1-D Lamination Models for Calculating the Magnetization Dynamics in Non-Oriented Soft Magnetic Steel Sheets

Iron-Loss and Magnetization Dynamics in Non-Oriented Electrical Steel: 1-D Excitations Up to High Frequencies

“…The presented PDE 7, combined with adequate BCs, can be solved for known ICs by using different approaches, such as by applying finite differences (FDs) [28], [42], [43], [49], [51], finite elements (FEs) [9], [34], [42]- [44], [57], mesh-free techniques [30], [36], [41], [48], spatial averaging methods [48], [50], [84], equivalent circuit approximation [62], fractional derivatives [32], [54], or by tackling the problem analytically [46]. Most of these approaches rely on some kind of discretization, whereas, usually, a system of non-linear Ordinary Differential Equations (ODEs) is obtained from the PDE (7).…”

“…Most of these approaches rely on some kind of discretization, whereas, usually, a system of non-linear Ordinary Differential Equations (ODEs) is obtained from the PDE (7). The size of the obtained ODE system depends on the applied method, as well as on excitation dynamics [48]. In this paper, a method is presented where the distribution of magnetic variables inside the sheet is approximated by using piecewise constant functions.…”

“…In this paper, a method is presented where the distribution of magnetic variables inside the sheet is approximated by using piecewise constant functions. The so-called Parametric Magneto-Dynamic (PMD) model of NO steel sheets is obtained using this method [48], [50], [84]. The presented method is based on (5) and (6), and gives a clear understanding of the underlying physical phenomena of non-linear diffusion of the electromagnetic field inside the discussed NO steel sheets.…”

“…In order to predict the iron-loss and magnetization behavior under such conditions accurately, it is indispensable to utilize a hysteresis model that is coupled directly to an eddy-current (lamination) model. This can be solved by using various approaches, where the lamination model is, e.g., based on Maxwell equations [9], [11], [23], [24], [27]- [36], [38]- [57], saturation wavefronts [58]- [60], equivalent circuits [37], [48], [61]- [63] or is included in the hysteresis model implicitly [43], [64], [65]. A comparison of different 1-D lamination models in terms of mathematical structure, implementation, computational performance, accuracy and spatial discretization can be found in [48].…”

Dynamic Modeling of a Serial Link Robot Laminated with Plastic Film

“…In magnetics, modeling of hysteresis losses [26][27][28], eddy current losses [29,30], and temperature effects [31] for magnetic laminations have been proposed under some conditions. Depending on those conditions, a 1-D model [32], a 2-D finite-element model [33], and a 3-D finite-element model [34] have been selected to analyze the laminated structure performance. However, we must derive the equations of motion and analyze the motions of laminated structures including a serial link robot from the viewpoint of robotics.…”