A simplified mathematical model development for the design of free-form cathode surface in electrochemical machining

Abstract

High-performance machining of free-form surfaces is highly critical in automotive, aerospace, and die-mold manufacturing industries. Therefore, electrochemical machining (ECM) process has been used in such cases in that sense. The most important challenges of using ECM process are the lack of accuracy and difficulty in designing proper machining tool (cathode) surfaces. In this article, a simplified mathematical model is presented to obtain a cathode surface for ECM of free-form surfaces which have high curvatures. In this theoretical approach, the finite-element method (FEM) is used to solve the 3-D Laplace equation and to determine the potential distribution between the anode (workpiece) and cathode (tool) surfaces. A compact and simple program was developed to obtain a proper cathode surface that only requires some nodal coordinates on the anode surface and boundary conditions. In this work, a trial cathode surface is constructed for a given gap distance. For the determined ECM parameters, cathode shape that satisfies the boundary conditions is obtained for the 45(th) layer. The results are compared with the literature and ANSYS Workbench for verification. The developed theoretical approach benefits simpler and faster FEM solutions, accurate cathode surface, and consequently correct form of machined surface.