Neural network-based simulation of fields and losses in electrical machines with ferromagnetic laminated cores

Due to the distribution of eddy currents inside ferromagnetic laminations, the accurate modeling of magnetic fields and losses in the laminated cores of electrical machines requires resolving individual laminations with a fine 3D discretization. This yields finite element models so huge and costly that they are unusable in daily industrial R&D. In consequence, hysteresis and eddy currents in laminations are often simply disregarded in the modeling: the laminated core is assumed to be made of a reversible (non lossy) saturable material, and magnetic losses are evaluated a posteriori, by means of Steinmetz-Bertotti like empirical formulas. However, in a context where industry is struggling to minutely assess the impact of magnetic losses on their devices, this simplified approach is more and more regarded as inaccurate and unsatisfactory. This paper proposes a solution to this issue, based on homogenization and on detailed mesoscopic simulations of eddy currents and hysteresis inside the laminations. The proposed approach results in a close-to-conventional 2D magnetic vector potential finite element model, but equipped with an irreversible parametric material law to represent the ferromagnetic stack. In each finite element, the parameters of the law are obtained from a neural network trained to best fit the detailed mesoscopic simulations of the laminations subjected to the same local magnetic field. This way, all aspects of the irreversible ferromagnetic response are appropriately accounted for in the finite element simulation, but at a computational cost drastically reduced with regard to a brute force 3D calculation, and comparable to that of conventional 2D finite element simulations.