{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T00:34:35Z","timestamp":1760229275861,"version":"build-2065373602"},"reference-count":38,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2022,6,7]],"date-time":"2022-06-07T00:00:00Z","timestamp":1654560000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Scientific Research Foundation of China Three Gorges Corporation","award":["202103471","JGAJ0302222001","52105551"],"award-info":[{"award-number":["202103471","JGAJ0302222001","52105551"]}]},{"name":"Scientific Research Foundation of China Three Gorges Construction Engineering Corporation","award":["202103471","JGAJ0302222001","52105551"],"award-info":[{"award-number":["202103471","JGAJ0302222001","52105551"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["202103471","JGAJ0302222001","52105551"],"award-info":[{"award-number":["202103471","JGAJ0302222001","52105551"]}],"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 proposes a displacement sensing method based on magnetic flux measurement. A bridge-structured magnetic circuit, formed by permanent magnets and two ferromagnetic cores, is designed and discussed. The analyses of the equivalent magnetic circuit and three-dimensional finite element simulations showed that the magnetic flux density changes linearly with the reciprocal of the sum of a constant and the displacement. A prototype sensor of the bridge structure is developed that consists of four permanent magnets as excitation, a Hall sensor as reception, and two ferromagnetic cores as the connection. Experiments have validated the feasibility of this method. The measured results show a good linearity between the sensor\u2019s output and the reciprocal of the sum of a constant and the displacement, with a correlation coefficient greater than 0.9995 across different measurement ranges. Additionally, the measured results significantly indicate that the proposed sensor is compatible with different ferromagnetic materials with a worst-case error of less than 5%. The proposed sensor has the advantages of low cost and good linearity; however, the test object is limited to ferromagnetic materials.<\/jats:p>","DOI":"10.3390\/s22124326","type":"journal-article","created":{"date-parts":[[2022,6,13]],"date-time":"2022-06-13T02:01:44Z","timestamp":1655085704000},"page":"4326","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":15,"title":["A Displacement Sensing Method Based on Permanent Magnet and Magnetic Flux Measurement"],"prefix":"10.3390","volume":"22","author":[{"given":"Jikai","family":"Zhang","sequence":"first","affiliation":[{"name":"National Center for Dam Safety Engineering Technology Research, Changjiang River Scientific Research Institute, Wuhan 430010, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yicheng","family":"Shi","sequence":"additional","affiliation":[{"name":"Three Gorges Construction Engineering Corporation, Beijing 101100, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yuewen","family":"Huang","sequence":"additional","affiliation":[{"name":"National Center for Dam Safety Engineering Technology Research, Changjiang River Scientific Research Institute, Wuhan 430010, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Cheng","family":"Liang","sequence":"additional","affiliation":[{"name":"Institute of Science and Technology, China Three Gorges Corporation, Beijing 100036, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yantong","family":"Dong","sequence":"additional","affiliation":[{"name":"Institute of Science and Technology, China Three Gorges Corporation, Beijing 100036, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2622-4769","authenticated-orcid":false,"given":"Yihua","family":"Kang","sequence":"additional","affiliation":[{"name":"School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1057-3932","authenticated-orcid":false,"given":"Bo","family":"Feng","sequence":"additional","affiliation":[{"name":"School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,6,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"9595","DOI":"10.1109\/TIE.2017.2726982","article-title":"Advances in Capacitive, Eddy Current, and Magnetic Displacement Sensors and Corresponding Interfaces","volume":"12","author":"George","year":"2017","journal-title":"IEEE Trans. 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