{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,16]],"date-time":"2026-03-16T17:11:13Z","timestamp":1773681073417,"version":"3.50.1"},"reference-count":40,"publisher":"MDPI AG","issue":"15","license":[{"start":{"date-parts":[[2019,8,5]],"date-time":"2019-08-05T00:00:00Z","timestamp":1564963200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51675304"],"award-info":[{"award-number":["51675304"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11890672"],"award-info":[{"award-number":["11890672"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Structural superlubricity (SSL) is a state of nearly zero friction and zero wear between two directly contacted solid surfaces. Recently, SSL was achieved in mesoscale and thus opened the SSL technology which promises great applications in Micro-electromechanical Systems (MEMS), sensors, storage technologies, etc. However, load issues in current mesoscale SSL studies are still not clear. The great challenge is to simultaneously measure both the ultralow shear forces and the much larger normal forces, although the widely used frictional force microscopes (FFM) and micro tribometers can satisfy the shear forces and normal forces requirements, respectively. Here we propose a hybrid two-axis force sensor that can well fill the blank between the capabilities of FFM and micro tribometers for the mesoscopic SSL studies. The proposed sensor can afford 1mN normal load with 10 nN lateral resolution. Moreover, the probe of the sensor is designed at the edge of the structure for the convenience of real-time optical observation. Calibrations and preliminary experiments are conducted to validate the performance of the design.<\/jats:p>","DOI":"10.3390\/s19153431","type":"journal-article","created":{"date-parts":[[2019,8,5]],"date-time":"2019-08-05T11:17:47Z","timestamp":1565003867000},"page":"3431","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["A Hybrid Two-Axis Force Sensor for the Mesoscopic Structural Superlubricity Studies"],"prefix":"10.3390","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5865-3288","authenticated-orcid":false,"given":"Taotao","family":"Sun","sequence":"first","affiliation":[{"name":"Center for Nano and Micro Mechanics, Tsinghua University, Beijing 100084, China"},{"name":"State Key Laboratory of Tribology, Tsinghua University, Beijing 100084, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhanghui","family":"Wu","sequence":"additional","affiliation":[{"name":"Center for Nano and Micro Mechanics, Tsinghua University, Beijing 100084, China"},{"name":"Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhihong","family":"Li","sequence":"additional","affiliation":[{"name":"Center for Nano and Micro Mechanics, Tsinghua University, Beijing 100084, China"},{"name":"National Key Laboratory of Science and Technology on Micro\/Nano Fabrication, Institute of Microelectronics, Peking University, Beijing 100871, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Quanshui","family":"Zheng","sequence":"additional","affiliation":[{"name":"Center for Nano and Micro Mechanics, Tsinghua University, Beijing 100084, China"},{"name":"Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Li","family":"Lin","sequence":"additional","affiliation":[{"name":"Center for Nano and Micro Mechanics, Tsinghua University, Beijing 100084, China"},{"name":"State Key Laboratory of Tribology, Tsinghua University, Beijing 100084, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,8,5]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1593","DOI":"10.1088\/0022-3719\/16\/9\/005","article-title":"Critical-Behavior at the Transition by Breaking of Analyticity in the Discrete Frenkel-Kontorova Model","volume":"16","author":"Peyrard","year":"1983","journal-title":"J. Phys. C Solid State Phys."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"126101","DOI":"10.1103\/PhysRevLett.92.126101","article-title":"Superlubricity of graphite","volume":"92","author":"Dienwiebel","year":"2004","journal-title":"Phys. Rev. Lett."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"235502","DOI":"10.1103\/PhysRevLett.111.235502","article-title":"Scaling Laws of Structural Lubricity","volume":"111","author":"Dietzel","year":"2013","journal-title":"Phys. Rev. Lett."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1718","DOI":"10.1021\/nn305722d","article-title":"Superlubric Sliding of Graphene Nanoflakes on Graphene","volume":"7","author":"Feng","year":"2013","journal-title":"ACS Nano"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"155702","DOI":"10.1088\/1361-6528\/aaac21","article-title":"Friction fluctuations of gold nanoparticles in the superlubric regime","volume":"29","author":"Dietzel","year":"2018","journal-title":"Nanot"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1800810","DOI":"10.1002\/advs.201800810","article-title":"Superlubricity of Graphite Sliding against Graphene Nanoflake under Ultrahigh Contact Pressure","volume":"5","author":"Li","year":"2018","journal-title":"Adv. Sci."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"7638","DOI":"10.1021\/acsnano.7b09083","article-title":"Interlayer Friction and Superlubricity in Single-Crystalline Contact Enabled by Two-Dimensional Flake-Wrapped Atomic Force Microscope Tips","volume":"12","author":"Liu","year":"2018","journal-title":"ACS Nano"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"205503","DOI":"10.1103\/PhysRevLett.108.205503","article-title":"Observation of Microscale Superlubricity in Graphite","volume":"108","author":"Liu","year":"2012","journal-title":"Phys. Rev. Lett."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"912","DOI":"10.1038\/nnano.2013.217","article-title":"Superlubricity in centimetres-long double-walled carbon nanotubes under ambient conditions","volume":"8","author":"Zhang","year":"2013","journal-title":"Nat. Nanotechnol."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"182","DOI":"10.1007\/s40544-014-0056-0","article-title":"Experimental advances in superlubricity","volume":"2","author":"Zheng","year":"2014","journal-title":"Friction"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"081405","DOI":"10.1103\/PhysRevB.94.081405","article-title":"Observation of normal-force-independent superlubricity in mesoscopic graphite contacts","volume":"94","author":"Vu","year":"2016","journal-title":"Phys. Rev. B"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"14314","DOI":"10.1039\/C7NR09628C","article-title":"Structural superlubricity in graphite flakes assembled under ambient conditions","volume":"10","author":"Deng","year":"2018","journal-title":"Nanoscale"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"894","DOI":"10.1038\/s41563-018-0144-z","article-title":"Robust microscale superlubricity in graphite\/hexagonal boron nitride layered heterojunctions","volume":"17","author":"Song","year":"2018","journal-title":"Nat. Mater."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"14029","DOI":"10.1038\/ncomms14029","article-title":"Robust microscale superlubricity under high contact pressure enabled by graphene-coated microsphere","volume":"8","author":"Liu","year":"2017","journal-title":"Nat. Commun."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"18","DOI":"10.1016\/S0924-4247(99)00283-6","article-title":"Fabrication of a novel scanning probe device for quantitative nanotribology","volume":"84","author":"Zijlstra","year":"2000","journal-title":"Sens. Actuators A Phys."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1016\/j.wear.2019.01.064","article-title":"Synergistic effects of electroless piston ring coatings and nano-additives in oil on the friction and wear of a piston ring\/cylinder liner pair","volume":"422","author":"Xu","year":"2019","journal-title":"Wear"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"435","DOI":"10.1016\/j.wear.2010.04.029","article-title":"On the scale dependence of coefficient of friction in unlubricated sliding contacts","volume":"269","author":"Achanta","year":"2010","journal-title":"Wear"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"485","DOI":"10.1038\/s41586-018-0704-z","article-title":"Structural superlubricity and ultralow friction across the length scales","volume":"563","author":"Hod","year":"2018","journal-title":"Nature"},{"key":"ref_19","first-page":"8853","article-title":"Measurement of the cleavage energy of graphite","volume":"6","author":"Wang","year":"2015","journal-title":"Nat. Commun."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"832","DOI":"10.1088\/0960-1317\/12\/6\/314","article-title":"A bulk microfabricated multi-axis capacitive cellular force sensor using transverse comb drives","volume":"12","author":"Sun","year":"2002","journal-title":"J. Micromech. Microeng."},{"key":"ref_21","first-page":"433","article-title":"A Six-Axis MEMS Force-Torque Sensor With Micro-Newton and Nano-Newtonmeter Resolution","volume":"18","author":"Beyeler","year":"2009","journal-title":"JMemS"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"025011","DOI":"10.1088\/0960-1317\/20\/2\/025011","article-title":"Three-axis micro-force sensor with sub-micro-Newton measurement uncertainty and tunable force range","volume":"20","author":"Muntwyler","year":"2010","journal-title":"J. Micromech. Microeng."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Michalowski, M., and Luczak, S. (2019). AFM cantilevers with spherical tip of millimeter size. J. Micromech. Microeng., 29.","DOI":"10.1088\/1361-6439\/aaee56"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Canale, L., Comtet, J., Nigu\u00e8s, A., Cohen, C., Clanet, C., Siria, A., and Bocquet, L. (2019). Nanorheology of interfacial water during ice gliding. arXiv.","DOI":"10.1103\/PhysRevX.9.041025"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"011101","DOI":"10.1063\/1.5052264","article-title":"The qPlus sensor, a powerful core for the atomic force microscope","volume":"90","author":"Giessibl","year":"2019","journal-title":"Rev. Sci. Instrum."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1007\/s11249-019-1134-2","article-title":"AFM at the Macroscale: Methods to Fabricate and Calibrate Probes for Millinewton Force Measurements","volume":"67","author":"Garabedian","year":"2019","journal-title":"Tribol. Lett."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"035601","DOI":"10.1088\/1361-6501\/aa57b8","article-title":"Advanced adhesion and friction measurement system","volume":"28","author":"Li","year":"2017","journal-title":"Meas. Sci. Technol."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Hou, B., Zhou, B., Li, X., Gao, Z., Wei, Q., and Zhang, R. (2019). An Analog Interface Circuit for Capacitive Angle Encoder Based on a Capacitance Elimination Array and Synchronous Switch Demodulation Method. Sensors, 19.","DOI":"10.3390\/s19143116"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"710","DOI":"10.1063\/1.1142072","article-title":"A New Force Sensor Incorporating Force-Feedback Control for Interfacial Force Microscopy","volume":"62","author":"Joyce","year":"1991","journal-title":"Rev. Sci. Instrum."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"24","DOI":"10.1016\/j.sna.2017.09.015","article-title":"Quad-seesaw-electrode type 3-axis tactile sensor with low nonlinearities and low cross-axis sensitivities","volume":"266","author":"Hata","year":"2017","journal-title":"Sens. Actuatorsa"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"095017","DOI":"10.1088\/1361-6439\/aa81bc","article-title":"Stand-alone differential capacitance force sensors with sub-nano-newton sensitivity","volume":"27","author":"Ye","year":"2017","journal-title":"J. Micromech. Microeng."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1687","DOI":"10.1109\/5.704274","article-title":"MEMS-based projection display","volume":"86","author":"Hornbeck","year":"1998","journal-title":"Proc. IEEE"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"3298","DOI":"10.1063\/1.1147411","article-title":"Calibration of frictional forces in atomic force microscopy","volume":"67","author":"Ogletree","year":"1996","journal-title":"Rev. Sci. Instrum."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"055108","DOI":"10.1063\/1.4804163","article-title":"The extended wedge method: Atomic force microscope friction calibration for improved tolerance to instrument misalignments, tip offset, and blunt probes","volume":"84","author":"Khare","year":"2013","journal-title":"Rev. Sci. Instrum."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"113704","DOI":"10.1063\/1.5041854","article-title":"Design and optimization of the diamagnetic lateral force calibration method","volume":"89","author":"Qu","year":"2018","journal-title":"Rev. Sci. Instrum."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"065105","DOI":"10.1063\/1.2209953","article-title":"Lateral force calibration of an atomic force microscope with a diamagnetic levitation spring system","volume":"77","author":"Li","year":"2006","journal-title":"Rev. Sci. Instrum."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"067205","DOI":"10.1103\/PhysRevLett.100.067205","article-title":"Self-retracting motion of graphite microflakes","volume":"100","author":"Zheng","year":"2008","journal-title":"Phys. Rev. Lett."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"3482","DOI":"10.1021\/acs.jpclett.7b01377","article-title":"Enhancement of Friction by Water Intercalated between Graphene and Mica","volume":"8","author":"Lee","year":"2017","journal-title":"J. Phys. Chem. Lett."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"36","DOI":"10.1007\/s11249-018-0984-3","article-title":"Isotope-and Thickness-Dependent Friction of Water Layers Intercalated Between Graphene and Mica","volume":"66","author":"Lee","year":"2018","journal-title":"Tribol. Lett."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"1504","DOI":"10.1016\/0304-3991(92)90473-W","article-title":"Rocking-Beam Force-Balance Approach to Atomic Force Microscopy","volume":"42","author":"Grigg","year":"1992","journal-title":"Ultramicroscopy"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/19\/15\/3431\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T13:08:47Z","timestamp":1760188127000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/19\/15\/3431"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,8,5]]},"references-count":40,"journal-issue":{"issue":"15","published-online":{"date-parts":[[2019,8]]}},"alternative-id":["s19153431"],"URL":"https:\/\/doi.org\/10.3390\/s19153431","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,8,5]]}}}