Prior procedures for cathode (tool) design in electrochemical machining have been plagued by limited applicability, inaccuracy, and nonconvergence. We develop and test a new approach to this problem which overcomes these difficulties by employing a finite element method within an optimization formulation. A least-squares minimization of the deviation of the simulated anode (workpiece) shape from that desired is performed, yielding a set of parameters in a predefined representation which uniquely define an optimal cathode shape. Cathode shapes are designed to produce a variety of anode shapes, even anode profiles with nearly discontinuous slope have been obtained.
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Acknowled#ements--This work was supported in part by the National Science Foundation under grant numbers CTS-9009924 and DMR-9058386, the Minnesota Supercomputer Institute, and the University of Minnesota Army High Performance Computing Research Center (under the auspices of Army Research Office contract number DAAL03-89-C-0038).