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

For citation:

Zakovorotny V. L., Pham D. T., Bykador V. S. Influence of a flexural deformation of a tool on self-organization and bifurcations of dynamical metal cutting system. Izvestiya VUZ. Applied Nonlinear Dynamics, 2014, vol. 22, iss. 3, pp. 40-52. DOI: 10.18500/0869-6632-2014-22-3-40-52

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Language: 
Russian
Heading: 
Applied Problems of Nonlinear Oscillation and Wave Theory
Article type: 
Article
UDC: 
621.91: 531.3
DOI: 
10.18500/0869-6632-2014-22-3-40-52

Influence of a flexural deformation of a tool on self-organization and bifurcations of dynamical metal cutting system

Autors: 
Zakovorotny Vilor Lavrentevich, Don State Technical University
Pham Dinh Tung, Le Kui Don State Technical University of Vietnam
Bykador Vitalij Sergeevich, Don State Technical University
Abstract: 

In the article we offer to consider case of a flexural deformation shifts of a tool when they are essential for nonlinear dynamics of cutting process. This situation is observed for drill deep  holes, because a boring bar has a small values of a flexural stiffness. In that case an angle of cutting  edge reduces and cutting forces increase if the deformation shifts also increased in velocity  direction. The last circumstance becomes occasion for positive feedback that essentially changes  dynamics of the cutting process. In the paper it is shown that process with positive feedback has the  bifurcation. In the first place we can observe bifurcation of fixed points. In the second place we can  watch if stiffness of cutting process is increased that limit cycles and chaotic attractors with limit region of attract are generated in neighborhood of fixed points. It is shown that attracting sets fundamentally depend on cutting parameters. The cutting parameters define cutting forces and the flexural deformation shifts of a tool.

Key words: 
dynamical system
attracting sets
chaotic attractor
bifurcations
cutting process of the materials
Reference: 
  1. Drozdov NA. To the question of machine vibrations during turning. Machines and tooling. 1937;12.
  2. Kashirin AI. Investigation of vibrations in metal cutting. Moscow-Leningrad: USSR Academy of Sciences; 1944. 282 p. (In Russian).
  3. Sokolovsky AP. Vibrations when working on metal cutting machines. Investigation of metal cutting oscillations. Moscow: Mashgiz; 1958. 294 p. (In Russian).
  4. Murashkin LS, Murashkin SL. Applied nonlinear machine mechanics. Leningrad: Mashinostroenie; 1977. 192 p. (In Russian).
  5. Albrecht P. Dynamics of the metal cutting process. Journal of engineening for industry. Transactions of the ASME.Ser.B. Moscow: Mir; 1965;87(4):40.
  6. Zharkov IS. Vibrations when machined with a blade tool. Leningrad: Mashinostroenie; 1987. 184 p. (In Russian).
  7. Tlusty I. Self-oscillations in metal cutting machines. Translation from Czech. Moscow: Mashgiz; 1956. 395 p.
  8. Kudinov VA. Dynamics of machine tools. Moscow: Mashinostroenie; 1967. 359 p. (In Russian).
  9. Elyasberg ME. Self-oscillations of metal cutting machines: Theory and practice. St. Petersburg: OKBS; 1993. 182 p.
  10. Weitz VL, Vasilkov DV. Tasks of dynamics, modeling and quality assurance in machining of smallhard workpieces. Russian Engineering Research. 1999;(6):9–13.
  11. Zakovorty VL, Fleck MB. Dynamics of the cutting process. Synergistic approach. Rostov-on-Don: DSTU; 2006. 876 p.
  12. Zakovorotny VL, Pham DT, Nguyen XC. MATHEMATICAL MODELING AND PARAMETRIC IDENTIFICATION OF DYNAMIC PROPERTIES OF THE SUBSYSTEMS OF THE CUTTING TOOL AND WORKPIECE IN THE TURNING. Scientific-educational and applied journal UNIVERSITY NEWS NORTH-CAUCASIAN REGION. TECHNICAL SCIENCES SERIES. 2011;2:38–46. (In Russian).
  13. Zakovorotny VL, Bordachev EV, Alekseychik MI. Dynamically monitors the state of the cutting process. Russian Engineering Research. 1998;12:6–13.
  14. Zakovorotny VL, Pham DT, Nguyen XC. MODELING OF TOOL DEFORMATION OFFSETTING TO WORKPIECE IN TURNING. Vestnik of Don State Technical University . 2010;10(7):1005-1015. (In Russian).
  15. Altintas Y, Budak E. Analytical prediction of stability lobes in milling. Ann. CIRP. 1995;44(1):357–362. DOI: 10.1016/S0007-8506(07)62342-7
  16. Balachandran B. Non-linear dynamics of milling process. Philos. Trans. Roy. Soc. 2001;359:793–819.
  17. Davies MA, Pratt JR. The stability of low immersion milling. Ann. CIRP. 2000; 49: 37–40.
  18. Gouskov AM, Voronov SA, Paris H, Batzer SA. Nonlinear dynamics of a machining system with two interdependent delays. Commun. Nonlin. Sci. Numer. Simul. 2002;7:207.
  19. Anishchenko VS. Complex fluctuations in simple systems. Moscow: Nauka; 1990. 312 p. (In Russian).
  20. Anishchenko VS, Vadivasova TE, Strelkova GI. Self-sustained oscillations of dynamical and stochastic systems and their mathematical image — an attractor. Izvestiya VUZ. Applied Nonlinear Dynamics. 2010;6(1):107–126.
  21. Neymark UI, Landa PS. Stochastic and chaotic fluctuations. Moscow: Nauka; 1987. 424 p. (In Russian).
  22. Li T-Y, Yorke JA. Period three implies chaos. Amer. Math. Monthly. 1975;82(10): 985–992.
  23. Lorens EN. Deterministic nonperiodic flow. J. Atmos. Sci. 1963;20(2):130–141. DOI: 10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2
  24. Dorfman JR. An Introduction to Chaos in Nonequilibrum Statistical Mechanics. Cambridge University Press; 1999. 288 p.
  25. Bobrov VF. Fundamentals of metal cutting theory. Moscow: Mashinostroenie; 1975. 344 p. (In Russian).
  26. Zakovorotniy VL, Pham DT, Chiem XN, Ryzhkin MN. DYNAMIC COUPLING MODELING FORMED BY TURNING IN CUTTING DYNAMICS PROBLEMS (VELOCITY COUPLING). Vestnik of Don State Technical University . 2011;11(2):137-146. (In Russian).
  27. Zakovorotniy VL, Pham DT, Chiem XN, Ryzhkin MN. DYNAMIC COUPLING MODELING FORMED BY TURNING IN CUTTING DYNAMICS PROBLEMS (positional coupling).Vestnik of Don State Technical University . 2011;11(3):301-311. (In Russian).
  28. Feigenbaum MJ. The transition to a periodic behavior in turbulent systems. Commun. Math. Phys. 1980;77(1):65–86. DOI: 10.1007/BF01205039
  29. Kabaldin YG. Self-organization and non-linear dynamics in the processes of friction and wear of the tool during cutting. Komsomolsk-on-Amur: KnASU; 2003. 175 p. (In Russian).
Received: 
18.03.2014
Accepted: 
05.05.2014
Published: 
31.10.2014
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