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

For citation:

Zakovorotny V. L., Gvindjiliya V. E. Bifurcations of attracting sets of cutting tool deformation displacements at the evolution of treatment process properties. Izvestiya VUZ. Applied Nonlinear Dynamics, 2018, vol. 26, iss. 5, pp. 20-38. DOI: 10.18500/0869-6632-2018-26-5-20-38

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Language: 
Russian
Heading: 
Applied Problems of Nonlinear Oscillation and Wave Theory
Article type: 
Article
UDC: 
621.9:531.3
DOI: 
10.18500/0869-6632-2018-26-5-20-38

Bifurcations of attracting sets of cutting tool deformation displacements at the evolution of treatment process properties

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

Aim. The aim of the investigation is to study the evolutionary properties changes of the dynamic cutting system and the bifurcation of the attracting sets of the deformation displacement of the tool due to the irreversible transformation of the energy input in coupling tool-processing are considered. Method. The mathematical modeling of the evolutionary system in form of the integro-differential functionally related systems is indicated, and the problem of bifurcation of the deformation displacement of the tool relatively to detail in the processing of evolution is considered. The example of the bifurcation and their influence on output properties of the processing. Novelty. In contrast to previously done researches in which the changes of this properties are determined by the set variations of the system parameters, for example, the rigidity of the workpiece, the evolution of the parameters is considered in the article as the natural process caused by the irreversible transformations of the energy in the cutting area. In this case the parameters of the dynamics (which is formed by the processing) depend on the phase work trajectories and the power of the irreversible transformations in the interface knots between the tool sides and the detail, and in the zone of the chip formation. Therefore the dynamic link parameters are considered as depending on the trajectories of the work and the power of the irreversible transformation in marked areas. Thus on the one side the parameters depend on these trajectories, on the another side their changing acts the work and the power of the irreversible transformation. Discussion. The important general regularities of the control of the processing on metal-cutting machines are not considered earlier. Their consist in coordination of the external control, for example, the NPC with the internal dynamic system changing evolutionarily. Their discussed here.  

Key words: 
dynamic system softheturning
system evolution
bifurcation of the attracting sets of the deformational displacement
Volterra operator
Reference: 
  1. Dalskiy A.M. Suslov A.G. Scientific Bases of Technology of Mechanical Engineering. M.: Mechanical Engineering, 2002. 684 p. (in Russian).
  2. Vasilyev A.S., Dalskiy A.M., Zolotarevskiy Y. M., Kondakov A.I. The Directing Formation of the Properties of Products of the Mechanical Engineering. M.: Mechanical Engineering, 2005, 352 p. (in Russian).
  3. Plotnikov A.L. The Control of the Parameters of the Bladed Process on the Machines with NCN. ONIKS, 2012. 231 p. (in Russian)
  4. Sosonkin V.L. The concept of the NCN system basis on PC. STIN, 1990, no. 11, pp. 9–14 (in Russian)
  5. Kozochkin M.P., Allenov D.G. The research of influence of wear of the cutting edge of the tool on deformations of a blanket of a detail. Vestnik MSTU «Stankin», 2015, no. 4 (35), pp. 22–29 (in Russian).
  6. Bekir Yalcin. Surface roughness and cutting forces in turning of tool steel with mixed ceramic and cubic boron nitride cutting tools. Transactions of the Canadian Society for Mechanical Engineering, 2015, vol. 39, no. 2.
  7. Borodkin N.N., Vasin S.A., Vasin L.A. Features of formation of the force field structure in the vicinity of the cutter top with a high-damping design of the toolholder. STIN, 2018, no. 4, pp. 19–26 (in Russian). 
  8. Zakovorotny V.L., Fam D.T., Nguen S.T., Rigkin M.N. Modeling of the dynamic communication formed by turning process in problems of dynamics of process of cutting (speed communication). Vestnik DSTU, 2011, vol. 11, no. 2 (53), pp. 137– 146 (in Russian).
  9. Zakovorotny V.L., Fam D.T., Nguen S.T., Rigkin M.N. Modeling of the dynamic communication formed by turning process in problems of dynamics of process of cutting (position communication). Vestnik DSTU, 2011, vol. 11, no. 3 (54), pp. 301– 311 (in Russian).
  10. Kudinov V.A. The dynamic of the machine. M.: Mechanical engineering, 1967, 359 p. (in Russian)
  11. Voronov C.A., Nepochatov A.V., Kiselev I.A. Criteria of the valuation stability of the milling process of the non-rigid parts. Scientific-educational and applied journal. University news, Engineering, 2011, no. 1, pp. 50–62 (in Russian).
  12. Veic V.L., Vasilkov D.V. Problems of dynamics, modeling and ensuring quality when machining low-rigid preparations, STIN, 1999, no. 6, pp. 9–13 (in Russian).
  13. Gorodetsky Y.I. The theory of the nonlinear vibrations and the dynamic of the machines. Vestnik of Lobachevsky University of Nizhni Novgorod, Series: Mathematical modeling and optimal control, 2001, no. 2, pp. 69–88 (in Russian).
  14. El’yasberg M.E. Self-Oscillation of the Cutting Machine: Theory and Practice. St. P.: OKBS, 1993, 182 p. (in Russian).
  15. Vasin S.A., Vasin L.A. Synergetic approach to the description of the origin and development of the self-oscillation when turning. Science Intensive Technologies in Mechanical Engineering, 2012, no. 1, pp. 11–16 (in Russian).
  16. Borodkin N.N., Vasin S.A., Vasin L.A. Prevention of the process of the emergence and development of self-oscillations whith turning cutters with structured tools. Izvestija Tulskogo Gosudarstvennogo Universiteta, Technical Science, 2014, no. 11–1, pp. 234–243 (in Russian).
  17. Voronov S.A., Kisilev I.A. Nonlinear problems of the dynamic of cutting processes. Mechanical Engineering and Engineering Education, 2017, no. 2(51), pp. 9–23 (in Russian).
  18. Gouskov A. M., Voronov S. A., Paris H., Batzer S. A. Nonlinear dynamics of a machining system with two interdependent delays, Commun. Nonlin. Sci. Numer. Simul., 2002, 7, pp. 207–221.
  19. KaoY.-C., NguyenN.-T., ChenM.-S., Su S.T. A prediction method of cutting force coefficients with helix angle of flat-end cutter and its application in a virtual threeaxis milling simulation system. The International Journal of Advanced Manufacturing Technology, 2015, Vol. 1, iss. 9–12, pp. 1793–1809.
  20. Warminski J., Litak G., Cartmell M.P., Khanin R., Wiercigroch M.. Approximate analytical solutions for primary chatter in the non-linear metal cutting model. Journal of Sound and Vibration, 2003, 259 (4), pp. 917–933.
  21. Stepan G. Delay-differential equation models for machine tool chatter In Nonlinear Dynamics of Material Processing and Manufacturing, ed. Moon F.C., NY: John Wiley, 1998, pp. 165–192.
  22. Stepan G., Insperge 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.
  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.
  24. Kufarev G.L., Naumov V.A. Influence of wear on cutting forces when turning. News of the Tomsk Polytechnical Institute of S.M. Kirov, 1966, vol. 147, pp. 187–192 (in Russian).
  25. Farouk Mahfoudi, Gautier List, Alain Molinari and Abdelhadi Moufki, Lakhdar Boulanouar. High speed turning for hard material with PCBN inserts: Tool wear analysis. Int. J. Machining and Machinability of Materials, 2008, vol. 3, no. 1/2, pp. 62–79.
  26. Zakovorotny V.L., Fam D.T., Bykador V.S. Self-organization and bifurcation of the dynamic system of metal cutting. Izvestia VUZ, Applied Nonlinear Dynamics, 2014, vol. 22, no. 3, pp. 26–39 (in Russian).
  27. Zakovorotny V.L., Fam D.T., Bykador V.S. The influence of bending deformations of the tool on the self-organization and bifurcation of the dynamic system of metal cutting. Izvestia VUZ, Applied Nonlinear Dynamics, 2014, vol. 22, no. 3, pp. 40–52 (in Russian).
  28. Zakovorotny V.L., Fam T.H. Parametric-excitation of the dynamic system of cutting. Vestnik of DSTU, 2013, vol. 13, no. 5–6(74), pp. 97–103 (in Russian).
  29. Zakovorotny V.L., Gvindjiliya V.E. The influence of kinematic perturbations towards longitudinal motion on shape-generating movement trajectories in cutting dynamic system. University News. North-Caucasian Region. Technical Sciences Series, 2016, no. 4 (192), pp. 67–76 (inRussian).
  30. Zakovorotny V.L., Gvindjiliya V.E. Bifurcations of attracting sets of deformation displacement of cutting tool depending on the spindle group beats. Izvestia VUZ, Applied Nonlinear Dynamics, 2017, vol. 25, no. 6, pp. 40–52 (in Russian).
  31. Haken G. Secrets of the Nature. Synergetic: the Doctrine of Interaction. M.-Izhevsk, Institute of the Computer Researches, 2003, 320 p. (in Russian)
  32. Prigogine I. From Being to Becoming. Moscow: Science, 1985, 296 p. (in Russian)
  33. Prigogine I., Stengers I. Order out of Chaos: Man’s New Dialogue with the Nature. M.: Progress, 1986. 432 p. (in Russian)
  34. Remada M., Rigal J. Evolution during time of tool wear and cutting forces in the case of hard turning with CBN inserts. Journal of Materials Processing Technology, 2006, vol. 178, pp. 67–75.
  35. Brzhozovsky B.M., Martynov V.V. The Control of Systems and Processes, Saratov, Saratov State Technical University, 2008, pp. 137–142 (in Russian).
  36. Zakovorotny, V.L., Bordachev E.V. Information support of the dynamic diagnostic system for cutting tool wear by the example of lathing. Journal of Machinery Manufacture and reliability, 1995, no. 3, pp. 95–103 (in Russian).
Received: 
17.05.2018
Accepted: 
20.06.2018
Published: 
31.10.2018
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