ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

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Zakovorotny V. L., Gvindjiliya V. E. Correlation of attracting sets of tool deformations with spatial orientation of tool elasticity and regeneration of cutting forces in turning. Izvestiya VUZ. Applied Nonlinear Dynamics, 2022, vol. 30, iss. 1, pp. 37-56. DOI: 10.18500/0869-6632-2022-30-1-37-56

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Correlation of attracting sets of tool deformations with spatial orientation of tool elasticity and regeneration of cutting forces in turning

Zakovorotny Vilor Lavrentevich, Don State Technical University
Gvindjiliya V. E., Don State Technical University

Nowadays, the dynamic cutting system is represented in the form of two subsystems — tool and workpiece, interacting through a nonlinear relationship formed by the cutting process. Such a representation determines the importance of studying the dynamics of the cutting process as the main factor influencing the efficiency of machines, the trajectories of the executive elements of which are set by CNC and are provided with high accuracy. However, in order to improve the efficiency of cutting, it is necessary to align the trajectories of the executive elements are defined by CNC with the changing dynamics of cutting, which introduces deviations in the program-defined trajectories. Purpose of this article is to consider the dependence of the dynamics of the cutting process on the spatial orientation of the cutting tool elasticity and the regenerative effect, and to find out the effect of the proposed dependence on the efficiency of the cutting process. All the issues discussed in the article are analyzed using the example of external shaft turning. Methods. The study is based on the methods of mathematical modeling and experimental dynamics. In contrast to the known studies, the dependence of the turnover lag time on the oscillatory displacements in the direction of the cutting speed, as well as the influence of the positive feedback formed in this case, is taken into account. In addition, changes in the sign of the internal feedback from the direction of deformations, as well as the influence of the regenerative effect on the generated attracting sets of deformations are taken into account. Results. Dependence of the system evolution on the elements of the stiffness matrix at different spindle speeds is disclosed. The properties of the system evolution depending on the ratio of the spindle rotation frequency and the eigenfrequencies of the tool subsystem, as well as the spatial distribution of the stiffness are studied. Conclusion. The frequency and time characteristics of the system are discussed. Conclusion is made about the possibility of efficiency increasing of the cutting process based on the coordination of the CNC program with the dynamic properties of the system.

This work was supported by Russian Foundation for Basic Research, grants No 19-08-00022 and No 20-38-90074
  1. Kudinov VA. Dynamics of Machines. Moscow: Mashinostroenie; 1967. 359 p. (in Russian).
  2. Hahn RS. On the theory of regenerative chatter in precision-grinding operations. Transactions of American Society of Mechanical Engineers. 1954;76:593–597.
  3. Tobias SA, Fishwick W. Theory of regenerative machine tool chatter. The Engineer. 1958;205(7): 199–203.
  4. Tobias SA. Machine Tool Vibrations. London: Blackie; 1965. 351 p.
  5. Tlusty J, Polacek M, Danek O, Spacek L. Selbsterregte Schwingungen an Werkzeugmaschinen. Berlin: Verlag Technik; 1962. 431 s. (in German). 
  6. Tlusty J, Ismail F. Basic non-linearity in machining chatter. CIRP Annals. 1981;30(1):299–304. DOI: 10.1016/S0007-8506(07)60946-9.
  7. Merritt HE. Theory of self-excited machine-tool chatter: Contribution to machine-tool chatter research. ASME Journal of Engineering. 1965;87(4):447–454. DOI: 10.1115/1.3670861.
  8. Altintas Y, Budak E. Analytical prediction of stability lobes in milling. CIRP Annals. 1995;44(1): 357–362. DOI: 10.1016/S0007-8506(07)62342-7.
  9. Eliasberg ME. Self-Oscillation of Machine Tools: Theory and Practice. Saint Petersburg: Osoboe KB Stankostroeniya; 1993. 180 p. (in Russian).
  10. Zakovorotny VL, Fam DT, Bykador VS. Self-organization and bifurcations of dynamical metal cutting system. Izvestiya VUZ. Applied Nonlinear Dynamics. 2014;22(3):26–39 (in Russian). DOI: 10.18500/0869-6632-2014-22-3-26-39.
  11. Zakovorotny VL, Gubanova AA, Lukyanov AD. Stability of shaping trajectories in milling: Synergetic concepts. Russian Engineering Research. 2016;36(11):956–964. DOI: 10.3103/S1068798X16110216.
  12. Zakovorotnyi VL, Gubanova AA, Luk’yanov AD. Parametric self-excitation of a dynamic endmilling machine. Russian Engineering Research. 2016;36(12):1033–1039. DOI: 10.3103/S1068798X16120194.
  13. Zakovorotny VL, Gvindzhiliya VE. Influence of spindle wobble in a lathe on the tool’s deformational-displacement trajectory. Russian Engineering Research. 2018;38(8):623–631. DOI: 10.3103/S1068798X1808018X.
  14. Zakovorotny VL, Gvindjiliya VE. Link between the self-organization of dynamic cutting system and tool wear. Izvestiya VUZ. Applied Nonlinear Dynamics. 2020;28(1):46–61 (in Russian). DOI: 10.18500/0869-6632-2020-28-1-46-61. 
  15. Veits VL, Vasilkov DV. Dynamics, modeling and quality assurance tasks in the machining of low-rigidity workpieces. Russian Engineering Research. 1999;(6):9–13 (in Russian).
  16. Zakovorotny VL, Fleck MB. The Dynamics of the Cutting Process. Synergetic Approach. Rostovon-Don: Terra; 2006. 876 p. (in Russian).
  17. Pontryagin LS. Selected Works of L.S. Pontryagin. Moscow: MAKS Press; 2004. 551 p. (in Russian).
  18. Tikhonov AN. Systems of differential equations with small parameters in senior derivatives. Mathematics of the USSR — Sbornik. 1952;31(3):575–586 (in Russian).
  19. Lipski J, Litak G, Rusinek R, Szabelski K, Teter A, Warminski J, Zaleski K. Surface quality of a work material influence on vibrations in a cutting process. Journal of Sound and Vibration. 2002;252:729–737. DOI: 10.1006/jsvi.2001.3943.
  20. Gorodetsky YI. Theory of nonlinear oscillations and machine tool dynamics. Vestnik of Lobachevsky University of Nizhni Novgorod. Series: Mathematical Modeling and Optimal Control. 2001;(2): 69–88 (in Russian).
  21. Balachandran B. Nonlinear dynamics of milling processes. Phil. Trans. R. Soc. A. 2001;359(1781): 793–819. DOI: 10.1098/rsta.2000.0755.
  22. Litak G, Rusinek R. Dynamics of a stainless steel turning process by statistical and recurrence analyses. Meccanica. 2012;47(6):1517–1526. DOI: 10.1007/s11012-011-9534-x.
  23. Gouskov AM, Voronov SA, Paris H, Batzer SA. Nonlinear dynamics of a machining system with two interdependent delays. Communications in Nonlinear Science and Numerical Simulation. 2002;7(4):207–221. DOI: 10.1016/S1007-5704(02)00014-X.
  24. Voronov SA, Ivanov II, Kiselev IA. Investigation of the milling process based on a reduced dynamic model of cutting tool. Journal of Machinery Manufacture and Reliability. 2015;44(1): 70–78. DOI: 10.3103/S1052618815010100.
  25. Zakovorotnyi VL, Lukyanov AD, Gubanova AA, Khristoforova VV. Bifurcation of stationary manifolds formed in the neighborhood of the equilibrium in a dynamic system of cutting. Journal of Sound and Vibration. 2016;368:174–190. DOI: 10.1016/j.jsv.2016.01.020.
  26. Litak G. Chaotic vibrations in a regenerative cutting process. Chaos, Solitons & Fractals. 2002;13(7):1531–1535. DOI: 10.1016/S0960-0779(01)00176-X.
  27. Namachchivaya NS, Beddini R. Spindle speed variation for the suppression of regenerative chatter. Journal of Nonlinear Science. 2003;13(3):265–288. DOI: 10.1007/s00332-003-0518-4.
  28. Wahi P, Chatterjee A. Self-interrupted regenerative metal cutting in turning. International Journal of Non-Linear Mechanics. 2008;43(2):111–123. DOI: 10.1016/j.ijnonlinmec.2007.10.010.
  29. Warminski J, Litak G, Lipski J, Wiercigroch M, Cartmell M. Vibrations in regenerative cutting process synthesis of nonlinear dynamical systems. Solid Mechanics and its Applications. 2000;73: 275–283.
  30. Stepan G, Szalai R, Insperger T. Nonlinear dynamics of high-speed milling subjected to regenerative effect. In: Radons G, Neugebauer R, editors. Nonlinear Dynamics of Production Systems. Hoboken, New Jersey: Wiley; 2004. P. 111–128. DOI: 10.1002/3527602585.ch7.
  31. Stepan G, Insperger T, Szalai R. Delay, parametric excitation, and the nonlinear dynamics of cutting processes. International Journal of Bifurcation and Chaos. 2005;15(9):2783–2798. DOI: 10.1142/S0218127405013642.
  32. Stepan G. Modelling nonlinear regenerative effects in metal cutting. Phil. Trans. R. Soc. A. 2001;359(1781):739–757. DOI: 10.1098/rsta.2000.0753.
  33. Moradi H, Bakhtiari-Nejad F, Movahhedy MR, Ahmadian MT. Nonlinear behaviour of the regenerative chatter in turning process with a worn tool: Forced oscillation and stability analysis. Mechanism and Machine Theory. 2010;45(8):1050–1066. DOI: 10.1016/j.mechmachtheory.2010.03.014.
  34. Gouskov AM, Guskov MA, Tung DD, Panovko GY. Modeling and investigation of the stability of a multicutter turning process by a trace. Journal of Machinery Manufacture and Reliability. 2018;47(4):317–323. DOI: 10.3103/S1052618818040052.
  35. Lapshin VP. The influence of the cutting speed of metals on the regeneration of the vibratory oscillations of the tool in machines of the turning group. Metal Working and Material Science. 2020;22(1):65–79 (in Russian). DOI: 10.17212/1994-6309-2020-22.1-65-79.
  36. Reith MJ, Bachrathy M, Stepan G. Improving the stability of multi-cutter turning with detuned dynamics. Machining Science and Technology. 2016;20(3):440–459. DOI: 10.1080/10910344.2016.1191029.
  37. Brissaud D, Gouskov A, Guibert N, Rech J. Influence of the ploughing effect on the dynamic behaviour of the self-vibratory drilling head. CIRP Annals. 2008;57(1):385–388. DOI: 10.1016/j.cirp.2008.03.101.
  38. Gouskov A, Gouskov M, Lorong P, Panovko G. Influence of flank face on the condition of chatter self-excitation during turning. International Journal of Machining and Machinability of Materials. 2017;19(1):17–40. DOI: 10.1504/IJMMM.2017.081186.
  39. Rusinek R, Wiercigroch M, Wahi P. Influence of tool flank forces on complex dynamics of cutting process. International Journal of Bifurcation and Chaos. 2014;24(9):1450115. DOI: 10.1142/S0218127414501156.
  40. Rusinek R, Wiercigroch M, Wahi P. Modelling of frictional chatter in metal cutting. International Journal of Mechanical Sciences. 2014;89:167–176. DOI: 10.1016/j.ijmecsci.2014.08.020.
  41. Grabec I. Chaos generated by the cutting process. Phys. Lett. A. 1986;117(8):384–386. DOI: 10.1016/0375-9601(86)90003-4.
  42. Wiercigroch M, Budak E. Sources of nonlinearities, chatter generation and suppression in metal cutting. Phil. Trans. R. Soc. A. 2001;359(1781):663–693. DOI: 10.1098/rsta.2000.0750.
  43. Wiercigroch M, Krivtsov AM. Frictional chatter in orthogonal metal cutting. Phil. Trans. R. Soc. A. 2001;359(1781):713–738. DOI: 10.1098/rsta.2000.0752.
  44. Masoumi F, Pellicano F, Samani FS, Barbieri M. Symmetry breaking and chaos-induced imbalance in planetary gears. Nonlinear Dynamics. 2015;80(1–2):561–582. DOI: 10.1007/s11071-014-1890-3.
  45. Zakovorotny VL, Gvindjiliya VE. The influence of fluctuation on the shape-generating trajectories stability with a turning. University News. North-Caucasian Region. Technical Sciences Series. 2017;(2(194)):52–61 (in Russian). DOI: 10.17213/0321-2653-2017-2-52-61.
  46. Zakovorotny VL, Gvindjiliya VE. The influence of the vibration on the tool shape-generating trajectories when turning. Metal Working and Material Science. 2019;21(3):42–58 (in Russian). DOI: 10.17212/1994-6309-2019-21.3-42-58.
  47. Zakovorotny VL, Gvindzhiliya VE. Synergetic concept of software control of machining processes on metal-cutting machines. BMSTU Journal of Mechanical Engineering. 2021;5(734):24–36 (in Russian). DOI: 10.18698/0536-1044-2021-5-24-36.
  48. Lyapunov AM. The General Problem of the Stability of Motion. Moscow: Gostekhizdat; 1950. 472 p. (in Russian).
  49. Zakovorotniy VL, Pham TH. Parametric self-excitation of cutting dynamic system. Advanced Engineering Research. 2013;13(5–6):97–103 (in Russian). DOI: 10.12737/1286.
  50. Besekersky VA, Popov EP. Theory of Automatic Control Systems. Moscow: Nauka; 1975. 768 p. (in Russian).
  51. Zakovorotniy V, Pham D, Nguyen X. Modeling of tool deformation offsetting to workpiece in turning. Advanced Engineering Research. 2010;10(7):1005–1015 (in Russian).
  52. Ryzhkin AA. Synergetics of Wear of Tool Materials During Blade Processing. Rostov-on-Don: Don State Technical University Publishing; 2019. 289 p. (in Russian).
  53. Push AV. Spindle Units: Quality and Reliability. Moscow: Mashinostroenie; 1992. 288 p. (in Russian). 
  54. Khusu AP, Vitenberg YR, Palmov VA. Roughness of Surfaces. Probabilistic Approach. Moscow: Nauka; 1975. 344 p. (in Russian).
  55. Zakovorotny VL, Flek MB, Lukyanov AD, Voloshin DA. Tool wear modeling using integral operators. Russian Engineering Research. 2004;(3):9–14 (in Russian).
  56. Zakovorotny VL, Gvindjiliya VE. Self-organization and evolution in dynamic friction systems. Journal of Vibroengineering. 2021;23(6):1418–1432. DOI: 10.21595/jve.2021.22033.
  57. Altintas Y, Kersting P, Biermann D, Budak E, Denkena B, Lazoglu I. Virtual process systems for part machining operations. CIRP Annals. 2014;63(2):585–605. DOI: 10.1016/j.cirp.2014.05.007.
  58. Kilic ZM, Altintas Y. Generalized mechanics and dynamics of metal cutting operations for unified simulations. International Journal of Machine Tools and Manufacture. 2016;104:1–13. DOI: 10.1016/j.ijmachtools.2016.01.006.