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Attractive manifolds in end milling

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Abstract

The attractive manifolds formed in end milling are analyzed. Such states are formed if the trajectories of steady periodic deformational tool displacements are unstable overall or in individual sections. In the dynamic milling system, attractive manifolds in the form of limit cycles, invariant tori, and strange (chaotic) attractors may appear. Bifurcations of attractive manifolds in parameter space are analyzed at length, with examples. Interest centers on how attractive manifolds affect manufacturing quality.

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References

  1. Drozdov, N.A., Vibrations of machine during turning process, Stanki Instrum., 1937, no. 22, pp. 21–25.

    Google Scholar 

  2. Zhestkost’, tochnost’ i vibratsii pri mekhanicheskoi obrabotke (Rigidness, Accuracy, and Vibrations during Mechanical Processing), Skragan, V.A., Ed., Moscow: Mashgiz, 1956.

  3. Il’nitskii, I.I., Kolebaniya v metallorezhushchikh stankakh i sposoby ikh ustraneniya (Oscillations in Metal-Cutting Machines and Their Elimination), Sverdlovsk: Mashgiz, 1958.

    Google Scholar 

  4. Kashirin, A.I., Issledovanie vibratsii pri rezanii (Analysis of Vibrations during Cutting), Moscow: Akad. Nauk SSSR, 1944.

    Google Scholar 

  5. Sokolovskii, A.P., Vibration at working on metal cutting machines, in Issledovanie kolebanii pri rezanii metallov (Vibration at Working on Metal Cutting Machines: Analysis of Vibrations at Metal Cutting), Moscow: Mashgiz, 1958, pp. 2–23.

    Google Scholar 

  6. Tlustý, J., Samobuzené Kmity v Obráběcích Strojích, Praha: Česk. Akad. Věd., 1954.

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  10. Zakovorotny, V.L., Lukyanov, A.D., Nguen, D.-A., and Fam, D.-T., 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 

  11. Zakovorotny, V.L. and Lukyanov, A.D., The problems of control of the evolution of the dynamic system interacting with the medium, Int. J. Mech. Eng. Autom., 2014, vol. 1, no. 5, pp. 271–285.

    Google Scholar 

  12. Zakovorotny, V.L., Bifurcations in the dynamic system of the mechanic processing in metal-cutting tools, J. Trans. Appl. Theor. Mech., 2015, vol. 10, pp. 102–116.

    Google Scholar 

  13. Zakovorotny, V.L., Fam, D.T., and Bykador, V.S., Self-organization and bifurcation of dynamic system for metal cutting, Izv. Vyssh. Uchebn. Zaved., Prikl. Nelineinaya Din., 2014, vol. 22, no. 3, pp. 26–40.

    Google Scholar 

  14. Zakovorotny, V.L., Fam, D.-T., and Bykador, V.S., Influence of flexural deformations of tool on self-organization and bifurcation of dynamic system of metal cutting, Izv. Vyssh. Uchebn. Zaved., Prikl. Nelineinaya Din., 2014, vol. 22, no. 3, pp. 40–53.

    Google Scholar 

  15. 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.

  16. 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  MathSciNet  MATH  Google Scholar 

  17. Sridhar, R., Hohn, R.E., and Long, G.W., A stability algorithm for the general milling process: contribution to machine tool chatter research-7, ASME J. Eng. Ind., 1968, vol. 90, no. 2, pp. 330–334.

    Article  Google Scholar 

  18. Altintas, Y. and Budak, E., Analytical prediction of stability lobes in milling, Ann. CIRP, 1995, vol. 44, no. 1, pp. 357–362.

    Article  Google Scholar 

  19. Tlusty, J. and Ismail, F., Special aspects of chatter in milling, ASME J. Vibrat., Stress, Reliab. Des., 1983, vol. 105, no. 1, pp. 24–32.

    Article  Google Scholar 

  20. Minis, I. and Yanushevsky, T., A new theoretical approach for the prediction of machine tool chatter in milling, Trans. ASME J. Eng. Ind., 1993, vol. 115, no. 2, pp. 1–8.

    Article  Google Scholar 

  21. Insperger, T. and Stepan, G., Stability of the milling process, Period. Polytech.-Mech. Eng., 2000, vol. 44, no. 1, pp. 47–57.

    Google Scholar 

  22. Budak, E. and Altintas, Y., Analytical prediction of chatter stability in milling. Part I: General formulation, ASME J. Dyn. Syst., Meas., Control, 1998, vol. 120, no. 6 (1), pp. 22–30.

    Article  Google Scholar 

  23. Budak, E. and Altintas, Y., Analytical prediction of chatter stability conditions for multi-degree of systems in milling. Part II: Applications, ASME J. Dyn. Syst., Meas., Control, 1998, vol. 120, no. 6 (1), pp. 31–36.

    Article  Google Scholar 

  24. Merdol, D. and Altintas, Y., Multi-frequency solution of chatter stability for low immersion milling, ASME J. Manuf. Sci. Eng., 2004, vol. 126, no. 3, pp. 459–466.

    Article  Google Scholar 

  25. Insperger, T., Mann, B., Stepan, G., and Bayly, P.V., Stability of up-milling and down-milling. Part 1: Alternative analytical methods, Int. J. Mach. Tools Manuf., 2003, vol. 43, no. 1, pp. 25–34.

    Article  Google Scholar 

  26. Kline, W.A., Devor, R.E., and Shareef, I.A., The prediction of surface accuracy in end milling, ASME J. Eng. Ind., 1982, vol. 104, no. 5, pp. 272–278.

    Article  Google Scholar 

  27. Elbestawi, M.A. and Sagherian, R., Dynamic modeling for the prediction of surface errors in milling of thin-walled sections, Theor. Comp. Fluid Dyn., 1991, vol. 25, no. 2, pp. 215–228.

    Google Scholar 

  28. Campomanes, M.L. and Altintas, Y., An improved time domain simulation for dynamic milling at small radial immersions, Trans. ASME. J. Manuf. Sci. Eng., 2003, vol. 125, no. 3, pp. 416–425.

    Article  Google Scholar 

  29. Paris, H., Peigne, G., and Mayer, R., Surface shape prediction in high-speed milling, Int. J. Mach. Tools Manuf., 2004, vol. 44, no. 15, pp. 1567–1576.

    Article  Google Scholar 

  30. Altintas, Y. and Lee, P., A general mechanics and dynamics model for helical end mills, Ann. CIRP, 1996, vol. 45, no. 1, pp. 59–64.

    Article  Google Scholar 

  31. Ozturk, E. and Budak, E., Modeling of 5-axis milling processes, Mach. Sci. Technol., 2007, vol. 11, no. 3, pp. 287–311.

    Google Scholar 

  32. Budak, E., Ozturk, E., and Tunc, L.T., Modeling and simulation of 5-axis milling processes, Ann. CIRP, 2009, vol. 58, no. 1, pp. 347–350.

    Article  Google Scholar 

  33. Voronov, S.A., Nepochatov, A.V., and Kiselev, I.A., Assessment criteria of stability of milling of non-rigid parts, Izv. Vyssh. Uchebn. Zaved., Mashinostr., 2011, no. 1 (610), pp. 50–62.

    Google Scholar 

  34. Voronov, S. and Kiselev, I., Dynamics of flexible detail milling, Proc. Inst. Mech. Eng., K, 2011, vol. 225, no. 3, pp. 1177–1186.

    Google Scholar 

  35. Zakovorotny, V.L., Gubanova, A.A., and Lukyanov, A.D., Stability of shaping trajectories in milling: synergetic concepts, Russ. Eng. Res., 2016, vol. 36, no. 11, pp. 956–964.

    Article  Google Scholar 

  36. Zakovorotny, V.L., Gubanova, A.A., and Luk’yanov, A.D., Parametric Self-Excitation of a Dynamic End-Milling Machine, Russ. Eng. Res., 2016, vol. 36, no. 12, pp. 1033–1039.

    Article  Google Scholar 

  37. Zakovorotny, V.L., Fam, D.-T., and Nguen, S.-T., 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 

  38. Zakovorotny, V.L., Fam, D.-T., Nguen, S.-T., and Ryzhkin, M.N., Modeling of dynamic coupling formed by turning in the tasks of cutting dynamics: speed relationship, Vestn. Donsk. Gos. Tekh. Univ., 2011, vol. 11, no. 2 (53), pp. 137–146.

    Google Scholar 

  39. Zakovorotny, V.L., Fam, D.-T., Nguen, S.-T., and Ryzhkin, M.N., Modeling of dynamic coupling formed by turning: positional relationship, Vestn. Donsk. Gos. Tekh. Univ., 2011, vol. 11, no. 3 (54), pp. 301–311.

    Google Scholar 

  40. Zakovorotnyj, V.L., Fam D.-T., and Nguen S.-T., Simulation of deformation shifts of the turning tool regards to the billet, Vestn. Donsk. Gos. Tekh. Univ., 2010, vol. 7 (50), pp. 1005–1015.

    Google Scholar 

  41. D’Angelo, R., Linear Time-Varying Systems: Analysis and Synthesis, Boston: Allyn and Bacon, 1970.

    MATH  Google Scholar 

  42. Pontryagin, L.S., Izbrannye trudy (Selected Research Works), Moscow: Nauka, 1988, vol. 2.

    MATH  Google Scholar 

  43. Tikhonov, A.N., Vasil’ev, A.B., and Volosov, V.M., Differential equations containing a small parameter, Tr. mezhdunar. simp. po nelineinym kolebaniyam (Proc. Int. Symp. on Nonlinear Oscillations), Kiev: Akad. Nauk UkrSSR, 1963, pp. 56–61.

    Google Scholar 

  44. 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 

  45. Zharkov, I.G., Vibratsii pri obrabotke lezviinym instrumentom (Vibrations Occurred during Edge Tool Implementation), Leningrad: Mashinostroenie, 1986.

    Google Scholar 

  46. Markov, A.I., Ul’trazvukovaya obrabotka materialov (Ultrasonic Processing of Materials), Moscow: Mashinostroenie, 1980.

    Google Scholar 

  47. Zakovorotny, 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. 75–81.

    Google Scholar 

  48. Zakovorotny, 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 

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Authors and Affiliations

  1. Don State Technical University, Rostov-on-Don, Russia

    V. L. Zakovorotny, A. A. Gubanova & A. D. Lukyanov

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  1. V. L. Zakovorotny
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  2. A. A. Gubanova
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  3. A. D. Lukyanov
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Correspondence to V. L. Zakovorotny.

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Original Russian Text © V.L. Zakovorotny, A.A. Gubanova, A.D. Lukyanov, 2016, published in STIN, 2016, No. 8, pp. 27–33.

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Zakovorotny, V.L., Gubanova, A.A. & Lukyanov, A.D. Attractive manifolds in end milling. Russ. Engin. Res. 37, 158–163 (2017). https://doi.org/10.3103/S1068798X17020198

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