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Pragmatic two-step homogenisation technique for ferromagnetic laminated cores

机译：铁磁叠片铁芯实用两步均质技术

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摘要

Electromagnetic fields and eddy currents in thin electrical steel laminations are governed by the laws of magnetodynamics with hysteresis. If the lateral dimension of the laminations is large with respect to their width, the fields and currents generated under arbitrary excitation inside a lamination can be resolved accurately by solving a one-dimensional finite element magnetodynamic problem across half the lamination thickness. This mesoscopic model is able to produce, by averaging the necessary information, a homogenised laminated core model, to be used in the macroscopic modelling of electrical devices involving ferromagnetic lamination stacks. As each evaluation of the homogenised model at the macroscale implies a finite element simulation at the mesoscale, a monolithic implementation of the homogenisation method would be extremely time-consuming. Hence the idea of this study to use system identification techniques to construct an algebraic approximation of the homogenised model, to be used as a conventional constitutive relationship in two- or three-dimensional macroscale simulations. This pragmatic two-step homogenisation approach turns out to be quite accurate and efficient in practice, and it entails no implementation in the FE code, provided the latter offers enough flexibility in the description of the material laws.
机译：薄电工钢叠片中的电磁场和涡流受磁滞定律控制。如果叠片的横向尺寸相对于其宽度较大，则通过解决叠片厚度一半的一维有限元磁动力问题，可以准确地解决叠片内部任意激励下产生的磁场和电流。该介观模型能够通过平均必要的信息来生成均质化的叠层铁心模型，以用于涉及铁磁叠片堆的电气设备的宏观建模。由于在宏观尺度上对均质化模型的每次评估都暗示着在中等尺度上的有限元模拟，因此，均质化方法的整体实现将非常耗时。因此，本研究的思想是使用系统识别技术构建均质化模型的代数近似，以用作二维或三维宏观模拟中的常规本构关系。事实证明，这种实用的两步均质化方法在实践中非常准确且有效，并且无需在FE代码中实施，只要FE代码在描述材料定律方面具有足够的灵活性即可。

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