Robust optimisation of machining conditions with tool life and surface roughness uncertainties

Abstract

The economics of the multi-pass turning problem is considered, while accounting for tool life uncertainty. The goal is to minimise the expected production cost per part, given the probability distribution for tool life, and with machining parameters being subject to practical constraints. The cost function accounts for machining cost, idling cost, tool changing cost as well as the cost associated with tool failure. A modified version of the particle swarm optimisation (PSO) algorithm, called the dynamic objective PSO (or DOPSO), is used for minimisation of the cost function. The decision variables include not only the machining parameters but also the tool replacement time. The equality constraint that the total desired depth of cut be achieved by an integral number of roughing passes and a single finishing pass is handled in a novel way, and together with including tool replacement time as a decision variable, this leads to lower costs than those cited by other comparable previous works. To handle uncertain constraints that lead to part failure when violated (e.g. desired surface finish), a robust formulation is also suggested through similar incorporation in the cost function, as for tool failure.