{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,25]],"date-time":"2026-06-25T16:31:08Z","timestamp":1782405068759,"version":"3.54.5"},"reference-count":23,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2021,10,15]],"date-time":"2021-10-15T00:00:00Z","timestamp":1634256000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The implications of the end effect for flux linkage and thrust ripple in a slot-less long-stator permanent magnet linear synchronous motor (LSPMLSM), are analyzed in this paper. Since it is affected by the end effect, the air-gap magnetic field density under the end permanent magnet is different from that under the non-end permanent magnet, leading to asymmetry in the thrust ripple. For this reason, we establish a dynamic permanent magnet flux linkage model, which proves that the end effect leads to sub-harmonics in the permanent magnet flux linkage. The motor\u2019s magnetic field distribution in the left and right parts is symmetrical. A thrust model taking into account the flux linkage sub-harmonics is established, from which the amplitude and period of the thrust ripple caused by the end effect can be calculated. There is no detent force for the slot-less LSPMLSM, and the end effect is the primary origin of the motor thrust ripple. In order to suppress the end effect, a method of increasing the end iron length is proposed, as a result of which the sub-harmonics in the flux linkage and the motor thrust ripple are effectively suppressed. Experimental and simulation results verify the results of this paper.<\/jats:p>","DOI":"10.3390\/sym13101939","type":"journal-article","created":{"date-parts":[[2021,10,17]],"date-time":"2021-10-17T23:25:15Z","timestamp":1634513115000},"page":"1939","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["End Effect Analysis of a Slot-Less Long-Stator Permanent Magnet Linear Synchronous Motor"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0101-0035","authenticated-orcid":false,"given":"Yue","family":"Zhou","sequence":"first","affiliation":[{"name":"Department of Electrical, Engineering Harbin Institute of Technology, Harbin 150001, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wenjun","family":"Zong","sequence":"additional","affiliation":[{"name":"Department of Electrical, Engineering Harbin Institute of Technology, Harbin 150001, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Qiang","family":"Tan","sequence":"additional","affiliation":[{"name":"Department of Electrical, Engineering Harbin Institute of Technology, Harbin 150001, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhenjiang","family":"Hu","sequence":"additional","affiliation":[{"name":"Department of Electrical, Engineering Harbin Institute of Technology, Harbin 150001, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Tao","family":"Sun","sequence":"additional","affiliation":[{"name":"Department of Electrical, Engineering Harbin Institute of Technology, Harbin 150001, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Liyi","family":"Li","sequence":"additional","affiliation":[{"name":"Department of Electrical, Engineering Harbin Institute of Technology, Harbin 150001, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2021,10,15]]},"reference":[{"key":"ref_1","first-page":"395","article-title":"Multiobjective Design Optimization of Ironless Permanent Magnet Linear Synchronous Motors for Improved Thrust and Reduced Thrust Ripple","volume":"416\u2013417","author":"Li","year":"2013","journal-title":"Appl. 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