Фрактальная геометрическая модель микроповерхности

Abstract

The article is devoted to the construction of spatial
 model of microsuface module of copper alloy. A real surface has a
 characteristic roughness associated with the material creating technology,
 so knowing the geometric parameters of the surface microstructure
 is very important in studying properties such as microhardness,
 friction, aero- and gas-dynamic resistance and catalytic
 activity towards reactions of heterogeneous recombination of atoms
 in the active centers. To obtain qualitative data on the microsuface
 morphology, without imposing on the sample to stringent requirements,
 used a scanning tunneling microscope. Building a model
 creates a need to recreate the surface topology to study its geometrical
 properties, expressed through the fractal dimension. Such
 a simulation should help to study the interaction mechanism between
 molecules of a rarefied gas with the flying vehicle surface in the
 solution of gas dynamics problems associated with heat and mass
 transfer. In MathCAD the calculation of geometric characteristics
 of a spatial model from the standpoint of the fractal theory for the
 formation of geometrical shapes and GOST 2789-73 requirements
 to control their numerical parameters. The example of procedural
 (algorithmic) construction of geometrical model equivalent to the
 real is given. It is shown that with sufficient for practical applications
 accuracy the surface topology can be described by the fractal
 patterns that take into account irregularities, both at the micro and
 nanoscale. The proposed algorithm makes it possible to broadcast
 a method of creating a fractal structure at any detail level.
 Its positive and negative features based on the midpoint displacement
 modernized algorithm use are noted. The algorithm
 correctness for modeling the other materials surfaces geometry is
 shown.