Thermal effect will greatly affect the engineering performance of high-temperature superconductors (HTSs) due to its strong dependence of electromagnetic parameters upon the local temperature. To advance the understanding of such thermal effects, a validated 3-D strong-coupled electromagnetic-thermal model for HTS bulk was established in commercial finite-element software COMSOL, which ensures the easy access and universality of the model. Jc(B,T) was employed to reflect both magnetic field and thermal field dependences of HTS in this model. In addition, the thermal transient equation and convective boundary condition were employed with experimentally measured HTS thermal conductivity and heat capacity to describe the thermal flux exchange between HTS and cryogenic medium. As an example of application, the established electromagnetic-thermal model was tailored to study the dynamic characteristics of a linear HTS magnetic levitation (maglev) bearing. The methodologies to numerically study the dynamic response of the linear HTS maglev bearing under free vibration state and typical operating excitations, e.g., earthquake, track irregularity, and crosswind, were put forward in this article. The influences of field cooling height, preload, and ambient temperature, were also studied, and promising methods to improve the system stability were put forward according to the obtained conclusions. The above-mentioned results are reasonable and keep in concert with former experimental and theoretical studies. Moreover, some results which are inaccessible in the 2-D models, for instance, the thermal field distribution inside HTS bulk, can also be obtained due to the versatility of the 3-D model. To conclude, the established HTS electromagnetic-thermal model could serve as a flexible and extensible simulation tool to study various applications of HTS bulk. Besides the application in linear HTS maglev bearing, which was systematically studied in this article, other potential applications, such as thermal analysis of HTS bulk in pulse magnetization process and HTS bulk-based electrical machines, can also be expected in future work.

中文翻译：

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HTS 散装体的 3-D 强耦合电磁热模型及其用于研究线性 HTS 磁悬浮轴承动态特性的用途

由于其电磁参数对局部温度的强烈依赖性，热效应将极大地影响高温超导体（HTS）的工程性能。为了加深对这种热效应的理解，在商用有限元软件 COMSOL 中建立了经过验证的 HTS 体 3-D 强耦合电磁-热模型，确保了模型的易用性和通用性。Jc(B,T) 用于反映该模型中 HTS 的磁场和热场依赖性。此外，热瞬态方程和对流边界条件与实验测量的 HTS 热导率和热容量一起用于描述 HTS 和低温介质之间的热通量交换。作为应用示例，建立的电磁热模型专门用于研究线性 HTS 磁悬浮 (maglev) 轴承的动态特性。本文提出了数值研究线性高温超导磁悬浮轴承在自由振动状态和典型运行激励（例如地震、轨道不平顺和侧风）下的动态响应的方法。还研究了现场冷却高度、预载和环境温度的影响，并根据所得结论提出了提高系统稳定性的有前景的方法。上述结果是合理的，与以往的实验和理论研究一致。此外，一些在二维模型中无法获得的结果，例如 HTS 体内部的热场分布，由于 3-D 模型的多功能性，也可以获得。总之，建立的 HTS 电磁热模型可以作为一种灵活且可扩展的仿真工具来研究 HTS 体的各种应用。除了本文系统研究的线性高温超导磁悬浮轴承的应用外，其他潜在的应用，如脉冲磁化过程中高温超导体的热分析和高温超导体基电机，也可以期待在未来的工作中。