Geodesic
Stationary electrochemical machining simulation applying to precision technologies
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 10 (2017) no. 4, pp. 15-25

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The modification of statement of electrochemical formation problem is offered for mathematical modelling of the precision technologies. As an example the process of cutting with a plate electrode-tool is considered. For the description of the technologies with high localization of the processes a stepwise function of current efficiency is used. It realizes for simulation of the anode dissolution process in passivating electrolytes under short impulse current. This function determines the movement rate of the anode boundary in the areas of an active electrochemical dissolution and also it defines the boundaries of the areas where dissolution is absent. The stationary and limiting-stationary machining problems are formulated and solved on the base of the offered model. The limiting model describes the maximum localization process. The stationary problem is characterized by the presence of anode surface part, on which the current density is equal to a critical value. Investigations in the whole range of ratio of the maximal and critical values of electrical field strength on the anode surface are carried out.
Keywords: electrochemical shaping; stepwise function; process localization; stationary model. 
@article{VYURU_2017_10_4_a1,
     author = {V. P. Zhitnikov and N. M. Sherykhalina and S. S. Porechny},
     title = {Stationary electrochemical machining simulation applying to precision technologies},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matemati\v{c}eskoe modelirovanie i programmirovanie},
     pages = {15--25},
     publisher = {mathdoc},
     volume = {10},
     number = {4},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VYURU_2017_10_4_a1/}
}
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V. P. Zhitnikov; N. M. Sherykhalina; S. S. Porechny. Stationary electrochemical machining simulation applying to precision technologies. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 10 (2017) no. 4, pp. 15-25. http://geodesic.mathdoc.fr/item/VYURU_2017_10_4_a1/