Log in

A time-space discretization method in milling stability prediction of thin-walled component

  • ORIGINAL ARTICLE
  • Published:
The International Journal of Advanced Manufacturing Technology Aims and scope Submit manuscript

Abstract

The stability prediction of thin-walled workpiece milling is an awkward problem due to the time variant of dynamic characteristics during milling process. Integrating the time discretization method for stability prediction mentioned in many articles, a novel time-space discretization method for thin-walled component milling stability prediction is proposed based on thin plate theory and mode superposition principle, which includes the effects of the engagement position between cutter and workpiece and multi-modes of the system. The results show that the method presented is very reliable and efficient, and its accuracy is also in good agreement with experimental results. Additionally, the method can be used to handle various complex boundary conditions by means of the updated Rayleigh-Ritz solutions together with the penalty method. Two case studies are performed to explain the validation of the method as well as milling experiments of a half-clamped thin plate.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (Germany)

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Yi W, Jiang ZL, Shao WX, Han XC, Liu WP (2015) Error compensation of thin plate-shape part with prebending method in face milling. Chin J Mech Eng 28:88–95

    Article  Google Scholar 

  2. Song QH, Ju GG, Liu ZQ, Ai X (2014) Subdivision of chatter-free regions and optimal cutting parameters based on vibration frequencies for peripheral milling process. Int J Mech Sci 83:172–183

    Article  Google Scholar 

  3. Tobias SA (1977) Machine tool vibration. China Machine Press, Bei**g

    Google Scholar 

  4. Smith S, Tlusty J (1990) Update on high-speed milling dynamics. Trans ASME J Eng Ind 112:142–149

    Article  Google Scholar 

  5. Altintas Y, Budak E (1995) Analytical prediction of stability lobes in milling. Ann CIRP 44:357–362

    Article  Google Scholar 

  6. Merdol SD, Altintas Y (2004) Multi frequency solution of chatter stability for low immersion milling. Trans ASME J Manuf Sci Eng 126:459–466

    Article  Google Scholar 

  7. Faassen RPH, Wouw VDN, Nijimeijer H, Oosterling JAJ (2007) An improved tool path model including periodic delay for chatter prediction in milling. J Comput Nonlinear Dyn 2:167–179

    Article  Google Scholar 

  8. Ding Y, Zhu LM, Zhang XJ, Ding H (2010) A full-discretization method for prediction of milling stability. Int J Mach Tools Manuf 50:502–509

    Article  Google Scholar 

  9. Bayly PV, Halley JE, Mann BP, Davies MA (2003) Stability of interrupted cutting by temporal finite element analysis. Trans ASME J Manuf Sci Eng 125:220–225

    Article  Google Scholar 

  10. Ding Y, Zhu LM, Zhang XJ, Ding H (2013) Stability analysis of milling via the differential quadrature method. Tans ASME J Manuf Sci Eng 135:044502–1–7

    Google Scholar 

  11. Totis G, Albertelli P, Sortino M, Monno M (2014) Efficient evaluation of process stability in milling with spindle speed variation by using the Chebyshev collocation method. J Sound Vib 333:646–668

    Article  Google Scholar 

  12. Lehotzky D, Insperger T, Khasawneh F, Stepan G (2016) Spectral element method for stability analysis of milling processes with discontinuous time-periodicity. Int J Adv Manuf Technol. doi:10.1007/s00170-016-9044-z

    Google Scholar 

  13. Song QH, Ai X, Tang WX (2011) Prediction of simultaneous dynamic stability limit of time-variable parameters system in thin-walled workpiece high-speed milling processes. Int J Adv Manuf Technol 55:883–889

    Article  Google Scholar 

  14. Luo M, Zhang DH, Wu BH, Zhou X (2011) Material removal process optimization for milling of flexible workpiece considering machining stability. Proc Inst Mech Eng B-J Eng Manuf 225:1263–1272

    Article  Google Scholar 

  15. Budak E, Altintas Y (1998) Analytical prediction of chatter stability in milling—part II: application of the general formulation to common milling systems. Trans ASME J Dyn Syst 120:31–36

    Article  Google Scholar 

  16. Ukar E, Campa FG, Sanchez JA, Rivero A (2005) The milling of airframe components with low rigidity: a general approach to avoid static and dynamic problems. Proc Inst Mech Eng B-J Eng Manuf 219:789–802

    Article  Google Scholar 

  17. Bravo U, Altuzarra O, Lopez de Lacalle LN, Sanchez JA, Campa FJ (2005) Stability limits of milling considering the flexibility of the workpiece and the machine. Int J Mach Tools Manuf 45:1669–1680

    Article  Google Scholar 

  18. Thevenot V, Arnaud L, Dessein G, Cazenave LG (2006) Integration of dynamic behaviour variations in the stability lobes method: 3D lobes construction and application to thin-walled structure milling. Int J Adv Manuf Technol 27:638–644

    Article  Google Scholar 

  19. Thevenot V, Arnaud L, Dessein G, Cazenave LG (2006) Influence of material removal on the dynamic behavior of thin-walled structures. Mach Sci Technol 10(3):275–287

    Article  Google Scholar 

  20. Song QH, Liu ZQ, Wan Y, Ju GG, Shi JH (2015) Application of Sherman-Morrison-Woodbury formulas in instantaneous dynamic of peripheral milling for thin-walled component. Int J Mech Sci 96–97:79–90

    Article  Google Scholar 

  21. Seguy S, Dessein G, Arnaud L (2008) Surface roughness variation of thin wall milling related to modal interactions. Int J Mach Tools Manuf 48:261–274

    Article  Google Scholar 

  22. Zhang XJ, **ong CH, Ding Y (2011) A new solution for stability prediction in flexible part milling in intelligent robotics and applications. Sprnger-Verlag, Berlin Heidelberg, pp. 452–464

    Google Scholar 

  23. Zhang XJ, **ong CH, Ding Y, Zhang XM (2010) Stability analysis in milling of thin-walled workpieces with emphasis on the structural effect. Proc Inst Mech Eng B-J Eng Manuf 224:589–608

    Article  Google Scholar 

  24. Ilanko S, Bharathy GK (2012) Positive and negative penalty parameters in optimization subjected to continuous constraints. Comput Struct 108–109:83–92

    Article  Google Scholar 

  25. Chakraverty S (2009) Vibration of plate: vibration basics for plates. CRC Press, Taylor & Francis Group, Boca Raton

    Google Scholar 

  26. Ilanko S, Monterrubio LE (2014) The Rayleigh-Ritz method for structural analysis. John Wiley & Sons, Inc., Hoboken

    Book  MATH  Google Scholar 

  27. Monterrubio LE, Ilanbo S (2015) Proof of convergence for a set of admissible functions for the Rayleigh-Ritz analysis of beams and plates and shells of rectangular planform. Comput Struct 147:236–243

    Article  Google Scholar 

  28. Richardson MH, Formenti DL (1982) Parameter estimation from frequency response measurements using rational fraction polynomials. Proc 1st Int Modal Anal Conf Orlando FL 1:167–186

    Google Scholar 

  29. Rao SS (2011) Mechanical vibration, 5th edn. Prentice Hall, Upper Saddle River

    Google Scholar 

  30. Song QH, Shi JH, Liu ZQ, Wan Y (2016) Dynamic analysis of rectangular thin plates of arbitrary boundary conditions under moving loads. Int J Mech Sci 117:16–29

    Article  Google Scholar 

  31. Altintas Y (2012) Manufacturing automation: metal cutting mechanics, machine tool vibrations, and CNC design, 2nd edn. Cambridge University Press, London

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Qinghua Song.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Song, Q., Shi, J., Liu, Z. et al. A time-space discretization method in milling stability prediction of thin-walled component. Int J Adv Manuf Technol 89, 2675–2689 (2017). https://doi.org/10.1007/s00170-016-9379-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00170-016-9379-5

Keywords

Navigation