Modeling of process of copying of a ledge form on an electrode-tool at electrochemical machining

2012 ◽  
Vol 9 (2) ◽  
pp. 95-100
Author(s):  
R.R. Muksimova
Keyword(s):  
Conformal Mapping ◽  
Numerical Solution ◽  
Complex Variable ◽  
Electrochemical Machining ◽  
Interelectrode Space ◽  
Electrode Tool ◽  
Boundary Problems ◽  
Analytical Functions ◽  
Definition Of ◽  
Electrochemical Shaping

Problems of modeling of a non-stationary electrochemical shaping are reduced to the solution of two boundary problems for definition of analytical functions of the complex variable: conformal mapping of the parametrical plane on physical and partial derivatives on time of interelectrode space points coordinates. Each of functions is obtained in the form of the sum of known function with singularities and two unknown functions defined by Schwartz or Keldysh – Sedov's formulas. One of unknown functions is intended for the description of a form of an electrode-tool, the second – the processed surface. Results of the numerical solution of problems with an electrode in the form of a circle and a plate are presented.

Investigation of solutions of non-stationary Hele-Shaw problems by means of a numerical filtration

2008 ◽  
Vol 6 ◽  
pp. 68-74
Author(s):  
V.P. Zhitnikov ◽  
O.R. Zinnatullina ◽  
G.I. Fedorova
Keyword(s):  
Variable Region ◽  
Physical Plane ◽  
Time Step ◽  
Boundary Problems ◽  
Analytical Functions ◽  
Definition Of ◽  
Points Approximation ◽  
Dirichlet’S Problem ◽  
Stationary Problems

The problem on each time step is reduced to the solution of three boundary problems for definition of analytical functions of complex variable: conformal mapping of parametric variable region on the physical plane, Dirichlet's problem for determination of intensity of electric field and Riemann – Hilbert's problem for calculation of partial derivatives on time of coordinates of interelectrode space points. Approximation by spline functions is made, the algorithms of the solution of non-stationary problems differing from known by the accuracy and stability are described. Results of the numerical solution are represented.

Numerical treatment of a singularity in a free boundary problem

1972 ◽  
Vol 330 (1583) ◽  
pp. 573-580 ◽  
Keyword(s):  
Free Boundary ◽  
Numerical Solution ◽  
Boundary Problem ◽  
Free Boundary Problem ◽  
Complex Variable ◽  
Free Boundary Problems ◽  
Separation Point ◽  
Free Boundaries ◽  
Boundary Problems ◽  
A Free Boundary Problem

The numerical solution of free boundary problems gives rise to many computational difficulties. One such difficulty is due to the singularity at the separation point between the fixed and free boundaries. A method is suggested which uses complex variable techniques to determine the shape of the free boundary near to the separation point. This complex variable solution is also used to improve the accuracy of the finite-difference solution in the neighbourhood of the singularity. The analytical study was incorporated into an algorithm for the numerical solution of a particular free boundary problem concerning the percolation of a fluid through a porous dam. Some numerical results for this problem are presented.

scholarly journals Selected Aspects of Electrochemical Micromachining Technology Development

Materials ◽  
2021 ◽  
Vol 14 (9) ◽  
pp. 2248
Author(s):  
Sebastian Skoczypiec ◽  
Piotr Lipiec ◽  
Wojciech Bizoń ◽  
Dominik Wyszyński
Keyword(s):  
Technology Development ◽  
Electrochemical Machining ◽  
Electrochemical Micromachining ◽  
Cylindrical Electrode ◽  
Electrode Tool ◽  
Geometrical Features ◽  
Tool Trajectory ◽  
Scaling Down ◽  
Sidewall Surface ◽  
Selection Of

The paper focuses on the fundamentals of electrochemical machining technology de-elopement with special attention to applications for micromachining. In this method, a material is removed during an anodic electrochemical dissolution. The method has a number of features which make it attractive technology for shaping parts with geometrical features in range of micrometres. The paper is divided into two parts. The first one covers discussion on: general characteristics of electrochemical machining, phenomena in the gap, problems resulting from scaling down the process and electrochemical micromachining processes and variants. The second part consists of synthetic overview of the authors’ research on localization of pulse electrochemical micromachining process and case studies connected with application of this method with use of universal cylindrical electrode-tool for shaping cavities in 1.4301 stainless steel. The latter application was conducted in two following variants: electrochemical contour milling and shaping carried out with sidewall surface of rotating tool. In both cases, the obtained shape is a function of electrode tool trajectory. Selection of adequate machining strategy allows to obtain desired shape and quality.

scholarly journals Conformal mapping of the Misner–Sharp mass from gravitational collapse

2016 ◽  
Vol 25 (07) ◽  
pp. 1650081 ◽  
Author(s):  
Fayçal Hammad
Keyword(s):  
Conformal Mapping ◽  
Gravitational Collapse ◽  
Conformal Transformation ◽  
Conformal Mappings ◽  
Conformal Transformations ◽  
Theories Of Gravity ◽  
Definition Of ◽  
Geometric Definition

The conformal transformation of the Misner–Sharp mass is reexamined. It has recently been found that this mass does not transform like usual masses do under conformal mappings of spacetime. We show that when it comes to conformal transformations, the widely used geometric definition of the Misner–Sharp mass is fundamentally different from the original conception of the latter. Indeed, when working within the full hydrodynamic setup that gave rise to that mass, i.e. the physics of gravitational collapse, the familiar conformal transformation of a usual mass is recovered. The case of scalar–tensor theories of gravity is also examined.

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