Geometry of real objects in shipbuilding and ship repair

Abstract

The article considers the modern engineering practice of designing and manufacturing that uses various analytical and graphic forms representing geometric objects. Both of these forms are characterized by the presence of two problems in terms of production practice: 1 - tools of modern geometry cannot operate with non-ideal forms and configurations of material objects; 2 - lack of methods and tools for describing patterns of generating geometric objects, from production lines to the structure that characterizes the relative location of surfaces. The generalized provisions of the geometry of non-ideal objects theoretically justified for formal synthesis and their elements have been presented, which avoids problems of geometric configuration in the practice of designing and developing manufacturing technologies in shipbuilding and ship repair. A special toolkit based on discrete mathematics is proposed for the formal description of the geometric configuration of non-ideal objects. The principles of geometry of real objects describe the structural-parametric representation of objects in a six-dimensional space that is defined by linear and angular vectors. The concepts of linear and angular vectors are analyzed. It has been stated that the presence of an angular vector simplifies the perception and makes easier calculating the processes of geometric transformations. A geometrical object refers to a closed subspace bounded by a single surface, a set of mating or intersecting surfaces. The examples of the real plane deviations from its reference, location of the planes for creating the ideal geometric configuration, variants of real images, forming the basis for six-dimensional space, structure of geometric configurations have been illustrated. It has been found that any specific part acting as a geometric object can be represented by a set of surfaces and the structure of their relationships, which contributes to the correctness of its manufacture. The use of six-dimensional space allows to describe the spatial geometric configurations of parts of various mechanisms with mathematical accuracy.