OBRABOTKAMETALLOV MATERIAL SCIENCE Том 23 № 3 2021 EQUIPMEN . INSTRUM TS Vol. 4 No. 1 2022 Introduction The development of science and technology sets the task of wide application in the designs of products of electrical engineering, instrumentation engineering, nuclear energy, rocket science, aircraft engineering, space technology, medicine and, more recently, in general engineering, new materials, which are subject to increased requirements for heat resistance, wear resistance, corrosion resistance and chemical resistance. Industrial enterprises are faced with the challenges of effi cient processing of the above materials. In the context of the development of a market economy, the most important factor in the success of an enterprise is the creation of technological processes that ensure the satisfaction of consumer needs. These include reducing the cost of manufacturing range while ensuring high performance characteristics of products, increasing the productivity of creating products with desired properties, for example, in the production of a friction pair, it is necessary to technologically ensure the optimal structure of the surface layer of the working surfaces of parts in the shortest possible time, creating a surface microrelief at the stage of machining parts close to equilibrium. This approach will reduce the running-in stage of the friction pair and increase its service life [1]. An analysis of existing research in the fi eld of material processing shows that, despite the presence of a large number of high-precision processing methods, such as ultrasonic, laser, high-speed milling, and others, grinding remains the most used and effi cient method in the manufacture of high-precision parts [2–6]. Grinding remains the most effi cient and effective method of fi nal fi nishing that is indispensable in the production of high-precision parts. The characteristic features of grinding materials are that the removal of the material roughness of the workpiece surface occurs due to the stochastic interaction of the grains of the abrasive material with the surface of the workpiece, in the presence of mutual oscillatory movements of the abrasive tool and the workpiece being processed. Considerable attention is paid to the study of grinding processes in the works of A.I. Grabchenko, V.L. Dobroskoka, V.I. Kalchenko, F.N. Novikova, M.D. Uzunyan, V.A. Fedorovich, L.N. Filimonova, A.V. Yakimov and other authors who, using various statistical and probabilistic methods, obtained calculated dependencies in relation to specifi c grinding schemes and conditions. The authors have shown that any conclusions about the number of working grains, about its percentage with grains on the surface of the wheel can have real meaning only in relation to specifi c conditions inherent in this process, which is associated with the nonstationarity of grinding operations. The fi rst mathematical models of abrasive-diamond machining, refl ecting the dynamic properties of processes, its stochastic nature, as well as the nonstationarity of the states of technological operations, were obtained and published by Yu.K. Novoselov in 1971. In 1975, publications of A.V. Korolev appeared, which used a similar approach. The above works have made a signifi cant contribution to the development of the theory of shaping of ground surfaces, however, it does not take into account the specifi cs of products processing in the presence of relative vibrations of the wheel and the workpiece on the output indicators of the grinding operation, therefore, it has a limited scope [7–10]. During processing workpieces with abrasive tools, the material is removed by a large number of grains that do not have a regular geometry and are randomly located on the working surface. This makes it necessary to apply probability theory and the theory of random processes in mathematical simulation of operations [11–14]. In real conditions, during grinding, the contact of the wheel with the workpiece is carried out with a periodically changing depth due to machine vibrations, tool shape deviations from roundness, unbalance of the wheel or insuffi cient rigidity of the workpiece. To eliminate the infl uence of vibrations in production, tools with soft ligaments are used, the value of longitudinal and transverse feeds is reduced, but all these measures lead to a decrease in the operation effi ciency, which is extremely undesirable. To avoid cost losses, mathematical models are needed that adequately describe the process, taking into account the infl uence of vibrations on the output indicators of the grinding process [15–19].
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