Heat conduction model for the calculation of the volume of molten metal in electric discharges

The craters obtained by electric sparks in electro-discharge machining are numerically calculated by use of a thermal model. The computational procedure is based on the exact solution of the related two-dimensional transient heat conduction problem in a finite or semi-infinite body subjected to a stepwise or time-dependent uniform heat flux over a small circular part of its upper surface. Optimal geometrical conditions, relative to a fast convergence and negligible influence of the boundaries, are demonstrated. By superposition of rectangular heat flux pulses over circular parts with different diameters, the influence of the channel widening can be investigated. It is shown that a theoretical model should include the possibility of accounting for the plasma channel widening in order to obtain acceptable agreement with experimental data or to predict the optimal operating conditions.