MATHEMATICAL MODEL OF TECHNOLOGICAL ASSEMBLY PROCESSES IN MACHINE-BUILDING AND REPAIR PRODUCTION

Abstract

In a logical representation, the technological process of assembling any mechanism or assembly, including the crank mechanism of the engine, can always be considered as one of the forms of displaying functional and constructive signs of searching for some objective function. (Research purpose) The research purpose is substantiating the effectiveness of original approaches to mathematical modeling of assembly processes in machine-building and repair industries. (Materials and methods) Conducted research using complete information about the modeling object as part of a unified system of mathematical modeling of assembly processes formed at the levels of abstraction of structure, logical and quantitative predicates. (Results and discussion) It has been shown that modern principles of mathematical modeling are based on the basic provisions of the theory of sets, graphs and mathematical logic. It was noted that of all the considered spaces of production systems describing assembly technological processes, the space of predicates of the mechanism and technological system is most closely related to the problem of ensuring a given accuracy of the closing link in a particular real dimensional chain. As a result of the assembly process, in general, parts or assemblies are transformed into a connected system of Cartesian bodies with a limited number of degrees of freedom. Mathematical modeling of assembly processes at the level of quantitative predicates is characterized by the least degree of response, but it gives a description in a more rigorous mathematical form that allows for a well-founded optimization of accuracy parameters and methods of performing technological techniques that provide unambiguous optimization. The applied value of modeling at the level of quantitative predicates is significantly higher than the description at the levels of structural and logical properties and relationships. (Conclusions) Mathematical modeling of assembly technological processes with a cybernetic approach at the levels of multiple, logical and quantitative predicates provides the best adequacy and applied significance in the case of building analytical models.