Analytical Calculation of Electromagnetic Performance for Slotless Permanent Magnet Motors Based on Improved Scalar Magnetic Potential Method
Li Hongjie1, Yang Jiangtao1, Guo Quan1,2, Huang Shoudao1
1. College of Electrical and Information Engineering Hunan University Changsha 410082 China; 2. Intelligent Manufacturing and Materials Engineering Gannan Institute of Science and Technology Ganzhou 341000 China
Abstract：Slotless permanent magnet (PM) motors have gained significant traction in applications demanding superior control performance, compact size, and lightweight design, such as new energy vehicles, aerospace, medical ventilators, and surgical tools. During the initial design phase, rapid and accurate evaluation of electromagnetic performance is crucial. While finite element analysis (FEA) offers precision, it is computationally intensive and time-consuming, especially for iterative parameter optimization. Analytical methods based on scalar magnetic potential (SMP) provide a fast alternative but have struggled to accurately capture the effects of armature reaction and PM remanence, limiting their predictive capability for loaded performance. This paper proposes an improved SMP-based semi-analytical model in the complex frequency domain for radial flux slotless PM motors. The core innovation lies in effectively integrating both armature reaction and PM remanence into the solution framework. Firstly, a two-dimensional semi-analytical model is established. The remanent magnetization of the PMs is explicitly incorporated into the formulation of Laplace's equation as a source term. Crucially, the armature reaction is equivalently represented by thin current sheets distributed along the inner and outer radial boundaries of the winding region. The interior of the winding region is treated as a vacuum, ensuring the curl of the magnetic field is zero within this domain. This treatment satisfies the fundamental requirement for applying the SMP method throughout the problem space. The governing Laplace equations for the PM region and the subdivided air-gap regions are derived in matrix form, incorporating harmonic components via Fourier series expansion up to a maximum order. The magnetization distributions for both radial and parallel magnetization patterns are rigorously defined in terms of Fourier series coefficients. Secondly, the model analyzes the influence of key design parameters-including the number of pole pairs, pole-arc coefficient, magnetization method, and winding spatial distribution-on the resulting armature reaction field and overall electromagnetic performance. Semi-analytical expressions for the critical electromagnetic quantities are derived: the radial and tangential air-gap flux densities, the back electromotive force (EMF), and the electromagnetic torque. The derivation distinguishes the harmonic order multiplied by the pole pairs equals ±1. Torque and EMF expressions account for winding topology and distribution factors. Thirdly, the accuracy of the proposed analytical method is validated through FEA simulations and experimental measurements. FEA comparisons for air-gap flux density under various load currents, pole pairs, magnetization types, and pole-arc coefficients demonstrate excellent waveform agreement, highlighting the model's ability to capture flux distortion due to armature reaction. Back-EMF and torque predictions for different motor configurations and current waveforms show negligible deviation from FEA results. Finally, a 6-coil-group, 4-pole (6S4P) slotless PM motor prototype was fabricated and tested. Measured no-load back-EMF waveforms align closely with both analytical and FEA predictions, with a minor amplitude discrepancy attributed to manufacturing and magnetization tolerances. Load torque measurements using a specialized test rig confirm the model's accuracy. The analytical torque deviates by only 1.26% from the measured value, closely matching FEA simulations. Measured air-gap flux density under load also validates the predicted distortion trends. In conclusion, the proposed improved SMP method incorporates armature reaction and remanence effects for slotless PM motors. FEA simulations and experiments validate its high accuracy for predicting key electromagnetic performance metrics, including flux density, back-EMF, and torque under load. This method provides an efficient, precise analytical tool for the initial design and optimization stages of slotless PM motors, serving as a viable alternative to computationally expensive FEA when frequent parameter adjustments are required.
李鸿杰, 杨江涛, 郭权, 黄守道. 基于改进型标量磁位法的无槽永磁电机电磁性能解析计算[J]. 电工技术学报, 2026, 41(14): 4718-4732.
Li Hongjie, Yang Jiangtao, Guo Quan, Huang Shoudao. Analytical Calculation of Electromagnetic Performance for Slotless Permanent Magnet Motors Based on Improved Scalar Magnetic Potential Method. Transactions of China Electrotechnical Society, 2026, 41(14): 4718-4732.
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2026, Vol. 41 
