All issues

A review of the problems of preparing accurate geometric models of steel ropes based on mathematical models without significant simplifications, taking into account the intended purpose of the model, is carried out. Possible approaches to the generation of precise geometric models of steel ropes that have no fundamental limitations on their integration in computational domains and the subsequent construction of finite element models based on them are shown. A generalized parameterized geometric model of single and double twist ropes and its algorithmic implementation using the OpenCASCADE Core Technology geometric modeling kernel in the Gmsh environment (open source software) is considered. The problems of using generic tabular data from steel rope assortment standards as initial data for constructing geometric models are considered. Methods of preliminary verification of collisions of a geometric model based on the initial data of a geometric model are given. Post-verification methods based on Boolean operations over rope wire bodies are given to identify incorrect results of generating models of wire bodies with curvilinear side surfaces based on the algorithm of sequential hierarchical construction of individual wires of single strand and sequential copying of it. Various methods of the process of constructing geometric models of rope wires by extrusion are shown: through a sequence of generatrix with the formation of a body limited by curvilinear surfaces, through a sequence of generatrix with the formation of a body limited by linearly approximated surfaces, and extrusion of one generatrix along a single guideline. The computational complexity of the geometric model generation and the required volume of RAM for the two most universal methods of creating a body of wire are investigated. A method for estimating the value of the step of the arrangement of the generatrix of a single wire is shown, and the influence of its value on the computational complexity of the procedure of wire construction is investigated. Recommendations are given for choosing the value of the radial gap between the layers of wires. An algorithmic implementation of the method for searching for collisions of a geometric model of a steel rope in a non-interactive mode is shown. Approaches to the formation of procedures for processing collisions are proposed. Approaches presented in the article can be implemented in the form of software modules for execution in the Gmsh environment, as well as for another environment using the OpenCascade Core Technology geometric modeling kernel. Such modules allow automation of the construction of accurate geometric models of steel ropes in any configuration without fundamental restrictions on subsequent use, both stand-alone and in the form of objects (primitives) suitable for integration in a third-party model.

In this paper a fluid flow between two close located rough surfaces depending on their location and discontinuity in contact areas is investigated. The area between surfaces is considered as the porous layer with the variable permeability, depending on roughness and closure of surfaces. For obtaining closure-permeability function, the flow on the small region of surfaces (100 $\mu$m) is modeled, for which the surfaces roughness profile created by fractal function of Weierstrass – Mandelbrot. The 3D-domain for this calculation fill out the area between valleys and peaks of two surfaces, located at some distance from each other. If the surfaces get closer, a contacts between roughness peaks will appears and it leads to the local discontinuities in the domain. For the assumed surfaces closure and boundary conditions the mass flow and pressure drop is calculated and based on that, permeability of the equivalent porous layer is evaluated.The calculation results of permeability obtained for set of surfaces closure were approximated by a polynom. This allows us to calculate the actual flow parameters in a thin layer of variable thickness, the length of which is much larger than the scale of the surface roughness. As an example, showing the application of this technique, flow in the gap between the billet and conical die in 3D-formulation is modeled. In this problem the permeability of an equivalent porous layer calculated for the condition of a linear decreased gap.

The article contains review of various estimation methods of combined extrusion process for the representative part, also analytical calculations and numerical simulation of this process using program DEFORM 3D. The comparative analysis of the results obtained by different methods was made. The assumptions of the main factors having a significant effect on the reliability of the results were formulated.

Flexible software for modeling polymeric film production by use of blown extrusion has been developed. It consists of library of mathematical models for extrusion and forming blown film, sub-system for changeover to new type of film and sub-system for investigation of extrusion and forming for film quality control under film production. The sub-system for changeover allows to choose the equipment of extrusion line on technical and economic indices, to synthesize 3D model of the line and to generate regulation ranges of regime parameters for given type of film. The sub-system for investigation allows to calculate temperature profiles of heating and cooling material, geometrical and optical characteristics of film depending on regime parameters for stages of extrusion and forming and to evaluate regime parameters ensuring given quality of polymeric film.