This paper proposes a dynamic state model of tool wear. This model is developed for the design of an adaptive observer which is used for on-line tool wear sensing in turning based on force measurement. The model treats flank wear and crater wear as state variables, cutting force as the output, and feed as the input. Relationships from the manufacturing literature are used in constructing this nonlinear model. Simulation results are presented for the nonlinear model, and eigenanalysis and controllability and observability analyses are performed on a linear model obtained by linearizing the nonlinear model about an operating point along its trajectory. The simulation results show good agreement with results in the manufacturing literature. The eigenanalysis shows the linear model to be unstable, reflecting the continually increasing nature of the wear processes modeled; and the model is shown to be controllable by feed and observable by cutting force for the cutting conditions considered in the paper.

Danai, K., & Ulsoy, A. G. (1987). A Dynamic State Model for On-Line Tool Wear Estimation in Turning. Journal of Engineering for Industry, 109(4), 396–399.