Dynamic Diagnostics of Limiting State of Milling Process Based on Poincaré Stroboscopic Mapping

  • A. A. GubanovaEmail author
Conference paper
Part of the Lecture Notes in Mechanical Engineering book series (LNME)


The article is devoted to the problem of diagnosing the limiting state of the milling process based on the Poincaré stroboscopic mapping. A method based on a contactless measurement of the distance between the cutter body and the measuring transducer is proposed. In this case, a sequence constructed on the basis of the Poincaré stroboscopic mapping is used, for which statistical estimates to determine the roughness, ripple, and mathematical expectation of the size over the entire treated surface are given. The results of the experiment made it possible to obtain effective algorithms for processing information, which, in the course of cutting, allow us to evaluate the limiting states of the process for obtaining information on the replacement of the tool and its readjustment. The dependencies obtained in the work as a whole coincides with the realistic approach to the estimation of the dynamics of milling processes occurring in metal-cutting machines. According to this approach, it is possible to provide unchanged values of the microroughness height due to the redistribution of the geometric component of the roughness determined by the feed, and the evolutionary component that depends on the trajectory of work and the power of irreversible transformations in the cutting zone.


Surface quality Milling Waviness Roughness Critical value 



I express my gratitude to my scientific supervisor Zakovorotniy Vilor Lavrentievich for valuable advice in the planning of research and recommendations on the design of the article.


  1. 1.
    Zakovorotny VL, Gubanova AA, Lukyanov AD (2017) Attractive manifolds in end milling. Russ Eng Res 37(2):158–163CrossRefGoogle Scholar
  2. 2.
    Goldberg S (1967) Henri Poincaré and Einstein’s Theory of Relativity. Am J Phys 35:934–944CrossRefGoogle Scholar
  3. 3.
    Hintikka J (2012) IF logic, definitions and the vicious circle principle. J Philos Logic 41(2):505–517MathSciNetCrossRefGoogle Scholar
  4. 4.
    Budak E, Altintas Y (1995) Modeling and avoidance of static form errors in peripheral milling of plates. J. Mach Tools Manuf 35(3):459–476CrossRefGoogle Scholar
  5. 5.
    Tsai JS, Liao CL (1999) Finite-element modelling of static surface errors in the peripheral milling of thin-walled workpiece. J. Mater Process Technol 94:235–246CrossRefGoogle Scholar
  6. 6.
    Paris H, Peigne G, Mayer R (2004) Surface shape prediction in high-speed milling. J Mach Tools Manuf 44(15):1567–1576CrossRefGoogle Scholar
  7. 7.
    Kersting P, Biermann D (2009) Simulation concept for predicting workpiece vibrations in five-axis milling. J. Mach Sci Technol 13(2):196–209CrossRefGoogle Scholar
  8. 8.
    Voronov S, Kiselev I (2011) Dynamics of flexible detail milling. J Multi-body Dyn 225(3):110–117Google Scholar
  9. 9.
    Lamikiz A, Lopez de Lacalle LN, Sanchez JA, Bravo U (2005) Calculation of the specific cutting coefficients and geometrical aspects in sculptured surface machining. J. Mach Sci Technol 9(3):411–436CrossRefGoogle Scholar
  10. 10.
    Surmann T, Enk D (2007) Simulation of milling tool vibration trajectories along changing engagement conditions. J. Mach Tools Manuf 47(9):1442–1448CrossRefGoogle Scholar
  11. 11.
    Guzel BU, Lazoglu I (2003) Sculpture surface machining: a generalized model of ball-end milling force system. J. Mach Tools Manuf 43(5):453–462CrossRefGoogle Scholar
  12. 12.
    Charpentier E, Ghys E, Lesne A (2010) The scientific legacy of Poincaré. Providence, American Mathematical Society, London Mathematical Society, London, RICrossRefGoogle Scholar
  13. 13.
    Goodman N (1969) Languages of art. An approach to a theory of symbols. Oxford University Press, LondonGoogle Scholar
  14. 14.
    Mette C (1986) Invariantentheorie als Grundlage des Konventionalismus. Überlegungen zur Wissenschaftstheorie Jules Henri Poincarés, Die blaue Eule, EssenGoogle Scholar
  15. 15.
    Zahar E (2001) Poincaré’s philosophy.From conventionalism to phenomenology. Open Court, LaSallezbMATHGoogle Scholar
  16. 16.
    Browder FE (1983) The mathematical heritage of Henri Poincaré. In: Proceedings of symposia in pure mathematics of the american mathematical society, vol 39. American Mathematical Society, ProvidenceGoogle Scholar
  17. 17.
    Darrigol O (2004) The mystery of the Einstein-Poincaré connection. Isis 95:614–626MathSciNetCrossRefGoogle Scholar
  18. 18.
    Goldfarb W (1985) Poincaré against the Logicists, in History and Philosophy of Modern Mathematics. In: Aspray W, Kitcher P (eds). Minnesota Press, Minneapolis, pp 61–81Google Scholar
  19. 19.
    Gray JJ (1991) Did Poincaré say set theory is a disease? Math Intell 13(1):19–22CrossRefGoogle Scholar
  20. 20.
    Vapnik VN, Chervonenkis AY (1974) Theory of pattern recognition. Nauka, Moscow, pp 55–60. (in Russia)Google Scholar

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Authors and Affiliations

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

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