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A novel precise integration-based updated numerical integration method for milling stability prediction

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Abstract

Stability lobe diagrams (SLDs) can be employed to determine the stability behavior of a milling process. Hence, SLD recognition is an important issue for an effective stable machining monitoring system. Various methods have been developed for prediction of milling stability. However, the main shortcoming of such methods is that they cannot accurately and efficiently predict milling stability. This study proposes a novel precise integration-based updated numerical integration method (PI-UNIM) that can be both accurate and efficient in milling stability prediction. The fifth-order Hermite interpolation polynomial for numerical integration formula derivation is addressed in this work. Transition matrix is obtained with the precise integration algorithm. The numerical results obtained using extensive simulation indicate that the proposed method can effectively recognize SLDs for not only low immersion milling situation but also high immersion milling situation. Empirical comparisons show that the proposed method performs better than existing methods in terms of computation accuracy and computation efficiency. A demonstrative example is provided to illustrate the usage of the proposed method.

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Data availability

The data associated with this study is publicly accessible on request.

Code availability

The source code implemented in Matlab available on request.

References

  1. Sridhar R, Hohn R, Long G (1968) A stability algorithm for the general milling process. J Eng Ind-T ASME 90:330–334

    Article  Google Scholar 

  2. Tlusty J, Ismail F (1983) Special aspects of chatter in milling. J Vib Acoust Stress Reliab Des-T ASME 105:24–32

    Article  Google Scholar 

  3. Smith S, Tlusty J (1993) Efficient simulation programs for chatter in milling. CIRP Ann-Manuf Techn 42:463–466

    Article  Google Scholar 

  4. Davies M, Pratt J, Dutterer B, Burns T (2002) Stability prediction for low radial immersion milling. J Manuf Sci E-T ASME 124:217–225

    Article  Google Scholar 

  5. Campomanes M, Altintas Y (2003) An improved time domain simulation for dynamic milling at small radial immersions. J Manuf Sci E-T ASME 125:416–422

    Article  Google Scholar 

  6. Altintas Y, Weck M (2004) Chatter stability of metal cutting and grinding. CIRP Ann-Manuf Techn 53:619–642

    Article  Google Scholar 

  7. Altintaş Y, Budak E (1995) Analytical prediction of stability lobes in milling. CIRP Ann Manuf Technol 44(1):357–362

    Article  Google Scholar 

  8. Merdol SD, Altintas Y (2004) Multi frequency solution of chatter stability for low immersion milling. J Manuf Sci Eng-Trans ASME 126(3):459–466

    Article  Google Scholar 

  9. Bayly P, Halley J, Mann B, Davies M (2003) Stability of interrupted cutting by temporal finite element analysis. J Manuf Sci Eng-Trans ASME 125(2):220–225

    Article  Google Scholar 

  10. Insperger T, Stépán G (2004) Updated semi-discretization method for periodic delay-differential equations with discrete delay. Int J Numer Methods Eng 61(1):117–141

    Article  MathSciNet  MATH  Google Scholar 

  11. Insperger T, Stépán G, Turi J (2008) On the higher-order semi-discretization for periodic delayed systems. J Sound Vib 313(1–2):334–341

    Article  Google Scholar 

  12. Altintas Y, Chan P (1992) In-process detection and suppression of chatter in milling. Int J Mach Tools Manuf 32(3):329–347

    Article  Google Scholar 

  13. Insperger T, Stepan G (2004) Stability analysis of turning with periodic spindle speed modulation via semidiscretization. J Vib Control 10(12):1835–1855

    Article  MATH  Google Scholar 

  14. Long X, Balachandran B (2010) Stability of up-milling and down-milling operations with variable spindle speed. J Vib Control 16(7–8):1151–1168

    Article  MathSciNet  MATH  Google Scholar 

  15. Ding Y, Niu J, Zhu LM, Ding H (2015) Numerical integration method for stability analysis of milling with variable spindle speeds. ASME J Vib Acoust 138(1):011010–011011

    Article  Google Scholar 

  16. Altıntas Y, Engin S, Budak E (1999) Analytical stability prediction and design of variable pitch cutters. J Manuf Sci Eng 121(2):173–178

    Article  Google Scholar 

  17. Sims N, Mann B, Huyanan S (2008) Analytical prediction of chatter stability for variable pitch and variable helix milling tools. J Sound Vib 317(3–5):664–686

    Article  Google Scholar 

  18. Wan M, Zhang W, Dang J, Yang Y (2010) A unified stability prediction method for milling process with multiple delays. Int J Mach Tools Manuf 50(1):29–41

    Article  Google Scholar 

  19. Ding Y, Zhu L, Zhang X, Ding H (2010) A full-discretization method for prediction of milling stability. Int J Mach Tools Manuf 50(5):502–509

    Article  Google Scholar 

  20. Ding Y, Zhu L, Zhang X, Ding H (2010) Second-order full-discretization method for milling stability prediction. Int J Mach Tools Manuf 50(10):926–932

    Article  Google Scholar 

  21. Quo Q, Sun Y, Jiang Y (2012) On the accurate calculation of milling stability limits using third-order full-discretization method. Int J Mach Tools Manuf 62:61–66

    Article  Google Scholar 

  22. Ji Y, Wang X, Liu Z, Yan Z (2018) An updated full-discretization milling stability prediction method based on the higher-order Hermite-Newton interpolation polynomial. Int J Adv Manuf Technol 95:2227–2242

    Article  Google Scholar 

  23. Huang C, Yang W, Cai X, Liu W, You Y (2020) An efficient third-order full-discretization method for prediction of regenerative chatter stability in milling. Shock Vib 1:1–16

    Google Scholar 

  24. Dai Y, Li H, Yang G, Peng D (2021) A novel method with Newton polynomial-Chebyshev nodes for milling stability prediction. Int J Adv Manuf Technol 112:1373–1387

    Article  Google Scholar 

  25. Li M, Zhang G, Huang Y (2013) Complete discretization scheme for milling stability prediction. Nonlinear Dyn 71(1–2):187–199

    Article  MathSciNet  Google Scholar 

  26. Huang T, Zhang X, Ding H (2013) An efficient linear approximation of acceleration method for milling stability prediction. Int J Mach Tools Manuf 74:56–64

    Article  Google Scholar 

  27. Huang T, Zhang X, Ding H (2017) A novel approach with smallest transition matrix for milling stability prediction. Nonlinear Dyn 90:95–104

    Article  MathSciNet  Google Scholar 

  28. Ding Y, Zhu L, Zhang X, Ding H (2011) Numerical integration method for prediction of milling stability. J Manuf Sci Eng-Trans ASME 133(3):031005–031009

    Article  Google Scholar 

  29. Zhang Z, Li H, Meng G, Liu C (2015) A novel approach for the prediction of the milling stability based on the Simpson method. Int J Mach Tools Manuf 99:43–47

    Article  Google Scholar 

  30. Ozoegwu CG (2016) High order vector numerical integration schemes applied in state space milling stability analysis. J Appl Math Comput 273:1025–1040

    Article  MathSciNet  MATH  Google Scholar 

  31. Dong X, Qiu Z (2020) Stability analysis in milling process based on updated numerical integration method. Mech Syst Signal Pr 137:0888–3270

    Article  Google Scholar 

  32. Dai Y, Li H, Xing X, Hao B (2018) Prediction of chatter stability for milling process using precise integration method. Precis Eng-J Int Soc Precis Eng Nanotechnol 52:152–157

    Google Scholar 

  33. Li H, Dai Y, Fan Z (2018) Improved precise integration method for chatter stability prediction of two-DOF milling system. Int J Adv Manuf Technol 101(5–8):1235–1246

    Google Scholar 

  34. Farkas M (1994) Periodic motions. Springer, Berlin

    Book  MATH  Google Scholar 

Download references

Funding

This study is funded by the Fundamental Research Funds for the Central Universities (NT2021019) and National Natural Science Foundation of China (51775279).

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Authors and Affiliations

  1. College of Mechanical and Electrical Engineering, Nanjing University of Aeronautics and Astronautics, 210016, Nanjing, People’s Republic of China

    WeiChao Liu, Wen-An Yang, YuXin Chen & YouPeng You

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  1. WeiChao Liu
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  2. Wen-An Yang
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  3. YuXin Chen
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  4. YouPeng You
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Correspondence to Wen-An Yang.

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Liu, W., Yang, WA., Chen, Y. et al. A novel precise integration-based updated numerical integration method for milling stability prediction. Int J Adv Manuf Technol 124, 2109–2126 (2023). https://doi.org/10.1007/s00170-022-10372-3

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  • DOI: https://doi.org/10.1007/s00170-022-10372-3

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