A mathematical model for the joint optimization of machining conditions and tool replacement policy with stochastic tool life in the milling process

Abstract

One major problem in the machining process is the optimization of tool replacement policy and machining condition simultaneously. Although many studies have been developed to optimize the machining process considering the stochastic tool life, they have not optimized these two problems together. Therefore, unlike these investigations, the objective of this study is to develop an integrated mathematical model for joint-optimization of tool replacement policy and machining condition given the dependence between them and various costs in the machining process. In this paper, the dependence of cutting tool life distribution and surface roughness of workpiece to the machining conditions is modeled based on a five-step methodology initially. For this purpose, empirical data of a milling process obtained via design of experiments (DOE) based on Box-Behnken design (BBD) is used. These data, converted by total time on test (TTT), transform and using an optimization process based on golden section search (GSS), the relation between machining conditions and parameters of the tool life distribution is obtained as a full quadratic model. The R2 values for the surface roughness, shape, and scale parameters in the full quadratic models are 89.61, 92.52, and 96.80% respectively, which confirms the adequacy of the proposed methodology. Then, a mathematical optimization model is proposed for multi-pass machining with considering costs related to tool replacement policies, direct labor costs, machining costs, loading/unloading of workpiece costs, and quality costs in a machining process. The proposed model of this study can optimize both of the tool replacement policy and the machining conditions simultaneously and also it can lead to choosing the optimized policy of the continuous or the discrete tool condition monitoring approaches. This model is implemented on a case study and its result is reported. For solving the mathematical model, the electromagnetism-like mechanism algorithm is used that has the proper performance to optimize the continuous spaces.