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The article is devoted to the development of an approach to improving the electroplating uniformity on the cathode surface, rotating around its axis, using a figured anode. A mathematical model of a stationary process with distributed coordinates, based on the equations of theoretical electrochemistry, has been developed for this approach. The problem for optimizing the anode shape according to the criterion for minimizing the non-uniformity of the deposited coating on the rotating cathode is formulated. The results of solving this problem are demonstrated on the example of the Zinc plating. Possible improvements to improve the accuracy of the calculation results for the developed mathematical model are given in the conclusion of the article.

Abstract. The paper presents the main factors that affect the uniformity of the thickness distribution of plating on the surface of the product. The experimental search for the optimal values of these factors is expensive and time-consuming. The problem of adequate simulation of coating processes is very relevant. The finite-difference approximation using seven-point and five-point templates in combination with the splitting method is considered as solution methods for the equations of the model. To study the correctness of the solution of equations of the mathematical model by these methods, the experiments were conducted on plating with a flat anode and cathode, which relative position was not changed in the bath. The studies have shown that the solution using the splitting method was up to 1.5 times faster, but it did not give adequate results due to the geometric features of the task under the given boundary conditions. IntroductionGalvanic coatings are applied for improving the surface's wear resistance, for protection against corrosion and for giving the product's presentation. The plating quality has a very strong influence on the operating characteristics of the finished products. Reducing unevenness plating is difficult due to different scattering ability of the electrolyte and the «boundary effect» [1]. Uneven thickness of the coating layer can lead to such negative factors as defects, an increase in power consumption and metal. Also subsequent mechanical processing of the finished product can be required. Technological and constructive factors influence the quality of galvanic coatings. Articles [2-4] study the influence on technological factors (such as current density, temperature, acidity and concentration of electrolyte components), on the quality of the plating. In articles [5,6], authors solved problems of searching a non-conductive screens' position and the number of additional anodes. As a rule, these problems are solved experimentally. However, the high cost of electrolytes, metals and energy does not allow numerous experiments. Mathematical modeling of electroplating processes is the way out. An important question, which arose after the formation of the equations of the mathematical model, is the choice of the solution methods. This is especially true in the case of using differential equations in partial derivatives.The aim of this work is studying the correctness using two variants of the implicit grid method (with seven-point and five-point templates in combination with the splitting method) for solving differential equations in partial derivatives of mathematical models of plating processes.

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