Geodesic
Quasi-stationary solution of a problem of electrochemical copying of a cogged surface
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2017), pp. 86-91.

Voir la notice de l'article provenant de la source Math-Net.Ru

We solve a problem of modeling of non-stationary electrochemical machining by an electrode-tool with cogged surface form. For modeling of process of anode dissolution we use the step function of a current efficiency. We find an exact (in quadratures) solution of a problem and obtain numerical results allowing to define a form of the processed surface in various moments of time.
Keywords: non-stationarity, current efficiency, step function. 
@article{IVM_2017_8_a8,
     author = {V. P. Zhitnikov and N. M. Sherykhalina and A. A. Zaripov and A. A. Sokolova},
     title = {Quasi-stationary solution of a problem of electrochemical copying of a cogged surface},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {86--91},
     publisher = {mathdoc},
     number = {8},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2017_8_a8/}
}
TY  - JOUR
AU  - V. P. Zhitnikov
AU  - N. M. Sherykhalina
AU  - A. A. Zaripov
AU  - A. A. Sokolova
TI  - Quasi-stationary solution of a problem of electrochemical copying of a cogged surface
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2017
SP  - 86
EP  - 91
IS  - 8
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2017_8_a8/
LA  - ru
ID  - IVM_2017_8_a8
ER  - 
%0 Journal Article
%A V. P. Zhitnikov
%A N. M. Sherykhalina
%A A. A. Zaripov
%A A. A. Sokolova
%T Quasi-stationary solution of a problem of electrochemical copying of a cogged surface
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2017
%P 86-91
%N 8
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2017_8_a8/
%G ru
%F IVM_2017_8_a8
V. P. Zhitnikov; N. M. Sherykhalina; A. A. Zaripov; A. A. Sokolova. Quasi-stationary solution of a problem of electrochemical copying of a cogged surface. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2017), pp. 86-91. http://geodesic.mathdoc.fr/item/IVM_2017_8_a8/

[1] Klokov V. V., Elektrokhimicheskoe formoobrazovanie, Izd-vo Kazansk. un-ta, Kazan, 1984

[2] Zhitnikov V. P., Oshmarina E. M., Fedorova G. I., “Ispolzovanie razryvnykh funktsii dlya modelirovaniya rastvoreniya pri statsionarnom elektrokhimicheskom formoobrazovanii”, Izv. vuzov. Matem., 2010, no. 10, 77–81

[3] Zhitnikov V. P., Oshmarina E. M., Fedorova G. I., “Tochnye resheniya dvukh zadach predelnogo kvazistatsionarnogo elektrokhimicheskogo formoobrazovaniya”, Izv. vuzov. Matem., 2011, no. 12, 21–29

[4] Zhitnikov V. P., Zaitsev A. N., Impulsnaya elektrokhimicheskaya razmernaya obrabotka, Mashinostroenie, M., 2007

[5] Muksimova R. R., Zhitnikov V. P., Sherykhalina N. M., Zaripov A. A., “Modelirovanie statsionarnogo i predelnogo elektrokhimicheskogo formoobrazovaniya v yacheike konechnoi shiriny”, Vestn. SPbGU GA, 2016, no. 4(13), 117—128