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Mathematical Modeling of Wear of Cutter on Back Edge by Taking into Account Beating and Kinematic Perturbations

  • V. L. Zakovorotny
  • V. E. Gvindjiliya
Conference paper
Part of the Lecture Notes in Mechanical Engineering book series (LNME)

Abstract

The study of the wear of the cutter on the back edge with the turning process by taking into account the beating and the kinematic perturbations on the basis of mathematical simulation or mathematical modeling of the wear is provided. The basis of the wear modeling assumes the concept of its link between the work and power of the irreversible transformation in the contact area of the tool back edge and detail. For this purpose, the Voltaire integral operator of the second kind regarding the phase trajectory of the power of the irreversible transformation to the implemented work is used. The trajectory of the power to the work is determined on the basis of the performed model and depends on the structure and the parameters of the dynamic model of the cutting system as well as the beats and the kinematical perturbations. The example of the dependence wear on the beats parameters is presented.

Keywords

Dynamic cutting system Beats of spindle Kinematic perturbations Wear rate Voltaire operator 

References

  1. 1.
    Chichinadze AV, Braun ED, Bushe NA et al (2001) Basis of tribology. Tutorial for technical universities. Second edn. revised and enlarged. In: Chichinadze AV (ed). Mashinostroenie, Moscow, 668 pGoogle Scholar
  2. 2.
    Regel’ VR, Slutsker AI, Tomashevskii EE (1974) The kinetic nature of the strength of solids. Nauka, Moscow (in Russian)Google Scholar
  3. 3.
    Fleischer G (1982) The question of quantification of friction and wear. Theoretical and applied problems of friction, wear and lubrication of machines. Nauka, Moscow: 285–296 (in Russian)Google Scholar
  4. 4.
    Bershadskiy LI (1981) Self-organizing and concepts of wear resistance of tribosistems. The Society “Knowledge”, Kiev: 1077–1092 (in Russian)Google Scholar
  5. 5.
    Zakovorotny VL, Marchak M, Usikov IV, Lukyanov AD (1998) Interrelation between tribosystem evolution and parameters of dynamic friction system. J Friction Wear 19(6):54–64Google Scholar
  6. 6.
    Zakovorotny VL, Fleck MB, Lukyanov AD, Voloshin DA (2004) Modeling of tool wear by using integral operators. STIN 3:9–14 (in Russian)Google Scholar
  7. 7.
    Zakovorotny VL, Lukyanov AD (2014) The problems of control of the evolution of the dynamic system interacting with the medium. Int J Mech Eng Autom 1(5):271–285Google Scholar
  8. 8.
    Zakovorotny VL (2004) Simulation of the evolutionary change in the processing on machine tools with integral operators. News of higher educational institutions. The North Caucasus region. Series: Natural Sciences 3:26–40. (in Russian)Google Scholar
  9. 9.
    Tlustyi I (1956) The oscillations in machine tools. Mashgiz Publication, Moscow, 395 pp (in Russian)Google Scholar
  10. 10.
    Tlusty J, Polacek A, Danek C, Spacek J (1962) Selbsterregte Schwingungenan Werkzeugmaschinen. VEB VerlagTechnik, BerlinGoogle Scholar
  11. 11.
    Tlusty J (2000) Manufacturing processes and equipment. Prentice Hall, NJGoogle Scholar
  12. 12.
    Tobias SA (1965) Machine tool vibrations. Blackie, LondonGoogle Scholar
  13. 13.
    Kudinov VA (1967) Dynamics of machines. Mashinostroenie, Moscow, 359 pp (in Russian)Google Scholar
  14. 14.
    El’yasberg ME (1993) Self-oscillations of metal cutting tools: theory and practice. OKB stankostroeniya, St. Petersburg (in Russian)Google Scholar
  15. 15.
    Weitz VL, Vasil’kov DV (1999) Problems of dynamics, modeling, and quality assurance for machining workpieces. STIN 6:9–13 (in Russian)Google Scholar
  16. 16.
    Stepan G (1998) Delay-differential equation models for machine tool chatter. In: Moon FC (ed) Nonlinear dynamics of material processing and manufacturing. Wiley, NY, pp 165–192Google Scholar
  17. 17.
    Stepan G, Insperge T, Szalai R (2005) Delay, parametric excitation, and the nonlinear dynamics of cutting processes. Int J Bifurcat Chaos 15(9):2783–2798MathSciNetCrossRefGoogle Scholar
  18. 18.
    Zakovorotny VL, Lukyanov AD, Gubanova AA, Khristoforova VV (2016) Bifurcation of stationary manifolds formed in the neighborhood of the equilibrium in a dynamic system of cutting. J Sound Vib 368:174–190CrossRefGoogle Scholar
  19. 19.
    Zakovorotny VL, Gubanova AA, Lukyanov AD (2016) Use of synergetic concept for the study of the stability of the morphogenetic trajectories of the associated milling. STIN 4:32–40 (in Russian)Google Scholar
  20. 20.
    Zakovorotny VL, Gubanova AA, Lukyanov AD (2016) Conditions of parametric excitation of a dynamic milling system with end mills. STIN 6:10–16 (in Russian)Google Scholar
  21. 21.
    Zakovorotny VL, Gubanova AA, Lukyanov AD (2016) The attracting set for end milling. STIN 8(8):27–33 (in Russian)Google Scholar
  22. 22.
    Zakovorotny VL, Bycador VS (2015) The link effect generated by the cutting process the dynamic of the system. STIN 12:18–24 (in Russian)Google Scholar
  23. 23.
    Zakovorotny V (2015) Bifurcations in the dynamic system of the mechanic processing in metal-cutting tools. WSEAS Trans Appl Theor Mech 10:102–116Google Scholar
  24. 24.
    Zakovorotny VL, Pham DT, Bycador VS (2014) The self-organization and bifurcation of the dynamic system of metal cutting, Izvestiya vuzov. Appl Nonlinear Dyn 22(3):26–39 (in Russian)Google Scholar
  25. 25.
    Zakovorotny VL, Pham DT, Bykador VS (2014) Influence of a flexural deformation of a tool on self-organization and bifurcations of dynamical metal cutting system, Izvestia VUZ. Appl. Nonlinear Dyn 22(3):40–53 (in Russian)Google Scholar
  26. 26.
    Zakovorotny VL, Tung PD, Chiem NX, Ryzhkin MN (2011) Dynamic coupling modeling formed by turning in cutting dynamics problems (velocity coupling). Vestnik of DSTU 11(2):137–147 (in Russian)Google Scholar
  27. 27.
    Zakovorotny VL, Tung PD, Chiem NX, Ryzhkin MN (2011) Dynamic coupling modeling formed by turning in cutting dynamics problems (position coupling). Vestnik of DSTU 11(3):30–38 (in Russian)Google Scholar
  28. 28.
    Haken H (2003) Secrets of nature. Synergetics: Doctrine of Interaction. Izhevsk: Institute of Computer Researches, Moscow (in Russian)Google Scholar
  29. 29.
    Zakovorotny VL, Lukyanov AD, Anh ND, Tung PD (2008) Synergistic system synthesis controlled dynamic of machine tools taking into account the evolution of relationships. Publishing center DGTU, Rostov on Donp, 324 pp (in Russian)Google Scholar
  30. 30.
    Zakovorotny VL, Flek MB (2006) Dynamics of cutting process. Synergetic approach. DSTU Publication Centre, Rostov-on-Don 876 pp (in Russian)Google Scholar
  31. 31.
    Zakovorotny VL, Huong PT (2013) Parametric self-excitation of cutting dynamic system. Vestnik of DSTU 5/6(74/75):97–104 (in Russian)Google Scholar
  32. 32.
    Zakovorotny VL, Gvindjilia VE (2017) Influence of kinematic perturbations on shape-generating movement trajectory stability. Proc Eng 206:157–162CrossRefGoogle Scholar
  33. 33.
    Zakovorotny VL, Bordachev EV (1995) Information support of a system of dynamic diagnostics of the tool wearout on the example of turning. Probl Mech Eng Reliab Mach 3:95–101 (In Russian)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Don State Technical UniversityRostov-on-DonRussia

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