Two-dimensional problem of electrochemical metal machining

The two-dimensional problem of the electrochemical dimensional machining of a metal is investigated within the framework of the model of an ideal stationary process, which makes it possible to use the analogy with the problems of fluid flows with free surfaces. In the problem considered the cathode (machining tool) takes the form of two parallel semi-infinite rectangular electrodes. The blank (anode) is a half-plane whose boundary is perpendicular to the cathodes. Depending on the relationship between the physical and geometrical parameters of the problem, on the machined part (anode) a projection symmetrical about the center line between the cathodes may be formed. Additional mechanical machining of the part is then required. In order to exclude such solutions, a condition is obtained for the mathematical parameters which determine the solution of the problem in the auxiliary complex plane. General and particular limiting cases are considered. For the cases considered the calculation results are presented in the form of plots of the shape of the part machined.