OBRABOTKAMETALLOV Vol. 23 No. 3 2021 MATERIAL SCIENCE EQUIPMENT. INSTRUMENTS 6 2 4 Research methodology Theoretical studies are carried out using the basic principles of system analysis, geometric theory of surface formation, cutting tool design, graph theory, mathematical and computer simulation. The selection of wheels for a manufacturing process takes place in several stages: selection of the abrasive material according to the task; search for the required type of wheel profile, taking into account its industrial purpose; development of a new design of modular grinding wheel. Achieving the required surface quality and productivity in the grinding process depends largely on the wheel used and its characteristics: the combination of machining and abrasive materials, dimensions, wheel design features, as well as the machining conditions and modes. Each of the characteristics described above is important in its own way and has an impact on the machining process. The choice of abrasive material and the determination of the optimum grit size also have an important influence on the grinding process and the achievement of the required product quality parameters. At the same time, it is important to maintain the high productivity of the grinding process [47–49]. The use of simulation in the design solution provides an opportunity to perform tool selection and analysis at various stages of design, as well as process and tool preparation in production. We have developed a simulation technique based on graphic modeling theory in order to effectively solve the tasks set. We have studied the existing designs of modular grinding wheels to solve the problem described above. The types of the abrasive part, the methods of fastening the abrasive cutting part on the body of the wheel, the materials used to manufacture the body, the characteristics of the body of the wheel and the fastening schemes were analyzed [50]. As a result of the analysis of existing wheel designs, the key structural elements are identified that make it possible to describe the design of the grinding wheel. The description of the abrasive part of the grinding wheel is based on the following elements: the design of the abrasive part (solid or segmented); the dimensional characteristics of the abrasive part, which determine the size and accuracy of the production of grinding elements; the abrasive material; the hardness of the wheel; the grit size; the bond; the shape of the elements and its quantity. The body part is defined by the type of its profile; dimensional parameters; material composition (such as steel or aluminum alloys); the presence or absence of coating. The fastening part is characterized by the method of fastening, which encompasses the type of connection of the abrasive part with the body part; the presence or absence of adjusting and fastening screws; its quantity and dimensional parameters. Furthermore, the model contains data about the intended purpose of the wheel; unbalance class; accuracy class; maximum speed; manufacturer information. The data analyzed has been used to construct a generalized graph-based model of modular grinding tool designs. This model contains all the constituent components that are included in the designs of various modular grinding wheels and displays the conditional constructive relationship. The grinding wheel design is a system of separate parts of the wheel design, or interconnected components, and is represented as an oriented graph. ( ) = , G Χ Ε , where X are vertices; E is an illustration of the set X in X or the relationship between the vertices of the graph (represented by connection lines). The relationship between the wheel elements and its characteristics is shown by vertex-edge connections {X1, lx1}, {X2, lx2}, ... etc. Each edge of a connected graph is a set of vertices, which is described by a subset of vertices and a subset of edges. An edge of a graph li is a set of vertices of a graph li Xi and simultaneously consists of elements X1, X2,...Xn, which can also be sets (Fig. 1). Thus 1 n i i i l X = = .
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