Calculation of the magnetic field of rotating machines. Part 4: Approximate determination of the field and the losses associated with eddy currents in conducting surfaces

The paper discusses the relationship between the eddy currents flowing inside a conducting material and the magnetic field outside. The particular problem of a current sheet carrying a sinusoidally distributed current parallel to a conducting magnetic slab is examined in detail. It is shown that this mathematical model is relevant to the calculation of eddy-current losses in many types of rotating machine. The investigation shows that the eddy-current loss in any conducting surface can be simply related to the tangential component of the field at the surface, if the problem fulfils certain conditions. These conditions are set out in the paper. As far as the calculation of the tangential field is concerned, it is shown that electromagnetic images (zero permeability) can be used to represent plane surfaces approximately for a surprisingly wide range of materials, even if these are magnetic. For more accurate representation, modified images are introduced. These may be difficult to formulate, but, where the analytical solution is known, modified images can shorten the labour of computation. Some experimental verification of the method of modified images is included in the paper.