Abstract
An analytical solution of the problem of electrochemical machining of metals by a curvilinear cathode tool with allowance for a discontinuous function that describes the dependence of the current efficiency on the current density is obtained. According to the hydrodynamic interpretation, the original problem reduces to the problem of the theory of ideal fluid flows with a free surface. It is demonstrated that the use of the proposed dependence of the current efficiency on the current density ensures the existence of three domains on an unknown treated surface; these domains have different laws of the distribution of the charge fraction spent on metal dissolution. Results calculated for various particular cases are presented.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
A. D. Davydov and E. Kozak, High-Velocity Electrochemical Machining (Nauka, Moscow, 1990) [in Russian].
V. P. Zhitnikov and A. N. Zaitsev, Pulsed Electrochemical Machining (Mashinostroenie, Moscow, 2008) [in Russian].
V. P. Zhitnikov, E. M. Oshmarina, and G. I. Fedorova, “Using Discontinuous Functions for Modeling Dissolution during Steady-State Electrochemical Machining,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 10, 77–81 (2010).
L. M. Kotlyar and N. M. Minazetdinov, “Evolution of the Shape of the Anode Boundary under Electrochemical Dimensional Machining of Metals,” Prikl. Mekh. Tekh. Fiz. 44 (3), 179–184 (2003) [J. Appl. Mech. Tech. Phys. 44 (3), 461–465 (2003)].
F. V. Sedykin, B. P. Orlov, and V. F. Matasov, “Investigation of the Anode Current Efficiency with Continuous and Pulsed Voltages,” Tekhnol. Mashinostr., No. 39, 3–7 (1975).
N. M. Minazetdinov, “One Problem of Electrochemical Machining of Metals with Allowance for Variability of the Current Efficiency for Anode Shaping Reactions,” Vestn. Ufim. Gos. Aviats. Univ. 16 (5), 154–159 (2012).
N. M. Minazetdinov, One Scheme of Electrochemical Machining of Metals by a Curvilinear Electrode Tool, Prikl. Mekh. Tekh. Fiz. 51 (2), 170–175 (2010) [J. Appl. Mech. Tech. Phys. 51 (2), 288–292 (2010)].
V. V. Klokov, Electrochemical Machining (Izd. Kazan. Univ., Kazan, 1984) [in Russian].
G. Birkhoff and E. Zarantonello, Jets, Wakes and Cavities (Academic Press, New York, 1957).
M. I. Gurevich, Theory of Ideal Fluid Jets (Nauka, Moscow, 1979) [in Russian].
M. A. Lavrent’ev and B. V. Shabat, Methods of the Theory of Complex Variable Functions (Nauka, Moscow, 1987) [in Russian].
E. T. Whitaker and J. H. Watson, A Course of Modern Analysis (Cambridge University Press, Cambridge, 1940).
L. M. Kotlyar, “One Case of an Ideal Fluid Jet Flow,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 2, 101–104 (1976).
L. M. Kotlyar and E. V. Skvortsov, Plane Steady-State Problems for a Fluid with an Initial gradient (Izd. Kazan. Univ., Kazan, 1979) [in Russian].
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © L.M. Kotlyar, N.M. Minazetdinov.
Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 57, No. 1, pp. 146–155, January–February, 2016. Original article submitted July 21, 2014.
Rights and permissions
About this article
Cite this article
Kotlyar, L.M., Minazetdinov, N.M. Modeling of electrochemical machining with the use of a curvilinear electrode and a stepwise dependence of the current efficiency on the current density. J Appl Mech Tech Phy 57, 127–135 (2016). https://doi.org/10.1134/S0021894416010144
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0021894416010144