Систематизация применений оператора параллельного переноса в моделировании плоских отсеков инструментальных поверхностей

Abstract

Рассматривается применение плоских отсеков как модулей моделей инструментальных поверхностей. Выполнен морфологический выбор элементарных представителей, образуемых действием оператора параллельного переноса, результаты которого визуализированы, математически описаны и поддержаны примером проектного использования. Представленный комплекс геометрических модулей и их математических описаний предлагается к многоотраслевому использованию в системах автоматизированного проектирования с инструментальной составляющей, ориентированных на обслуживание формообразующих машиностроительных и других технологий.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.