Advanced soft- and hard-magnetic material models for the numerical simulation of electrical machines

The development of energy-efficient electrical machines requires an accurate knowledge of the soft- and hard-magnetic material behavior already in the design stage. Accurate numerical models are required which offer the ability of better understanding and modelling in an appropriate accuracy. With such model properties on the one hand accurate simulations can be performed and on the other hand the best possible material choice for a particular application, i.e. for an electrical machine, can be done. The soft-magnetic material constitutes the magnetic core of an electrical machine and its properties. On that account, the accurate prediction of iron losses of soft-magnetic materials for various frequencies and magnetic flux densities, i.e., arbitrary magnetic field waveforms, is eminent for the design of electrical machines [1]. For this purpose different phenomenological iron-loss models were proposed, which describe the loss-generating effects, i.e., hysteresis, non-local eddy currents and anomalous eddy currents. Most of these suffer from poor accuracy for not considering the effect of high frequencies and high material utilization as well as the material degradation due to the magneto-elastic coupling [2, 3, 5]. This paper presents a comparison of common iron-loss models. The IEM-formula used, resolves the limitation by introducing a high-order term of the magnetic flux density and considers the alteration of material-dependent loss-parameters due to the magneto-elastic coupling [3]. The knowledge of the magnetic property deterioration due to induced residual stress occurring during the manufacturing or operation of the electrical machine is indispensable for the contemporary design. It has been widely ascertained that processing of electrical steel laminations significantly alters the magnetic properties of the electrical steel [2–6]. Cutting induces plastic deformation and residual stress in the laminations. Due to their strong sensitivity to mechanical stress, the magnetic properties are locally degraded near the cut edge. The extent of the degradation depends substantially on the process characteristics, i.e., the cutting procedure and cutting parameters in combination with material properties, such as mechanical strength and grain size [4–6]. In [7] a continuous material model for an efficient numerical model of the local magnetization was introduced. By replacing numerically expensive sliced models, the continuous model (CM) is independent of the discretization and converges in the case of coarse meshes to the sliced model [7]. Measured single-sheet specimens are used to identify the different model parameters. In Fig. 1 results on hysteresis loss distribution are presented. The vital advantage of the proposed CM is that properties depend only on the distance to the cut edge. For improved estimation of penetration depth and mechanical stress distribution, novel experimental procedures are utilized [8] and mechanical simulations are evaluated [6] to further advance the cut-edge model. Permanent magnets are central to the electromagnetic energy conversion process in permanent-magnet synchronous and flux-switching machines. In order to design the magnetic circuit and a magnetizing circuit for post-assembly magnetization as well as to analyze the resistance to being demagnetized during the simulation of electrical machines, it is indispensable to describe the magnetization behavior of the permanent magnets accurately. However, due to the complex interplay of the non-linear and hysteretic magnetization behavior and the magnetic anisotropy, it is a complex problem. Commonly, simplified models are used, which are based on empirical and phenomenological approaches. These describe the major loop of the permanent magnets only. However, the magnetization state of the permanent magnet depends on the magnetic and thermic history, i.e., it is indispensable to account for minor loops or incompletely magnetized permanent magnets. In this paper, a pragmatic methodology to replicate the hysteresis of permanent magnets is presented, which uses first-order return curves and the magnetization behavior starting from the virgin state for model-parameter identification [10]. Efficient parametric models with low additional computational effort are perfectly suited for the finite-element analysis. Starting from these advanced models of soft- and hard-magnetic materials, a methodology for selecting the optimal steel grade during the design-stage of electrical machines in due consideration of the application-specific requirements on torque-speed operating points, i.e., all have to meet the requirements of the same driving cycle, is presented [1]. This allows one to study the effect of different electrical steel grades on the operational characteristics along the torque-speed map [11]. In order to determine the efficiency of each combination of machine topology and lamination type, the iron-loss model with material degradation is used in combination with a machine simulation scheme of the entire operating range of the machine. In the light of this, this paper will give an overview on the current modeling approaches applied at the Institute of Electrical Machines (IEM) for soft- and hard-magnetic materials in the simulation of rotating electrical machines.