Magnetic dipole collectives for modelling the ferromagnetic material characteristics in electrical machines

现代电机电磁场数值计算采用磁化曲线来描述铁件的非线性铁磁材料特性。平均磁化曲线是通过从环形试样测试仪或爱泼斯坦框架进行测量而获得的。科学文献提供了不同的滞后模型，这些模型或者基于数学或物理方程，或者具有现象学性质。常见的模型是例如Preisach模型、Jiles-Atherton模型和Landau-Lifshitz模型。前两个描述的宏观，瞬态行为的磁化强度依赖于外部磁场强度的常微分方程。然而，这两种模型都忽略了机器的活动铁部件内的局部磁场分布。然而，Landau-Lifshitz模型描述了铁磁材料的微观行为。基于不同的相互作用，基本偶极子（磁化矢量）的排列进行了数学优化，以最小化系统的总自由能。这些相互作用可以从基于原子尺度下材料的晶体结构和纹理的物理关系推导出来。本项目详细研究的模型抽象了Landau-Lifshitz模型提供的物理关系，并将其转换为宏观网格。因此，对磁偶极子的二维和三维集合进行了全面的初步研究。在这项研究中得到的结果表明，模拟值和测量值之间的定性良好的协议。由于Landau-Lifshitz模型的上述抽象，属于所研究模型的参数集的物理关系暂时丢失，因此，所提出的模型的集体内的偶极子根据杂散场、交换场和各向异性场相互作用。为了重建这种关系，首先有必要制定一个标准化的参数识别过程，这是尽可能的，由样品上的物理观测和不同的激发条件的指导。在第二步中，从所发现的定性关系中，将推导出参数集和测量的滞后行为之间的定量连接。综上所述，本项目的目的是全面研究引入的偶极子模型在考虑材料样品上的不同外部影响的情况下定量模拟和预测宏观结构的滞后行为的能力。

Modern numerical electromagnetic field computation of electrical machines uses the magnetization curve to describe the nonlinear ferromagnetic material characteristics of the iron parts. The mean magnetization curves are obtained by measurements taken from a ring specimen tester or an Epstein frame. The scientific literature provides different hysteresis models which are either based on mathematical or physical equations or which are of phenomenological nature. Common models are e.g. the Preisach model, the Jiles-Atherton model and the Landau-Lifshitz model. The first two of them describe the macroscopic, transient behaviour of the magnetization dependent on the external magnetic field intensity as ordinary differential equations. However, both of these models neglect the local magnetic field distribution within the active iron parts of the machine.However, the Landau-Lifshitz model describes the microscopic behaviour of ferromagnetic materials. Based on different interactions, the alinement of elementary dipoles (magnetization vectors) is optimized mathematically to minimize the total free energy of the system. The interactions can be derived from physical relations that are based on the crystal structure and the texture of the material at the atomic scale.The model investigated in detail in this project abstracts the physical relations provided by the Landau-Lifshitz model and transfers them to a macroscopic grid. Therefore, comprehensive preliminary studies with two- and three-dimensional collectives of magnetic dipoles were performed. The results obtained in this studies show a qualitative good agreement between simulated and measured values. The dipoles within the collective of the presented model interact according to the stray-, exchange and anisotropy field, as it they are formulated in the Landau-Lifshitz-Model.Because of the above-mentioned abstraction of the Landau-Lifshitz-Model the physical relationship of the parameter set, which belongs to the model under investigation, is lost for the moment. In order to rebuild this relationship, first it is necessary to develop a standardized parameter identification process that is, as far as possible, guided by physical observations on the sample and the different excitation conditions. In a second step, from the found qualitative relationships, quantitative connections between the parameter set and the measured hysteresis behaviour will be deduced.Summing up, the aim of this project is a comprehensive investigation of the introduced dipole model in term of its abilities of imitating and predicting quantitatively the hysteresis behaviour of macroscopic structures considering different external influences on the material sample.