Abstract
The dynamic reorganization of the deformational displacements in the cutting system during its evolution is considered. In the present work, instead of regarding dynamic reorganization as due to specified change in the parameters—for instance, the workpiece rigidity—parameter evolution is treated as a natural process associated with irreversible energy transformation in the machine zone. In that case, the dynamic relationships formed in the process depend on the work and power of irreversible transformations at contact of the tool faces with the workpiece and also in the chip-formation zone. Therefore, the parameters of such relationships will depend on the work and power trajectories of the irreversible transformations in those regions. On the one hand, the parameters depend on those trajectories; on the other, change in those parameters affects the work and power of the irreversible transformations. In the present work, the goal is to model this functionally coupled dynamic system.
Similar content being viewed by others
REFERENCES
Haken, H., Erfolgsgeheimnisse der Natur. Synergetik: Die Lehre vom Zusammenwirken, Stuttgart: Deutsche Verlags-Anstalt, 1981.
Prigogine, I., From Being to Becoming: Time and Complexity in the Physical Sciences, San Francisco: W.H. Freeman, 1980.
Prigogine, I. and Stengers, I., Order Out of Chaos: Man’s New Dialogue with Nature, New York: Bantam Books, 1984.
Zakovorotnyi, V.L. and Flek, M.B., Dinamika protsessa rezaniya. Sinergeticheskii podkhod (Dynamics of Cutting Process: Synergetic Approach), Rostov-on-Don: Terra,2006.
Zakovorotnyi, V.L., Luk’yanov, A.D., Nguen, D.-A., and Fam, D.T., Sinergeticheskii sistemnyi sintez upravlyaemoi dinamiki metallorezhushchikh stankov s uchetom evolyutsii svyazei (Synergetic System Synthesis of Controlled Dynamics of Metal Cutting Machines, Taking into Account the Evolution of Relations), Rostov-on-Don: Donsk. Gos. Tekh. Univ., 2008.
Hahn, R.S., On the Theory of Regenerative Chatter in Precision Grinding Operation, Trans. ASME, 1954, vol. 76, pp. 356–260.
Kudinov, V.A., Dinamika stankov (Dynamics of Machines), Moscow: Mashinostroenie, 1967.
Tlustý, J. and Ismail, F., Basic non-linearity in machining chatter, Ann. CIRP, 1981, vol. 30, pp. 299–304.
Tlustý, J., Samobuzené Kmity v Obrábecích Strojích, Prague: Cesk. Akad. Ved., 1954.
Tobias, S.A., Machine Tool Vibrations, London: Blackie, 1965.
Veits, V.L. and Vastil’kov, D.V., Dynamics, modeling, and quality maintenance at the machine treatment of small hard billets, Stanki Instrum., 1999, no. 6, pp. 9–13.
Voronov, S.A., Nepochatov, A.V., and Kiselev, I.A., Assessment criteria of stability of milling of non-rigid parts, Izv. Vyssh. Uchebn. Zaved., Mashinostr., 2011, no. 1 (610), pp. 50–62.
Guskov, A.G., Guskov, M.A., Dinh Dyk Tung, and Panovko, G.Ya., Modeling and investigation of the stability of a multicutter turning process by a trace, J. Mach. Manuf. Reliab., 2018, vol. 47, no. 4, pp. 317–323.
Gorodetskii, Yu.I., Theory of nonlinear fluctuations and machine dynamics, Vestn. Nizhegorod. Univ. im. N.I. Lobachevskogo, Ser.: Matem. Model. Optim. Upr., 2001, no. 2, pp. 69–88.
Balachandran, B., Nonlinear dynamics of milling process, Philos. Trans. R. Soc., A, 2001, vol. 359, pp. 793–819.
Litak, G., Chaotic vibrations in a regenerative cutting process, Chaos, Solitons Fractals, 2002, vol. 13, pp. 1531–1535.
Litak, G. and Rusinek, R., Dynamics of a stainless steel turning process by statistical and recurrence analyses, Mechanic, 2012, vol. 47, pp. 1517–1526.
Namachchivaya, N.S. and Beddini, R., Spindle speed variation for the suppression of regenerative chatter, J. Nonlinear Sci., 2003, vol. 13, pp. 265–288.
Wahi, P. and Chatterjee, A., Self-interrupted regenerative metal cutting in turning, J. Nonlinear Mech., 2008, vol. 43, pp. 111–123.
Warminski, J., Litak, G., Lipski, J., et al., Chaotic vibrations in regenerative cutting process, Proc. IUTAM/IFToMM Symp. on Synthesis of Nonlinear Dynamical Systems, Riga, Latvia, August 24–28, 1998, Dordrecht: Springer-Verlag, 2000, vol. 73, pp. 275–284.
Stépán, G., Szalai, R., and Insperger, T., Nonlinear dynamics of high-speed milling subjected to regenerative effect, in Nonlinear Dynamics of Production Systems, Radons, G. and Neugebauer, R., Eds., Weinheim: Wiley, 2004, pp. 111–127.
Stépán, G., Modeling nonlinear regenerative effects in metal cutting, Philos. Trans. R. Soc., A, 2001, vol. 359, pp. 739–757.
Gouskov, A.M., Voronov, S.A., Paris, H., and Batzer, S.A., Nonlinear dynamics of a machining system with two interdependent delays, Commun. Nonlinear Sci. Numer. Simul., 2002, vol. 7, pp. 207–221.
Voronov, S.A. and Kiselev, I.A., Nonlinear dynamic problems for cutting processes, Mashinostr., Inzh. Obraz., 2017, no. 2 (51), pp. 9–23.
Vasin, S.A. and Vasin, L.A., The nature of the occurrence and development of auto-oscillations during turning: synergistic approach, Naukoemkie Tekhnol. Mashinostr., 2012, no. 1, pp. 11–16.
Rusinek, R., Wiercigroch, M., and Wahi, P., Influence of tool flank forces on complex dynamics of cutting process, Int. J. Bifurcation Chaos, 2014, vol. 24, no. 9, art. ID 1450115.
Rusinek, R., Wiercigroch, M., and Wahi, P., Modeling of frictional chatter in metal cutting, Int. J. Mech. Sci., 2014, vol. 89, pp. 167–176. https://doi.org/10.1016/j.ijmecsci.2014.08.020
Zakovorotnyi, V.L. and Fam, T.Kh., Parametric self-excitation of dynamics system of cutting, Vestn. Donsk. Gos. Tekh. Univ., 2013, nos. 5–6, pp. 97–103.
Grabec, I., Chaos generated by the cutting process, Phys. Lett. A, 1986, vol. 117, pp. 384–386.
Lipski, J., Litak, G., Rusinek, R., et al., Surface quality of a work material’s influence on the vibrations of the cutting process, J. Sound Vib., 2002, vol. 252, pp. 737–739.
Wiercigroch, M. and Budak, E., Sources of nonlinearities, chatter generation and suppression in metal cutting, Philos. Trans. R. Soc., A, 2001, vol. 359, pp. 663–693.
Wiercigroch, M. and Krivtsov, A.M., Frictional chatter in orthogonal metal cutting, Philos. Trans. R. Soc., A, 2001, vol. 359, pp. 713–738.
Zakovorotny, V.L., Lukyanov, A.D., Gubanova, A.A., and Khristoforova, V.V., Bifurcation of stationary manifolds formed in the neighborhood of the equilibrium in a dynamic system of cutting, J. Sound Vib., 2016, vol. 368, pp. 174–190.
Voronov, S.A., Ivanov, I.I., and Kiselev, I.A., Investigation of the milling process based on a reduced dynamic model of cutting tool, J. Mach. Manuf. Reliab., 2015, vol. 44, no. 1, pp. 70–78.
Zakovorotny, V., Bifurcations in the dynamic system of the mechanic processing in metal–cutting tools, WSEAS Trans. Appl. Theor. Mech., 2015, vol. 10, pp. 102–116.
Zakovorotnyi, V.L. and Gvindzhiliya, V.E., Influence of fluctuations on stability of molding trajectories during turning, Izv. Vyssh. Uchebn. Zaved., Sev.-Kavk. Reg., Tekh. Nauki, 2017, no. 2 (194), pp. 52–61.
Zakovorotnyi, V.L. and Gvindzhiliya, V.E., Influence of the motion error of the lathe turning elements on the trajectory of the shaping motions, Vestn. Donsk. Gos. Tekh. Univ., 2017, vol. 17, no. 1 (88), pp. 35–46.
Zakovorotny, V.L. and Gvindzhiliya, V.E., Influence of spindle wobble in a lathe on the tool’s deformational-displacement trajectory, Russ. Eng. Res., 2018, vol. 38, no. 8, pp. 623–631.
Zakovorotnyi, V.L. and Gvindzhiliya, V.E., Evolution of the dynamic cutting system with irreversible energy transformation in the machining zone, Stanki Instrum., 2018, no. 12, pp. 17–25.
Zakovorotny, V.L. and Gvindjilia, V.E., Influence of kinematic perturbations on shape-generating movement trajectory stability, Procedia Eng., 2017, vol. 206, pp. 157–162.
Zakovorotny, V.L. and Gvindzhiliya, V.E., Evolution of the dynamic cutting system with irreversible energy transformation in the machining zone, Russ. Eng. Res., 2019, vol. 39, no. 5, pp. 423–430.
Funding
Financial support was provided by the Russian Foundation for Basic Research (grant 19-08-00022).
Author information
Authors and Affiliations
Corresponding authors
Additional information
Translated by B. Gilbert
About this article
Cite this article
Zakovorotnyi, V.L., Gvindjiliya, V.E. & Lapshin, V.P. Dynamics of Tool Deformation in the Cutting System. Russ. Engin. Res. 41, 246–251 (2021). https://doi.org/10.3103/S1068798X21030230
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.3103/S1068798X21030230