Systematization of applications of the operator of parallel transport in modeling of flat compartments of tool surfaces
DOI:
https://doi.org/10.15587/2312-8372.2015.51279Keywords:
tool surface, modeling, multi-parameter mappings, operator of parallel transport, flat compartment, systematizationAbstract
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.References
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Copyright (c) 2016 Нина Викторовна Зубкова, Татьяна Евгеньевна Третяк, Юрий Григорьевич Гуцаленко
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