Systematization of applications of the operator of parallel transport in modeling of flat compartments of tool surfaces

Authors

  • Нина Викторовна Зубкова National Technical University «Kharkiv Polytechnic Institute», 21, Frunze Str., Kharkiv, Ukraine, 61002, Ukraine https://orcid.org/0000-0001-8200-7924
  • Татьяна Евгеньевна Третяк National Technical University «Kharkiv Polytechnic Institute», 21, Frunze Str., Kharkiv, Ukraine, 61002, Ukraine https://orcid.org/0000-0003-4429-7072
  • Юрий Григорьевич Гуцаленко National Technical University «Kharkiv Polytechnic Institute», 21, Frunze Str., Kharkiv, Ukraine, 61002, Ukraine https://orcid.org/0000-0001-6571-5363

DOI:

https://doi.org/10.15587/2312-8372.2015.51279

Keywords:

tool surface, modeling, multi-parameter mappings, operator of parallel transport, flat compartment, systematization

Abstract

The application of the flat compartments as modules of the models of tool surfaces for machine-building and other purpose in industries with the shape-generating technologies has been considered. The main purpose of the study is allocation and systematization the basic typical elementary flat compartments of tool surfaces, the use of which by means of the operator of parallel transport allows to reproduce virtually any of them. The application of the theory of multi-parameter affine mappings of the space and some of the results of our research in the direction of its applied unification have been discussed in this paper. A systematic morphological selection of elementary flat compartments of tool surfaces formed by the action of the operator of parallel transport, the results of which are visualized and mathematically described, was made in this paper. The methodical example of the practical application of development is being shown. The presented complex of geometric modules and their mathematical descriptions is being offered for a diversified use in computer-aided design to development with tool component, service-oriented to shape-generating machine-building and other technologies. The proposed system of flat compartments formed by the action of the operator of parallel transport allows to perform modeling of tool production objects of any complexity, from a flat in planning application to a complex profile shape-generating edge in manufacture of turbine blade.

Author Biographies

Нина Викторовна Зубкова, National Technical University «Kharkiv Polytechnic Institute», 21, Frunze Str., Kharkiv, Ukraine, 61002

Candidate of Technical Sciences, Associate Professor

Department of the Mechanical Engineering Integrated Technologies named after M. F. Semko

Татьяна Евгеньевна Третяк, National Technical University «Kharkiv Polytechnic Institute», 21, Frunze Str., Kharkiv, Ukraine, 61002

Senior Lecturer

Department of the Mechanical Engineering Integrated Technologies named after M. F. Semko

Юрий Григорьевич Гуцаленко, National Technical University «Kharkiv Polytechnic Institute», 21, Frunze Str., Kharkiv, Ukraine, 61002

Senior Researcher

Department of the Mechanical Engineering Integrated Technologies named after M. F. Semko

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Published

2015-09-22

How to Cite

Зубкова, Н. В., Третяк, Т. Е., & Гуцаленко, Ю. Г. (2015). Systematization of applications of the operator of parallel transport in modeling of flat compartments of tool surfaces. Technology Audit and Production Reserves, 5(7(25), 48–51. https://doi.org/10.15587/2312-8372.2015.51279

Issue

Vol. 5 No. 7(25) (2015): Fundamental and applied researches: integration into the world scientometric databases

Section

Mechanical Engineering Technology: Original Research

License

Copyright (c) 2016 Нина Викторовна Зубкова, Татьяна Евгеньевна Третяк, Юрий Григорьевич Гуцаленко

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