Simultaneous determination of optimal machining conditions and tool replacement policies in constrained machining economics problems by geometric programming

This paper presents an analytical model for the simultaneous determination of the optimal machining conditions (cutting speed and feed) and the optimal tool replacement policy in constrained machining economics problems by geometric programming. The optimal preventive tool replacement policy is initially determined as a tool life fractile (independent of the underlying tool life distribution) and then it is expressed as actual tool life by utilizing the underlying tool life distribution applicable to the combination of tool material, workpiece properties, and machining conditions. Constraints on the optimal values of cutting speeds, feeds, and/or optimal tool replacement policy based on maximum allowable values and/or surface finish requirements are handled through the optimization of the dual objective function. It is shown that the optimal cost distribution does not depend on the cost coefficients in the objective function. Finally, the model is applied to two-stage systems where the necessary conditions are derived for increasing the synchronization between the two stages.