Modeling of electrochemical micromachining of cylindrical hole surface by eccentric cathode

Electrochemical machining (ECM) of the inner surface of cylindrical workpiece (WP) with an eccentric rotating cylinder tool-electrode (TE) is studied theoretically using a new mathematical model. The proposed model uses a moving coordinate system bound to the rotating WP. In this case, only the variation in the position of TE center during its orbital movement is taken into account. In addition, for convenient solution and analysis of results, the mathematical model was presented in the dimensionless form in order to reduce the number of parameters. The local one-dimensional approximation is used to calculate the distribution of the current density. It enables determining the distribution of the current density not from the solution of Laplace's equation, but using a simple analytical equation. Three dimensionless parameters are proposed to characterize the properties of the workpiece material, the electrolyte solution and working conditions, and also the dimensions of the electrodes and the rate of their relative motion. These parameters are used in the numerical solution and analysis of the results. The obtained relationship between the accuracy and productivity of ECM with an eccentric rotating TE can be used to optimize the process. The error in the shape of workpiece surface is analyzed within the proposed model. The relation between the error of machining and the minimum interelectrode gap is revealed. A two-stage ECM scheme is proposed to reduce the shape error.