Theoretical and computational investigation of the electrochemical machining process for characteristic cases of a stepped moving tool eroding a plane surface

A theoretical and computational investigation into the electrochemical machining (ECM) process for the case of a moving stepped tool eroding an initially flat surface is presented. Five parametric variations of the basic geometry of the stepped tool machining process are possible, depending on the relative distance between the moving tool and eroded work. For each of the five cases, and based on one-dimensional theory, formulae have been developed to predict the minimum depth of working material that must initially be provided to enable a particular step size to be machined to a specified tolerance. The computer simulation of the ECM process which has been developed is based on the finite element method (FEM). The geometry of tool, electrolyte and work is simulated by means of a two-dimensional mesh of square elements. A system of macros has been developed which interact internally with an FE package to move component boundaries systematically to simulate both tool movement and surface erosion. Such boundary movements are accomplished automatically and continuously without user intervention during a simulation run. The algorithms employed to achieve characteristically different erosion rates are described. Results both from one-dimensional ECM theory and from the computer simulations of the characteristic cases are presented. Comparisons show that there is good agreement between computer predictions and theory. The differential erosion process is fundamental to all ECM processes. Complex shapes evolve because of spatial differences in erosion rates. Thus the one-dimensional results presented here for the formation of a step should provide a basis for comparisons between spatially separated regions of one-dimensional differential erosion on bodies of arbitrary shape.