Three-dimensional chatter stability prediction of milling based on the linear and exponential cutting force model

  • Yiqing YangEmail author
  • Qiang Liu
  • Bin Zhang


Stability lobes are widely used to avoid chatter which restricts the machining quality and productivity. A lot of work has been done to predict the stability lobes fast and accurately. However, most of them are based on the linear force model, and the chatter stability limit is formulated as independent on the feed rate, which is inconsistent with the machining practice. By referencing with the zero-order solution, this paper investigates the chatter stability prediction based on the exponential force model. Focusing on the cutters with a lead angle (i.e., inserted face mill, the ball-end mill, and bull-nose end mill) where chatter is likely to be brought up in Z direction, the stability model is extended to three-dimensional. Taylor equation is utilized to linearize the exponential expressions when computing the directional coefficients in order to solve the stability limit analytically as the linear force model. Simulation results show that the exponential force model agrees with the measurements as well as the linear force model in the cutting force prediction, and it is able to demonstrate the feed rate effect on the stability limit. The stability limit is found to be increased as the feed rate increases, which is evidenced by the time domain simulation. Cutting tests are performed in the end to verify the stability model. The proposed model could be reduced to either X/Y dimensional or linear force model-based stability model by further simplifications.


Milling Chatter stability Three-dimensional Exponential force model Face mill 


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  1. 1.
    Tlusty J, Ismail F (1981) Basic nonlinearity in machining chatter. CIRP Ann Manuf Technol 30(1):21–25CrossRefGoogle Scholar
  2. 2.
    Altintas Y (2012) Manufacturing automation. Cambridge University Press, CambridgeGoogle Scholar
  3. 3.
    Altintas Y, Stepan G, Merdol D, Dombovari Z (2008) Chatter stability of milling in frequency and discrete time domain. CIRP J Manuf Sci Technol 1(1):35–44CrossRefGoogle Scholar
  4. 4.
    Tang A, LIU Z (2009) Three-dimensional stability lobe and maximum material removal rate in end milling of thin-walled plate. Int J Adv Manuf Technol 43(1–2):33–39CrossRefGoogle Scholar
  5. 5.
    Zatarain M, Bediaga I, Munoa J, Insperger T (2010) Analysis of directional factors in milling: importance of multi-frequency calculation and of the inclusion of the effect of the helix angle. Int J Adv Manuf Technol 47(5–8):535–542CrossRefGoogle Scholar
  6. 6.
    Iglesias A, Munoa J, Ciurana J (2013) Optimisation of face milling operations with structural chatter using a stability model based process planning methodology. Int J Adv Manuf Technol. doi: 10.1007/s00170-013-5199-z CrossRefGoogle Scholar
  7. 7.
    Insperger T, Stépán G (2002) Semi-discretization method for delayed systems. Int J Numer Methods Eng 55(5):503–518MathSciNetCrossRefGoogle Scholar
  8. 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(5):502–509CrossRefGoogle Scholar
  9. 9.
    Liu YL, Zhang DH, Wu BH (2012) An efficient full-discretization method for prediction of milling stability. Int J Mach Tools Manuf 63:44–48CrossRefGoogle Scholar
  10. 10.
    Jensen SA, Shin YC (1999) Stability analysis in face milling operations, part 2: experimental validation and influencing factors. J Manuf Sci Eng 121(4):606–614CrossRefGoogle Scholar
  11. 11.
    Faassen RPH, Van de Wouw N, Oosterling JAJ, Nijmeijer H (2003) Prediction of regenerative chatter by modeling and analysis of high-speed milling. Int J Mach Tools Manuf 43(14):1437–1446CrossRefGoogle Scholar
  12. 12.
    Budak E (2006) Analytical models for high performance milling. Part I: cutting forces, structural deformations and tolerance integrity. Int J Mach Tools Manuf 46(12–13):1478–1488CrossRefGoogle Scholar
  13. 13.
    Muñoa J, Zatarain M, Bediaga I, Peigné G (2006) Stability study of the milling process using an exponential force model in frequency domain. CIRP—2nd International HPC Conference, VancouverGoogle Scholar
  14. 14.
    Altintas Y (2001) Analytical prediction of three dimensional chatter stability in milling. JSME Int J 44(3):717–723CrossRefGoogle Scholar
  15. 15.
    Campa FJ, López de Lacalle LN, Lamikiz A, Sánchez JA (2007) Selection of cutting conditions for a stable milling of flexible parts with bull-nose end mills. J Mater Process Technol 191(1–3):279–282CrossRefGoogle Scholar
  16. 16.
    Engin S, Altintas Y (2001) Mechanics and dynamics of general milling cutters. Part I: helical end mills. Int J Mach Tools Manuf 41(15):2195–2212CrossRefGoogle Scholar
  17. 17.
    Campomanes ML, Altintas Y (2003) An improved time domain simulation for dynamic milling at small radial immersions. J Manuf Sci Eng 125(3):416–422CrossRefGoogle Scholar
  18. 18.
    Li HZ, Li XP, Chen XQ (2003) A novel chatter stability criterion for the modeling and simulation of the dynamic milling process in the time domain. Int J Adv Manuf Technol 22(9–10):619–625CrossRefGoogle Scholar

Copyright information

© Springer-Verlag London 2014

Authors and Affiliations

  1. 1.School of Mechanical Engineering and AutomationBeihang UniversityBeijingChina

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