{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:04:35Z","timestamp":1760241875576,"version":"build-2065373602"},"reference-count":19,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2018,10,9]],"date-time":"2018-10-09T00:00:00Z","timestamp":1539043200000},"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":["U1709206, 51465027, 51275465"],"award-info":[{"award-number":["U1709206, 51465027, 51275465"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004731","name":"Natural Science Foundation of Zhejiang Province","doi-asserted-by":"publisher","award":["LZ16E050001"],"award-info":[{"award-number":["LZ16E050001"]}],"id":[{"id":"10.13039\/501100004731","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>A spherical joint is a commonly used mechanical hinge with the advantages of compact structure and good flexibility, and it becomes a key component in many types of equipment, such as parallel mechanisms, industrial robots, and automobiles. Real-time detection of a precision spherical joint clearance is of great significance in analyzing the motion errors of mechanical systems and improving the transmission accuracy. This paper presents a novel method for the micro-clearance measurement with a spherical differential capacitive sensor (SDCS). First, the structure and layout of the spherical capacitive plates were designed according to the measuring principle of capacitive sensors with spacing variation. Then, the mathematical model for the spatial eccentric displacements of the ball and the differential capacitance was established. In addition, equipotential guard rings were used to attenuate the fringe effect on the measurement accuracy. Finally, a simulation with Ansoft Maxwell software was carried out to calculate the capacitance values of the spherical capacitors at different eccentric displacements. Simulation results indicated that the proposed method based on SDCS was feasible and effective for the micro-clearance measurement of the precision spherical joints with small eccentricity.<\/jats:p>","DOI":"10.3390\/s18103366","type":"journal-article","created":{"date-parts":[[2018,10,9]],"date-time":"2018-10-09T11:10:44Z","timestamp":1539083444000},"page":"3366","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["A Novel Method for the Micro-Clearance Measurement of a Precision Spherical Joint Based on a Spherical Differential Capacitive Sensor"],"prefix":"10.3390","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0084-0910","authenticated-orcid":false,"given":"Wen","family":"Wang","sequence":"first","affiliation":[{"name":"School of Mechanical Engineering, Hangzhou Dianzi University, Hangzhou 310018, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1540-1793","authenticated-orcid":false,"given":"He","family":"Yang","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Hangzhou Dianzi University, Hangzhou 310018, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Min","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Hangzhou Dianzi University, Hangzhou 310018, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3768-2714","authenticated-orcid":false,"given":"Zhanfeng","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Hangzhou Dianzi University, Hangzhou 310018, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guang","family":"Shi","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Hangzhou Dianzi University, Hangzhou 310018, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Keqing","family":"Lu","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Hangzhou Dianzi University, Hangzhou 310018, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kui","family":"Xiang","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Zhejiang University, Hangzhou 310027, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bingfeng","family":"Ju","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Zhejiang University, Hangzhou 310027, China"},{"name":"State Key Lab of Fluid Power &amp; Mechatronic Systems, Zhejiang University, Hangzhou 310027, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,10,9]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.precisioneng.2005.01.001","article-title":"Measurement and characterization of precision spherical joints","volume":"30","author":"Robertson","year":"2006","journal-title":"Precis. Eng."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1239","DOI":"10.1016\/S0094-114X(99)00076-2","article-title":"Uncertainty analysis of planar and spatial robots with joint clearances","volume":"35","author":"Zhu","year":"2000","journal-title":"Mech. Mach. Theory"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"045102","DOI":"10.1088\/1361-6501\/aa912e","article-title":"Online monitoring of dynamic tip clearance of turbine blades in high temperature environments","volume":"29","author":"Han","year":"2018","journal-title":"Meas. Sci. Technol."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Garcia, I., Przysowa, R., Amorebieta, J., and Zubia, J. (2016). Tip-clearance measurement in the first stage of the compressor of an aircraft engine. Sensors, 16.","DOI":"10.3390\/s16111897"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Zhang, J., Duan, F., Niu, G., Jiang, J., and Li, J. (2017). A blade tip timing method based on a microwave sensor. Sensors, 17.","DOI":"10.3390\/s17051097"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1177\/1687814017748020","article-title":"Simulating eddy current sensor outputs for blade tip timing","volume":"10","author":"Jamia","year":"2018","journal-title":"Adv. Mech. Eng."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"14","DOI":"10.1016\/S0924-4247(04)00482-0","article-title":"Tubomachinery blade vibration amplitude measurement through tip timing with capacitance tip clearance probes","volume":"118","author":"Lawson","year":"2005","journal-title":"Sens. Actuators A Phys."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"312","DOI":"10.1016\/S0924-4247(01)00833-0","article-title":"System level simulation of a double stator wobble electrostatic micromotor","volume":"99","author":"Endemano","year":"2002","journal-title":"Sens. Actuators A Phys."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1016\/j.sna.2004.08.030","article-title":"Nonlinear compensation of active electrostatic bearings supporting a spherical rotor","volume":"119","author":"Han","year":"2005","journal-title":"Sens. Actuators A Phys."},{"key":"ref_10","first-page":"257","article-title":"Modelling and linearization for long-range spherical gap measurement","volume":"23","author":"Han","year":"2002","journal-title":"Chin. J. Sci. Instrum."},{"key":"ref_11","unstructured":"Gao, Z.Y. (2004). Electrostatically Suspended Gyroscope Technology, Tsinghua University Press. (In Chinese)."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Hill, D.A., Letendre, T., and Mills, H.A. (July, January 30). Embedded, real-time DSP control of an electrostatically suspended gyroscope. Proceedings of the 2004 American Control Conference, Boston, MA, USA.","DOI":"10.23919\/ACC.2004.1384421"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Liu, J.H., Wang, H., Chang, K., Li, X., and Wang, Q.L. (2015, January 20\u201323). Design and test of displacement transducer for an electrode-insulated electrostatically suspended gyroscope. Proceedings of the 2015 IEEE International Conference on Applied Superconductivity and Electromagnetic Devices, Shanghai, China.","DOI":"10.1109\/ASEMD.2015.7453645"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"513","DOI":"10.1016\/j.sna.2005.12.007","article-title":"Initial levitation of an electrostatic bearing system without bias","volume":"130\u2013131","author":"Han","year":"2006","journal-title":"Sens. Actuators A Phys."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Baxter, L.K. (1997). Capacitive Sensors: Design and Applications, IEEE Press.","DOI":"10.1109\/9780470544228"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"897","DOI":"10.1088\/0022-3735\/19\/11\/002","article-title":"Application of capacitance techniques in sensor design","volume":"19","author":"Heerens","year":"1986","journal-title":"J. Phys. E Sci. Instrum."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1458","DOI":"10.1166\/sl.2011.1651","article-title":"Impact of fringe effect on measuring accuracy of planar capacitive sensors","volume":"9","author":"Wang","year":"2011","journal-title":"Sens. Lett."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"827","DOI":"10.4028\/www.scientific.net\/AMM.303-306.827","article-title":"Key technique for inner hole diameter measure with capacitive probe","volume":"303\u2013306","author":"Ma","year":"2013","journal-title":"Appl. Mech. Mater."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"98","DOI":"10.1109\/TMTT.1980.1130017","article-title":"Effect of fringing fields on the capacitance of circular microsrip disk","volume":"28","author":"Weng","year":"1980","journal-title":"IEEE Trans. Microw. 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