The predetermination of the magnetic properties of ferromagnetic laminae at power and audio frequencies

In order to explain the discrepancies which exist between results obtained experimentally and those determined from the classical solution of the behaviour of ferromagnetic laminae when subjected to a.c. magnetization, a more rigorous solution has been obtained by taking account of the variation of both the permeability and hysteresis loop, with changes in the maximum flux density, throughout the thickness of the lamination. A method of harmonic analysis has been utilized to represent the relationship which exists, at any instant of time, between the m.m.f. and flux density across the section of the lamination, in order that the quantities of fundamental and harmonic frequency may be separately investigated. Calculations to determine the total iron loss have shown that, for the range of frequency and flux density covered, only the quantities of fundamental frequency need be considered in the more usual practical case of sinusoidal waveform of applied voltage, or alternatively, of sinusoidal excitation current. Contrary to the classical solution, it is shown that the m.m.f. and flux density at any point in the lamination are not necessarily in phase, even when the usual hysteresis effect is negligible. In consequence, an energy loss occurs which is additional to the usual conception of eddy-current and hysteresis loss. The physical explanation of the existence of the additional loss suggests that it may conveniently be designated as the ?differential hysteresis loss.? The range of application of the theoretical expression for the iron loss is subject to an upper limit, corresponding approximately with the knee of the magnetization curve. An alternative solution is put forward for values of magnetizing force beyond this point. Tests have been carried out on samples of both Mumetal and silicon steel, to cover a wide range of frequencies and flux densities. The theoretical value of loss calculated from the new formulae accounts for the greater part of the measured value- without introducing a fictitious value for the permeability. A comparison of the measured and calculated values gives a useful indication of the inhomogeneity of the material. It is noted that a reduction in lamination thickness results in an increase of the hysteresis loss and a reduction of the permeability, the latter effect tending to increase the eddy-current loss. This is of particular importance at low audio-frequency operation, where a reduction of lamination thickness can result in an appreciably higher total loss.