A multivariate hybrid approach applied to AISI 52100 hardened steel turning optimization

This paper presents an alternative hybrid approach, combining response surface methodology (RSM) and principal component analysis (PCA) to optimize multiple correlated responses in a turning process. Since a great number of manufacturing processes present sets of correlated responses, this approach could be extended to many applications. As a case study, the turning process of the AISI 52100 hardened steel is examined considering three input factors: cutting speed (Vc), feed rate (f) and depth of cut (d). The outputs considered were: the mixed ceramic tool life (T), processing cost per piece (Kp), cutting time (Ct), the total turning cycle time (Tt), surface roughness (Ra) and the material removing rate (MRR). The aggregation of these targets into a single objective function is conducted using the score of the first principal component (PC1) of the responses’ correlation matrix and the experimental region (Ω) is used as the main constraint of the problem. Considering that the first principal component cannot be enough to represent the original data set, a complementary constraint defined in terms of the second principal component score (PC2) is added. The original responses have the same weights and the multivariate optimization lead to the maximization of MRR while minimize the other outputs. The kind of optimization assumed by the multivariate objective function can be established examining the eigenvectors of the correlation matrix formed with the original outputs. The results indicate that the multiresponse optimization is achieved at a cutting speed of 238 m/min, with a feed rate of 0.08 mm/rev and at a depth of cut of 0.32 mm.