The Geometry of Non-ideal Objects in Process Engineering for Processing Parts on Machine Tools

Abstract

AbstractThe paper discusses creating the theoretical background and formal techniques for the synthesis of technology for the geometric configuration of a part, which is a key problem in the development of modern CAPP systems. At the theoretical level, identifying the relationship between the design (geometry) of the part and the technology of its manufacture is important. Studies have shown that the modern tools of traditional geometry have two problems leading to the impossibility of describing the geometric structure of real machine parts. The first one is the inability to operate with non-ideal forms and configurations of material objects. The second problem is the use of already existing objects, regardless of their geometric configuration building scheme. The Geometry of Non-ideal Objects proposed by the authors solves these problems since it allows describing not only the composition (surfaces) but also the structure (dimensional relationships) of real geometric configurations in six-dimensional space. The paper shows a formal relationship between the real part design and a set of its processing technologies in the six-dimensional space.KeywordsGeometryNon-ideal objectsGeometric configurationsProcess engineeringManufacturing technologyMetal-cutting machine tools