Equivalent circuit of solid iron core for impact excitation problems

In designing machines and apparatus with solid or partly solid magnetic circuits, it is necessary to predetermine the flux/time and current/time curves to obtain a desired rapidity of response. This requires precise knowledge of the damping action of eddy currents. Rigorous analysis of the problem for a core of rectangular section, taking into account the resistance of the magnetising winding, is difficult to obtain and has not been attempted so far in published work. The problem is all the more complicated when the nonlinearity of the material of the iron core is taken into consideration. The paper presents a method of reducing the solid iron core to a circuit analogous to that of a transformer with short-circuited secondary winding. The basis for obtaining the circuit is the eddy-current expression under alternating magnetisation for a solid iron core of large width/depth ratio, obtained from Maxwell equations. The equivalent circuit consists of secondary resistance and leakage reactance, which depend on the shape of the section and the electrical and magnetic characteristics of the material. The circuit obtained for constant permeability is then extended for use under nonlinear conditions. This method of obtaining the equivalent circuit results in an original treatment of the problem and gives an insight into the phenomena involved in the magnetisation of a core due to impact excitation. The results obtained from this theory compare favourably with test results.