MODELLING OF LIMIT STATIONARY PROCESS OF THE ELECTROCHEMICAL AXISYMMETRIC SHAPING

The method of definition of a form of the machining surface (anode) by an electrode tool (cathode) is offered when modeling a limit-stationary electrochemical shaping. The problem is reduced to the solution of a boundary problem for definition of two analytical functions of the complex variable. The first function makes conformal mapping of region of parametrical variable on the physical plane. For its determination Schwartz's integral and a spline interpolation are used. For determination of potential and stream function of an axisymmetric field integration transformations of the second analytical function are used. Analytical function is defined in the form of the sum of two addends. The first addend considers singularities of function so that the second had no singularities. The second function is defined by Schwartz's integral. Interpolation by spline functions is made, thus coefficients of splines are derivatives of these functions by means of which strength vector components are calculated. The limit-stationary axisymmetric problem is solved by method of collocations. It is shown that in the limit-stationary mode on the machined surface two zones are formed: a workpiece material dissolution zone with constant value of the module of intensity of electric field and a zone of lack of dissolution where the module of intensity is less than critical value. Results of the numerical solution are presented. The error estimation of the obtained results is carried out. The comparison with results of the solution of a plane problem is carried out, which showed qualitative coincidence of them.

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