OBRABOTKAMETALLOV Vol. 23 No. 3 2021 MATERIAL SCIENCE EQUIPMENT. INSTRUMENTS 4 1 2 Conclusions 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 [20–22]. 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. One of the ways to determine the parameters of a technological system is a full-scale experiment. Experimental confi rmation of the results was carried out on a CNC grinding machine Knuth RSM 500 CNC in the Common Use Center “Engineering and industrial design” SevGU when processing elements of the experimental system – a pump developed at Sevastopol State University. The design of this product includes parts (leading rotor) made of VT3-1 titanium alloy, the quality parameters of which are ensured only during grinding operations. References 1. Novoselov Y., Bogutsky V., Shron L. Patterns of removing material in workpiece – grinding wheel contact area. Procedia Engineering, 2017, vol. 206, pp. 991–996. DOI: 10.1016/j.proeng.2017.10.583. 2. Kassen G., Werner G. Kinematische Kenngrößen des Schleifvorganges [Kinematic parameters of the grinding process]. Industrie-Anzeiger = Industry Scoreboard, 1969, no. 87, pp. 91–95. (In German). 3. 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. 4. 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. 5. 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. 6. Leonesio M., Parenti P., Cassinari A., Bianchi G., Monn M. A time-domain surface grinding model for dynamic simulation. Procedia CIRP, 2012, vol. 4, pp. 166–171. DOI: 10.1016/j.procir.2012.10.030. 7. Sidorov D., Sazonov S., Revenko D. Building a dynamic model of the internal cylindrical grinding process. Procedia Engineering, 2016, vol. 150, pp. 400–405. DOI: 10.1016/j.proeng.2016.06.739. 8. Zhang N., Kirpitchenko I., Liu D.K. Dynamic model of the grinding process. Journal of Sound and Vibration, 2005, vol. 280, pp. 425–432. DOI: 10.1016/j.jsv.2003.12.006. 9. Ahrens M., Damm J., Dagen M., Denkena B., Ortmaier T. Estimation of dynamic grinding wheel wear in plunge grinding. Procedia CIRP, 2017, vol. 58, pp. 422–427. DOI: 10.1016/j.procir.2017.03.247. 10. Garitaonandia I., Fernandes M.H., Albizuri J. Dynamic model of a centerless grinding machine based on an updated FE model. International Journal of Machine Tools and Manufacture, 2008, vol. 48, pp. 832–840. DOI: 10.1016/j.ijmachtools.2007.12.001. 11. Tawakolia T., Reinecke H., Vesali A. An experimental study on the dynamic behavior of grinding wheels in high effi ciency deep grinding. Procedia CIRP, 2012, vol. 1, pp. 382–387. DOI: 10.1016/j.procir.2012.04.068. 12. Jung J., Kim P., Kim H., Seok J. Dynamic modeling and simulation of a nonlinear, non-autonomous grinding system considering spatially periodic waviness on workpiece surface. Simulation Modeling Practice and Theory, 2015, vol. 57, pp. 88–99. DOI: 10.1016/j.simpat.2015.06.005.
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