Analysis and Design of a Polygonal Oblique Beam for the Butterfly Vibratory Gyroscope with Improved Robustness to Fabrication Imperfections
Abstract
:1. Introduction
2. Structural Design and Theoretical Analysis
2.1. The Operating Principles of the Gyroscope
2.2. Structural Design and Operation Principles
2.3. Spindle Azimuth Angle
2.4. Capacitance Sensitivity
- , the related angular velocities of the rotations;
- , the angular accelerations of the rotations;
- , the moments of inertia of the bending axis;
- , the moments of inertia of the torsion axis;
- , the resonant frequency of the driving mode;
- , the resonant frequency of the sensing mode.
- , the related quality factors of the driving mode;
- , the related quality factors of the sensing mode;
- , the angle rate input;
- , the amplitude of the direct voltage;
- , the amplitude of the alternating voltage; and
- , the velocity coupling coefficient. The formula can be expressed as
2.5. Fabrication Imperfection Analysis
3. A Comparison and Analysis of the Tolerance of Different Cross-Sections
4. Tolerance Capability Analysis
4.1. Alignment Error
4.2. Silicon Thickness Error
4.3. Etching Depth Error
4.4. Upper Width Error
4.5. Bottom Width Error
4.6. DRIE Verticality Error
5. Quadrature Analysis
5.1. Simulation Model
5.2. Comparison Date
6. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
References
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Gyro Width | Gyro Height | Mass Width | Mass Height | Oblique Beam Width | Support Beam Width | Support Beam Height |
---|---|---|---|---|---|---|
6000 | 6000 | 1400 | 1600 | 60 | 70 | 220 |
Alignment Error | Silicon Thickness Error | Etching Depth Error | Upper Width Error | Bottom Width Error | DRIE Verticality Error |
---|---|---|---|---|---|
Red Dashed | |||||
Error Types | Polygonal Cross-Section Beam | Convex Cross-Section Beam |
---|---|---|
Alignment error | 6.24089 | 12.5886 |
Silicon thickness error | 2.48747 | 4.19936 |
Etching depth error | 0.77974 | 0.75824 |
Upper width error | 0.57613 | 5.50023 |
Bottom width error | 3.11562 | 7.33358 |
DRIE verticality error | 0.99716 | 1.88352 |
Cross-Section Type | Displacement Direction | A | B | C | D |
---|---|---|---|---|---|
Polygonal cross-section beam | Driving direction (X) | 0.078 | 0.016 | 1.051 | 0.754 |
Sensing direction (Z) | 10.725 | 4.467 | 10.113 | 5.514 | |
Convex cross-section beam | Driving direction (X) | 0.591 | 0.758 | 0.247 | 0.296 |
Sensing direction (Z) | 23.059 | 24.673 | 33.511 | 13.083 |
Cross-Section Type | Symmetry Point | Driving Direction (X) | Sensing Direction (Z) |
---|---|---|---|
Polygonal cross-section beam | A-B | 1.118 | * |
C-D | 1.021 | * | |
A-C | * | 1.534 | |
B-D | * | 1.824 | |
Convex cross-section beam | A-B | 1.109 | * |
C-D | 1.05 | * | |
A-C | * | 9.155 | |
B-D | * | 2.039 |
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Ou, F.; Hou, Z.; Wu, X.; Xiao, D. Analysis and Design of a Polygonal Oblique Beam for the Butterfly Vibratory Gyroscope with Improved Robustness to Fabrication Imperfections. Micromachines 2018, 9, 198. https://doi.org/10.3390/mi9050198
Ou F, Hou Z, Wu X, Xiao D. Analysis and Design of a Polygonal Oblique Beam for the Butterfly Vibratory Gyroscope with Improved Robustness to Fabrication Imperfections. Micromachines. 2018; 9(5):198. https://doi.org/10.3390/mi9050198
Chicago/Turabian StyleOu, Fenlan, Zhanqiang Hou, Xuezhong Wu, and Dingbang Xiao. 2018. "Analysis and Design of a Polygonal Oblique Beam for the Butterfly Vibratory Gyroscope with Improved Robustness to Fabrication Imperfections" Micromachines 9, no. 5: 198. https://doi.org/10.3390/mi9050198