Probabilistic model of surface layer removal when grinding brittle non-metallic materials

OBRABOTKAMETALLOV Vol. 23 No. 2 2021 15 TECHNOLOGY References 1. Malkin S., Guo C. Grinding technology: theory and applications of machining with abrasives. New York, Industrial Press, 2008. 372 р . ISBN 978-0-8311-3247-7. 2. Hou Z.B., Komanduri R. On the mechanics of the grinding process. Pt. 1. Stochastic nature of the grinding process. International Journal of Machine Tools and Manufacture, 2003, vol. 43, pp. 1579–1593. DOI: 10.1016/ S0890-6955(03)00186-X. 3. Lajmert P., Sikora V., Ostrowski D. A dynamic model of cylindrical plunge grinding process for chatter phenomena investigation. MATEC Web of Conferences , 2018, vol. 148, pp. 09004–09008. DOI: 10.1051/ matecconf/20181480900. Probabilistic model of surface layer removal when grinding brittle non-metallic materials Sergey Bratan a, * , Stanislav Roshchupkin b , Alexander Kharchenko c , Anastasia Chasovitina d Sevastopol State University, 33 Universitetskaya str., Sevastopol, 299053, Russian Federation a https://orcid.org/0000-0002-9033-1174 , bratan@gmail.com, b https://orcid.org/0000-0003-2040-2560, st.roshchupkin@yandex.ru , c https://orcid.org/0000-0003-1704-9380, khao@list.ru , d https://orcid.org/0000-0001-6800-9392, nastya.chasovitina@mail.ru Obrabotka metallov (tekhnologiya, oborudovanie, instrumenty) = Metal Working and Material Science. 2021 vol. 23 no. 2 pp. 6–16 ISSN: 1994-6309 (print) / 2541-819X (online) DOI: 10.17212/1994-6309-2021-23.2-6-16 Obrabotka metallov - Metal Working and Material Science Journal homepage: http://journals.nstu.ru/obrabotka_metallov ARTICLE INFO Article history : Received: 15 March 2021 Revised: 29 March 2021 Accepted: 14 April 2021 Available online: 15 June 2021 Keywords : Sanding fragile materials Abrasive grain Contact area of the workpiece with the tool Likelihood of material removal Microcutting Brittle chipping Bulk fracture probability ABSTRACT Introduction. The fi nal quality of products is formed during fi nishing operations, which include the grinding process. It is known that when grinding brittle materials, the cost of grinding work increases signi fi cantly. It is possible to reduce the scatter of product quality indicators when grinding brittle materials, as well as to increase the reliability and ef fi ciency of the operation, by choosing the optimal parameters of the technological system based on dynamic models of the process. However, to describe the regularities of the removal of particles of a brittle non- metallic material and the wear of the surface of the grinding wheel in the contact zone, the known models do not allow taking into account the peculiarities of the process in which micro-cutting and brittle chipping of the material are combined. Purpose of the work: to create a new probabilistic model for removing the surface layer when grinding brittle non-metallic materials. The task is to study the laws governing the removal of particles of brittle non-metallic material in the contact zone. In this work, the removal of material in the contact zone as a result of microcutting and brittle chipping is considered as a random event. The research methods are mathematical and physical simulation using the basic provisions of the theory of probability, the laws of distribution of random variables, as well as the theory of cutting and the theory of a deformable solid. Results and discussion. The developed mathematical models make it possible to trace the effect on material removal of the overlap of single cuts on each other when grinding holes in ceramic materials. The proposed dependences show the regularity of 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 upon contact of the treated surface with an abrasive tool and the proposed analytical dependences are valid for a wide range of grinding modes, wheel characteristics and a number of other technological factors. The obtained expressions make it possible to fi nd the amount of material removal also for schemes of end, fl at and circular external grinding, for which it is necessary to know the amount of removal increment due to brittle fracture during the development of microcracks in the surface layer. One of the ways to determine the magnitude of this increment is to simulate the crack formation process using a computer. The presented results con fi rm the prospects of the developed approach to simulate the processes of mechanical processing of brittle non-metallic materials. For citation: Bratan S.M., Roshchupkin S.I., Kharchenko A.O., Chasovitina A.S. Probabilistic model of surface layer removal when grinding brittle non-metallic materials. Obrabotka metallov (tekhnologiya, oborudovanie, instrumenty) = Metal Working and Material Science , 2021, vol. 23, no. 2, pp. 6–16. DOI: 10.17212/1994-6309-2021-23.2-6-16. (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