OBRABOTKAMETALLOV Vol. 24 No. 1 2022 45 EQUIPMENT. INSTRUMENTS The effect of the relative vibrations of the abrasive tool and the workpiece on the probability of material removing during fi nishing grinding Sergey Bratan 1, a,*, Stanislav Roshchupkin 1, b, Anastasia Chasovitina 1, c, Kapil Gupta2, d 1 Sevastopol State University, 33 Universitetskaya str., Sevastopol, 299053, Russian Federation 2 University of Johannesburg, 7225 John Orr Building Doornfontein Campus, Johannesburg, 2028, South Africa a https://orcid.org/0000-0002-9033-1174, serg.bratan@gmail.com, b https://orcid.org/0000-0003-2040-2560, st.roshchupkin@yandex.ru, c https://orcid.org/0000-0001-6800-9392, nastya.chasovitina@mail.ru, d https://orcid.org/0000-0002-1939-894X, kgupta@uj.ac.za Obrabotka metallov (tekhnologiya, oborudovanie, instrumenty) = Metal Working and Material Science. 2022 vol. 24 no. 1 pp. 33–47 ISSN: 1994-6309 (print) / 2541-819X (online) DOI: 10.17212/1994-6309-2022-24.1-33-47 Obrabotka metallov - Metal Working and Material Science Journal homepage: http://journals.nstu.ru/obrabotka_metallov ART I CLE I NFO Article history: Received: 30 December 2021 Revised: 21 January 2022 Accepted: 15 February 2022 Available online: 15 March 2022 Keywords: Grinding of titanium Abrasive grain Microcutting The contact area of the workpiece with the tool Probability of material removing Probability of material not removing Funding The work was carried out with the support of the Priority-2030 program of Sevastopol State University (strategic project No. 2). Acknowledgements Research were conducted at core facility “Structure, mechanical and physical properties of materials”. ABSTRACT Introduction. 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. 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. 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. The purpose of the work is to create a theoretical and probabilistic model of material removing during fi nishing and fi ne grinding, which allows, taking into account the relative vibrations of the abrasive tool and the workpiece, to trace the patterns of its removal in the contact zone. The research methods are mathematical and physical simulation using the basic provisions of probability theory, the laws of distribution of random variables, as well as the theory of cutting and the theory of deformable solids. Results and discussion. The developed mathematical models allow tracing the effect on the removal of the material of the superimposition of single sections on each other during the fi nal grinding of materials. The proposed dependencies show the regularity of the stock removal within the arc of contact of the grinding wheel with the workpiece. The considered features of the change in the probability of material removal when the treated surface comes into contact with an abrasive tool in the presence of vibrations, the proposed analytical dependences are valid for a wide range of grinding modes, wheel characteristics and a number of other technological factors. The expressions obtained allow fi nding the amount of material removal also for the schemes of end, profi le, fl at and round external and internal grinding, for which it is necessary to know the magnitude of relative vibrations. However, the parameters of the technological system do not remain constant, but change over time, for example, as a result of wear of the grinding wheel. To assess the state of the technological system, experimental studies are carried out taking into account the above changes over the period of durability of the grinding wheel. For citation: Bratan S.M., Roshchupkin S.I., Chasovitina A.S., Gupta K. The effect of the relative vibrations of the abrasive tool and the workpiece on the probability of material removing during fi nishing grinding. Obrabotka metallov (tekhnologiya, oborudovanie, instrumenty) = Metal Working and Material Science, 2022, vol. 24, no. 1, pp. 33–47. DOI: 10.17212/1994-6309-2022-24.1-33-47. (In Russian). ______ * Corresponding author Bratan Sergey M., D. Sc. (Engineering), Professor Sevastopol State University 33 Universitetskaya str, 299053, Sevastopol, Russian Federation Tel.: +7 (978)7155019, e-mail: serg.bratan@gmail.com
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