One problem of the theory of dimensional electrochemical machining of metals

A method is proposed for determining the shape of the anode-article boundary for a given shape of the cathode-tool in plane problems of the theory of dimensional electrochemical machining of metals. Under the assumptions used, the boundary of the anode-article is divided into the working zone, where metal dissolution occurs, and an adjacent zone, where the treatment (dissolution) is terminated. The initial problem is reduced to a problem of a fictitious plane-parallel potential flow of an ideal fluid with a nonlinear condition on the free surface. The point of separation of the fictitious flow from the solid boundary corresponds to the point separating these two zones of the anode boundary. The Brillouin-Will condition of smooth separation is imposed at the separation point to construct a closed system of equations determining the problem solution. © AIK/Nauka 2009

Modeling of electrochemical machining with the use of a curvilinear electrode and a stepwise dependence of the current efficiency on the current density

© 2016, Pleiades Publishing, Ltd.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

MATHEMAТICAL SIMULAТION AND REALIZATION OF ЕСМ PROCESS OF DROP DIES

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One problem of the theory of dimensional electrochemical machining of metals

A method is proposed for determining the shape of the anode-article boundary for a given shape of the cathode-tool in plane problems of the theory of dimensional electrochemical machining of metals. Under the assumptions used, the boundary of the anode-article is divided into the working zone, where metal dissolution occurs, and an adjacent zone, where the treatment (dissolution) is terminated. The initial problem is reduced to a problem of a fictitious plane-parallel potential flow of an ideal fluid with a nonlinear condition on the free surface. The point of separation of the fictitious flow from the solid boundary corresponds to the point separating these two zones of the anode boundary. The Brillouin-Will condition of smooth separation is imposed at the separation point to construct a closed system of equations determining the problem solution. © AIK/Nauka 2009

One scheme of electrochemical machining of metals by a curvilinear electrode tool

The nonlinear plane problem of the evolution of the shape of the metal surface (anode) during electrochemical machining by a curvilinear cathode of symmetric shape is solved. A condition is obtained which allows one to determine the position of the point of transition from the zone of anodic metal dissolution to the region in which machining stops. © 2010 Springer Science+Business Media, Inc

Cavitation flow of an ideal incompressible fluid in the electrochemical machining of metals

© 2017 Elsevier Ltd The limiting simplest model of the non-linear two-dimensional problem of the electrochemical machining of metals taking account of the attached cavitation is constructed on the basis of a model of an ideal electrochemical shaping process and the theory of ideal incompressible fluid jets. A solution is obtained related to the determination of the steady shape of the surface of the component (anode) taking account of the cavity formed in the machining on the cathode tool boundary. The results of the calculations show that the model reflects the qualitative effects related to the effect of the added cavity on the shape of the machined component

Cavitation flow of an ideal incompressible fluid in the electrochemical machining of metals

© 2017 Elsevier Ltd The limiting simplest model of the non-linear two-dimensional problem of the electrochemical machining of metals taking account of the attached cavitation is constructed on the basis of a model of an ideal electrochemical shaping process and the theory of ideal incompressible fluid jets. A solution is obtained related to the determination of the steady shape of the surface of the component (anode) taking account of the cavity formed in the machining on the cathode tool boundary. The results of the calculations show that the model reflects the qualitative effects related to the effect of the added cavity on the shape of the machined component

Modeling of electrochemical machining with the use of a curvilinear electrode and a stepwise dependence of the current efficiency on the current density

© 2016, Pleiades Publishing, Ltd.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