发表机构
TU Darmstadt; Tampere University; Rio de Janeiro State University; Universidade Federal do Rio de Janeiro（达姆施塔特工业大学; 坦佩雷大学; 里约热内卢州立大学; 里约热内卢联邦大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出一种基于固定网格的超导磁轴承建模方法，通过坐标变换处理运动效应，结合有限元法，准确高效地模拟悬浮力，验证结果与实验高度吻合。
AI 中文摘要
超导磁轴承（SMB）的数值模拟因高温超导体与磁导轨之间的相对运动而变得复杂，这通常需要反复更新几何形状和网格。我们提出了一种基于固定网格的方法来模拟运动引起的效应，其中坐标变换仅应用于运动区域之间的空气区域。该变换可以包含在依赖于时间的各向异性材料张量中，从而使模拟过程中的网格以及其余公式保持不变。为了提供数值示例，该方法采用有限元方法在二维中实现，使用$j$-$a$公式，并与均质化和电路耦合相结合，用于涂层导体的双交叉回路。开源模型实现已公开提供。所提出的方法经过验证，并与现有的建模方法和文献中关于SMB的实验结果进行了对比。给出了两个模拟示例，在这两个示例中，固定网格模型预测的悬浮力与实验结果一致，$R^2$值均高于0.99。对于一个验证问题，结果表明在网格细化下，固定网格模型如预期地收敛到重新划分网格的参考解。对于一个经历垂直和水平平移的SMB，均质化固定网格模型再现了完全解析的运动几何参考模型的横向力响应。此外，均质化固定网格模型在计算上比参考模型更高效，表明自由度和计算时间显著减少。结果证明了基于固定网格的方法能够准确且高效地模拟平移运动。
英文摘要
Numerical simulations of superconducting magnetic bearings (SMBs) are complicated by the relative motion between high temperature superconductors and the magnetic guideway, which commonly requires repeated updates of the geometry and mesh. We present a fixed-mesh based approach for modeling the motion induced effects in which a coordinate transformation is applied only to the air region between the moving regions. The transformation can be included in a time-dependent anisotropic material tensor, leaving the mesh during the simulation and the rest of the formulation unchanged. To provide numerical examples, the approach is implemented in 2D using the finite element method with the $j$-$a$ formulation and is combined with homogenization and circuit coupling for double-crossed loops of coated conductors. The open-source model implementations are made available. The proposed approach is verified and validated against existing modeling approaches and experimental results from the literature for SMBs. Two simulation examples are presented, and in both of them the levitation force predicted by the fixed-mesh model agrees with the experimental results, yielding $R^2$ values above 0.99. For a verification problem, it is shown that the fixed-mesh model converges towards the remeshed reference solution under mesh refinement as expected. For an SMB undergoing vertical and horizontal translations, the homogenized fixed-mesh model reproduces the lateral-force response of a fully resolved moving-geometry reference model. Additionally, the homogenized fixed-mesh model is computationally more efficient than the reference model, indicating a significant reduction in the number of degrees of freedom and the computation time. The results demonstrate accurate and computationally efficient simulation of translational motion with the fixed-mesh based approach.
