Permeability of Magnetic Cores with Air Gaps

The influence of the geometric dimensions of the cut core and the number and size of air gaps on the effective permeability was investigated. Using dimensional analysis, an equation was obtained that relates the permeability of the cut core to the simplest dimensionless combination of the mean magnetic flux length l, single air gap length l₁, the cross-sectional area S of the core, and gap number n. Permeability calculated from the geometric parameters of the cut core was compared with the effective permeability obtained using a two-dimensional FEMM simulation. Simulation has shown that the equation derived from dimensional analysis provides the best fit. The influence of each significant parameters l, l₁, n, and S on cut core permeability is demonstrated. Experimental results have shown that an equation derived from dimensional analysis can be used to predict cut core permeability. In this case, one should take into account the residual air gap that forms after cutting the core. A method for assessing the residual air gap is proposed.