Optimal shape of additively manufactured magnetic cores.

Additive manufacturing enables the fabrication of next-generation electrical machines with unprecedented topological complexity and design freedom. Due to this design freedom, no consensus has been achieved on the optimal shapes for air-gapped soft magnetic cores -- flux guides - that maximize transmitted magnetic flux for a given volume while maintaining eddy current losses at an acceptable level and ensuring sufficient mechanical stiffness. We research topological optimality in terms of transmitting magnetic flux, while favouring mechanical stability when the amount of flux transmitted is similar. We demonstrate that the optimal core shape is close to a structure we term the 'H-comb': a configuration of thin sheets interconnected by a central bridge, forming a double-sided comb in cross-section perpendicular to the magnetic flux flow. We also develop a mathematical framework for optimally dimensioning these flux guides, providing guidelines for determining appropriate sheet and gap thicknesses based on specific material properties and operating frequencies. We fabricated a series of H-comb-shaped magnetic cores and conducted flux measurements. Across the practically relevant frequency range, the deviation between theoretical predictions and experimental results remains below 10%.