Modeling of electrochemical machining by point electrode tool with a jump anode potential change

Abstract

The distribution of the electric field in the electrolyte near the contact point of two detail parts with different values of the anode potential is investigated. The problem is relevant in connection with the development of technologies for welds machining in order to dissolve material layers that retain residual tension and do not create new tension. The methods of the theory of functions of a complex variable are used to solve the problem, since a stationary electric field with the properties of solenoidality and potentiality is considered. A singularity of the complex potential at the contact point is found by the method of conformal mappings. The solution of the problem is sought as the sum of a known function with a singularity and a function without singularities, which is defined as a power series with unknown coefficients. The coefficients are determined numerically by the collocation method, i.e. the problem is reduced to solving of equations system. The Gauss method is used for this purpose. The problems with the specified dependence of the anode potential on the current density is solved. The errors estimates have shown that by the developed method allows determining the desired parameters with sufficient accuracy. The distributions of the anode potential and components of strength on the surface of the detail are found. The resulting forms of stream lines allowed us to adequately describe the electric field which is the result of the superposition of the field of a point source and the field arising from the potential difference in different parts of the detail.