{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:56:43Z","timestamp":1760241403379,"version":"build-2065373602"},"reference-count":33,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2018,1,31]],"date-time":"2018-01-31T00:00:00Z","timestamp":1517356800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Science Foundation of China","doi-asserted-by":"publisher","award":["61474034"],"award-info":[{"award-number":["61474034"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012166","name":"National Basic Research Program of China","doi-asserted-by":"publisher","award":["2012CB934100"],"award-info":[{"award-number":["2012CB934100"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Natural Science Foundation of Heilongjiang Province of China","award":["F201418"],"award-info":[{"award-number":["F201418"]}]},{"name":"the State Key Laboratory of Urban Water Resource and Environment (Harbin Institute of Technology)","award":["2016TS 06"],"award-info":[{"award-number":["2016TS 06"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Stable rotor levitation is a challenge for rotational gyroscopes (magnetically suspended gyroscopes (MSG) and electrostatically suspended gyroscopes (ESG)) with a ring- or disk-shaped rotor, which restricts further improvement of gyroscope performance. In addition, complicated pick-up circuits and feedback control electronics propose high requirement on fabrication technology. In the proposed gyroscope, a ball-disk shaped rotor is supported by a water-film bearing, formed by centrifugal force to deionized water at the cavity of the lower supporting pillar. Water-film bearing provides stable mechanical support, without the need for complicated electronics and control system for rotor suspension. To decrease sliding friction between the rotor ball and the water-film bearing, a supherhydrophobic surface (SHS) with nano-structures is fabricated on the rotor ball, resulting in a rated spinning speed increase of 12.4% (under the same driving current). Rotor is actuated by the driving scheme of brushless direct current motor (BLDCM). Interaction between the magnetized rotor and the magnetic-conducted stator produces a sinusoidal rotor restoring torque, amplitude of which is proportional to the rotor deflection angle inherently. Utilization of this magnetic restoring effect avoids adding of a high amplitude voltage for electrostatic feedback, which may cause air breakdown. Two differential capacitance pairs are utilized to measure input angular speeds at perpendicular directions of the rotor plane. The bias stability of the fabricated gyroscope is as low as 0.5\u00b0\/h.<\/jats:p>","DOI":"10.3390\/s18020415","type":"journal-article","created":{"date-parts":[[2018,1,31]],"date-time":"2018-01-31T12:41:24Z","timestamp":1517402484000},"page":"415","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["A Rotational Gyroscope with a Water-Film Bearing Based on Magnetic Self-Restoring Effect"],"prefix":"10.3390","volume":"18","author":[{"given":"Dianzhong","family":"Chen","sequence":"first","affiliation":[{"name":"MEMS Center, Harbin Institute of Technology, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaowei","family":"Liu","sequence":"additional","affiliation":[{"name":"MEMS Center, Harbin Institute of Technology, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4917-746X","authenticated-orcid":false,"given":"Haifeng","family":"Zhang","sequence":"additional","affiliation":[{"name":"MEMS Center, Harbin Institute of Technology, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hai","family":"Li","sequence":"additional","affiliation":[{"name":"Center for Integrated Spintronic Devices, Hangzhou Dianzi University, Hangzhou 310018, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3830-7385","authenticated-orcid":false,"given":"Rui","family":"Weng","sequence":"additional","affiliation":[{"name":"School of Software and Microelectronics, Harbin University of Science and Technology, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ling","family":"Li","sequence":"additional","affiliation":[{"name":"MEMS Center, Harbin Institute of Technology, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wanting","family":"Rong","sequence":"additional","affiliation":[{"name":"MEMS Center, Harbin Institute of Technology, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhongzhao","family":"Zhang","sequence":"additional","affiliation":[{"name":"Communication Research Center, Harbin Institute of Technology, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,1,31]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1639","DOI":"10.1109\/JSEN.2007.908921","article-title":"Zero-rate output and quadrature compensation in vibratory MEMS gyroscopes","volume":"7","author":"Saukoski","year":"2007","journal-title":"IEEE Sens. J."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Elsayed, M., Nabki, F., Sawan, M., and El-Gamal, M. (2011, January 19\u201322). A 5 V Gyroscope with 3 aF\/\u00b0\/s Sensitivity, 0.6\u00b0\/\u221ahr Mechanical Noise and Drive-Sense Crosstalk Minimization. Proceedings of the 2011 International Conference on Microelectronics (ICM), Hammamet, Tunisia.","DOI":"10.1109\/ICM.2011.6177338"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"469","DOI":"10.1016\/S0924-4247(97)80307-X","article-title":"Modelling and testing of a frictionless levitated micromotor","volume":"61","author":"Williams","year":"1997","journal-title":"Sens. Actuators"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1016\/S0924-4247(00)00292-2","article-title":"Development of a levitated micromotor for application as a gyroscope","volume":"82","author":"Shearwood","year":"2000","journal-title":"Sens. Actuators"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"651","DOI":"10.1016\/j.sna.2006.03.002","article-title":"The study of an electromagnetic levitating micromotor for application in a rotating gyroscope","volume":"132","author":"Zhang","year":"2006","journal-title":"Sens. Actuators"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"681","DOI":"10.1049\/el:20080528","article-title":"Variable-capacitance micromotor with levitated diamagnetic rotor","volume":"44","author":"Liu","year":"2008","journal-title":"Electron. Lett."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"431","DOI":"10.1007\/s00542-009-0935-x","article-title":"An innovative micro-diamagnetic levitation system with coils applied in micro-gyroscope","volume":"16","author":"Liu","year":"2010","journal-title":"Microsyst. Technol."},{"key":"ref_8","unstructured":"Dauwalter, C.R., and Ha, J.C. (2004, January 26\u201329). A high performance magnetically suspended MEMS spinning wheel gyroscope. Proceedings of the PLANS 2004\u2014Position Location and Navigation Symposium, Monterey, CA, USA."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1109\/MAES.2005.1397145","article-title":"Magnetically suspended MEMS spinning wheel gyroscope","volume":"20","author":"Dauwalter","year":"2005","journal-title":"IEEE Aerosp. Electron. Syst. Mag."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1357","DOI":"10.1016\/j.isatra.2014.03.009","article-title":"Dynamic characteristics of the rotor in a magnetically suspended control moment gyroscope with active magnetic bearing and passive magnetic bearing","volume":"53","author":"Tang","year":"2014","journal-title":"ISA Trans."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Torti, R., Gondhalekar, V., Tran, H., Selfors, B., Bart, S., and Maxwell, B. (1994, January 13). Electrostatically suspended and sensed micromechanical rate gyroscope. Proceedings of the SPIE\u2019s International Symposium on Optical Engineering and Photonics in Aerospace Sensing, Orlando, FL, USA.","DOI":"10.1117\/12.179613"},{"key":"ref_12","unstructured":"Esashi, M. (2002, January 24). Saving energy and natural resource by micro-nanomachining. Proceedings of the Fifteenth IEEE International Conference on Micro Electro Mechanical Systems, Las Vegas, NV, USA."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"2468","DOI":"10.1143\/JJAP.42.2468","article-title":"Electrostatically levitated ring-shaped rotational gyroscope\/accelerometer","volume":"42","author":"Murakoshi","year":"2003","journal-title":"Jpn. J. Appl. Phys."},{"key":"ref_14","unstructured":"Nakamura, S. (November, January 30). MEMS inertial sensor toward higher accuracy & multi-axis sensing. Proceedings of the 2005 IEEE Sensors, Irvine, CA, USA."},{"key":"ref_15","unstructured":"Kraft, M., and Evans, A. (2000, January 27\u201329). System level simulation of an electrostatically levitated disk. Proceedings of the 2000 International Conference on Modeling and Simulation of Microsystems, San Diego, CA, USA."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"423","DOI":"10.1088\/0960-1317\/11\/4\/324","article-title":"Modelling and design of an electrostatically levitated disk for inertial sensing applications","volume":"11","author":"Kraft","year":"2001","journal-title":"J. Micromech. Microeng."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"S11","DOI":"10.1088\/0960-1317\/13\/4\/302","article-title":"Electronic interface design for an electrically floating micro-disk","volume":"13","author":"Gindila","year":"2003","journal-title":"J. Micromech. Microeng."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1088\/0960-1317\/13\/4\/311","article-title":"Electroplating moulds using dry film thick negative photoresist","volume":"13","author":"Kukharenka","year":"2003","journal-title":"J. Micromech. Microeng."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Damrongsak, B., and Kraft, M. (November, January 30). A micromachined electrostatically suspended gyroscope with digital force feedback. Proceedings of the 2005 IEEE Sensors, Irvine, CA, USA.","DOI":"10.1049\/ic:20060468"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Damrongsak, B. (2006, January 28). Design and simulation of a micromachined electrostatically suspended gyroscope. Proceedings of the Seminar on MEMS Sensors and Actuators, London, UK.","DOI":"10.1049\/ic:20060468"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"4586","DOI":"10.3390\/s90604586","article-title":"Development of a prototype miniature silicon microgyroscope","volume":"9","author":"Xia","year":"2009","journal-title":"Sensors"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"417","DOI":"10.1006\/jsvi.2001.4163","article-title":"The influence of control system design on the performance of vibratory gyroscopes","volume":"255","author":"Loveday","year":"2002","journal-title":"J. Sound Vib."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1382","DOI":"10.1109\/JMEMS.2011.2167663","article-title":"Force rebalance controller synthesis for a micromachined vibratory gyroscope based on sensitivity margin specifications","volume":"20","author":"Cui","year":"2011","journal-title":"J. Microelectromech. Syst."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"721","DOI":"10.1109\/JMEMS.2012.2185218","article-title":"Rotary Liquid Droplet Microbearing","volume":"21","author":"Yoxall","year":"2012","journal-title":"J. Microelectromech. Syst."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1109\/JMEMS.2013.2262592","article-title":"Electrostatic side-drive rotary stage on liquid-ring bearing","volume":"23","author":"Sun","year":"2014","journal-title":"J. Microelectromech. Syst."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1781","DOI":"10.1039\/c001211d","article-title":"Capillary motor driven by electrowetting","volume":"10","author":"Takei","year":"2010","journal-title":"Lab Chip"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"417","DOI":"10.1007\/s11340-008-9165-x","article-title":"Measurement of dynamic properties of viscoelastic materials","volume":"49","author":"Kulik","year":"2009","journal-title":"Exp. Mech."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"503","DOI":"10.1017\/S0022112087003288","article-title":"A model for the dynamics of polymers in laminar shear flows","volume":"185","author":"Keyes","year":"1987","journal-title":"J. Fluid Mech."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"512","DOI":"10.1103\/PhysRevLett.63.512","article-title":"Scale-dependent enhancement and damping of vorticity disturbances by polymers in elongational flow","volume":"63","author":"Rabin","year":"1989","journal-title":"Phys. Rev. Lett."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1017\/S0022112004000291","article-title":"On the coherent drag-reducing and turbulence-enhancing behaviour of polymers in wall flows","volume":"514","author":"Dubief","year":"2004","journal-title":"J. Fluid Mech."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Chen, D., Liu, X., Zhang, H., Li, H., Weng, R., Li, L., and Zhang, Z. (2017). Friction reduction for a rotational gyroscope with mechanical support by fabrication of a biomimetic superhydrophobic surface on a ball-disk shaped rotor and the application of a water film bearing. Micromachines, 8.","DOI":"10.3390\/mi8070223"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"5065","DOI":"10.1021\/la034123j","article-title":"Equation for slip of simple liquids at smooth solid surface","volume":"19","author":"Spikes","year":"2003","journal-title":"Langmuir"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"591","DOI":"10.1631\/FITEE.1500454","article-title":"Micro-Angle Tilt Detection for the Rotor of a Novel Rotational Gyroscope with 0.47\u2019\u2019 Resolution","volume":"18","author":"Li","year":"2016","journal-title":"Front. Inf. Technol. Electron. Eng."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/18\/2\/415\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T14:53:20Z","timestamp":1760194400000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/18\/2\/415"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,1,31]]},"references-count":33,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2018,2]]}},"alternative-id":["s18020415"],"URL":"https:\/\/doi.org\/10.3390\/s18020415","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2018,1,31]]}}}