Analytical methods for minimizing cogging torque in permanent-magnet machines

Li Zhu, S. Z. Jiang, Z. Q. Zhu, C. C. Chan

Research output: Journal article publicationJournal articleAcademic researchpeer-review

367 Citations (Scopus)


Cogging torque in permanent-magnet machines causes torque and speed ripples, as well as acoustic noise and vibration, especially in low speed and direct drive applications. In this paper, a general analytical expression for cogging torque is derived by the energy method and the Fourier series analysis, based on the air gap permeance and the flux density distribution in an equivalent slotless machine. The optimal design parameters, such as slot number and pole number combination, skewing, pole-arc to pole-pitch ratio, and slot opening, are derived analytically to minimize the cogging torque. Finally, the finite-element analysis is adopted to verify the correctness of analytical methods.

Original languageEnglish
Pages (from-to)2023-2031
Number of pages9
JournalIEEE Transactions on Magnetics
Issue number4
Publication statusPublished - Apr 2009


  • Cogging torque
  • Energy method
  • Fourier series
  • Permanent-magnet machines
  • Torque ripple

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Electrical and Electronic Engineering


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