Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Stability of ball-end milling on warped surface: semi-analytical and experimental analysis


This paper presents a study of warped surface machining with ball-end milling. A specific model based on the classical stability lobe theory was used and improved with important aspects. The non-linear effect of radial allowance on the contact angle was integrated by an original averaging method. The cutting coefficients are updated in order to follow effective radius and cutting velocity. An original experimental procedure was developed in order to compute the cutting coefficient for various inclined surfaces. More complete experimental analysis was conducted in order to study the effect of machining parameters on the stability of inclined surface milling. The comparison between experiment and simulation shows good correlation for the prediction of stable cutting condition.

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


  1. 1.

    Tobias SA, Fishwick W (1958) Theory of regenerative machine tool chatter. Engineer-London 205(199–203):238–239

  2. 2.

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

  3. 3.

    Budak E (2006) Analytical models for high performance milling—part I: cutting forces, structural deformations and tolerance integrity. Int J Mach Tool Manu 46:1478–1488

  4. 4.

    Budak E (2006) Analytical models for high performance milling—part II: process dynamics and stability. Int J Mach Tool Manu 46:1489–1499

  5. 5.

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

  6. 6.

    Altintas Y (2001) Analytical prediction of three dimensional chatter stability in milling. JSME Int J C-Mech SY 44:717–723

  7. 7.

    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 49:1053–1062

  8. 8.

    Mousseigne M, Landon Y, Seguy S, Dessein G, Redonnet JM (2013) Predicting the dynamic behaviour of torus milling tools when climb milling using the stability lobes theory. Int J Mach Tool Manu 65:47–57

  9. 9.

    Chao S, Altintas Y (2016) Chatter free tool orientations in 5-axis ball-end milling. Int J Mach Tool Manu 106:89–97

  10. 10.

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

  11. 11.

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

  12. 12.

    Insperger T, Mann BP, Stépán G, Bayly PV (2003) Stability of up-milling and down-milling, part 1: alternative analytical methods. Int J Mach Tool Manu 43:25–34

  13. 13.

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

  14. 14.

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

  15. 15.

    Mann BP, Insperger T, Bayly PV, Stépán G (2003) Stability of up-milling and down-milling, part 2: experimental verification. Int J Mach Tool Manu 43:35–40

  16. 16.

    Insperger T, Mann BP, Surmann T, Stépán G (2008) On the chatter frequencies of milling processes with runout. Int J Mach Tool Manu 48:1081–1089

  17. 17.

    Zhang X, Zhang J, Pang B, Wu DD, Zheng XW, Zhao WH (2016) An efficient approach for milling dynamics modeling and analysis with varying time delay and cutter runout effect. Int J Adv Manuf Tech doi:10.1007/s00170-016-8671-8

  18. 18.

    Zatarain M, Muñoa J, Peigné G, Insperger T (2006) Analysis of the influence of mill helix angle on chatter stability. CIRP Ann-Manuf Techn 55:365–368

  19. 19.

    Seguy S, Arnaud S, Insperger T (2014) Chatter in interrupted turning with geometrical defects: an industial case study. Int J Adv Manuf Tech 75:45–56

  20. 20.

    Insperger T, Stépán G, Bayly PV, Mann BP (2003) Multiple chatter frequencies in milling processes. J Sound Vib 262:333–345

  21. 21.

    Stépán G, Szalai R, Insperger T (2005) Nonlinear dynamics of high-speed milling subjected to regenerative effect. In: Radons G, Neugebauer R (eds) Nonlinear dynamics of production systems. Weinheim, Wiley-VCH Verlag. doi:10.1002/3527602585.ch7

  22. 22.

    Stépán G, Insperger T, Szalai R (2005) Delay, parametric excitation, and the nonlinear dynamics of cutting processes. Int J Bifurcat Chaos 15:2783–2798

  23. 23.

    Seguy S, Insperger T, Arnaud L, Dessein G, Peigné G (2011) Suppression of period doubling chatter in high-speed milling by spindle speed variation. Mach Sci Technol 15:153–171

  24. 24.

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

  25. 25.

    Ozoegwu CG, Omenyi SN, Ofochebe SM (2015) Hyper-third order full-discretization methods in milling stability prediction. Int J Mach Tool Manu 92:1–9

  26. 26.

    Tang X, Peng F, Yan R, Gong Y, Li Y, Jiang L (2016) Accurate and efficient prediction of milling stability with updated full-discretization method. Int J Adv Manuf Tech doi:10.1007/s00170-016-8923-7

  27. 27.

    Wang S, Geng L, Zhang Y, Liu K, Ng T (2015) Chatter-free cutter postures in five-axis machining. P I Mech Eng B-J Eng doi:10.1177/0954405415615761

  28. 28.

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

  29. 29.

    Liu X, Cheng K (2005) Modelling the machining of peripheral milling. Int J Mach Tool Manu 45:1301–1320

  30. 30.

    Surmann T, Enk D (2007) Simulation of milling tool vibration trajectories along changing engagement conditions. Int J Mach Tool Manu 47:1442–1448

  31. 31.

    Arnaud L, Gonzalo O, Seguy S, Jauregi H, Peigné G (2011) Simulation of low rigidity part machining applied to thin walled structures. Int J Adv Manuf Tech 54:479–488

  32. 32.

    Ahmadi K, Ismail F (2011) Analytical stability lobes including nonlinear process damping effect on machining chatter. Int J Mach Tool Manu 51:296–308

  33. 33.

    Ahmadi K, Ismail F (2010) Machining chatter in flank milling. Int J Mach Tool Manu 51:75–85

  34. 34.

    Shtehin OO (2014) Vyznachennya kutiv vrizannya ta vykhodu pry obrobtsi pokhylykh poverkhon sferychnymy kintsevimi frezamy [definition of start and exit angles in ball end milling of inclined surfaces]. Visnyk ZHDTU – Reporter of ZSTU 3(70):62–67 [in Ukrainian]

  35. 35.

    Cosma M (2007) Horizontal path strategy for 3D–CAD analysis of chip area in 3-axes ball nose end milling. 7th International Multidisciplinary Conference, Baia Mare, Romania

Download references

Author information

Correspondence to S. Seguy.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Shtehin, O.O., Wagner, V., Seguy, S. et al. Stability of ball-end milling on warped surface: semi-analytical and experimental analysis. Int J Adv Manuf Technol 89, 2557–2569 (2017).

Download citation


  • Chatter
  • Milling
  • Stability lobes
  • Warped surface