ПРОГРЕССИВНЫЕ ТЕХНОЛОГИИ В МАШИНОСТРОЕНИИ THE ADVANCED TECHNOLOGIES IN MECHANICAL ENGINEERING УДК 658.512 ON SOME METHODS OF FORMALIZATION OF APPROACHES TO TECHNOLOGICAL OPERATIONS DESIGN This paper considers several approaches to and variants of descriptions of technological operations (TO) design, and a range of methods for formalization of these approaches and descriptions. <...> The paper presents a mathematical interpretation of technological operations via base set (BS) elements, which includes revealing and defining the TO extrinsic properties and their intrinsic construction with the use of (X) parameters. <...> The operations are divided (structured) in accordance with decomposition of a functional model properties, and then G-type criteria are formed which allows to describe the mapping relation of the TO subject and its transfer function FnM (TO) product, or by lexicographical means for approach to automated design etc. <...> Keywords: technological operation, base set elements, decomposition of properties, functional model, automated design. <...> Manufacturing TO design is usually performed with the use of both technical, manufacturing and empirical presentations of an object. <...> The environment is a system, which is extrinsic to the object and has a particular set of properties. <...> The condition of the environment for each specific object shall be characterized by a vector Z. By a design object we understand an artificial material object which must be manufactured for solving a specific problem and which is characterized by a sum total of extrinsic Y and X properties. <...> By a model М(О) in the signature (the signature is M2 , ., Мk ) , (r1 , r2 model; аа — is an injective mapping, which puts each name (unique name, identifier) in correspondence with a relation Rn understood as a set of identifiers (names) of the relations which are part of a model, together with additional information on their location) WW we designate the pair Мббаасс, where М = {Mi }k — is a base set of a from the signature WW, relation rn corresponding location [1]. 136 Проблемы машиностроения и автоматизации, № 3 – 2008 of the manufacturing object models М(О) can be defined as sets (M1 ) with given sets of named and, , r2 , , ., (М1 , М2 values of their elements can be directly interpreted with regard to the subject either as the values of extrinsic or intrinsic properties of a TO, or the values of properties of the operation environment, or properties <...>