The modication of statement of electrochemical formation problem is oered 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 eciency 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 denes 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 oered 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 eld strength on the anode surface are carried out.
The method of precision electrochemical machining is studied by using a model in which the current output has the form of a step function of current density. The problems of maximum stationary and quasistationary machining are formulated and solved, which made it possible to study the nonstationary process with sufficient accuracy.
The quasi-stationary problem for modelling the process of electrochemical cutting with a plate electrode-tool is formulated. The formulation of the problem is based on the use of a stepwise function of current efficiency from the current density. Thus three areas with various conditions are formed on the machined surface. The usual stationarity condition is used in the area of high current densities. In the area of low current densities the dissolution is absent and the initial form of the boundaries remains. In the intermediate zone, the current density at each point is equal to the critical value. The presence of boundary conditions on each section of the machined surface allows to formulate a boundary problem for the analytical function of the complex variable and to find the shape of the boundary at any moment, regardless of the background. The solutions of quasi-stationary and non-stationary problems are compared, and the range of existence of quasi-stationary solutions is found.
Self-similar (at preservation of geometrical similarity of borders) solutions of non-stationary Hele-Shaw problems in connection to an electrochemical shaping are considered. The problem of a flow about an arch of a circle on which the border condition for Zhukovsky’s function has the form similar to a boundary condition of a self-similar problem is used for the solution.
The problem of modeling of process of electrochemical machining of metal by means of a flat electrode tool is considered. Modeling of non-stationary process of formation of a ledge on metal billet is carried out taking into account variable function of a current efficiency. Application of a method of a filtration for estimation of machining parameters is described.
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