Информационные технологии интеллектуальной поддержки принятия решений, Информационные технологии интеллектуальной поддержки принятия решений 2018

Размер шрифта: 
The application of jump-like function of current efficiency for simulation of non-stationary electrochemical formation
K. O. Sherykhalin, A. A. Sokolova

Изменена: 2019-11-02


In the numerical solution, the problem of modeling nonstationary formation is reduced to the solution of three boundary problems for determining of analytic functions of a complex variable at each time step: a conformal mapping of parametric variable domain onto the physical plane, the Dirichlet problem for determining the electric field strength and the Riemann-Hilbert problem from the calculation of partial derivatives with respect to time coordinates of the points of the interelectrode space (images of points on the boundary of the parametric plane are fixed). The integral transformations of analytic function are used to determine the strength in contrast to the plane problem. The spline functions approximation is realized, the algorithms for general solution of nonstationary axisymmetric problems are described, which are differ from the known ones taking into account the jump of the dependence of the current efficiency on the current density. The results of a numerical investigation of stationary configurations are presented.

Ключевые слова

jump-like function; simulation; non-stationary electrochemical formation


1.            Zhitnikov V.P., Zaytsev A.N. “Pulse electrochemical dimensional machining”. Mashinistroenie, Мoscow, 2008.

2.            Zhitnikov V.P., Zinnatullina O.R., Oshmarina E.M., Fedorova G.I. “Electrochemical formation simulation for restriction on dissolution”. Scientific-technical bulletin of SPb polytechnic Univ. Saint-Petersburg. 2009, 4 (82): 221-224.

3.            Zhitnikov V.P., Oshmarina E.M., Fedorova G.I. “The use of discontinuous functions for modeling the dissolution process of steady-state electrochemical shaping”. Russian Mathematics. 2010, 54 (10): 67-70.

4.            Zhitnikov V.P., Sherykhalina N.M., Porechny S.S. “Stationary electrochemical machining simulation applying to precision technologies” Bulletin of the South Ural State University. Ser. Mathematical Modelling, Programming & Computer Software (Bulletin SUSU MMCS, Chelyabinsk, Russia). 2017, 10 (4): 15-25.

5.            Pology G.N. “Generalization of the theory of analytic functions of a complex variable”. Kiev Univ:, Kiev, 1965.

6.            Sherykhalina N.M., Zinnatullina O.R., Sokolova A.A. “Simulation of stationary process of electrochemical axisymmetric formation by point tool-electrode”.The progress of modern science. Belgorod. 2017,. 2 (8): 137-144.

7.            Zhitnikov V.P., Zinnatullina O.R., Porechny S.S., Sherykhalina N.M. “Determining the limiting solutions of nonstationary axisymmetric Hele-Shaw problems”. Journal of Applied Mechanics and Technical Physics, 2009,. 50 (4): 617-627.

8.            Polubarinova-Kochina P.Y. “Nonstationary moving at filtration theory”. Applied Mathematics and mechanics,. 1945, 9: 79-90.

9.            Galin L.A. “Nonstationary filtration with free boundaries”. DAN USSR, 1945, 47: 246-249.

10.          Zhitnikov V.P., Sherykhalina N.M., Zaripov A.A. “Modelling of precision steady-state and non-steady-state electrochemical machining by wire electrode-tool”. Journal of Materials Processing Technology, 2016, 235: 49-54.