Extending the Steinmetz Equation: Incorporating Mechanical Stress Effects in Ferrite Core Loss Calculations

This paper extends the Generalized Steinmetz Equation (GSE) to account for the influence of mechanical stress on ferrite core losses. Experimental measurements are used to quantify the effects of compressive and tensile stresses on the relative permeability and the core losses of different ferrite materials. Mechanical stress is found to significantly affect the core losses, depending on the relative orientation of the magnetic flux density and the applied mechanical stress. Specifically, the losses monotonically increase when the flux and compressive stress vectors are parallel, while perpendicular vectors lead to a more complex response depending on the level of mechanical stress. The measured loss characteristics are translated in an extension of the GSE (X-GSE), which is validated for different ferrite materials, and provides a useful tool for a first rough estimation of the core losses under mechanical stresses. Finally, FEM simulations demonstrate how thermally induced mechanical stresses in a ferrite core can redistribute the magnetic flux and therefore impact the resulting core losses, which underlines the importance of considering the stress dependence of core losses in ferrite, especially in the development of magnetic components to be encapsulated in incompressible materials.