Uncertainty analysis of force coefficients during micromilling of titanium alloy



Predicting process forces in micromilling is difficult due to complex interaction between the cutting edge and the work material, size effect, and process dynamics. This study describes the application of Bayesian inference to identify force coefficients in the micromilling process. The Metropolis-Hastings (MH) algorithm Markov chain Monte Carlo (MCMC) approach has been used to identify probability distributions of cutting, edge, and ploughing force coefficients based on experimental measurements and a mechanistic model of micromilling. The Bayesian inference scheme allows for predicting the upper and lower limits of micromilling forces, providing useful information about stability boundary calculations and robust process optimization. In the first part of the paper, micromilling experiments are performed to investigate the influence of micromilling process parameters on machining forces, tool edge condition, and surface texture. Under the experimental conditions used in this study, built-up edge formation is observed to have a significant influence on the process outputs in micromilling of titanium alloy Ti6Al4V. In the second part, Bayesian inference was explained in detail and applied to model micromilling force prediction. The force predictions are validated with the experimental measurements. The paper concludes with a discussion of the effectiveness of employing Bayesian inference in micromilling force modeling considering special machining cases.


Micromilling Mechanistic modeling Bayesian inference Markov chain Monte Carlo Uncertainty analysis 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Dornfeld D, Min S, Takeuchi Y (2006) Recent advances in mechanical micromachining. CIRP Ann Manuf Technol 55(2):745–768CrossRefGoogle Scholar
  2. 2.
    Chae J, Park SS, Freiheit T (2006) Investigation of micro-cutting operations. Int J Mach Tools Manuf 46:313–332CrossRefGoogle Scholar
  3. 3.
    Schmitz TL, Couey J, Marsh E, Mauntler N, Hughes D (2007) Runout effects in milling: surface finish, surface location error, and stability. Int J Mach Tools Manuf 47:841–851CrossRefGoogle Scholar
  4. 4.
    Afazov SM, Ratchev SM, Segal J, Popov AA (2012) Chatter modelling in micro-milling by considering process nonlinearities. Int J Mach Tools Manuf 56:28–38CrossRefGoogle Scholar
  5. 5.
    Malekian M, Park SS, Jun MBG (2009) Modeling of dynamic micro-milling cutting forces. Int J Mach Tools Manuf 49:586–598CrossRefGoogle Scholar
  6. 6.
    Zhang X, Ehmann KF, Yu T, Wang W (2016) Cutting forces in micro-end-milling processes. Int J Mach Tools Manuf 107:21–40CrossRefGoogle Scholar
  7. 7.
    Srinivasa YV, Shunmugam MS (2013) Mechanistic model for prediction of cutting forces in micro end-milling and experimental comparison. Int J Mach Tools Manuf 67:18–27CrossRefGoogle Scholar
  8. 8.
    Jin X, Altintas Y (2012) Prediction of micro-milling forces with finite element method. J Mater Process Technol 212:542–552CrossRefGoogle Scholar
  9. 9.
    Karandikar JM, Schmitz TL, Abbas AE (2014) Application of Bayesian inference to milling force modeling. J Manuf Sci Eng 136(2):021017CrossRefGoogle Scholar
  10. 10.
    Karandikar JM, Abbas AE, Schmitz TL (2014) Tool life prediction using Bayesian updating—part 1: milling tool life model using a discrete grid method. Precis Eng 38(1):9–17CrossRefGoogle Scholar
  11. 11.
    Karandikar JM, Abbas AE, Schmitz TL (2014) Tool life prediction using Bayesian updating—part 2: turning tool life using a Markov chain Monte Carlo approach. Precis Eng 38(1):18–27CrossRefGoogle Scholar
  12. 12.
    Niaki FA, Ulutan D, Mears L (2016) Parameter inference under uncertainty in end-milling γ-strengthened difficult-to-machine alloy. J Manuf Sci Eng 138 / 061014-1Google Scholar
  13. 13.
    Mehta P, Kuttolamadom M, Mears L (2017) Mechanistic force model for machining process—theory and application of Bayesian inference. Int J Adv Manuf Technol. doi: 10.1007/s00170-017-0064-0
  14. 14.
    Cao Z, Li H (2015) Investigation of machining stability in micro milling considering the parameter uncertainty. Adv Mech Eng:1–8. doi: 10.1177/1687814015575982
  15. 15.
    Jaffery SI, Khan M, Ali L, Mativenga PT (2016) Statistical analysis of process parameters in micromachining of Ti-6Al-4V alloy. Proc Inst Mech Eng B J Eng Manuf 230(6):1017–1034CrossRefGoogle Scholar
  16. 16.
    Jaffery SI, Driver N, Mativenga PT (2010) Analysis of process parameters in the micromachining of Ti-6Al-4V alloy. Proceedings of the 36th international MATADOR conference. Springer, London, 2010.Google Scholar
  17. 17.
    Hitchcock DB A history of the Metropolis–Hastings algorithm, The American StatisticianGoogle Scholar
  18. 18.
    Andrieu C, De Freitas N, Doucet A, Jordan MI (2003) An introduction to MCMC for machine learning. Mach Learn 50(1–2):5–43CrossRefMATHGoogle Scholar
  19. 19.
    Hoff PD (2009) A first course in Bayesian statistical methods. Springer Science & Business MediaGoogle Scholar
  20. 20.
    Chae J, Park SS (2007) High frequency bandwidth measurements of micro cutting forces. Int J Mach Tools Manuf 47(9):1433–1441CrossRefGoogle Scholar
  21. 21.
    Oliaei SNB, Karpat Y (2016) Investigating the influence of built-up edge on forces and surface roughness in micro scale orthogonal machining of titanium alloy Ti6Al4V. J Mater Process Technol 235:28–40CrossRefGoogle Scholar
  22. 22.
    Characterization of areal surface texture. R. Leach Editor. Springer ISBN 978-3-642-36457-0Google Scholar
  23. 23.
    Wang Z, Kovvuri V, Araujo A, Bacci M, Hung WNP, Bukkapatnam STS (2016) Built-up-edge effects on surface deterioration in micro milling processes. J Manuf Process. doi: 10.1016/j.jmapro.2016.03.016
  24. 24.
    Duncan GS, Kurdi M, Schmitz T, Snyder J Uncertainty propagation for selected analytical milling stability limit analyses. Trans NAMRI/SME 34:17–24Google Scholar
  25. 25.
    Davies M, Dutterer B, Pratt J, Schaut A (1998) On the dynamics of high-speed milling with long, slender endmills. Ann CIRP 47(1):55–60CrossRefGoogle Scholar

Copyright information

© Springer-Verlag London 2017

Authors and Affiliations

  1. 1.Department of Industrial EngineeringBilkent UniversityAnkaraTurkey
  2. 2.Micro System Design and Manufacturing Center, Department of Mechanical EngineeringBilkent UniversityAnkaraTurkey
  3. 3.UNAM–Institute of Materials Science and NanotechnologyAnkaraTurkey

Personalised recommendations