OBRABOTKAMETALLOV Vol. 23 No. 3 2021 MATERIAL SCIENCE EQUIPMENT. INSTRUMENTS 6 2 4 of the tool and the thermodynamics of cutting (fig. 7, b and c). In our opinion, depending on the cutting speed, it is necessary to take into account molecular-mechanical interactions, such as the formation and breaking of adhesive bonds. Its formation and breakage depend on the speed of tool movements relative to the workpiece. A number of key findings emerged from the study. 1. The quality of creating a digital twin of the cutting process on metal cutting machines depends on the depth of penetration of the models used in this process into the physics of interactions between the tool and the workpiece through the cutting zone. 2. Trajectories of forming motions of the tool relative to the workpiece, considered in the unity of the trajectories of the machine tool actuators and deformation displacements of the tool tip relative to the workpiece specified by the CNC system, adequately reflect the geometrical topology of the workpiece surface formed by cutting. However, the adequacy of such representation is limited by the frequency range, which depends, firstly, on the selective properties of the interacting subsystems on the side of the tool and the workpiece; secondly, it is limited by the possibility of measuring high-frequency vibrational displacements of the tool tip relative to the workpiece, as well as independent, not included in the dynamic cutting system, physical interactions in the cutting zone. 3. Mathematical modeling of the dynamic cutting system based on the mechanics of interaction between the tool and the workpiece allows to adequately predict the macro geometry of the part formed by cutting, but not the properties of surface roughness, much less the properties of the surface layer. For predicting microrelief, mathematical models that reveal the connection of trajectories of machine tool actuating elements taking into account elastic deformations into geometrical topology should be compositional. In addition to the mechanics of tool and workpiece interactions through the dynamic coupling formed by the cutting process, it is necessary to include thermodynamic and molecular interactions, as well as to take into account the plastic deformation of surface layers. 4. The present studies are limited to linearized models valid for small perturbations and for the case of stable trajectories. For large perturbations, it is necessary to additionally take into account nonlinear interaction effects, which will be analyzed in our next publications. References 1. Altintas Y. Manufacturing automation: metal cutting mechanics, machine tool vibrations, and CNC design. UK, Cambridge University Press, 2012. 366 p. DOI: 10.1017/CBO9780511843723. 2. Altintas Y., Brecher C., Weck M., Witt S. Virtual machine tool. CIRP Annals, 2005, vol. 54 (2), pp. 115–138. DOI: 10.1016/S0007-8506(07)60022-5. 3. Erkorkmaz K., Altintas Y., Yeung C.-H. Virtual computer numerical control system. CIRP Annals, 2006, vol. 55 (1), pp. 399–402. DOI: 10.1016/S0007-8506(07)60444-2. 4. Altintas Y., Kersting P., Biermann D., Budak E., Denkena B. Virtual process systems for part machining operations. CIRP Annals, 2014, vol. 63 (2), pp. 585–605. DOI: 10.1016/j.cirp.2014.05.007. 5. Gao W., Ibaraki S., Donmez M.A., Kono D., Mayer J.R.R., Chen Y.-L., Szipka K., Archenti A., Linares J.- M., Suzuki N. Machine tool calibration: Measurement, modeling, and compensation of machine tool errors International. International Journal of Machine Tools and Manufacture, 2023, vol. 187, p. 104017. DOI: 10.1016/j. ijmachtools.2023.104017. 6. Estman L., Merdol D., Brask K.-G., Kalhori V., Altintas Y. Development of machining strategies for aerospace components, using virtual machining tools. New Production Technologies in Aerospace Industry. Cham, Springer, 2014, pp. 63–68. DOI: 10.1007/978-3-319-01964-2_9. 7. Kilic Z.M., Altintas Y. Generalized mechanics and dynamics of metal cutting operations for unified simulations. International Journal of Machine Tools and Manufacture, 2016, vol. 104, pp. 1–13. DOI: 10.1016/j. ijmachtools.2016.01.006. 8. Soori M., Arezoo B. Virtual machining systems for CNC milling and turning machine tools: a review. International Journal of Engineering and Technology, 2020, vol. 18, pp. 56–104. 9. Lin M.-T., Huang T.-Y., Tsai M.-S., Wu S.-K. Virtual simulation of five-axis machine tool with consideration of CNC interpolation, servo dynamics, friction, and geometric errors. Journal of the Chinese Institute of Engineers, 2017, vol. 40 (7), pp. 1–12. DOI: 10.1080/02533839.2017.1372221.
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