Voltage impact excitation of rectangular solid iron core

Voltage impact excitation of a solid iron core creates eddy currents in the core, retarding the rise of flux. An analysis of the problem involves the simultaneous solution of partial and ordinary differential equations. The boundary condition for the partial differential equation contains an unknown quantity, which is variable with respect to time in the ordinary differential equation associated with the physical system. Such situations are commonly termed field-circuit problems. The paper presents the method of eigenvalues for solving linear field-circuit problems. The eigenfunctions are mutually orthogonal, enabling an exact fit of the boundary condition by a linear combination of these eigenfunctions. The final equations, when applied to a practical voltage-impact-excitation problem, show favourable agreement with experimental results for current and flux transients. A special and interesting feature of the paper is the predetermination of contours of constant magnetising force and eddy-current-density distribution within the rectangular section during the transient period. The contours, obtained rigorously for the first time, give insight into the phenomena involved in the magnetisation of a rectangular solid iron core.