Analysis and computer simulation of the electrochemical machining process: A stepped moving tool eroding a plane surface

This paper presents a theoretical and computational investigation of the electrochemical machining (ECM) process, for the important practical case of a stepped tool eroding an initially flat work surface. A fully automatic computer package based on the finite element method (FEM) has been developed which simulates the two-dimensional ECM process. To provide theoretical benchmarks for the computer simulation, differential erosion of a step has been analysed in terms of the one-dimensional processes on either side of it. To facilitate this analysis, the basic erosion equation has been approximated by a simple exponential relation, which becomes increasingly exact as time increases. This has enabled explicit equations for the time required to machine a step to be developed. This simple theoretical model both provides insight into the ECM process and facilitates design estimates of the time required to erode a step to a given tolerance. Five characteristic cases of erosion with a stepped tool have been summarized in parametric form. For one of these cases, results from the two-dimensional computer simulation have been compared with theory; there is good agreement. It is intended that the computer results from the four remaining cases will be presented in a later companion paper which will provide additional information on the computer package and the two-dimensional results from it.