Application of Bayesian Inference to Milling Force Modeling

Jaydeep M. Karandikar, Tony L. Schmitz and Ali E. Abbas Abstract

This paper describes the application of Bayesian inference to the identification of force coefficients in milling. Mechanistic cutting force coefficients have been traditionally determined by performing a linear regression to the mean force values measured over a range of feed per tooth values. This linear regression method, however, yields a deterministic result for each coefficient and requires testing at several feed per tooth values to obtain a high level of confidence in the regression analysis. Bayesian inference, on the other hand, provides a systematic and formal way of updating beliefs when new information is available while incorporating uncertainty. In this work, mean force data is used to update the prior probability distributions (initial beliefs) of force coefficients using the Metropolis-Hastings (MH) algorithm Markov chain Monte Carlo (MCMC) approach. Experiments are performed at different radial depths of cut to determine the corresponding force coefficients using both methods and the results are compared. Introduction In metal cutting operations, the cutting force can be modeled using the chip area and empirical constants that depend on the tool-workpiece combination. The mechanistic cutting force coefficients are determined using a linear regression to the mean force values measured over a range of feed per tooth values [1]. However, the least squares method has two limitations. First, the method required testing at several feed per tooth values to achieve a high level of confidence in the regression. Second, for micromilling applications or machining parameters (radial and axial depth) resulting