Abstract Modelling hysteresis behaviour is an essential task in transient analysis of electrical machines. A curve fitting approach based on isoparametric elements is proposed in this work. A hysteresis loop is split into sub-curves and each sub-curve has been modelled in terms of a second degree polynomial using three data points. Thus the model requires few data points to model a complete loop. The model equations can be easily derived using predefined shape functions of an isoparametric element without using any curve fitting algorithms. The proposed approach has been applied to model hysteresis data of two different materials, namely, grain-oriented (GO) laminations and soft magnetic composites (SMC). Symmetrical minor loops of GO materials with magnetization along any arbitrary direction are modelled for the first time. The calculated results are in close agreement with measured values. Compared to existing methods, the proposed technique in this paper is simple to understand and computationally efficient.

中文翻译：

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一种对包括各向异性和对称次环在内的铁磁磁滞进行建模的等参方法

摘要 迟滞行为建模是电机瞬态分析中的一项基本任务。本文提出了一种基于等参单元的曲线拟合方法。磁滞回线被分成子曲线，并且每个子曲线都使用三个数据点根据二次多项式建模。因此，该模型需要很少的数据点来模拟一个完整的循环。可以使用等参元素的预定义形状函数轻松导出模型方程，而无需使用任何曲线拟合算法。所提出的方法已应用于两种不同材料的磁滞数据建模，即晶粒取向 (GO) 叠片和软磁复合材料 (SMC)。首次对沿任意方向磁化的 GO 材料的对称小环进行建模。计算结果与实测值非常吻合。与现有方法相比，本文提出的技术易于理解且计算效率高。