Tool life prediction using Bayesian updating. Part 1: Milling tool life model using a discrete grid method

• A Taylor tool life model for milling that uses an exponent, n, and a constant, C, is developed.
• Bayesian inference is applied to estimate the two model constants using a discrete grid method.
• Tool wear tests are performed using an uncoated carbide tool and 1018 steel work material.
• Test results are used to update initial beliefs predict tool life using a probability density function.

According to the Taylor tool life equation, tool life reduces with increasing cutting speed following a power law. Additional factors can also be added, such as the feed rate, in Taylor-type models. Although these models are posed as deterministic equations, there is inherent uncertainty in the empirical constants and tool life is generally considered a stochastic process. In this work, Bayesian inference is applied to estimate model constants for both milling and turning operations while considering uncertainty.In Part 1 of the paper, a Taylor tool life model for milling that uses an exponent, n, and a constant, C, is developed. Bayesian inference is applied to estimate the two model constants using a discrete grid method. Tool wear tests are performed using an uncoated carbide tool and 1018 steel work material. Test results are used to update initial beliefs about the constants and the updated beliefs are then used to predict tool life using a probability density function. In Part 2, an extended form of the Taylor tool life equation is implemented that includes the dependence on both cutting speed and feed for a turning operation. The dependence on cutting speed is quantified by an exponent, p, and the dependence on feed by an exponent, q; the model also includes a constant, C. Bayesian inference is applied to estimate these constants using the Metropolis–Hastings algorithm of the Markov Chain Monte Carlo (MCMC) approach. Turning tests are performed using a carbide tool and MS309 steel work material. The test results are again used to update initial beliefs about the Taylor tool life constants and the updated beliefs are used to predict tool life via a probability density function.