar I, McKee K. A Detailed Analysis of the Dynamic Behavior of a MEMS Vibrating Internal Ring Gyroscope. Micromachines. 2024; 15(9):1107. https://doi.org/10.3390/mi15091107
Chicago/Turabian StyleGill, Waqas Amin, Ian Howard, Ilyas Mazhar, and Kristoffer McKee. 2024. "A Detailed Analysis of the Dynamic Behavior of a MEMS Vibrating Internal Ring Gyroscope" Micromachines 15, no. 9: 1107. https://doi.org/10.3390/mi15091107