Losses in ferromagnetic laminations due to saturation

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Abstract
The discrepancy between experimentally determined core losses and those calculated using the classical expressions for ferromagnetic laminations is well known. The paper presents an analytical solution that takes account of the saturation of the lamination material. In laminations, over the usual range of flux densities and frequencies encountered in core-loss calculations, only the fundamental frequency need be considered in the more usual case of applied voltage or excitation current of sinusoidal waveform. The present analysis makes use of the magnetisation curve relating the fundamental quantities (B1/H1) obtained from the d.c. magnetisation (or B/H) curve. The solution is obtained for the B1/H1 curve of the equation B1=μ(H1+aH13+cH15), where the coefficients a and c that govern the nonlinearity may be positive or negative. The hysteresis effect is accounted for by replacing the actual loop by an ellipse which has the same area and maximum value of magnetisation.Contrary to the well known ideas of constant permeability, it is shown that the magnetising force and the flux density at any point inside the lamination are not necessarily in phase, even when the hysteresis effect is not present. As a result, an extra loss appears additional to the usual eddy-current and hysteresis loss components.The expressions obtained are applicable for laminations in which the ratio of the magnetising force at the surface to that at the centre is nearly unity. The validity of the theory has been verified by applying it to the experimental results available in literature and agreement is found to be satisfactory both at power and low audio frequencies. The analysis provides simple expressions which are useful for quick computation compared with the usual graphical and numerical methods normally employed in nonlinear problems.

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