The Effect of the Bending Beam Width Variations on the Discrepancy of the Resulting Quadrature Errors in MEMS Gyroscopes
In this paper, we develop a new approach in order to understand the origin of the quadrature error in MEMS gyroscopes. As the width of the flexure springs is a critical parameter in the MEMS design, it is necessary to investigate the impact of the width variations on the stiffness coupling, which ca...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-04-01
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| Series: | Micromachines |
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| Online Access: | https://www.mdpi.com/2072-666X/13/5/655 |
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| author | Alexandre Azier Najib Kacem Bernard Chaumet Noureddine Bouhaddi |
| author_facet | Alexandre Azier Najib Kacem Bernard Chaumet Noureddine Bouhaddi |
| author_sort | Alexandre Azier |
| collection | DOAJ |
| description | In this paper, we develop a new approach in order to understand the origin of the quadrature error in MEMS gyroscopes. As the width of the flexure springs is a critical parameter in the MEMS design, it is necessary to investigate the impact of the width variations on the stiffness coupling, which can generate a quadrature signal. To do so, we developed a method to determine the evolution of the stiffness matrix of the gyroscope springs with respect to the variation of the bending beams width of the springs through finite element analysis (FEA). Then, a statistical analysis permits the computation of the first two statistical moments of the quadrature error for a given beam width defect. It turns out that even small silicon etching defects can generate high quadrature level with up to a root mean square (RMS) value of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1220</mn><mo>°</mo><mo>/</mo><mi mathvariant="normal">s</mi></mrow></semantics></math></inline-formula> for a bending beam width defect of 0.9%. Moreover, the quadrature error obtained through simulations has the same order of magnitude as the ones measured on the gyroscopes. This result constitutes a great help for designing MEMS gyroscopes, as the consideration of the bending beams width defects is needed in order to avoid high quadrature error. |
| first_indexed | 2024-03-10T03:25:10Z |
| format | Article |
| id | doaj.art-86a0b261f79a474881998800ec203384 |
| institution | Directory Open Access Journal |
| issn | 2072-666X |
| language | English |
| last_indexed | 2024-03-10T03:25:10Z |
| publishDate | 2022-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Micromachines |
| spelling | doaj.art-86a0b261f79a474881998800ec2033842023-11-23T12:11:07ZengMDPI AGMicromachines2072-666X2022-04-0113565510.3390/mi13050655The Effect of the Bending Beam Width Variations on the Discrepancy of the Resulting Quadrature Errors in MEMS GyroscopesAlexandre Azier0Najib Kacem1Bernard Chaumet2Noureddine Bouhaddi3Department of Applied Mechanics, FEMTO-ST Institute, CNRS/UFC/ENSMM/UTBM, University Bourgogne Franche-Comté, 25000 Besançon, FranceDepartment of Applied Mechanics, FEMTO-ST Institute, CNRS/UFC/ENSMM/UTBM, University Bourgogne Franche-Comté, 25000 Besançon, FranceThales Avionics, 26027 Valence, FranceDepartment of Applied Mechanics, FEMTO-ST Institute, CNRS/UFC/ENSMM/UTBM, University Bourgogne Franche-Comté, 25000 Besançon, FranceIn this paper, we develop a new approach in order to understand the origin of the quadrature error in MEMS gyroscopes. As the width of the flexure springs is a critical parameter in the MEMS design, it is necessary to investigate the impact of the width variations on the stiffness coupling, which can generate a quadrature signal. To do so, we developed a method to determine the evolution of the stiffness matrix of the gyroscope springs with respect to the variation of the bending beams width of the springs through finite element analysis (FEA). Then, a statistical analysis permits the computation of the first two statistical moments of the quadrature error for a given beam width defect. It turns out that even small silicon etching defects can generate high quadrature level with up to a root mean square (RMS) value of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1220</mn><mo>°</mo><mo>/</mo><mi mathvariant="normal">s</mi></mrow></semantics></math></inline-formula> for a bending beam width defect of 0.9%. Moreover, the quadrature error obtained through simulations has the same order of magnitude as the ones measured on the gyroscopes. This result constitutes a great help for designing MEMS gyroscopes, as the consideration of the bending beams width defects is needed in order to avoid high quadrature error.https://www.mdpi.com/2072-666X/13/5/655MEMSgyroscopeinertial sensorquadrature signaltechnology defects |
| spellingShingle | Alexandre Azier Najib Kacem Bernard Chaumet Noureddine Bouhaddi The Effect of the Bending Beam Width Variations on the Discrepancy of the Resulting Quadrature Errors in MEMS Gyroscopes Micromachines MEMS gyroscope inertial sensor quadrature signal technology defects |
| title | The Effect of the Bending Beam Width Variations on the Discrepancy of the Resulting Quadrature Errors in MEMS Gyroscopes |
| title_full | The Effect of the Bending Beam Width Variations on the Discrepancy of the Resulting Quadrature Errors in MEMS Gyroscopes |
| title_fullStr | The Effect of the Bending Beam Width Variations on the Discrepancy of the Resulting Quadrature Errors in MEMS Gyroscopes |
| title_full_unstemmed | The Effect of the Bending Beam Width Variations on the Discrepancy of the Resulting Quadrature Errors in MEMS Gyroscopes |
| title_short | The Effect of the Bending Beam Width Variations on the Discrepancy of the Resulting Quadrature Errors in MEMS Gyroscopes |
| title_sort | effect of the bending beam width variations on the discrepancy of the resulting quadrature errors in mems gyroscopes |
| topic | MEMS gyroscope inertial sensor quadrature signal technology defects |
| url | https://www.mdpi.com/2072-666X/13/5/655 |
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