【目的】双定子轴向磁通永磁电机的磁路沿轴向和周向两个方向分布,需采用三维有限元法进行电磁性能分析。尽管三维有限元法计算精度高,但也存在计算资源需求大、求解时间长等问题。本文提出一种可以准确考虑非线性迭代的等效磁网络法,以实现对该类电机电磁性能的快速精确计算。【方法】首先,针对该类电机的三维磁路特征,将电机沿径向划分为多个独立切片,并将每个切片等效为二维直线电机,从而建立考虑铁心饱和的准三维分层磁网络模型。其次,针对传统磁网络模型在非线性求解中存在的收敛困难、鲁棒性差等问题,提出一种基于Sigmoid函数的动态松弛因子迭代策略。该策略利用Sigmoid函数的连续平滑特性动态调节松弛因子,在迭代初期实现快速收敛,在迭代末期实现高精度稳定求解。最后,以一台双定子轴向磁通永磁电机为例,将计算结果与三维有限元结果进行对比分析,说明所提方法的正确性与可行性。【结果】所建立的准三维分层磁网络模型能够准确反映该电机的磁场分布特性,气隙磁密、空载反电动势及电磁转矩的计算结果与有限元仿真结果吻合较好,误差在工程允许范围内。在非线性迭代性能方面,所提出的Sigmoid函数动态松弛因子策略显著改善了迭代收敛特性。与传统固定松弛因子法相比,该策略具有更强的鲁棒性,收敛过程更为平稳,在不同饱和程度下均能保持稳定的收敛性能,有效避免了深度饱和区域可能出现的迭代发散问题。【结论】本文提出的基于准三维分层磁网络模型和Sigmoid函数动态松弛因子的电磁性能分析方法,兼顾了计算精度与效率,且具有良好的通用性,可推广应用于其他类型轴向磁通电机及复杂磁路结构的电磁性能分析。

[Objective] The magnetic circuit of dual-stator axial-flux permanent magnet motors is distributed along both the axial and circumferential directions, requiring three-dimensional finite element method for electromagnetic performance analysis. Although the three-dimensional finite element method offers high computational accuracy, it also presents challenges such as high computational resource demands and long solution times. This paper proposes an equivalent magnetic network method that accurately accounts for nonlinear iterations, enabling fast and precise calculation of the electromagnetic performance of such motors. [Methods] First, considering the three-dimensional magnetic circuit characteristics of this motor, the motor was divided radially into multiple independent slices, with each slice equivalently modeled as a two-dimensional linear motor, thereby a quasi-three-dimensional layered magnetic network model that accounts for iron core saturation was established. Second, to overcome the convergence difficulties and poor robustness of traditional magnetic network models in nonlinear solutions, an iterative strategy with a dynamic relaxation factor based on the Sigmoid function was proposed. This strategy utilized the continuous and smooth characteristics of the Sigmoid function to dynamically adjust the relaxation factor, achieving fast convergence in the initial iteration stages and high-precision stable solutions in the final stages. Finally, taking a dual-stator axial-flux permanent magnet motor as an example, the calculated results were compared and analyzed with three-dimensional finite element results , demonstrating the correctness and feasibility of the proposed method. [Results] The established quasi-three-dimensional layered magnetic network model was able to accurately reflect the magnetic field distribution characteristics of this motor. The calculated results of air-gap flux density, no-load back electromotive force, and electromagnetic torque agreed well with the finite element simulation results, and the errors were within the engineering allowable range. In terms of nonlinear iteration performance, the proposed Sigmoid function dynamic relaxation factor strategy significantly improved the iterative convergence characteristics. Compared with the traditional fixed relaxation factor method, this strategy exhibited stronger robustness, the convergence process was more stable, it maintained stable convergence performance under different saturation levels, and it effectively avoided the iterative divergence problem that might occur in the deep saturation region. [Conclusion] The electromagnetic performance analysis method proposed in this paper, which is based on the quasi-three-dimensional layered magnetic network model and the Sigmoid function dynamic relaxation factor, balances computational accuracy and efficiency. This method possesses good generality and can be extended to the electromagnetic performance analysis of other types of axial-flux motors with complex magnetic circuit structures.

国家自然科学基金青年科学基金项目（52207041）