Finite element computer investigation of the electrochemical machining process for a parabolically shaped moving tool eroding an arbitrarily shaped workpiece

This paper describes a computational investigation into the electrochemical machining (ECM) process for the case of a tool of fixed parabolic shape, moving at a uniform speed while eroding a stationary work surface initially of arbitrary shape. The numerical simulation of this two-dimensional moving boundary problem is based on the finite element method (FEM). The improved algorithms presented here, which model the erosion process at the work surface, remove certain limitations of the previous square mesh method. In ECM, as time increases, the eroded surface approaches more closely to an equilibrium shape. One-dimensional ECM theory is briefly reviewed in order to provide a background to the physical factors which influence this equilibrium state. A general equilibrium criterion is derived which is first used as part of a check on the test data, and later made the basis of an iterative design method. The present paper is divided into two sections. In the first, the modular computer package, which simulates the continuous erosion process, is described. A parabolically shaped tool was selected to allow the final equilibrium work shape generated after a number of time steps to be checked. These checks demonstrated excellent agreement between computer predictions and theory; they constitute a successful validation of the methodology. In the second part of the paper, the inverse of the above process is considered. Algorithms are described which, starting from the specified work shape, iteratively generate the tool shape required to produce that work shape. This avoids the multiple trial and error runs normally associated with the evolution of a tool shape in practice.