Air-Gap Permeance and Reluctance Network Models for Analyzing Vibrational Exciting Force of In-Wheel PMSM

Zaixin Song, Chunhua Liu, Yong Chen, Rundong Huang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

16 Citations (Scopus)


There is recognized interest in in-wheel motors for vehicle traction. Studies have gradually focused the design of in-wheel motors on electro-mechanical vibration, subject to the demand of driving comfort. It is crucial to model, analyze, and minimize the air-gap exciting force, the dominant source of vibration. In order to qualitatively and quantitatively study the air-gap vibrational exciting force and evaluate its characteristic for an in-wheel outer-runner permanent magnet synchronous machine (PMSM), this research proposes an air-gap permeance model (APM) and a unique adaptive reluctance network model (ARNM). In the process of motor design, APM is a quick means of determining dominant radial force density (RFD) harmonics and minimizing specific components that may produce considerable vibration. Morphing surface-mounted magnets and nonuniform air-gap length are guided by design optimization which complicates the analysis. Yet, proposed ARNM can account for this geometry variation and handle deformed gap geometry by using modified equation-based local permeance and residual flux. The speed and accuracy of proposed model are verified through the comparison of flux density and force mapping data between the calculation by proposed analytical model and the simulation by finite element tools. A 3-kW prototype is fabricated and tested to explore the effectiveness of ARNM-based performance prediction.

Original languageEnglish
Pages (from-to)7122-7133
Number of pages12
JournalIEEE Transactions on Vehicular Technology
Issue number7
Publication statusPublished - 1 Jul 2022
Externally publishedYes


  • Air-gap permeance
  • In-wheel motor
  • Radial force density
  • Reluctance network
  • Traction

ASJC Scopus subject areas

  • Automotive Engineering
  • Aerospace Engineering
  • Electrical and Electronic Engineering
  • Applied Mathematics


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