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

Abstract

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.