{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:19:06Z","timestamp":1760242746235,"version":"build-2065373602"},"reference-count":33,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2016,5,18]],"date-time":"2016-05-18T00:00:00Z","timestamp":1463529600000},"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>An in situ measurement of micro-friction torque in MEMS gas bearings, which has been a challenging research topic for years, is realized by a system designed in this paper. In the system, a high accuracy micro-force sensor and an electronically-driven table are designed, fabricated and utilized. With appropriate installation of the sensor and bearings on the table, the engine rotor can be driven to rotate with the sensor using a silicon lever beam. One end of the beam is fixed to the shaft of the gas bearing, while the other end is free and in contact with the sensor probe tip. When the sensor begins to rotate with the table, the beam is pushed by the sensor probe to rotate in the same direction. For the beam, the friction torque from the gas bearing is balanced by the torque induced by pushing force from the sensor probe. Thus, the friction torque can be calculated as a product of the pushing force measured by the sensor and the lever arm, which is defined as the distance from the sensor probe tip to the centerline of the bearing. Experimental results demonstrate the feasibility of this system, with a sensitivity of 1.285 mV\/\u03bcN\u00b7m in a range of 0 to 11.76 \u03bcN\u00b7m when the lever arm is 20 mm long. The measuring range can be modified by varying the length of the lever arm. Thus, this system has wide potential applications in measuring the micro-friction torque of gas bearings in rotating MEMS machines.<\/jats:p>","DOI":"10.3390\/s16050726","type":"journal-article","created":{"date-parts":[[2016,5,18]],"date-time":"2016-05-18T10:10:24Z","timestamp":1463566224000},"page":"726","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Measuring Micro-Friction Torque in MEMS Gas Bearings"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0956-3833","authenticated-orcid":false,"given":"Xudong","family":"Fang","sequence":"first","affiliation":[{"name":"School of Materials Science &amp; Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Huan","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Optoelectronic Engineering, Xi\u2019an Technological Univeristy, Xi\u2019an 710032, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2016,5,18]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1269","DOI":"10.1016\/j.jct.2006.03.001","article-title":"Construction, calibration and testing of a micro-combustion calorimeter","volume":"38","author":"Camarillo","year":"2006","journal-title":"J. Chem. Thermodyn."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1016\/j.energy.2007.07.014","article-title":"Biodiesel fuel in diesel micro-turbine engines: Modelling and experimental evaluation","volume":"33","author":"Nascimento","year":"2008","journal-title":"Energy"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1168","DOI":"10.1016\/j.physleta.2007.09.041","article-title":"Performance analysis of a thermosize micro\/nano heat engine","volume":"372","author":"Nie","year":"2008","journal-title":"Phys. Lett. A"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"3067","DOI":"10.1016\/j.proci.2008.06.002","article-title":"Heat loss reduction and hydrocarbon combustion in ultra-micro combustors for ultra-micro gas turbines","volume":"32","author":"Sakurai","year":"2009","journal-title":"Proc. Combust. Inst."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"2373","DOI":"10.1016\/j.applthermaleng.2008.12.005","article-title":"Improvement of micro-combustion stability through electrical heating","volume":"29","author":"Zhou","year":"2009","journal-title":"Appl. Therm. Eng."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"3099","DOI":"10.1016\/j.proci.2008.07.017","article-title":"Demonstration of an external combustion micro-heat engine","volume":"32","author":"Cho","year":"2009","journal-title":"Proc. Combust. Inst."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"108","DOI":"10.1016\/j.polymdegradstab.2009.11.047","article-title":"Investigation of the flammability of different textile fabrics using micro-scale combustion calorimetry","volume":"95","author":"Yang","year":"2010","journal-title":"Polymer Degrad. Stab."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"456","DOI":"10.1007\/s00542-004-0369-4","article-title":"Micro gas bearings fabricated by deep x-ray lithography","volume":"10","author":"Kim","year":"2004","journal-title":"Microsyst. Technol."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"537","DOI":"10.1115\/1.1924428","article-title":"Tribological study of microbearings for MEMS applications","volume":"127","author":"Kim","year":"2005","journal-title":"J. Tribol."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"254","DOI":"10.1115\/1.1897739","article-title":"Scaling Laws for Ultra-Short Hydrostatic Gas Journal Bearings","volume":"127","author":"Spakovszky","year":"2005","journal-title":"J. Vib. Acoust."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"306","DOI":"10.1115\/1.1828455","article-title":"Modal and nodal EHD analysis for gas journal bearings","volume":"127","author":"Boedo","year":"2005","journal-title":"J. Tribol."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1115\/1.1897738","article-title":"Hydrostatic gas journal bearings for micro-turbomachinery","volume":"127","author":"Liu","year":"2005","journal-title":"J. Vib. Acoust."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1016\/j.triboint.2004.01.003","article-title":"Numerical prediction of slip flow effect on gas-lubricated journal bearings for mems\/mst-based micro-rotating machinery","volume":"38","author":"Lee","year":"2005","journal-title":"Tribol. Int."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"116","DOI":"10.1088\/0960-1317\/14\/1\/016","article-title":"Effects of the slip velocity boundary condition on the characteristics of microbearings","volume":"14","author":"Ren","year":"2004","journal-title":"J. Micromech. Microeng."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"711","DOI":"10.1115\/1.1792676","article-title":"Hydrodynamic performance of gas microbearings","volume":"126","author":"Kim","year":"2004","journal-title":"J. Tribol."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1115\/1.1498273","article-title":"Development of high-speed gas bearings for high-power density microdevices","volume":"125","author":"Ehrich","year":"2002","journal-title":"J. Eng. Gas Turbines Power"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"368","DOI":"10.1115\/1.1308000","article-title":"Low-order models for very short hybrid gas bearings","volume":"123","author":"Savoulides","year":"2001","journal-title":"J. Tribol."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1087","DOI":"10.1016\/j.triboint.2009.12.029","article-title":"A novel tribometer for the measurement of friction in MEMS","volume":"43","author":"Ku","year":"2010","journal-title":"Tribol. Int."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"863","DOI":"10.1016\/j.sna.2006.10.008","article-title":"Measurement of static and dynamic friction coefficients of sidewalls of bulk-microfabricated MEMS devices with an on-chip micro-tribotester","volume":"135","author":"Guo","year":"2007","journal-title":"Sens. Actuators A Phys."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1007\/s11249-010-9696-z","article-title":"Evolution of wear characteristics and frictional behavior in mems devices","volume":"41","author":"Subhash","year":"2011","journal-title":"Tribol. Lett."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"580","DOI":"10.1016\/j.wear.2005.02.070","article-title":"In situ wear studies of surface micromachined interfaces subject to controlled loading","volume":"260","author":"Flater","year":"2006","journal-title":"Wear"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"887","DOI":"10.1016\/j.triboint.2011.03.004","article-title":"Performance and stability analysis of gas-lubricated journal bearings in MEMS","volume":"44","author":"Zhang","year":"2011","journal-title":"Tribol. Int."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"263","DOI":"10.1109\/JMEMS.2009.2013407","article-title":"Dynamic friction and wear in a planar-contact encapsulated microball bearing using an integrated microturbine","volume":"18","author":"McCarthy","year":"2009","journal-title":"Microelectromech. Syst."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.sna.2011.08.003","article-title":"Design and characterization of MEMS micromotor supported on low friction liquid bearing","volume":"177","author":"Chan","year":"2012","journal-title":"Sens. Actuators A Phys."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"772","DOI":"10.1016\/j.triboint.2011.01.008","article-title":"Experimental measurement of the friction torque on hydrodynamic plain journal bearings during start-up","volume":"44","author":"Bouyer","year":"2011","journal-title":"Tribol. Int."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1016\/S0924-4247(97)80510-9","article-title":"Frictional study of micromotor bearings","volume":"63","author":"Beerschwinger","year":"1997","journal-title":"Sens. Actuators A Phys."},{"key":"ref_27","unstructured":"FT-S1000 Micro Force Sensing Probe. Available online: http:\/\/www.femtotools.com\/fileadmin\/datasheets\/FT-S1000_Datasheet.pdf."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"883","DOI":"10.1016\/j.measurement.2006.11.018","article-title":"A novel self-decoupled four degree-of-freedom wrist force\/torque sensor","volume":"40","author":"Song","year":"2007","journal-title":"Measurement"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"6669","DOI":"10.3390\/s130506669","article-title":"Fast estimation of strains for cross-beams six-axis force\/torque sensors by mechanical modeling","volume":"13","author":"Ma","year":"2013","journal-title":"Sensors"},{"key":"ref_30","first-page":"1","article-title":"Finite element analysis for elastic body of new 4-axis wrist force sensor","volume":"3","author":"Qin","year":"2003","journal-title":"J. Transcluction Technol."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1016\/j.sna.2012.11.035","article-title":"Design and characterization of a novel, robust, tri-axial force sensor","volume":"192","author":"Baki","year":"2013","journal-title":"Sens. Actuators A Phys."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1016\/j.sna.2005.01.006","article-title":"Characterization of a novel hybrid silicon three-axial force sensor","volume":"123","author":"Valdastri","year":"2005","journal-title":"Sens. Actuators A Phys."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"370","DOI":"10.1016\/j.sna.2005.01.007","article-title":"Design and fabrication of a hybrid silicon three-axial force sensor for biomechanical applications","volume":"120","author":"Beccai","year":"2005","journal-title":"Sens. Actuators A Phys."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/16\/5\/726\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T19:24:05Z","timestamp":1760210645000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/16\/5\/726"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,5,18]]},"references-count":33,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2016,5]]}},"alternative-id":["s16050726"],"URL":"https:\/\/doi.org\/10.3390\/s16050726","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2016,5,18]]}}}