The algorithm of transformation of polygonal models to simplify the calculation of galvanic processes


DOI: 10.34759/trd-2022-127-24

Аuthors

Lazeev A. S.*, Litovka Y. V.**

Tambov State Technical University, 106, Sovetskaya, Tambov, 392000, Russia

*e-mail: a.lazzeev@mail.ru
**e-mail: polychem@list.ru

Abstract

Electrochemical coatings provide special properties of the surface of the parts. In the aircraft industry, electroplating coatings are widely used to protect against corrosion and increase the wear resistance of steel and aluminum parts.

Efficient specification of the shape of a part in automated control systems for galvanic processes can be organized by exporting drawings for subsequent software processing where complex mathematical calculations associated with surfaces are not required. To solve problems that require complex calculations, various polygonal meshes are divided into simpler shapes. An algorithm for calculating the electric field in a galvanic electrolyte is presented, and the need for a mathematical description of the cathode surface to set the boundary conditions is shown. The paper considers the issues of creating algorithms for converting three-dimensional polygonal models into voxel format to reduce computational complexity, which is estimated by indicators: the time of the algorithm and the amount of memory occupied. The algorithm for converting a polygonal model into a voxel model has the form:

  • the octal tree for the model is being built;
  • all non-empty vertices of the octal tree are bypassed, each of them is divided into a grid and then a request is made for each cell to enter the polygon into the cell. Bypassing only filled vertices allows you to reduce the constant with computational complexity.

When comparing the most productive «naive» algorithm, which has complexity O(n(1/h)3) with the algorithm developed in this article, which has complexity O((log n)∙(1/h)3), an increase in efficiency up to four hundred thousand times.

The resulting geometric mathematical model reduces the search time for optimal parameters of the galvanic cell, especially when using modern effective optimization methods.


Keywords:

vibration, vibration diagnostics, spectral analysis, production of blanks, crystallization, non-destructive

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