{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,13]],"date-time":"2026-07-13T10:07:47Z","timestamp":1783937267107,"version":"3.55.0"},"reference-count":23,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2015,11,17]],"date-time":"2015-11-17T00:00:00Z","timestamp":1447718400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>To avoid the oscillation of four unequal masses seen in previous triaxial linear gyroscopes, a modified silicon triaxial gyroscope with a rotary wheel is presented in this paper. To maintain a large sensitivity and suppress the coupling of different modes, this novel gyroscope structure is designed be perfectly symmetrical with a relatively large size of about 9.8 mm \u00d7 9.8 mm. It is available for differentially detecting three-axis angular rates simultaneously. To overcome the coupling between drive and sense modes, numerous necessary frames, beams, and anchors are delicately figured out and properly arranged. Besides, some frequency tuning and feedback mechanisms are addressed in the case of post processing after fabrication. To facilitate mode matched function, a new artificial fish swarm algorithm (AFSA) performed faster than particle swarm optimization (PSO) with a frequency split of 108 Hz. Then, by entrusting the post adjustment of the springs dimensions to the finite element method (FEM) software ANSYS, the final frequency splits can be below 3 Hz. The simulation results demonstrate that the modal frequencies in drive and different sense modes are respectively 8001.1, 8002.6, 8002.8 and 8003.3 Hz. Subsequently, different axis cross coupling effects and scale factors are also analyzed. The simulation results effectively validate the feasibility of the design and relevant theoretical calculation.<\/jats:p>","DOI":"10.3390\/s151128979","type":"journal-article","created":{"date-parts":[[2015,11,17]],"date-time":"2015-11-17T10:23:41Z","timestamp":1447755821000},"page":"28979-29002","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["A Mode Matched Triaxial Vibratory Wheel Gyroscope with Fully Decoupled Structure"],"prefix":"10.3390","volume":"15","author":[{"given":"Dunzhu","family":"Xia","sequence":"first","affiliation":[{"name":"School of Instrument Science and Engineering, Key Laboratory of Micro Inertial Instrument and Advanced Navigation Technology of the Ministry of Education, Southeast University, Nanjing 210096, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lun","family":"Kong","sequence":"additional","affiliation":[{"name":"School of Instrument Science and Engineering, Key Laboratory of Micro Inertial Instrument and Advanced Navigation Technology of the Ministry of Education, Southeast University, Nanjing 210096, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Haiyu","family":"Gao","sequence":"additional","affiliation":[{"name":"School of Instrument Science and Engineering, Key Laboratory of Micro Inertial Instrument and Advanced Navigation Technology of the Ministry of Education, Southeast University, Nanjing 210096, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2015,11,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"113001","DOI":"10.1088\/0960-1317\/19\/11\/113001","article-title":"The development of micro-gyroscope technology","volume":"19","author":"Liu","year":"2009","journal-title":"J. Micromech. Microeng."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"2176","DOI":"10.3390\/s130202176","article-title":"A micro dynamically tuned gyroscope with adjustable static capacitance","volume":"13","author":"Xia","year":"2013","journal-title":"Sensors"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"25101","DOI":"10.1088\/0957-0233\/26\/2\/025101","article-title":"Silicon microgyroscope temperature prediction and control system based on BP neural network and Fuzzy-PID control method","volume":"26","author":"Xia","year":"2015","journal-title":"Meas. Sci. Technol."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1394","DOI":"10.3390\/s140101394","article-title":"The Development of Micromachined Gyroscope Structure and Circuitry Technology","volume":"14","author":"Xia","year":"2014","journal-title":"Sensors"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"444","DOI":"10.1109\/JMEMS.2005.844799","article-title":"An x-axis single-crystalline silicon microgyroscope fabricated by the extended SBM process","volume":"14","author":"Kim","year":"2005","journal-title":"J. Microelectromech. Syst."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Guo, Z., Yang, Z., Zhao, Q., Lin, L.T., Ding, H.T., Liu, X.S., Cui, J., Xie, H., and Yan, G.Z. (2010). A lateral-axis micromachined tuning fork gyroscope with torsional Z-sensing and electrostatic force-balanced driving. J. Micromech. Microeng., 20.","DOI":"10.1088\/0960-1317\/20\/2\/025007"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Zhao, Q., Lin, L., Yang, Z., Dong, L., and Yan, G. (2013, January 3\u20136). A micromachined vibrating wheel gyroscope with folded beams. Proceedings of the 2013 IEEE Sensors, Baltimore, MD, USA.","DOI":"10.1109\/ICSENS.2013.6688220"},{"key":"ref_8","unstructured":"ST Microelectronics L3G4200D-3-Axis Digital Output Gyroscope. Available online: http:\/\/www.st.com."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"347","DOI":"10.1109\/JMEMS.2013.2273802","article-title":"Shock impact reliability and failure analysis of a three-axis MEMS gyroscope","volume":"23","author":"Li","year":"2014","journal-title":"J. Microelectromec. Syst."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Walther, A., Desloge, B., Lejuste, C., Coster, B., Audebert, P., and Willienmin, J. (2013). Development of a 3D capacitive gyroscope with reduced parasitic capacitance. J. Micromech. Microeng., 23.","DOI":"10.1088\/0960-1317\/23\/2\/025013"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Vigna, B. (2011, January 5\u20137). Tri-axial MEMS gyroscopes and Six Degree-Of-Freedom Motion Sensors. Proceedings of the 2011 IEEE Electron Devices Meeting (IEDM), Washington, DC, USA.","DOI":"10.1109\/IEDM.2011.6131635"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1016\/j.sna.2010.01.005","article-title":"Experimental analysis and characterization of electrostatic-drive tri-axis micro-gyroscope","volume":"158","author":"Tsai","year":"2010","journal-title":"Sens. Actuators A"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Wang, M., Jiao, J., Yan, P., Mi, B.W., and Qi, S. (2014). A novel tri-axis MEMS gyroscope with in-plane tetra-pendulum proof masses and enhanced sensitive springs. J. Micromech. Microeng., 24.","DOI":"10.1088\/0960-1317\/24\/4\/045002"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"239","DOI":"10.1016\/S0924-4247(01)00732-4","article-title":"Decoupled microgyros and the design principle DAVED","volume":"95","author":"Geiger","year":"2002","journal-title":"Sens. Actuators A"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"707","DOI":"10.1109\/JMEMS.2005.845400","article-title":"A single-crystal silicon symmetrical and decoupled MEMS gyroscope on an insulating substrate","volume":"14","author":"Alper","year":"2005","journal-title":"J. Microelectromec. Syst."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"398","DOI":"10.1109\/JMEMS.2011.2178116","article-title":"High-range angular rate sensor based on mechanical frequency modulation","volume":"21","author":"Zotov","year":"2012","journal-title":"J. Microelectromec. Syst."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"16929","DOI":"10.3390\/s150716929","article-title":"Design and Analysis of a Novel Fully Decoupled Tri-axis Linear Vibratory Gyroscope with Matched Modes","volume":"15","author":"Xia","year":"2015","journal-title":"Sensors"},{"key":"ref_18","unstructured":"Fowles, G., and Cassiday, G. (1999). Analytical Mechanics, Saunders College Publishing."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1593","DOI":"10.1109\/JSSC.2009.2016996","article-title":"A sub-0.2\u00b0\/h bias drift micromechanical silicon gyroscope with automatic CMOS mode-matching","volume":"44","author":"Sharma","year":"2009","journal-title":"IEEE J. Solid-State Circuits"},{"key":"ref_20","unstructured":"Fedder, G.K. (1994). Simulation of Microelectromechanical Systems. [Ph.D. Thesis, University of California]."},{"key":"ref_21","first-page":"1","article-title":"A Solution Quality Assessment Method for Swarm Intelligence Optimization Algorithms","volume":"183809","author":"Zhang","year":"2014","journal-title":"Sci. World J."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Shen, M., Li, L., and Liu, D. (2014, January 19\u201320). Research and Application of Function Optimization Based on Artificial Fish Swarm Algorithm. Proceedings of the 4th International Conference on Computer Engineering and Networks (CENet2014), Shanghai, China.","DOI":"10.1007\/978-3-319-11104-9_23"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"965","DOI":"10.1007\/s10462-012-9342-2","article-title":"Artificial fish swarm algorithm: A survey of the state-of-the-art, hybridization, combinatorial and indicative applications","volume":"42","author":"Neshat","year":"2014","journal-title":"Artif. Intell. Rev."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/15\/11\/28979\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T20:52:12Z","timestamp":1760215932000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/15\/11\/28979"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,11,17]]},"references-count":23,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2015,11]]}},"alternative-id":["s151128979"],"URL":"https:\/\/doi.org\/10.3390\/s151128979","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,11,17]]}}}