A direct analytical solution to the tool design problem in electrochemical machining under steady state conditions

A method for the direct computation of two-dimensional electrochemical machining tool designs is described. The required workpiece geometry is represented by a Fourier series. Conformal transformation is then used to express the tool shape in series form, each term being a direct analytical function of the corresponding workpiece harmonic. Tool designs are thus achieved without numerical iteration. The model has been experimentally validated for a required workpiece geometry consisting of two harmonics, for which a tool was designed and manufactured. An In 718-15 per cent NaCl workpiece-electrolyte system was used to produce a machined surface, whose Fourier transform was obtained. The measured and predicted harmonic amplitudes agree closely. This harmonic design method is also shown to give insight into the relationship and limitations between tool design and achievable workpiece detail.