OBRABOTKA METALLOV

Introduction. Tool vibrations accompanying the cutting process are largely related to the long-established regenerative effect, which significantly affects the dynamic characteristics of the metal cutting process, which is indicated in numerous foreign publications of leading European specialists in the field of Metalworking. In the works of some Russian scientists specializing in the analysis of metal cutting processes on metal-cutting machines, the position of the existence of an optimal cutting speed that provides the best quality of the processed surface and the greatest tool life is considered. Therefore, the paper considers the question of the probable connection of this optimal speed with the regeneration of tool vibrations during metal turning. Objective: the possibility of assessing the influence of the regenerative effect on the dynamics of the processing process is considered, without taking into account additional influences on the process, both from the machine side and from the cutting process itself, in order to determine the existence of optimal cutting modes. The study investigated: a mathematical model describing the dynamics of tool vibrations in the conditions of metal processing on machines of the turning group, while only the case of longitudinal turning of the product is considered. Research methods: on the basis of mathematical modeling of the dynamic cutting system, three variants of the possible behavior of the processing process are considered, taking into account the influence on the regeneration of tool vibrations, the period of rotation of the spindle with the part fixed in it. As the first case, a neutral variant in which this period is not associated with the carrier frequency of the speed of axial deformations of the tool is considered. The second option determined the optimal speed of rotation of the spindle, which completely coincided with the carrier frequency of the speed of axial deformations of the tool. The third option shows the worst-case version of the spindle rotation speed, which makes the spindle oscillation period such that the regenerative effect is maximized. Results and discussion. The results of modeling are presented, revealing the dynamics of the system, taking into account the three options selected for the specified spindle speed of the machine. The results of research show that even in the simplest description of cutting forces, the dynamics of the system is quite complex, which is significantly affected by the regenerative effect revealed in the work. The numerical experiment confirms the theory proposed in the paper about the existence of an optimal processing speed, in terms of the influence of tool vibration regeneration on the cutting process. The results obtained are in line with well-known domestic works devoted to the practical analysis of the possibility of building optimal cutting systems and link them with the work of leading European experts in the field of dynamics of metal processing processes.

1. Hahn R.S. On the theory of regenerative chatter in precision grinding operation. Transactions of American Society of Mechanical Engineers, 1954, vol. 76, pp. 356–260.

2. Tobias S.A., Fishwick W. Theory of regenerative machine tool chatter. The Engineer, 1958, vol. 205, no. 7, pp. 199–203.

3. Merritt H.E. Theory of self-excited machine-tool chatter: contribution to machine-tool chatter research – 1. Journal of Engineering for Industry, 1965, vol. 87, no. 4, pp. 447–454. DOI: 10.1115/1.3670861.

4. Hanna N.H., Tobias S.A. A theory of nonlinear regenerative chatter. Journal of Engineering for Industry, 1974, vol. 96, no. 1, pp. 247–255.

5. Tlusty I., Ismail F. Basic non-linearity in Machining Chatter. CIRP Annals, 1981, vol. 30, pp. 299–304. DOI: 10.1016/S0007-8506(07)60946-9.

6. Altintas Y., Budak E. Analytical prediction of stability lobes in milling. CIRP Annals, 1995, vol. 44, no. 1, pp. 357–362. DOI: 10.1016/S0007-8506(07)62342-7.

7. Insperger T., Stépán G. Stability of the milling process. Periodica Polytechnica Mechanical Engineering, 2000, vol. 44, no. 1, pp. 47–57.

8. Wiercigroch M., Budak E. Sources of nonlinearities, chatter generation and suppression in metal cutting. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2001, no. 359, pp. 663–693. DOI: 10.1098/rsta.2000.0750.

9. Grabec I. Chaos generated by the cutting process. Physics Letters A, 1986, vol. 117, no. 8, pp. 384–386. DOI: 10.1016/0375-9601(86)90003-4.

10. Balachandran B. Nonlinear dynamics of milling process. Philosophical Transactions of the Royal Society A: Mathematical Physical and Engineering Sciences, 2001, vol. 359, pp. 793–819.

11. Stepan G. Modelling nonlinear regenerative e?ects 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.2000.07537.

12. 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.

13. Namachchivaya S., Beddini. Spindle speed variation for the suppression of regenerative chatter. Journal of Nonlinear Science, 2003, vol. 13, no. 3, pp. 265–288. DOI: 10.1007/s00332-003-0518-4.

14. Wahi P., Chatterjee A. Regenerative tool chatter near a codimension 2 Hopf point using multiple scales. Nonlinear Dynamics, 2005, vol. 40, no. 4, pp. 323–338.

15. 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. 9, pp. 2783–2798. DOI: 10.1142/S0218127405013642.

16. 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, no. 8, pp. 1050–1066. DOI: 10.1016/j.mechmachtheory.2010.03.014.

17. 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.

18. Gouskov A.M., Voronov S.A., Kvashnin A.S. Vliyanie krutil'nykh kolebanii na protsess vibrosverleniya [Influence of torsion vibrations on process of vibration-drilling]. Vestnik MGTU im. N.E. Baumana. Seriya: Mashinostroenie = Herald of the Bauman Moscow State Technical University. Series: Mechanical Engineering, 2007, no. 1 (66), pp. 3–19.

19. Vasin S.A., Vasin L.A. Sinergeticheskii podkhod k opisaniyu prirody vozniknoveniya i razvitiya avtokolebanii pri tochenii [Synergetic approach to describing the nature and development of self-oscillations in turning]. Naukoemkie tekhnologii v mashinostroenii = Science Intensive Technologies in Mechanical Engineering, 2012, no. 1, pp. 11–16.

20. Voronin A.A. Vliyanie ul'trazvukovykh kolebanii na protsess rezaniya zharoprochnykh splavov [Influence of the ultrasound oscillations on the cutting process of the high-temperature alloy]. Stanki i instrument = Machines and Tooling, 1960, no. 11, pp. 15–18.

21. Zakovorotny V.L., Lapshin V.P., Gubanova A.A. Opredelenie optimal'nykh traektorii pri obrabotke s uchetom evolyutsii protsessa rezaniya [Determination of optimal trajectories during processing taking into account the evolution of the cutting process]. Vestnik Donskogo gosudarstvennogo tekhnicheskogo universiteta = Vestnik of Don State Technical University, 2014, vol. 14, no. 3 (78). DOI: 10.12737/5715.

22. Zakovorotny V.L., Lapshin V.P., Babenko T.S. Assessing the regenerative effect impact on the dynamics of deformation movements of the tool during turning. Procedia Engineering, 2017, vol. 206, pp. 68–73. DOI: 10.1016/j.proeng.2017.10.439.

23. Zakovorotny V.L., Lukyanov A.D., Gubanova A.A., Khristoforova V.V. Bifurcation of stationary manifolds formed in the neighborhood of the equilibrium in a dynamic system of cutting. Journal of Sound and Vibration, 2016, vol. 368, pp. 174–190. DOI: 10.1016/j.jsv.2016.01.020.

24. Lapshin V.P., Turkin I.A. Dynamic influence of the spindle servo drive on the drilling of deep narrow holes. Russian Engineering Research, 2015, vol. 35, no. 10, pp. 795–797. DOI: 10.3103/S1068798X15100111.

25. Ryzhkin A.A., Shuchev K.G., Klimov M.M. Obrabotka materialov rezaniem [Processing of materials by cutting]. Rostov-on-Don, Feniks Publ., 2008. 418 p. ISBN 978-5-7890-0413-X.

26. Vul'f A.M. Rezanie metallov [Cutting of metals]. Leningrad, Mashinostroenie Publ., 1973. 496 p.

27. Zorev N.N. Voprosy mekhaniki protsessa rezaniya metallov [Questions of mechanics of metal cutting process]. Moscow, Mashgiz Publ., 1956. 367 p.

28. Makarov A.D. Optimizatsiya protsessov rezaniya [Optimization of cutting processes]. Moscow, Mashinostroenie Publ., 1976. 278 p.

29. Popov E.P., Pal'tov I.P. Priblizhennye metody issledovaniya nelineinykh avtomaticheskikh sistem [Approximate methods for studying nonlinear automatic systems]. Moscow, Mashgiz Publ., 1960. 792 p.