The electrochemical machining process is mathematically modeled as a linear potential problem in two dimension assuming constant properties of the electrolyte. The model is then used for optimization of tool shape for a desired workpiece shape as well as for simulation of the metal removal process. The method of deriving shape sensitivity formulas based on boundary integral equation is utilized and implemented for numerical calculations using BEM. The tool shape to be designed is represented by a spline.
The transient shape of workpiece for a given electric potential and a feed rate are successively obtained and equilibrium configurations studied. A straight tool, a curved tool and a rectangular tool are used for numerical examples and their solutions compared with available analytic solutions. A tool design example is taken to optimize a curved tool for the workpiece shape obtained earlier by the simulation. The objective function is to get the final equilibrium configuration. The optimized shape agrees well with the original curved tool.
