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Cutting-system dynamics

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Abstract

The attractive sets formed in the vicinity of equilibrium (asymptotically stable orbital limiting cycles, two-dimensional invariant tori, and chaotic attractors) are analyzed. The bifurcations of the system in parameter space and the space of control parameters are considered. General laws of stability loss of the equilibrium in a cutting system are outlined.

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References

  1. Nicolis, G. and Prigogine, I., Exploring Complexity: An Introduction, New York: W.H. Freeman, 1989.

    Google Scholar 

  2. Haken, H., Information and Self-Organization. A Macroscopic Approach to Complex Systems, Berlin: Springer-Verlag, 1988.

    Book  MATH  Google Scholar 

  3. Sinergetika i problemy teorii upravleniya (Synergetic and Problems of Management Theory), Kolesnikov, A.A., Ed., Moscow: Fizmatlit, 2004.

  4. Tlustý, J., Samobuzené Kmity v Obrábecích Strojích, Praha: Cesk. Akad. Ved., 1954.

    Google Scholar 

  5. Tlustý, J., Polacek, A., Danek, C., and Spacek, J., Selbsterregte Schwingungen an Werkzeugmaschinen, Berlin: VEB Verlag Technik, 1962.

    Google Scholar 

  6. Tlusty, J., Manufacturing Processes and Equipment, Upper Saddle River, NJ: Prentice Hall, 2000.

    Google Scholar 

  7. Tobias, S.A., Machine Tool Vibrations, London: Blackie, 1965.

    Google Scholar 

  8. Kudinov, V.A., Dinamika stankov (Dynamics of Machines), Moscow: Mashinostroenie, 1967.

    Google Scholar 

  9. El’yasberg, M.E., Avtokolebaniya metallorezhushchikh stankov: teoriya i praktika (Auto-Oscillations of Machine Tools: Theory and Practice), St. Petersburg: Osoboe Konstr. Byuro Stankostr., 1993.

  10. Veits, V.L. and Vastil’kov, D.V., Dynamics, modeling, and quality maintenance at the machine treatment of small hard billets, Stanki Instrum., 1999, no. 6, pp. 9–13.

    Google Scholar 

  11. Zakovorotnyj, V.L. and Flek, M.B., Dinamika protsessa rezaniya. Sinergeticheskii podkhod (Dynamics of Cutting Process: Synergetic Approach), Rostov-on-Don: Terra, 2006.

    Google Scholar 

  12. Zakovorotnyj, V.L., Fam Din Tung, and Nguen Suan Tiem, Mathematical modeling and parametric identification of dynamic properties of the tool and billet subsystem, Izv. Vyssh. Uchebn. Zaved., Sev.-Kavk. Reg., Tekh. Nauki, 2011, no. 2, pp. 38–46.

    Google Scholar 

  13. Stepan, G., Delay-differential equation models for machine tool chatter, in Nonlinear Dynamics of Material Processing and Manufacturing, Moon, F.C., Ed., New York: Wiley, 1998, pp. 165–192.

    Google Scholar 

  14. Stepan, G., Insperge, T., and Szalai, R., Delay, parametric excitation, and the nonlinear dynamics of cutting processes, Int. J. Bifurcation Chaos Appl. Sci. Eng., 2005, vol. 15, no. 9, pp. 2783–2798.

    Article  MATH  Google Scholar 

  15. Zakovorotnyj, V.L., Luk’yanov, A.D., Nguen Dong An, and Fam Din Tung, Sinergeticheskii sistemnyi sintez upravlyaemoi dinamiki metallorezhushchikh stankov s uchetom evolyutsii svyazei (Synergetic System Synthesis of Controlled Dynamics of Metal Cutting Machines, Taking into Account the Evolution of Relations), Rostov-on-Don: Donsk. Gos. Tekh. Univ., 2008.

    Google Scholar 

  16. Zharkov, I.G., Vibratsii pri obrabotke lezviinym instrumentom (Vibrations Occurred during Edge Tool Implementation), Leningrad: Mashinostroenie, 1987.

    Google Scholar 

  17. Kashirin, A.I., Issledovanie vibratsii pri rezanii metallov (Analysis of Vibration at the Metal Cutting), Moscow: Akad. Nauk SSSR, 1944.

    Google Scholar 

  18. Sokolovskii, A.P., Vibratsii pri rabote na metallorezhushchikh stankakh. Issledovanie kolebanii pri rezanii metallov (Vibration at Working on Machines: Analysis of Vibrations in Metal Cutting), Moscow: Mashgiz, 1958, pp. 15–18.

    Google Scholar 

  19. Corpus, W.T. and Endres, W.J., Added stability lobes in machining processes that exhibit periodic time variation. Part 1: An analytical solution, J. Manuf. Sci. Eng., 2004, no. 126, pp. 467–474.

    Article  Google Scholar 

  20. Gouskov, A.M., Voronov, S.A., Paris, H., and Batzer, S.A., Nonlinear dynamics of a machining system with two interdependent delays, Commun. Nonlinear Sci. Numer. Simul., 2002, no. 7, pp. 207–221.

    Article  MATH  Google Scholar 

  21. Zakovorotnyj, V.L. and Fam Thy Hyong, Parametric self-excitation of dynamic cutting system, Vestn. Donsk. Gos. Tekh. Univ., 2013, vols. 74–75, nos. 5–6, pp. 97–104.

    Google Scholar 

  22. Mathieu, E., Memoire sur le mouvement vibratoire d'une membrane de forme elliptique, J. Math. Pure Appl., 1968, no. 13, pp. 137–203.

    Google Scholar 

  23. Floquet, M.G., Equations differentielles lineaires a coefficients peridiques, Ann. Sci. Ec. Norm. Super., 1883, no. 12, pp. 47–89.

    MathSciNet  Google Scholar 

  24. Litak, G., Chaotic vibrations in a regenerative cutting process, Chaos, Solitons Fractals, 2002, no. 13, pp. 1531–1535.

    Article  MATH  Google Scholar 

  25. Grabec, I., Chaotic dynamics of the cutting process, J. Mach. Tools Manuf., 1988, no. 28, pp. 19–50.

    Article  Google Scholar 

  26. Litak, G., Chaotic vibrations in a regenerative cutting process, Chaos, Solitons Fractals, 2002, no. 13, pp. 1531–1535.

    Article  MATH  Google Scholar 

  27. Wiercigroch, M., Chaotic vibrations of a simple model of the machine tool-cutting system, ASME J. Vib. Acoust., 1997, no. 119, pp. 468–542.

    Article  Google Scholar 

  28. Wiercigroch, M. and Cheng, A.H.-D., Chaotic and stochastic dynamics of orthogonal metal cutting, Chaos, Solitons Fractals, 1997, no. 8, pp. 715–740.

    Article  MATH  Google Scholar 

  29. Kabaldin, Yu.G., Samoorganizatsiya i nelineinaya dinamika v protsessakh treniya i iznashivaniya instrumenta pri rezanii (Self-Organization and Nonlinear Dynamics in the Friction and Wear Processes of Cutting Instrument), Komsomolsk-on-Amur: Komsomolsk-na-Amur. Gos. Tekh. Univ., 2003.

    Google Scholar 

  30. Feigenbaum, M.J., Quantitative universality for a class of nonlinear transformations, J. Stat. Phys., 1978, vol. 19, pp. 25–52.

    Article  MathSciNet  MATH  Google Scholar 

  31. Murashkin, L.S. and Murashkin, S.L., Prikladnaya nelineinaya mekhanika stankov (Applied Nonlinear Mechanics of Machines), Leningrad: Mashinostroenie, 1977.

    Google Scholar 

  32. Warminski, J., Litak, G., Cartmell, M. P., Khanin, R., and Wiercigroch, M., Approximate analytical solutions for primary chatter in the non-linear metal cutting model, J. Sound Vib., 2003, vol. 259, no. 4, pp. 917–933.

    Article  Google Scholar 

  33. van der Pol, F. and Strutt, M.J.O., On the stability of the solutions of Mathieu's equation, Philos. Mag. J. Sci., 1928, no. 5, pp. 18–38.

    Article  MATH  Google Scholar 

  34. Zakovorotnyj, V.L., Fam Din Tung, and Nguen Suan Tiem, Mathematical modeling and parametric identification of dynamic properties of the tool and the billet subsystem at turning, Izv. Vyssh. Uchebn. Zaved., Sev.- Kavk. Reg., Tekh. Nauki, 2011, no. 2, pp. 38–46.

    Google Scholar 

  35. Zakovorotnyj, V.L., Fam Din Tung, and Nguen Suan Tiem, Simulation of deformation shifts of the tool regards to the billet during turning, Vestn. Donsk. Gos. Tekh. Univ., 2010, vol. 10, no. 7, pp. 1005–1015.

    Google Scholar 

  36. Lyapunov, A.M., Obshchaya zadacha ob ustoichivosti dvizheniya. Sobranie sochinenii (General Problem of Motion Stability: Collection of Research Works), Moscow: Akad. Nauk SSSR, 1956, vol. 2.

    Google Scholar 

  37. Merkin, D.R., Vvedenie v teoriyu ustoichivosti dvizheniya (Introduction to the Theory of Motion Stability), Moscow: Nauka, 1987.

    MATH  Google Scholar 

  38. Likhadanov, V.M., The effect of forces on the stability of motion, Prikl. Matem. Mekh., 1974, vol. 38, pp. 246–253.

    Google Scholar 

  39. Likhadanov, V.M., Stabilization of potential systems, Prikl. Matem. Mekh., 1975, vol. 39, pp. 53–58.

    MathSciNet  Google Scholar 

  40. Zakovorotnyj, V.L., Bordachev, E.V., and Alekseichik, M.I., Dynamic monitoring of the status of the cutting process, Stanki Instrum., 1998, no. 12, pp. 6–12.

    Google Scholar 

  41. Zakovorotnyj, V.L. and Ladnik, I.V., Compilation of information model of the dynamic system of the metalcutting machine for the diagnosis of treatment process, Probl. Mashinostr. Nadezhnosti Mash., 1991, no. 4, pp. 75–79.

    Google Scholar 

  42. Zakovorotnyj, V.L. and Bordachev, E.V., Information support of the dynamic diagnostics system of the cutting tool wear by the example of turning, Probl. Mashinostr. Nadezhnosti Mash., 1995, no. 3, pp. 95–101.

    Google Scholar 

  43. Ostaf’ev, V.A., Antonyuk, V.S., and Tymchik, G.S., Diagnosis of the metal treatment process, Tekhnika, 1991, pp. 54–55.

    Google Scholar 

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Correspondence to V. L. Zakovorotnyi.

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Original Russian Text © V.L. Zakovorotnyi, V.S. Bykador, 2015, published in STIN, 2015, No. 12, pp. 18–24.

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Zakovorotnyi, V.L., Bykador, V.S. Cutting-system dynamics. Russ. Engin. Res. 36, 591–598 (2016). https://doi.org/10.3103/S1068798X16070182

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  • DOI: https://doi.org/10.3103/S1068798X16070182

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