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<p>The closed-slot stator structure is an effective way of suppressing cogging torque in permanent magnet synchronous machines (PMSMs). However, a closed-form analytical relationship between the slot bridge thickness and the resulting cogging torque has not yet been established. To address this issue, this paper derives, for the first time, a closed-slot structure analytical expression that relates cogging torque to the closed-slot bridge thickness while accounting for localized magnetic saturation. The cogging torque under linear conditions is first obtained using the energy method in conjunction with the closed-slot geometry. To improve computational accuracy, an iterative nonlinear magnetic circuit model (NMCM) is then introduced. This method iteratively updates the bridge permeance based on the material’s actual <i>B</i>–<i>H</i> characteristics, thereby accurately incorporating the saturation-dependent permeability variation into the analytical model. The analysis reveals distinct physical boundaries for the suppression efficacy of the slot bridge. When the bridge thickness is below the critical saturation threshold, the permeability collapses to near-unity. The bridge then behaves magnetically as an extended air-gap, and the suppression effect is lost. When the thickness exceeds the optimal suppression range, excessive flux shunting reduces the main magnetic flux. Based on this analytical relationship, a predictive criterion for optimal bridge thickness selection is proposed, significantly reducing the need for extensive parametric finite element analysis (FEA). A 30-pole, 90-slot submersible PMSM is taken as a case study. The analytically predicted optimal thickness range (0.3–0.6&#xa0;mm) agrees well with FEA. Static cogging torque and no-load back EMF measurements on a closed-slot prototype validate the NMCM predictions under the no-load PM excited condition. The analytical framework established in this paper provides a generalized theoretical foundation for the direct design of closed‑slot PMSMs with respect to cogging torque reduction, with on‑load behavior evaluated via FEA.</p>

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Analytical modeling of cogging torque in closed-slot PMSMs incorporating slot bridge saturation effects

  • 期刊论文

  • 发表日期：

    2026年7月14日

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  • Gaoyuan Fan,
  • Luyao Wang,
  • Tianxiang Zhu,
  • Xiaohua Bao

摘要

The closed-slot stator structure is an effective way of suppressing cogging torque in permanent magnet synchronous machines (PMSMs). However, a closed-form analytical relationship between the slot bridge thickness and the resulting cogging torque has not yet been established. To address this issue, this paper derives, for the first time, a closed-slot structure analytical expression that relates cogging torque to the closed-slot bridge thickness while accounting for localized magnetic saturation. The cogging torque under linear conditions is first obtained using the energy method in conjunction with the closed-slot geometry. To improve computational accuracy, an iterative nonlinear magnetic circuit model (NMCM) is then introduced. This method iteratively updates the bridge permeance based on the material’s actual B–H characteristics, thereby accurately incorporating the saturation-dependent permeability variation into the analytical model. The analysis reveals distinct physical boundaries for the suppression efficacy of the slot bridge. When the bridge thickness is below the critical saturation threshold, the permeability collapses to near-unity. The bridge then behaves magnetically as an extended air-gap, and the suppression effect is lost. When the thickness exceeds the optimal suppression range, excessive flux shunting reduces the main magnetic flux. Based on this analytical relationship, a predictive criterion for optimal bridge thickness selection is proposed, significantly reducing the need for extensive parametric finite element analysis (FEA). A 30-pole, 90-slot submersible PMSM is taken as a case study. The analytically predicted optimal thickness range (0.3–0.6 mm) agrees well with FEA. Static cogging torque and no-load back EMF measurements on a closed-slot prototype validate the NMCM predictions under the no-load PM excited condition. The analytical framework established in this paper provides a generalized theoretical foundation for the direct design of closed‑slot PMSMs with respect to cogging torque reduction, with on‑load behavior evaluated via FEA.