OBRABOTKAMETALLOV technology Vol. 25 No. 1 2023 the cutting process, is determined by a combination of the following factors: the incident characteristics of the cutting force (according to N.N. Zorev), the minimum coefficient of friction caused by the transition of friction from adhesive to diffusion nature and the dependence of the force pushing the tool from the preheated processing zone. However, it should be added here that another important factor determining the optimality of the cutting process according to A.D. Makarov is the regenerative effect inherent in the model of the cutting control system, which has a significant impact on the stability of the cutting system dynamics. All this together allows us to formulate the following scientific position: the most optimal, with regard to a cutting speed (cutting temperature), will be the mode in which the incident characteristic of the cutting force (according to N.N. Zorev) reaches its minimum value, the coefficient of friction on the tool flank will be in the vicinity of the point of the local minimum, pushing the tool force will not exceed a certain pre-known value and, at the same time, the value of the cutting speed should be in the vicinity of a certain minimum of self-excitation of the cutting system during the regeneration of vibrations due to cutting along the “trace”. From a practical point of view, the conducted research shows the possibility of introducing new measuring and computing subsystems that, based on a synthesized mathematical model, can determine the most optimal cutting modes in real time. References 1. Stépán G. Modelling nonlinear regenerative effects in metal cutting. Philosophical Transactions of The Royal Society A: Mathematical Physical and Engineering Sciences, 2001, vol. 359, pp. 739–757. DOI: 10.1098/ rsta.2000.0753. 2. Litak G. Chaotic vibrations in a regenerative cutting process. Chaos, Solitons and Fractals, 2002, vol. 13, pp. 1531–1535. DOI: 10.1016/S0960-0779(01)00176-X. 3. Namachchivaya S., Beddini R. Spindle speed variation for the suppression of regenerative chatter. Journal of Nonlinear Science, 2003, vol. 13, pp. 265–288. DOI: 10.1007/s00332-003-0518-4. 4. Wahi P., Chatterjee A. Regenerative tool chatter near a codimension 2 Hopf point using multiple scales. Nonlinear Dynamics, 2005, vol. 40, iss. 4, pp. 323–338. 5. Stépán G., Insperger T., Szalai R. Delay, parametric excitation, and the nonlinear dynamics of cutting processes. International Journal of Bifurcation and Chaos, 2005, vol. 15, no. 09, pp. 2783–2798. DOI: 10.1142/ S0218127405013642. 6. Moradi H., Bakhtiari-Nejad F., Movahhedy M.R., Ahmadian M.T. Nonlinear behaviour of the regenerative chatter in turning process with a worn tool: forced oscillation and stability analysis. Mechanism and Machine Theory, 2010, vol. 45, iss. 8, pp. 1050–1066. DOI: 10.1016/j.mechmachtheory.2010.03.014. 7. Gouskov A.M., Voronov S.A., Paris H., Batzer S.A. Nonlinear dynamics of a machining system with two interdependent delays. Communications in Nonlinear Science and Numerical Simulation, 2002, vol. 7, no. 4, pp. 207– 221. DOI: 10.1016/S1007-5704(02)00014-X. 8. Lapshin V.P. Turning tool wear estimation based on the calculated parameter values of the thermodynamic subsystem of the cutting system. Materials, 2021, vol. 14, no. 21, p. 6492. DOI: 10.3390/ma14216492. 9. Lapshin V.P., Khristoforova V.V., Nosachev S.V. Vzaimosvyaz’ temperatury i sily rezaniya s iznosom i vibratsiyami instrumenta pri tokarnoi obrabotke metallov [Relationship of temperature and cutting force with tool wear and vibration in metal turning]. Obrabotka metallov (tekhnologiya, oborudovanie, instrumenty) = Metal Working and Material Science, 2020, vol. 22, no. 3, pp. 44–58. DOI: 10.17212/1994-6309-2020-22.3-44-58. 10. Zakovorotny V.L., Gvindjiliya V.E. Evolution of the dynamic cutting system with irreversible energy transformation in the machining zone. Russian Engineering Research, 2019, vol. 39, no. 5, pp. 423–430. DOI: 10.3103/ S1068798X19050204. 11. Zakovorotny V.L., Gvinjiliya V.E. Svyaz’ prityagivayushchikh mnozhestv deformatsii instrumenta s prostranstvennoi orientatsiei uprugosti i regeneratsiei sil rezaniya pri tochenii [Correlation of attracting sets of tool deformations with spatial orientation of tool elasticity and regeneration of cutting forces in turning]. Izvestiya vuzov. Prikladnaya nelineinaya dinamika = Izvestiya VUZ. Applied Nonlinear Dynamics, 2022, vol. 30 (1), pp. 37–56. DOI: 10.18500/0869-6632-2022-30-1-37-56. 12. Zakovorotny V.L., Gvinjiliya V.E. Self-organization and evolution in dynamic friction systems. Journal of Vibroengineering, 2021, vol. 23, iss. 6, pp. 1418–1432. DOI: 10.21595/jve.2021.22033.
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