Skip to main content
SpringerLink
Log in

An updated model of stability prediction in five-axis ball-end milling

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

Abstract

The intention of this paper is to present an updated model to predict stability limits of five-axis ball-end milling. Two-degree of freedom five-axis ball-end milling system in consideration of regenerative effect and helix angle is first concluded into a delay differential equation (DDE) with time-varying coefficients. As the time period being carved up evenly into a certain number of elements, the discrete map of system response is determined with the assistance of generalized precise integration method (GPIM). Then, in a single tooth passing period, the analytic cutter-workpiece engagement (CWE) is extracted by an intersection of spatial surface technique to ascertain the instantaneous cutting angles. Taking the advantage of these angles, the transition matrix denoting the given machining state is established to predict the process stability. The validity of the predictive model is verified in a five-axis CNC machine tool by close accordance with the experimental results. Lastly, a set of comparisons and discussions are developed to demonstrate the feature of this updated predictive model.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. Balachandran B, Zhao MX (2000) A mechanics based model for study of dynamics of milling operations. Meccanica 35(2):89–109

    Article  MATH  Google Scholar 

  2. Xinhua L, 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 

  3. Long XH, Balachandran B (2007) Stability analysis for milling process. Nonlinear Dynam 49(3):349–359

    Article  MATH  Google Scholar 

  4. Bo Q, Liu H, Lian M, Wang Y, Liu K (2018) The influence of supporting force on machining stability during mirror milling of thin-walled parts. Int J Adv Manuf Technol. https://doi.org/10.1007/s00170-018-3113-4

  5. Ismail F, Soliman E (1997) A new method for the identification of stability lobes in machining. Int J Mach Tools Manuf 37(6):763–774

    Article  Google Scholar 

  6. Solis E, Peres CR, Jiménez JE, Alique JR, Monje JC (2004) A new analytical–experimental method for the identification of stability lobes in high-speed milling. Int J Mach Tools Manuf 44(15):1591–1597

    Article  Google Scholar 

  7. Quintana G, Ciurana J, Ferrer I, Rodríguez CA (2009) Sound mapping for identification of stability lobe diagrams in milling processes. Int J Mach Tools Manuf 49(3):203–211

    Article  Google Scholar 

  8. 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 

  9. Altintas Y, Budak E (1995) Analytical prediction of stability lobes in milling. Cirp Ann-Manuf Technol 44(1):357–362

    Article  Google Scholar 

  10. Merdol S, Altintas Y (2004) Multi frequency solution of chatter stability for low immersion milling. J Manuf Sci E-T ASME 126(3):459–466

    Article  Google Scholar 

  11. Altintas Y, Shamoto E, Lee P (1999) Analytical prediction of stability lobes in ball end milling. J Manuf Sci E-T ASME 121(4):586–592

    Article  Google Scholar 

  12. Li Z, Yang Z, Peng Y (2016) Prediction of chatter stability for milling process using Runge-Kutta-based complete discretization method. Int J Adv Manuf Technol 86:943–952

    Article  Google Scholar 

  13. Lin Z, Huang X, Akhtar M (2011) Chatter stability of low-immersion milling in multi-frequency with helix angle. J Comput Theor Nanos 4(6):2076–2081

    Google Scholar 

  14. Insperger T, Stepan G (2004) Updated semi-discretization method for periodic delay-differential equations with time-interval delay. Int J Numer Meth Eng 61(1):117–141

    Article  MATH  Google Scholar 

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

    Article  Google Scholar 

  16. Insperger T (2010) Full-discretization and semi-discretization for milling stability prediction: some comments. Int J Mach Tools Manuf 50(7):658–662

    Article  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  18. Huang T, Zhang X, Zhang X (2013) An efficient linear approximation of acceleration method for milling stability prediction. Int J Mach Tools Manuf 74(8):56–64

    Article  Google Scholar 

  19. Dai Y, Li H, Hao B (2018) An improved full-discretization method for chatter stability prediction. Int J Adv Manuf Technol 96(9–12):3503–3510

    Article  Google Scholar 

  20. Zhang X, Xiong C, Ding Y (2016) Prediction of chatter stability in high speed milling using the numerical differentiation method. Int J Adv Manuf Technol 89(9–12):1–10

    Google Scholar 

  21. Ding Y, Zhu L, Zhang X, Ding H (2011) Milling stability analysis using the spectral method. Sci China Ser E Technol Sci 54(12):3130–3136

    Article  MATH  Google Scholar 

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

    Article  Google Scholar 

  23. 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. https://doi.org/10.1007/s00170-018-2910-0

  24. Lu Y, Ding Y, Zhu L (2017) Dynamics and stability prediction of five-axis flat-end milling. J Manuf Sci E-T ASME 139(6):061015

    Article  Google Scholar 

  25. Shamoto E, Akazawa K (2009) Analytical prediction of chatter stability in ball end milling with tool inclination. Cirp Ann-Manuf Technol 58(1):351–354

    Article  Google Scholar 

  26. Hayasaka T, Ito A, Shamoto E (2016) Generalized design method of highly-varied-helix end mills for suppression of regenerative chatter in peripheral milling. Precis Eng 48:45–59

    Article  Google Scholar 

  27. Ozturk E, Budak E (2010) Dynamics and stability of five-axis ball-end milling. J Manuf Sci E-T ASME 132(2):237–247

    Article  Google Scholar 

  28. Sun C (2016) Altintas Y (2016) chatter free tool orientations in 5-axis ball-end milling. Int J Mach Tools Manuf 106:89–97

    Article  Google Scholar 

  29. Li Z, Zhu L (2018) An accurate method for determining cutter-workpiece engagements in five-axis milling with a general tool considering cutter runout. J Manuf Sci Eng 140(2):021001

    Article  Google Scholar 

  30. Ozturk E, Tunc L, Budak E (2011) Analytical methods for increased productivity in five-axis ball-end milling. Int J Mechatronics M 4(3–4):238–265

    Google Scholar 

  31. 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 

  32. 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 

  33. Kiswanto G, Hendriko H, Duc E (2014) An analytical method for obtaining cutter workpiece engagement during a semi-finish in five-axis milling. Comput Aided Des 55(3):81–93

    Article  Google Scholar 

  34. Dai Y, Li H, Wei Z, Zhang H (2018) Chatter stability prediction for five-axis ball end milling with precise integration method. J Manuf Process 32:20–31

    Article  Google Scholar 

  35. Lee P, Altintaş Y (1996) Prediction of ball-end milling forces from orthogonal cutting data. Int J Mach Tool Manu 36(9):1059–1072

    Article  Google Scholar 

  36. Sims N (2015) Fast chatter stability prediction for variable helix milling tools. Archive P I Mech E C 230(1):203–210

    Google Scholar 

  37. Zatarain M, Muñoa J, Peigné G (2006) Analysis of the influence of mill helix angle on chatter stability. Cirp Ann-Manuf Technol 55(1):365–368

    Article  Google Scholar 

  38. Turner S, Merdol D, Altintas Y (2007) Modeling of the stability of variable helix end mills. Int J Mach Tools Manuf 47(9):1410–1416

    Article  Google Scholar 

  39. Wang C, Zhang X, Cao H (2017) Milling stability prediction and adaptive chatter suppression considering helix angle and bending. Int J Adv Manuf Technol 11:1–13

    Google Scholar 

Download references

Funding

This work was financially supported by National Natural Science Foundation of China (51575075) and Collaborative Innovation Center of Major Machine Manufacturing in Liaoning.

Author information

Authors and Affiliations

  1. School of Mechanical Engineering, Dalian University of Technology, Dalian, 116024, China

    Yuebang Dai, Hongkun Li, Jianglei Dong, Qiang Zhou & Shengxian Liu

  2. Shenyang Blower Works Group Corporation Co. Ltd., Shenyang, 100869, China

    Jianhua Yong

Authors
  1. Yuebang Dai
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hongkun Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jianglei Dong
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Qiang Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Jianhua Yong
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Shengxian Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hongkun Li.

Additional information

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Dai, Y., Li, H., Dong, J. et al. An updated model of stability prediction in five-axis ball-end milling. Int J Adv Manuf Technol 103, 3293–3306 (2019). https://doi.org/10.1007/s00170-019-03508-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00170-019-03508-5

Keywords

Search

Navigation