Geometry Problems in Formalizing the Creation of Machining Processes on Machine Tools

Abstract

Introduction: The main problems hindering the creation of fully automatic systems of design of parts and technologies of their production are considered. The search for and formalization of regularities and relationships between the design parameters of parts and the technology of their production is an urgent task. At the same time, it has not yet been possible to create a unified general theory of geometric construction and transformation of objects at the macro level. Purpose: To show and formulate the key problems of formalizing the design process and identify possible ways to solve them. Methods: The study uses a wide range of methods of algebra, geometry, and discrete mathematics, as well as the main provisions of the geometry of non-ideal objects. Results: The need for fundamental laws of generation of geometric configurations and their elements is a key formalization problem. The geometry of non-ideal objects allows us to formally solve these problems. A geometric object is represented in six-dimensional space (three linear and three angular dimensions) with binary non-uniform metrics. The considered geometry has a principal possibility to formally generate geometric configurations of objects and their elements. The geometrical structure of a part is unambiguously connected with a set of technological schemes providing the mutual arrangement of surfaces during machining. Rules for the formal generation of a complete set of technological structures that are guaranteed to provide the specified parameters during the machining of parts. Conclusion: Sets of surfaces and relations between them define the individual structure of geometric configuration for each specific object. This individuality can be effectively used for the formal recognition of geometric objects. The geometry of non-ideal objects can serve as a fundamental basis for the formal theory of the creation of original technological processes of their processing.