用于带桥径向磁通磁齿轮设计与快速分析的参数化非线性磁等效电路
Methods for Accelerating and Stabilizing Nonlinear Magnetic Equivalent-Circuit Analysis
AI总结：
本文提出参数化二维非线性MEC模型，可快速准确分析带桥或无桥RFMG，并经140,000种设计验证，结果吻合FEA且速度最高提升100倍。
摘要：
磁齿轮相比机械齿轮具有显著优势，包括非接触式动力传递，但其优化和商业化需要高效且准确的建模工具。本文提出首个快速、准确的二维非线性磁等效电路（MEC）模型，用于径向磁通磁齿轮（RFMG），能够分析带桥的设计；桥是关键结构元件，会引入强烈的局部磁饱和。所提出的模型通过参数化几何结构和自适应磁通管分布，系统地纳入非线性效应，同时保持快速仿真时间。稳健的初始化策略确保其在多种设计中的可靠性能。针对非线性有限元分析（FEA）进行的大量验证，证实了该模型在转矩和磁通密度预测方面的准确性。对140,000种设计开展的全面参数研究表明，其结果与FEA高度吻合，而仿真速度最高可提升100倍。与以往的MEC方法不同，该模型为分析带桥或不带桥的广泛RFMG设计提供了通用且计算高效的解决方案，因此特别适合大规模设计优化。
英文摘要：
Design and optimization of electromagnetic devices require models that converge reliably and quickly and can represent intense localized magnetic saturation. This paper presents a parameterized 2D nonlinear magnetic equivalent circuit (MEC) and proposes solution methods for it: an approximate Jacobian that is symmetric positive definite, so each Newton-Raphson iteration can use sparse Cholesky factorization with fill-reducing reordering, and Anderson mixing as step control. These methods are compared with alternative nonlinear iterations, linear solvers, and step-control methods in convergence, computational cost, and prediction accuracy. Radial-flux magnetic gears (RFMGs) with structural bridges serve as a challenging test case, because their thin bridges exhibit intense local saturation. The methods are evaluated on three bridged base designs and on 1,024 bridged designs, each paired with the same design without the bridge. On the base designs, Newton-Raphson iteration with the approximate Jacobian reached much lower residuals than fixed-point iteration, which converged for none of them. Sparse Cholesky factorization with reordering was the fastest linear solver tested. Across the 1,024 design pairs, full-step Newton-Raphson converged for 193 bridged and 564 bridge-free designs, whereas Anderson mixing converged for 1,003 and 1,022 and required fewer iterations. Bridged designs converged less often and more slowly under every method. The nonlinear MEC was 2.17 and 1.84 times faster than fixed-mesh nonlinear finite element analysis (FEA) in total computation time for the bridged and bridge-free populations. The median outer-rotor torque discrepancy relative to FEA was 0.22%, and the Spearman rank correlations of the design rankings were at least 0.9996.
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