Prediction of ball end milling forces based on special turning experiment data

  • Weijian Huang
  • Xi Li
  • Yanfen Zhang
  • Guangdong Liang
  • Weiwei Gao


In milling processes, the prediction of cutting forces plays an important role in machining quality improvement. A novel cutting force model for ball end mills is presented in this paper. The cutting forces acting on infinitesimal cutting edges are set as a binary function of inclination angle and uncut chip thickness in order to consider the local helix angle variation along the cutting edge. The function is obtained by surface fitting based on special turning experiment data. Two position vectors are presented for describing the machining states of the tool and calculating the uncut chip thickness and the tool contact area. The resultant cutting force is calculated by numerical integration of cutting forces acting on the engaged infinitesimal cutting edges. The predictions from the proposed model are verified by milling experiments.


Ball end mill Cutting force Special turning experiment Binary function Two position vectors 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.



This work was supported by the National Natural Science Foundation of China (51075170). The authors would like to thank Yongjie Chen for providing the experimental equipment and Wenjun Li, Ning Li, Dong Zhang, and Ding Chen for their assistance with the experimental work.


  1. 1.
    Altintas Y (2000) Manufacturing automation: metal cutting mechanics, machine tool vibrations, and CNC. Cambridge University Press, CambridgeGoogle Scholar
  2. 2.
    Ozturk E, Tunc LT, Budak E (2009) Investigation of lead and tilt angle effects in 5-axis ball-end milling processes. Int J Mach Tool Manu 49(14):1053–1062CrossRefGoogle Scholar
  3. 3.
    Lee P, Altintas Y (1996) Prediction of ball-end milling forces from orthogonal cutting data. Int J Mach Tool Manu 36(9):1059–1072CrossRefGoogle Scholar
  4. 4.
    Budak E, Altintaş Y, Armarego EJA (1996) Prediction of milling force coefficients from orthogonal cutting data. J Eng Ind 118(2):216–224Google Scholar
  5. 5.
    Ko JH, Cho DW (2005) 3D ball-end milling force model using instantaneous cutting force coefficients. J Manuf Sci Eng 127(1):1–12CrossRefGoogle Scholar
  6. 6.
    Liu XW, Cheng K, Longstaff AP, Widiyarto MH, Ford D (2005) Improved dynamic cutting force model in ball-end milling. Part i: theoretical modelling and experimental calibration. Int J Adv Manuf Technol 26(5–6):457–465CrossRefGoogle Scholar
  7. 7.
    Cao Q, Zhao J, Han S, Chen X (2012) Force coefficients identification considering inclination angle for ball-end finish milling. Precis Eng 36(2):252–260CrossRefGoogle Scholar
  8. 8.
    Huang T, Zhang X, Ding H (2013) Decoupled chip thickness calculation model for cutting force prediction in five-axis ball-end milling. Int J Adv Manuf Technol 69(5–8):1203–1217CrossRefGoogle Scholar
  9. 9.
    Wojciechowski S, Maruda RW, Nieslony P, Krolczyk GM (2016) Investigation on the edge forces in ball end milling of inclined surfaces. Int J Mech Sci 119:360–369CrossRefGoogle Scholar
  10. 10.
    Lazoglu I, Liang SY (2000) Modeling of ball-end milling forces with cutter axis inclination. J Manuf Sci Eng 122(1):3–11CrossRefGoogle Scholar
  11. 11.
    Tsai CL, Liao YS (2008) Prediction of cutting forces in ball-end milling by means of geometric analysis. J Mater Process Technol 205(1):24–33CrossRefGoogle Scholar
  12. 12.
    Kim GM, Cho PJ, Chu CN (2000) Cutting force prediction of sculptured surface ball-end milling using z-map. Int J Mach Tool Manu 40(2):277–291CrossRefGoogle Scholar
  13. 13.
    Lamikiz A, Lacalle LNLD, Sánchez JA, Salgado MA (2004) Cutting force estimation in sculptured surface milling. Int J Mach Tool Manu 44(14):1511–1526CrossRefGoogle Scholar
  14. 14.
    Wei ZC, Wang MJ, Cai YJ, Wang SF (2013) Prediction of cutting force in ball-end milling of sculptured surface using improved z-map. Int J Adv Manuf Technol 68(5–8):1167–1177CrossRefGoogle Scholar
  15. 15.
    Zhang L, Feng J, Wang Y, Chen M (2009) Feed rate scheduling strategy for free-form surface machining through an integrated geometric and mechanistic model. Int J Adv Manuf Technol 40(11–12):1191–1201CrossRefGoogle Scholar
  16. 16.
    Tukora B, Szalay T (2012) Multi-dexel based material removal simulation and cutting force prediction with the use of general-purpose graphics processing units. Adv Eng Softw 43(1):65–70CrossRefGoogle Scholar
  17. 17.
    Zhang X, Yu TWW (2014) Modeling, simulation, and optimization of five-axis milling processes. Int J Adv Manuf Technol 74(9–12):1611–1624CrossRefGoogle Scholar
  18. 18.
    Tuysuz O, Altintas Y, Feng HY (2013) Prediction of cutting forces in three and five-axis ball-end milling with tool indentation effect. Int J Mach Tools Manuf 66(2):66–81CrossRefGoogle Scholar
  19. 19.
    Cao Q, Zhao J, Li Y, Zhu L (2013) The effects of cutter eccentricity on the cutting force in the ball-end finish milling. Int J Adv Manuf Technol 69(9–12):2843–2849CrossRefGoogle Scholar
  20. 20.
    Yao ZQ, Liang XG, Luo L, Hu J (2013) A chatter free calibration method for determining cutter runout and cutting force coefficients in ball-end milling. J Mater Process Technol 213(9):1575–1587CrossRefGoogle Scholar
  21. 21.
    Wang SB, Geng L, Zhang YF, Liu K, Ng TE (2015) Cutting force prediction for five-axis ball-end milling considering cutter vibrations and run-out. Int J Mech Sci 96–97:206–215CrossRefGoogle Scholar
  22. 22.
    Lu Y, Takeuchi Y, Takahashi I, Anzai M (2005) An integrated system development for ball end mill design, creation and evaluation. Int J Adv Manuf Technol 25(7–8):628–646CrossRefGoogle Scholar
  23. 23.
    Wang M, Gao L, Zheng Y (2014) An examination of the fundamental mechanics of cutting force coefficients. Int J Mach Tool Manu 78(1):1–7CrossRefGoogle Scholar
  24. 24.
    Saglam H, Unsacar F, Yaldiz S (2006) Investigation of the effect of rake angle and approaching angle on main cutting force and tool tip temperature. Int J Mach Tool Manu 46(2):132–141CrossRefGoogle Scholar

Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2018

Authors and Affiliations

  1. 1.National NC System Engineering Research Center, School of Mechanical Science and EngineeringHuazhong University of Science and TechnologyWuhanChina

Personalised recommendations