Research Papers

Parameter Inference Under Uncertainty in End-Milling γ′-Strengthened Difficult-to-Machine Alloy

[+] Author and Article Information
Farbod Akhavan Niaki, Laine Mears

International Center for Automotive Research,
Clemson University,
Greenville, SC 29607

Durul Ulutan

Mechanical Engineering,
Bucknell University,
Lewisburg, PA 17837

Manuscript received August 19, 2015; final manuscript received March 10, 2016; published online April 15, 2016. Assoc. Editor: Radu Pavel.

J. Manuf. Sci. Eng 138(6), 061014 (Apr 15, 2016) (10 pages) Paper No: MANU-15-1429; doi: 10.1115/1.4033041 History: Received August 19, 2015; Revised March 10, 2016

Nickel-based alloys are those of materials that are maintaining their strength at high temperature. This feature makes these alloys a suitable candidate for power generation industry. However, high wear rate and tooling cost are known as the challenges in machining Ni-based alloys. The high wear rate causes a rapid failure of the tool, and therefore, fewer data will be available for model development. In addition, variations in material properties and hardness, residual stress, tool runout, and tolerances are some uncontrollable effects adding uncertainties to the currently developed models. To address these challenges, a probabilistic Bayesian approach using Markov Chain Monte Carlo (MCMC) method has been used in this work. The MCMC method is a powerful tool for parameter inference and quantification of embedded uncertainties of models. It is shown that by adding a prior probability to the observation probability, fewer experiments are required for inference. This is specifically useful in model development for difficult-to-machine alloys where high wear rate lowers the cardinality of the dataset. The combined Gibbs–Metropolis algorithm as a subset of MCMC method has been used in this work to quantify the uncertainty of the unknown parameters in a mechanistic tool wear model for end-milling of a difficult-to-machine Ni-based alloy. Maximum of 18% error and average error of 11% in the results show a good potential of this modeling in prediction of parameters in the presence of uncertainties when limited experiments are available.

Copyright © 2016 by ASME
Your Session has timed out. Please sign back in to continue.



Grahic Jump Location
Fig. 1

Price comparison of different materials (source: McMaster-Carr)

Grahic Jump Location
Fig. 2

Gibbs sampler algorithm

Grahic Jump Location
Fig. 3

Metropolis algorithm

Grahic Jump Location
Fig. 4

Milling schematic [29]

Grahic Jump Location
Fig. 5

Data acquisition with NI-cRIO9103

Grahic Jump Location
Fig. 6

Cutting power of test 3: Vc = 50 m/min and f = 0.1 mm/rev

Grahic Jump Location
Fig. 7

Measured flank wear for tests 1–4: (a) test 1—Vc = 25 m/min and f = 0.1 mm/rev, (b) test 2—Vc = 25 m/min and f = 0.2 mm/rev, (c) test 3—Vc = 50 m/min and f = 0.1 mm/rev, and (d) test 4—Vc = 50 m/min and f = 0.2 mm/rev

Grahic Jump Location
Fig. 8

Flowchart of combined Gibbs–Metropolis algorithm

Grahic Jump Location
Fig. 9

Pilot run samples: (a) trace plot and (b) samples autocorrelation (diverged chain)

Grahic Jump Location
Fig. 10

Main run samples: (a) trace plot and (b) samples autocorrelation (converged chain)

Grahic Jump Location
Fig. 11

Prior and posterior distributions after main run: (a) prior probability of Ki and Kj, (b) posterior probability of K1 and K2, (c) posterior probability of K3 and K1, and (d) posterior probability of K3 and K2

Grahic Jump Location
Fig. 12

Distribution of parameters for prior belief, pilot run, and main run (the y-axis is not normalized)

Grahic Jump Location
Fig. 13

Gamma distribution of the inverse of measurement error variance

Grahic Jump Location
Fig. 14

Posterior predictive distribution algorithm

Grahic Jump Location
Fig. 15

Posterior predictive distribution, measured spindle power (-o- sign)—validation tests 1–4

Grahic Jump Location
Fig. 16

Evolution of mean (E[Ki]) and variance (Var[Ki]) of parameters after 50 runs




Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In