A two-stage approach for modeling inverse S-shaped wear processes of cutting tools

Wear is one of major failure causes of cutting tools. Monitoring the wear process of a cutting tool and predicting its residual life have attracted wide attentions. A stochastic wear process model that relates the wear amount to cumulative cutting time is needed so as to make the inspection and replacement decisions of the cutting tool. The wear amount as a function of cutting time is often inverse S-shaped. That is, the wear rate curve is bathtub-shaped. The works that explicitly model inverse S-shaped wear processes are rare. This paper presents a two-stage approach for modeling this type of wear processes. The proposed approach divides the process into two stages with the inflection point of the wear curve as the boundary of stages. The task in the first stage is to collect data and the tasks in the second stage are to predict residual life and make inspection and replacement decisions. The stochastic wear process model obtained from the proposed approach is simple and realistic, and does not need many data. A real-world example is included to illustrate the simplicity and appropriateness of the proposed approach.