{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:59:33Z","timestamp":1760241573083,"version":"build-2065373602"},"reference-count":31,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2018,6,6]],"date-time":"2018-06-06T00:00:00Z","timestamp":1528243200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Nature Science Foundation of China","award":["No. 51575026","No. 51235002"],"award-info":[{"award-number":["No. 51575026","No. 51235002"]}]},{"name":"National Key Basic Research Program of China (973 program)","award":["2014CB046406"],"award-info":[{"award-number":["2014CB046406"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Conventional single-layer magnet arrays are widely utilized in electromagnetic linear machines. The objective of this paper is to analyze various types of novel dual-layer magnet arrays, either in similar or different patterns, to compare their flux field distribution and increase flux density in the machine. High flux density helps to improve the sensitivity of electromagnetic displacement sensors or actuator thrust. The design concept of magnet arrays are presented. The machine space is divided into several regions according to the magnetic properties. The corresponding magnetic field distribution is formulated based on magnetic vector potential and Laplace\u2019s equations. Numerical computation is conducted to validate the developed magnetic field model. A systematic comparison of magnetic field of various magnet arrays is carried out. It shows that the dual Halbach magnet array can generate relatively high and constant flux density, which may help to produce strong signals. A research prototype and an experimental testbed are developed to validate the analytical model of dual Halbach array. This study provides a general framework for the design and analysis of dual-layer magnet arrays with various magnetization patterns. It can be extended to multiple-layer designs in radial direction.<\/jats:p>","DOI":"10.3390\/s18061854","type":"journal-article","created":{"date-parts":[[2018,6,6]],"date-time":"2018-06-06T07:38:15Z","timestamp":1528270695000},"page":"1854","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Comparative Study of the Dual Layer Magnet Array in a Moving-Coil Tubular Linear PM Motor"],"prefix":"10.3390","volume":"18","author":[{"given":"Liang","family":"Yan","sequence":"first","affiliation":[{"name":"School of Automation Science and Electrical Engineering, Beihang University, Beijing 100191, China"}]},{"given":"Lu","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Automation Science and Electrical Engineering, Beihang University, Beijing 100191, China"}]},{"given":"Lei","family":"Peng","sequence":"additional","affiliation":[{"name":"School of Automation Science and Electrical Engineering, Beihang University, Beijing 100191, China"}]},{"given":"Zongxia","family":"Jiao","sequence":"additional","affiliation":[{"name":"School of Automation Science and Electrical Engineering, Beihang University, Beijing 100191, China"}]}],"member":"1968","published-online":{"date-parts":[[2018,6,6]]},"reference":[{"key":"ref_1","unstructured":"Boldea, I., and Nasar, S.A. 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