Detent Force Minimization of Double‐Sided Permanent Magnet Linear Synchronous Machine with 120° Phase Belt Toroidal Windings by Slot‐Shift Structure

Jikai Si, Xiaobao Chai, Rui Nie*, Yihua Hu, Yingsheng Li

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Double‐sided permanent magnet linear synchronous machine with 120° phase belt toroidal windings (120°‐TWDSPMLSM) suffers from large detent force due to the end effect and slot effect. Many existing methods can reduce the detent force of the 120°‐TWDSPMLSM effectively. But they also minimize the back electromotive force (back‐EMF) and thrust simultaneously. To alleviate this problem, this paper adopts a method of combining slot‐shift structure with rearranging the 120° phase belt toroidal windings (120°‐TW) to suppress the detent force and improve the back‐EMF and thrust of the 120°‐TWDSPMLSM simultaneously. First, the slots on the two sides of the primary part are stagger by an optimal distance to reduce the detent force. The models of the detent force, including the end force and cogging force, is established theoretically, and then verified by finite‐element analysis (FA). Then, the 120°‐TW are rearranged to improve the back‐EMF and average thrust. And the electromagnetic characteristics of the 120°‐TWDSPMLSM under different shifted distances are analyzed and compared in detail. Finally, the result shows that the detent force of optimized machine is 70.19% lower than that of the original machine, and the thrust fluctuation reduces 19.21%. Besides, the back‐EMF of optimized machine is 6.84% lower than that of the original machine, but 31.86 higher than the machine with shifting slots and without rearranging the 120°‐TW. Therefore, the optimal method in this paper is available in the detent force reduction and thrust improvement of the 120°‐DSPMLSM.

Original languageEnglish
Article number943
Number of pages14
Issue number3
Publication statusPublished - 27 Jan 2022

Bibliographical note

Funding Information:
Funding: This research was funded by Natural Science Foundation of China under grant number 51777060, in part by the Major Special Project for Collaborative Innovation in Zhengzhou under grant number 20XTZX12023 and the China Postdoctoral Science Foundation under grant number 2020M682342. Besides, this research was also funded by the Science and Technology Funds of North China Institute of Science and Technology under grant number JSJ1204B and JD2013B01.


  • 120° phase belt toroidal windings
  • Detent force
  • Double‐sided
  • Electromagnetic characteristic
  • Permanent magnet linear synchronous machine
  • Slot‐shift

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