Abstract
In this paper, the objective is to derive the variational formulation of the electrochemical machining problem (ECM for short) and to evaluate the numerical solution using the direction Ritz method. This problem is of degenerate problem which has so many difficulties to be solved using other approach. 1. Introducation As an alternative to definition to mechanical machining problem, a piece of metal can sometimes be shaped by using it as an anode in electrolytic cell with an appropriately shaped cathode. This represent a moving boundary value problem, because the anode surface is moved toward the cathode at constant velocity, and products of the erosion of the anode are swept away by the electrolytes, which is pumped through the space between the electrodes, [12]. 2. The mathematical model of the problem The two dimensional ECM problem will be considered for two electrodes shown in Fig. (1). the space between the electrodes is filled by an appropriate electrolyte. A voltage is placed across the electrodes and these causes are removal of material from the anode, [5]. We will solve equation ECM of an anode surrounded by circular cathode, the conductivity in the gap between the electrodes is considered constant [5]. This problem is formally identical to one-phase Stefan problem with zero heat capacity [13].
Published Version
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