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Talent Recruitment Program of Hebei Province","award":["E2024203259"],"award-info":[{"award-number":["E2024203259"]}]},{"name":"Hebei Province Basic Research Program Proof of Concept Project","award":["2024YFE0114600"],"award-info":[{"award-number":["2024YFE0114600"]}]},{"name":"Hebei Province Basic Research Program Proof of Concept Project","award":["CXXM20240010"],"award-info":[{"award-number":["CXXM20240010"]}]},{"name":"Hebei Province Basic Research Program Proof of Concept Project","award":["E2023203007"],"award-info":[{"award-number":["E2023203007"]}]},{"name":"Hebei Province Basic Research Program Proof of Concept Project","award":["BJ2025115"],"award-info":[{"award-number":["BJ2025115"]}]},{"name":"Hebei Province Basic Research Program Proof of Concept Project","award":["A2025006"],"award-info":[{"award-number":["A2025006"]}]},{"name":"Hebei Province Basic Research Program Proof of Concept Project","award":["E2024203259"],"award-info":[{"award-number":["E2024203259"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The ironless tubular permanent magnet synchronous linear motor (TPMSLM) is in high demand for high-precision servo control applications due to its advantages of having zero cogging effect and high dynamic response. However, its electromagnetic field analysis model has not yet been perfected. This paper aims to accurately predict the magnetic field distribution and electromagnetic performance parameters of an ironless TPMSLM. Taking the axially magnetized ironless TPMSLM as an example, and disregarding the influence of the armature magnetic field on the air gap magnetic field, a simplified analytical model of the TPMSLM is established in the cylindrical coordinate system based on the equivalent magnetization current method (EMC), and the analytical formula for the air gap magnetic flux density is then derived. Subsequently, by applying electromagnetic field theory and the analytical formula for the magnetic flux density in the air gap, analytical expressions for the back electromotive force (back EMF) and thrust are derived, reducing analytical complexity while maintaining accuracy. The accuracy and practicality of the proposed analytical formulas are validated through comparisons with finite element analysis (FEA) and experimental prototypes. This analytical approach facilitates the optimization of linear motor parameters and the study of thrust fluctuation suppression, thereby laying the foundation for high-precision servo control of linear motors.<\/jats:p>","DOI":"10.3390\/sym17091480","type":"journal-article","created":{"date-parts":[[2025,9,8]],"date-time":"2025-09-08T10:29:07Z","timestamp":1757327347000},"page":"1480","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Electromagnetic Analysis and Experimental Validation of an Ironless Tubular Permanent Magnet Synchronous Linear Motor"],"prefix":"10.3390","volume":"17","author":[{"given":"Weiyi","family":"Shao","sequence":"first","affiliation":[{"name":"School of Mechanical Engineering, Yanshan University, Qinhuangdao 066004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Pengda","family":"Xing","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Yanshan University, Qinhuangdao 066004, China"},{"name":"Qinhuangdao Daze Electromechanical Equipment Co., Qinhuangdao 066004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bo","family":"Deng","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Yanshan University, Qinhuangdao 066004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Caiyi","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Yanshan University, Qinhuangdao 066004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yang","family":"Liu","sequence":"additional","affiliation":[{"name":"Qinhuangdao Daze Electromechanical Equipment Co., Qinhuangdao 066004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hanzhang","family":"Zhao","sequence":"additional","affiliation":[{"name":"Qinhuangdao Daze Electromechanical Equipment Co., Qinhuangdao 066004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3679-3893","authenticated-orcid":false,"given":"Yan","family":"Peng","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Yanshan University, Qinhuangdao 066004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,9,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Zong, R.W., and Lin, G.B. 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