{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,5]],"date-time":"2026-04-05T09:06:34Z","timestamp":1775379994583,"version":"3.50.1"},"reference-count":23,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2018,5,29]],"date-time":"2018-05-29T00:00:00Z","timestamp":1527552000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Key Research and Development 301 Plan Project of Zhejiang Province","award":["No.2018C01036"],"award-info":[{"award-number":["No.2018C01036"]}]},{"DOI":"10.13039\/501100001809","name":"the National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["No.61376117"],"award-info":[{"award-number":["No.61376117"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"the National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["No.61411136003"],"award-info":[{"award-number":["No.61411136003"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>This paper discusses the vibration-induced error in non-ideal MEMS tuning fork gyroscopes (TFGs). Ideal TFGs which are thought to be immune to vibrations do not exist, and imbalance between two gyros of TFGs is an inevitable phenomenon. Three types of fabrication imperfections (i.e., stiffness imbalance, mass imbalance, and damping imbalance) are studied, considering different imbalance radios. We focus on the coupling types of two gyros of TFGs in both drive and sense directions, and the vibration sensitivities of four TFG designs with imbalance are simulated and compared. It is found that non-ideal TFGs with two gyros coupled both in drive and sense directions (type CC TFGs) are the most insensitive to vibrations with frequencies close to the TFG operating frequencies. However, sense-axis vibrations with in-phase resonant frequencies of a coupled gyros system result in severe error outputs to TFGs with two gyros coupled in the sense direction, which is mainly attributed to the sense capacitance nonlinearity. With increasing stiffness coupled ratio of the coupled gyros system, the sensitivity to vibrations with operating frequencies is cut down, yet sensitivity to vibrations with in-phase frequencies is amplified.<\/jats:p>","DOI":"10.3390\/s18061755","type":"journal-article","created":{"date-parts":[[2018,5,30]],"date-time":"2018-05-30T03:04:27Z","timestamp":1527649467000},"page":"1755","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Vibration-Induced Errors in MEMS Tuning Fork Gyroscopes with Imbalance"],"prefix":"10.3390","volume":"18","author":[{"given":"Xiang","family":"Fang","sequence":"first","affiliation":[{"name":"The Key Laboratory of RF Circuits and System of Ministry of Education, College of Electronic and Information, Hangzhou Dianzi University, Hangzhou 310018, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Linxi","family":"Dong","sequence":"additional","affiliation":[{"name":"The Key Laboratory of RF Circuits and System of Ministry of Education, College of Electronic and Information, Hangzhou Dianzi University, Hangzhou 310018, China"},{"name":"State Key Laboratory of Functional Materials for Informatics, Chinese Academy of Sciences, Shanghai 200050, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2507-5776","authenticated-orcid":false,"given":"Wen-Sheng","family":"Zhao","sequence":"additional","affiliation":[{"name":"The Key Laboratory of RF Circuits and System of Ministry of Education, College of Electronic and Information, Hangzhou Dianzi University, Hangzhou 310018, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Haixia","family":"Yan","sequence":"additional","affiliation":[{"name":"Department of Mechanics, School of Information Engineering, Hangzhou Dianzi University, Hangzhou 310018, China"},{"name":"State Key Laboratory for Manufacturing Systems Engineering, Xi\u2019an Jiaotong University, Xi\u2019an 710049, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kwok Siong","family":"Teh","sequence":"additional","affiliation":[{"name":"Department of Mechanics, School of Engineering, San Francisco State University, San Francisco, CA 94132, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8599-7249","authenticated-orcid":false,"given":"Gaofeng","family":"Wang","sequence":"additional","affiliation":[{"name":"The Key Laboratory of RF Circuits and System of Ministry of Education, College of Electronic and Information, Hangzhou Dianzi University, Hangzhou 310018, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,5,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1640","DOI":"10.1109\/5.704269","article-title":"Micromachined inertial sensors","volume":"86","author":"Yazdi","year":"1998","journal-title":"Proc. IEEE"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Prikhodko, I.P., Zotov, S.A., Trusov, A.A., and Shkel, A.M. (2011, January 5\u20139). Sub-degree-per-hour silicon MEMS rate sensor with 1 million Q-factor. Proceedings of the International Conference on Solid-State Sensors, Actuators and Microsystems (TRANSDUCERS), Beijing, China.","DOI":"10.1109\/TRANSDUCERS.2011.5969216"},{"key":"ref_3","unstructured":"Cho, J., Gregory, J.A., and Najafi, K. (February, January 29). High-Q, 3kHz single-crystal-silicon cylindrical rate-integrating gyro (CING). Proceedings of the IEEE International Conference on Micro Electro Mechanical Systems (MEMS), Paris, France."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1640","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. Microelectromech. Syst."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1651","DOI":"10.3390\/s130201651","article-title":"Design of a novel MEMS gyroscope array","volume":"13","author":"Wang","year":"2013","journal-title":"Sensors"},{"key":"ref_6","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_7","unstructured":"Shkel, A.M. (2006, January 25\u201327). Type I and type II micromachined vibratory gyroscopes. Proceedings of the IEEE PLANS, Position Location and Navigation Symposium, San Diego, CA, USA."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1860","DOI":"10.1109\/JSSC.2002.804345","article-title":"Single-chip surface micromachined integrated gyroscope with 50\/spl deg\/\/h Allan deviation","volume":"37","author":"Geen","year":"2002","journal-title":"IEEE J. Solid-State Circuits"},{"key":"ref_9","unstructured":"Zaman, M.F., Sharma, A., and Ayazi, F. (2006, January 22\u201326). High performance matched-mode tuning fork gyroscope. Proceedings of the IEEE International Conference on Micro Electro Mechanical Systems (MEMS), Istanbul, Turkey."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1016\/j.microrel.2017.06.019","article-title":"Signal integrity in capacitive and piezoresistive single-and multi-axis MEMS gyroscopes under vibrations","volume":"75","author":"Giacci","year":"2017","journal-title":"Microelectron. Reliab."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"2453","DOI":"10.3390\/s150202453","article-title":"Analysis of frequency response and scale-factor of tuning fork micro-gyroscope operating at atmospheric pressure","volume":"15","author":"Ding","year":"2015","journal-title":"Sensors"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1061\/(ASCE)0893-1321(2003)16:2(65)","article-title":"Integrated microelectromechanical gyroscopes","volume":"16","author":"Xie","year":"2003","journal-title":"J. Aerosp. Eng."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Schofield, A.R., Trusov, A.A., Acar, C., and Shkel, A.M. (2007, January 10\u201314). Anti-phase driven rate gyroscope with multi-degree of freedom sense mode. Proceedings of the International Conference on Solid-State Sensors, Actuators and Microsystems (TRANSDUCERS), Lyon, France.","DOI":"10.1109\/SENSOR.2007.4300351"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Yoon, S.W., Lee, S.W., Perkins, N.C., and Najafi, K. (2007, January 28\u201331). Vibration sensitivity of MEMS tuning fork gyroscopes. Proceedings of the IEEE Conference on Sensors, San Diego, CA, USA.","DOI":"10.1109\/ICSENS.2007.4388349"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Schofield, A.R., Trusov, A.A., and Shkel, A.M. (2007, January 28\u201331). Multi-degree of freedom tuning fork gyroscope demonstrating shock rejection. Proceedings of the IEEE Conference on Sensors, Atlanta, GA, USA.","DOI":"10.1109\/ICSENS.2007.4388350"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"32","DOI":"10.1016\/j.sna.2012.04.022","article-title":"Vibration-induced errors in MEMS tuning fork gyroscopes","volume":"180","author":"Yoon","year":"2012","journal-title":"Sens. Actuators A Phys."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1593","DOI":"10.1109\/JSSC.2009.2016996","article-title":"A Sub-0.2\u2218\/hr 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_18","doi-asserted-by":"crossref","first-page":"1144","DOI":"10.1109\/JSEN.2006.881432","article-title":"Modal coupling in micromechanical vibratory rate gyroscopes","volume":"6","author":"Phani","year":"2006","journal-title":"IEEE Sens. J."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"797","DOI":"10.1007\/s00542-012-1510-4","article-title":"Frequency response of in-plane coupled resonators for investigating the acceleration sensitivity of MEMS tuning fork gyroscopes","volume":"18","author":"Singh","year":"2012","journal-title":"Microsyst. Technol."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1313","DOI":"10.1007\/s00542-014-2185-9","article-title":"Acceleration sensitivity of tuning fork gyroscopes: Theoretical model, simulation and experimental verification","volume":"21","author":"Guan","year":"2015","journal-title":"Microsyst. Technol."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1007\/s00542-004-0438-8","article-title":"A novel tuning fork gyroscope with high Q-factors working at atmospheric pressure","volume":"11","author":"Chen","year":"2005","journal-title":"Microsyst. Technol."},{"key":"ref_22","unstructured":"Yin, Y., Wang, S., Wang, C., and Yang, B. (2010, January 20\u201323). Structure-decoupled dual-mass MEMS gyroscope with self-adaptive closed-loop detection. Nano\/Micro Engineered and Molecular Systems (NEMS). Proceedings of the IEEE International Conference on Nano\/Micro Engineered and Molecular Systems (NEMS), Xiamen, China."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Yang, B., Wang, X., Deng, Y., and Hu, D. (2016). Mechanical Coupling Error Suppression Technology for an Improved Decoupled Dual-Mass Micro-Gyroscope. Sensors, 16.","DOI":"10.3390\/s16040503"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/18\/6\/1755\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:06:26Z","timestamp":1760195186000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/18\/6\/1755"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,5,29]]},"references-count":23,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2018,6]]}},"alternative-id":["s18061755"],"URL":"https:\/\/doi.org\/10.3390\/s18061755","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,5,29]]}}}