The two-dimensional problem of the electrochemical machining of metals with a periodic cathode tool

The problem of the electrochemical machining of metals with a periodic cathode tool in the form of a lattice of plates is formulated and solved. The hydrodynamic analogue of the initial problem is the problem of a plane-parallel potential circulating flow of an ideal incompressible fluid around plate electrodes. Auxiliary schemes are considered in order to specify the initial data and conditions determining the parameters of the problem. The steady-state shapes of the anode boundaries are found. It is shown that different anode boundaries are obtained due to a change in the electric field characteristics provided that the properties of the metal and the electrolyte, the geometry of the electrode tool and its rate of advance are identical.