Tool-life modelling as a stochastic process

Abstract

In a previous paper [G. Galante, A. Lombardo, A. Passannanti, Proceedings of XXXVII Scientific Meeting of the Italian Statistical Society, 1994, p. 553] the Authors proposed to model cutting tool wear behaviour as a stochastic process with independent Gaussian increments plus drift. Such a model implies that the tool-life, i.e. the time to reach a fixed value of flank wear, has an inverse Gaussian probability distribution. The model has several practical and theoretical advantages. In fact, it is based on an easily and cheaply experimentally verifiable wear behaviour hypothesis, it is more flexible because it is not limited to a particular wear level and, finally, the data are better exploited for the estimation of the distribution parameters. In the present paper that model is verified under different working conditions. Moreover, by varying the cutting parameters, a relation between these and the tool-life is obtained. It is shown that the well-known Taylor's equation can be considered as a first order approximation of the proposed model.