Parametric design of technological processes based on multidimensional geometric modelling

Abstract

A method of parametric design of technological processes has been developed based on the theory of multidimensional geometry using elements of parametrization, multidimensional computational geometry and geometric modelling. The method allows a technological process to be described by a hypersurface defined by a set of lines of one- or two-dimensional frames in a multidimensional complex plot. Its parameters are regarded as a certain set of points and lines of a space which is defined as an intersection of the frame lines by hyperplanes of a given level. The article proposes a computer implementation of the method which provides a solution to engineering problems with required accuracy. A geometric model of a thread stitching technological process has been obtained. The model allows to set a parameter range and determine the modes of obtaining compounds of a given quality in a wide range of possible solutions depending on the package of product materials, the number of process equipment parameters and process criteria.