Simplifying Random Particle Structures Within Soft Magnetic Composite Materials for the Optimization of 3-D-FEM Simulations

This article investigates the simulative approximation for simplifying the complex random particle arrangement within a soft magnetic composite (SMC) material by cubic atomic lattice structures. The implemented 3-D finite element model (FEM) can calculate the relative permeability of different particle arrangements in the form of a geometric replication of a volume section of the SMC material. We demonstrate the determination of the relative permeability in dependency of the volume fraction from an SMC material with the simulation, and the results are consistent with established analytical formulas, based on the demagnetization factor and relative permeability of the soft magnetic particles. The utilization of cubic atomic lattice structures is investigated in respect of reducing the computational complexity. The four atomic lattice structures introduced here each correspond to a fixed volume fraction. By varying the relative permeability of the soft magnetic particles, the simulation results reveal a maximum achievable relative permeability for the polydisperse cubic face-centered particle structure of 45.5. Furthermore, the relative permeability of several self-manufactured toroidal SMC cores with different particle size distributions was measured, and we investigated the measurement uncertainty in detail. The measurement results indicate that the particle size distribution has no influence on the relative permeability of the compound material. Especially, the simulation model of the monodisperse cubic primitive particle structure with a volume fraction of 52.36% replicates the measurement results with high conformity. In conclusion, it is possible to simplify the random particle structure in SMC materials within a specific range of volume fractions. Thereby, for volume fractions over 50%, a tradeoff between model complexity and accuracy is necessary.