Pragmatic two-step homogenisation technique for ferromagnetic laminated cores

Electromagnetic fields and eddy currents in thin electrical steel laminations are governed by the laws of magnetodynamics with hysteresis. If the lateral dimension of the laminations is large with respect to their width, the fields and currents generated under arbitrary excitation inside a lamination can be resolved accurately by solving a one-dimensional finite element magnetodynamic problem across half the lamination thickness. This mesoscopic model is able to produce, by averaging the necessary information, a homogenised laminated core model, to be used in the macroscopic modelling of electrical devices involving ferromagnetic lamination stacks. As each evaluation of the homogenised model at the macroscale implies a finite element simulation at the mesoscale, a monolithic implementation of the homogenisation method would be extremely time-consuming. Hence the idea of this study to use system identification techniques to construct an algebraic approximation of the homogenised model, to be used as a conventional constitutive relationship in two- or three-dimensional macroscale simulations. This pragmatic two-step homogenisation approach turns out to be quite accurate and efficient in practice, and it entails no implementation in the FE code, provided the latter offers enough flexibility in the description of the material laws.