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access icon free Lyapunov–Krasovskii approach to the stability analysis of the milling process

© The Institution of Engineering and Technology
Received 09/11/2017, Accepted 26/02/2018, Revised 06/02/2018, Published 27/02/2018

Self-excited milling vibrations represent an important problem in the manufacturing industry. This study presents an out-of-process analysis based on the Lyapunov–Krasovskii approach which provides operational guidelines for the proper selection of the cutting parameters to guarantee a stable vibration-free process. The proposed approach considers a time-delay two degree of freedom model and takes advantage of some useful tools of the control theory developed for time-delay systems such as the descriptor method and the Bessel–Legendre inequalities.

Inspec keywords: delay systems; vibrations; Lyapunov methods; cutting; linear matrix inequalities; milling; asymptotic stability; stability; delays

Other keywords: out-of-process analysis; milling process; Lyapunov–Krasovskii approach; proper selection; time-delay systems; self-excited milling vibrations; important problem; stable vibration-free process; manufacturing industry; time-delay two degree; operational guidelines; stability analysis

Subjects: Stability in control theory; Algebra; Distributed parameter control systems

References

    1. 1)
      • 28. Park, P.G., Ko, J.W., Jeong, C.: ‘Reciprocally convex approach to stability of systems with time-varying delays’, Automatica, 2011, 47, (1), pp. 235–238.
    2. 2)
      • 35. Ramírez Jerónimo, L.F.: ‘Modelado y análisis de vibraciones en el proceso de fresado’. MSc thesis, Universidad Autónoma del Estado de México, Engineering Faculty, 2017.
    3. 3)
      • 13. Li, Z., Yang, Z., Peng, Y., et al: ‘Prediction of chatter stability for milling process using Runge-Kutta-based complete discretization method’, Int. J. Adv. Manuf. Technol., 2016, 86, pp. 943–952.
    4. 4)
      • 34. Ma, Y., Wan, M., Zhang, W.: ‘Effect of cutter runout on chatter stability of milling process’. 9th Int. Conf. on Digital Enterprise Technology, 2016, vol. 56, pp. 115–118.
    5. 5)
      • 11. Yan, Z., Wang, X., Liu, Z., et al: ‘Third-order updated full-discretization method for milling stability prediction’, Int. J. Adv. Manuf. Technol., 2017, 92, pp. 2299–2309.
    6. 6)
      • 15. Minis, I., Yanushevski, R.: ‘A new theorical approach for the prediction of machine tool chatter in milling’, ASME J. Eng. Ind., 1993, 115, pp. 1–8.
    7. 7)
      • 20. Munoa, J., Beudaert, X., Dombovari, Z., et al: ‘Chatter suppression techniques in metal cutting’ CIRP Ann. Manuf. Technol., 2016, 65, (2), pp. 785–808.
    8. 8)
      • 12. Wan, M., Ma, Y.C., Zhang, W.H., et al: ‘Study on the construction mechanism of stability lobes in milling process with multiple modes’, Int. J. Adv. Manuf. Technol., 2015, 79, pp. 589–603.
    9. 9)
      • 8. Kuljanic, E., Totis, G., Sortino, M.: ‘Vibrations and chatter in machining: state of the art and new approaches’. Proc. of the 8th Int. Conf. Advanced Manufacturing Systems and Technology, Udine International Centre for Mechanical Sciences, 2008.
    10. 10)
      • 23. Fridman, E.: ‘Tutorial on Lyapunov-based methods for time-delay systems’, Eur. J. Control, 2014, 20, (6), pp. 271–283.
    11. 11)
      • 22. Gu, K., Kharitonov, V.L., Chen, J.: ‘Stability of time-delay systems’ (Birkhäuser, New York, USA, 2003).
    12. 12)
      • 27. Zeng, H.B., He, Y., Wu, M., et al: ‘Free-matrix-based integral inequality for stability analysis of systems with time-varying delay’, IEEE Trans. Autom. Control, 2015, 60, (10), pp. 2768–2772.
    13. 13)
      • 14. Altintas, Y., Weck, M.: ‘Chatter stability of metal cutting and grinding’, CIRP Ann. – Manuf. Technol., 2004, 53, (2), pp. 619–642.
    14. 14)
      • 19. Mei, Y., Mo, R., Sun, H., et al: ‘Chatter detection in milling based on singular spectrum analysis’, Int. J. Adv. Manuf. Technol., 2017, pp. 1–12.
    15. 15)
      • 1. Quintana, G., Ciurana, J.: ‘Chatter in machining processes: a review’, Int. J. Mach. Tool Manuf., 2011, 51, pp. 363–376.
    16. 16)
      • 30. Liu, K., Seuret, A., Xia, Y.Q.: ‘Stability analysis of systems with time-varying delays via the second-order Bessel–Legendre inequality’, Automatica, 2017, 76, pp. 138–142.
    17. 17)
      • 6. Sridhar, R., Hohn, R.E., Long, G.W.: ‘A stability algorithm for general milling process. Contribution to Machine Tool Chatter Research’, ASME J. Eng. Ind., 1968, 90, pp. 330–334.
    18. 18)
      • 18. Iglesias, A., Munoa, J., Ciurana, J., et al: ‘Analytical expressions for chatter analysis in milling operations with one dominant mode’, J. Sound Vib., 2016, 375, pp. 403–421.
    19. 19)
      • 10. Insperger, T., Stépán, G.: ‘Semi-discretization for time-delay systems’ (Applied Mathematical Sciences, Springer, USA, 2011), 178.
    20. 20)
      • 7. Opitz, H., Bernardi, F.: ‘Investigation and calculation of chatter behaviour of lathes and milling machines’, CIRP Ann. – Manuf. Technol., 1970, 18, pp. 335–343.
    21. 21)
      • 32. Seuret, A., Gouaisbaut, F.: ‘Delay-dependent reciprocally convex combination lemma’. Rapport LAAS n16006, 2016.
    22. 22)
      • 5. Gomez, M.A., Ochoa, G., Mondié, S.: ‘Necessary exponential stability conditions for linear periodic time-delay systems’, Int. J. Robust Nonlinear Control, 2016, 26, (18), pp. 3996–4007.
    23. 23)
      • 24. Seuret, A., Gouaisbaut, F.: ‘Wirtinger-based integral inequality: application to time-delay systems’, Automatica, 2013, 49, pp. 2860–2866.
    24. 24)
      • 4. Altintas, Y.: ‘Manufacturing automation: metal cutting mechanics, machine tools vibrations, and CNC design’ (Cambridge University Press, USA, 2012, 2nd edn.).
    25. 25)
      • 29. Seuret, A., Gouaisbaut, F.: ‘Hierarchy of LMI conditions for the stability analysis of time-delay systems’, Syst. Control Lett., 2015, 81, pp. 1–7.
    26. 26)
      • 33. Zhang, X.M., Han, Q.L., Seuret, A., et al: ‘An improved reciprocally convex inequality and an augmented Lyapunov–Krasovskii functional for stability of linear systems with time-varying delay’, Automatica, 2017, 84, pp. 221–226.
    27. 27)
      • 25. Zhang, X.M., Han, Q.L.: ‘Robust H∞ filtering for a class of uncertain linear systems with time-varying delay’, Automatica, 2008, 44, pp. 157–166.
    28. 28)
      • 21. Fridman, E.: ‘Introduction to time-delay systems: analysis and control’ (Systems and Control: Foundations and Applications, Birkhäuser, Israel, 2014).
    29. 29)
      • 2. Tlusty, J., Polacek, M.: ‘The stability of machine tools against self-excited vibration in machining’, ASME Int. Res. Prod. Eng., 1963, 1, pp. 465–474.
    30. 30)
      • 31. Liu, K., Seuret, A.: ‘Comparison of bounding methods for stability analysis of systems with time-varying delays’, J. Franklin Inst., 2017, 354, (7), pp. 2979–2993.
    31. 31)
      • 9. Bayly, P.V., Halley, J.E., Mann, B.P., et al: ‘Stability of interrupted cutting by temporal finite element analysis’, Trans. ASME J. Manuf. Sci. Eng., 2002, 125, pp. 220–225.
    32. 32)
      • 17. Hajdu, H., Insperger, T., Bachrathy, D., et al: ‘Prediction of robust stability boundaries for milling operations with extended multi-frequency solution and structured singular values’, J. Manuf. Process., 2017, 30, pp. 281–289.
    33. 33)
      • 3. Tobias, S.A., Fishwick, W.: ‘Theory of regenerative machine tool chatter’, Engineering, 1958, 205, pp. 199–203.
    34. 34)
      • 26. Zhang, X.M., Han, Q.L.: ‘Abel lemma-based finite-sum inequality and its application to stability analysis for linear discrete time-delay systems’, Automatica, 2013, 57, pp. 199–202.
    35. 35)
      • 16. Altintas, Y., Budak, E.: ‘Analytical prediction of stability lobes in milling’, CIRP Ann. – Manuf. Technol., 1995, 44, (1), pp. 357–362.
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