A novel instantaneous uncut chip thickness model for mechanistic cutting force model in micro-end-milling

  • Yudong Zhou
  • Yanling Tian
  • Xiubing Jing
  • Kornel F. Ehmann


Modeling of cutting force plays a vital role in characterizing the micro-end-milling processes, including tool wear and surface quality as well as machining stability. It is well recognized that precise determination of instantaneous uncut chip thickness (IUCT) is essential for cutting force prediction, while the presence of tool run-out and material elastic recovery have an equally important influence. On the basis of the IUCT model considering run-out, elastic recovery is innovatively integrated into the surfaces generated by the previously passing tool tips to improve the accuracy of IUCT model. Subsequently, a novel IUCT model is proposed in this paper that considers trochoidal trajectory of tool tip, run-out, minimum chip thickness, elastic recovery, and variety in entry/exit angles. Also, it can be found that the elastic recovery has a significant effect upon IUCT (especially at small feed rate) based on the numerical analysis of the IUCT model, and meanwhile the role of elastic recovery is mainly affected by run-out, minimum chip thickness and elastic recovery rate. Furthermore, it is worth noting that entry/exit angles may change at small feed rate when taking into account elastic recovery. Then, the IUCT model and non-linear cutting force coefficients are integrated into the mechanistic cutting force model and used to predict cutting force. The predicted cutting force is found to be well in harmony with the experimental results; as a result, the developed theoretical cutting force model in this work can be used in real-time machining process monitoring as well as adaptive control of machining process.


Micro-end-milling Cutting forces Elastic recovery Chip thickness 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bissacco G, Hansen HN, Slunsky J (2008) Modelling the cutting edge radius size effect for force prediction in micro milling. CIRP Ann Manuf Technol 57(1):113–116CrossRefGoogle Scholar
  2. 2.
    Chae J, Park SS, Freiheit T (2006) Investigation of micro-cutting operations. Int J Mach Tool Manu 46(3–4):313–332CrossRefGoogle Scholar
  3. 3.
    Filiz S, Romero LA, Ozdoganlar OB (2008) An analytical model for micro-endmill dynamics. J Vib Control 14(8):1125–1150CrossRefMATHGoogle Scholar
  4. 4.
    Patra RSAK (2014) Modeling and simulation of mechanical micro-machining—a review. Mach Sci Technol 18(3):323–347CrossRefGoogle Scholar
  5. 5.
    Dornfeld D, Min S, Takeuchi Y (2006) Recent advances in mechanical micromachining. CIRP Ann Manuf Technol 55(2):745–768CrossRefGoogle Scholar
  6. 6.
    Zhou L, Peng FY, Yan R (2015) Analytical modeling and experimental validation of micro end-milling cutting forces considering edge radius and material strengthening effects. Int J Mach Tool Manu 97:29–41CrossRefGoogle Scholar
  7. 7.
    Brousseau EB, Dimov SS, Pham DT (2010) Some recent advances in multi-material micro- and nano-manufacturing. Int J Adv Manuf Technol 47(1–4):161–180CrossRefGoogle Scholar
  8. 8.
    Srinivasa YV, Shunmugam MS (2013) Mechanistic model for prediction of cutting forces in micro end-milling and experimental comparison. Int J Mach Tool Manu 67(2):18–27CrossRefGoogle Scholar
  9. 9.
    Lai X, Li H, Li C (2008) Modelling and analysis of micro scale milling considering size effect, micro cutter edge radius and minimum chip thickness. Int J Mach Tool Manu 48(1):1–14CrossRefGoogle Scholar
  10. 10.
    Wan M, Zhang WH (2006) Calculations of chip thickness and cutting forces in flexible end milling. Int J Adv Manuf Technol 29(7–8):637–647CrossRefGoogle Scholar
  11. 11.
    Yoon HS, Ehmann KF (2016) Dynamics and stability of micro-cutting operations. Int J Mech Sci 115-116:81–92CrossRefGoogle Scholar
  12. 12.
    Li H, Wu B (2016) Development of a hybrid cutting force model for micromilling of brass. International Journal of Mechanical Sciences 115-116:586–595CrossRefGoogle Scholar
  13. 13.
    Oliveira FBD, Rodrigues AR, Coelho RT, Souza AFD (2015) Size effect and minimum chip thickness in micromilling. Int J Mach Tool Manu 89:39–54CrossRefGoogle Scholar
  14. 14.
    Vogler MP, Kapoor SG, DeVor RE (2004) On the modeling and analysis of machining performance in micro-endmilling, part II: cutting force prediction. J Manuf Sci Eng 126(4):695–705CrossRefGoogle Scholar
  15. 15.
    Vogler MP, Devor RE, Kapoor SG (2004) On the modeling and analysis of machining performance in micro-endmilling, part I: surface generation. J Manuf Sci Eng 126(4):685–694CrossRefGoogle Scholar
  16. 16.
    Zhang X, Ehmann KF, Yu T (2016) Cutting forces in micro-end-milling processes. Int J Mach Tool Manu 107:21–40CrossRefGoogle Scholar
  17. 17.
    Bao WY, Tansel IN (2000) Modeling micro-end-milling operations. Part I: analytical cutting force model. Int J Mach Tool Manu 40(15):2155–2173CrossRefGoogle Scholar
  18. 18.
    Bao WY, Tansel IN (2000) Modeling micro-end-milling operations. Part II: tool run-out. Int J Mach Tool Manu 40(15):2175–2192CrossRefGoogle Scholar
  19. 19.
    Vogler MP, Devor RE, Kapoor SG (2003) Microstructure-level force prediction model for micro-milling of multi-phase materials. J Manuf Sci Eng 125(2):202–209CrossRefGoogle Scholar
  20. 20.
    Rodríguez P, Labarga JE (2015) Tool deflection model for micromilling processes. Int J Adv Manuf Technol 76(1):199–207CrossRefGoogle Scholar
  21. 21.
    Jun MBG, Liu X, Devor RE, Kapoor Shiv G (2006) Investigation of the dynamics of microend milling-part I: model development. J Manuf Sci Eng 128(4):893–900CrossRefGoogle Scholar
  22. 22.
    Li C, Lai X, Li H (2007) Modeling of three-dimensional cutting forces in micro-end-milling. J Micromech Microeng 17(4):671–678CrossRefGoogle Scholar
  23. 23.
    Mamedov A, Lazoglu I (2016) An evaluation of micro milling chip thickness models for the process mechanics. Int J Adv Manuf Technol 87(5):1–7Google Scholar
  24. 24.
    Li K, Zhu K, Mei T (2016) A generic instantaneous undeformed chip thickness model for the cutting force modeling in micromilling. Int J Mach Tool Manu 105:23–31CrossRefGoogle Scholar
  25. 25.
    Jing X, Li H, Wang J, Tian Y (2014) Modelling the cutting forces in micro-end-milling using a hybrid approach. Int J Adv Manuf Technol 73(9):1647–1656CrossRefGoogle Scholar
  26. 26.
    Li HZ, Liu K, Li XP (2001) A new method for determining the undeformed chip thickness in milling. J Mater Process Technol 113(1–3):378–384CrossRefGoogle Scholar
  27. 27.
    Park SS, Malekian M (2009) Mechanistic modeling and accurate measurement of micro end milling forces. CIRP Ann Manuf Technol 58(1):49–52CrossRefGoogle Scholar
  28. 28.
    Malekian M, Park SS, Jun MBG (2009) Modeling of dynamic micro-milling cutting forces. Int J Mach Tool Manu 49(7):586–598CrossRefGoogle Scholar
  29. 29.
    Malekian M, Park SS, Um K (2008) Investigation of micro plowing forces through conical scratch tests. Trans SME-NAMRI 36(1):293–300Google Scholar
  30. 30.
    Gonzalo O, Jauregi H, Uriarte LG (2009) Prediction of specific force coefficients from a FEM cutting model. Int J Adv Manuf Technol 43(3):348–356CrossRefGoogle Scholar

Copyright information

© Springer-Verlag London Ltd. 2017

Authors and Affiliations

  • Yudong Zhou
    • 1
  • Yanling Tian
    • 1
  • Xiubing Jing
    • 1
  • Kornel F. Ehmann
    • 2
  1. 1.Key Laboratory of Equipment Design and Manufacturing Technology, School of Mechanical EngineeringTianjin UniversityTianjinChina
  2. 2.Department of Mechanical EngineeringNorthwestern UniversityEvanstonUSA

Personalised recommendations