The electrochemical machining (ECM) of cylindrical hole surface by a partially insulated eccentric cylindrical tool-electrode (cathode) is theoretically studied using the numerical simulation based on the mathematical model of primary current density distribution. The Laplace equation with boundary conditions is solved numerically using the boundary element method combined with the fast multipole method (FMM-BEM method). The distributions of the current density over the workpiece surface and tool-electrode (TE) surface are obtained. The effect of the angle of non-insulated TE part \({\uptheta }_{\text{TE}}\) and the minimal interelectrode gap S0 on the degree of localization of anodic metal dissolution (the ECM accuracy) and on the average current density (the ECM productivity) is studied. It is shown that partial insulation of TE surface enhances ECM accuracy but reduces productivity due to a decrease of TE surface area. The distribution of the current density over partially insulated TE reveals a significant edge effect at the boundary between the insulated and non-insulated TE parts, which has a strong effect on the ECM productivity. It is shown that a decrease in the ECM productivity due to a decrease in TE surface area is partially compensated by an increase in the average current density due to the edge effect. An approximate analytical solution of the problem enables us to estimate the effect of partial insulation of the TE surface on the productivity and accuracy of electrochemical machining of a cylindrical hole with an eccentric TE. The results of numerical and analytical solutions agree well.
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