Abstract
This work discusses the Bayesian parameter inference method for a mechanistic force model for machining. Bayesian inference methods have gained popularity recently owing to their intuitiveness and ease with which empirical knowledge may be combined with experimental data considering the uncertainty. The first part of the paper discusses Bayesian parameter inference and Markov Chain Monte Carlo (MCMC) methods. MCMC method effectiveness has been further analyzed by (1) changing the number of particles in MCMC estimation and (2) changing the MCMC move step size. The second part of the paper discusses two example applications as nonlinear mechanistic force model coefficient identification. The Bayesian inference scheme performs prediction of the cutting force coefficients from the training data. Using these coefficients and input parameters to the model, the cutting force is predicted. This prediction is validated using experimental data, and it is demonstrated that with very few parameter updates the predicted force converges with the measured cutting force. The paper is concluded with the discussion of future work.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Zhang G, Hwang T, Ratnakar R (1993) Mathematical modeling of the uncertainty for improving quality in machining operations. doi:10.1109/ISUMA.1993.366723
Kalpakjian S, Schmid S (2002) Manufacturing processes for engineering materials, 4th edn. Prantice Hall, USA
Bernoardo J, Smith A (1994) Bayesian theory, 1st edn. West Sussex, Wiley
Gilks WR, Richardson S, Spiegelhalter DJ (1996) Eds., Markov Chain Monte Carlo in practice, 1 ed., Chapman & Hall/CRC
Hastings WK (1970) Monte Carlo sampling methods using Markov chains and their applications. Biometrika 57(1):97–109
Metropolis N, Rosenbluth AW, Rosenbluth MN, Teller AH, Teller E (1953) Equations of state calculations by fast computing machines. J Chem Phys 21:1087–1092
Müller P (1991) A generic approach to posterior integration and gibbs sampling. Purdue University, Indiana
Merchant E (1945) Mechanics of the metal cutting process. I. Orthogonal cutting and a type 2 chip. J Appl Phys 16(5):267–275
Rao DN, Krishna PV, Srikant RR (2008) Surface model and tool-wear prediction model for solid lubricant-assisted turning. Engineering Tribology 222(J5):657–665
Guo PQ, Huang CZ, Zhao P (2004) Cutting force model for contour surface machining of gear indexing cam with flat end milling. Advances in Material Manufacturing Scienece and Technology 471-472:122–126
Wu DW (1988) Comprehensive dynamics cutting force model and its application to wave removing process. J Eng Ind 110(2):153–161
Schmitz TL, Karandikar J, Kim NH, Abbas A (2011) Uncertainty in machining: workshop summary and contributions. J Manuf Sci Eng 133:051009–051001 9
Barry J, Byrne G, Lennon D (2001) Observations on chip formation and acoustic emission in machining Ti-6Al-4V alloy. Int J Mach Tool Manuf 41:1055–1070
Yang X, Liu R (1999) Machining titanium and its alloys. Mach Sci Technol 3(1):107–139
Obikawa T, Usui E (1996) Computational machining of titanium alloy- finite element modeling and a few results. Transactions of the ASME 118:208–215
C Engineering. [Online]. Available: http://www.caron-eng.com/download-files/tmac-8.pdf
Mehta P, Kuttolamadom M, Mears L (2012) Machining process power monitoring: Bayesian update of machining power model. In Proceedings of Seventh Annual International Manufacturing Science and Engineering Conference, Notre Dame, pp 745–752
Mehta P, Werner A, Mears L (2015) Condition based maintenance-systems integration and intelligence using naive Bayesian classification and sensor fusion. J Intell Manuf 26(2):331–346
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Mehta, P., Kuttolamadom, M. & Mears, L. Mechanistic force model for machining process—theory and application of Bayesian inference. Int J Adv Manuf Technol 91, 3673–3682 (2017). https://doi.org/10.1007/s00170-017-0064-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00170-017-0064-0