Machining economics with phase-type distributed tool lives and periodic maintenance control

A Markov decision model is proposed to update dynamically the optimal cutting speed and tool replacement policy based on information gathered on-line about tool wear. The underlying tool wear process is modeled as a continuous Markov chain, while the mean time to malfunction is dependent on the cutting speed through the Taylor tool life equation. We show that under appropriate assumptions the generator matrix of the underlying Markov chain exhibits a separability property that greatly facilitates the solution procedure. The procedure is demonstrated through a numerical example. The proposed model can lead to substantial savings since the optimal machining parameters are computed based on actual tool wear information instead of empirically predetermined estimates for the tool life parameters.