A multivariate surface roughness modeling and optimization under conditions of uncertainty

Correlated responses can be written in terms of principal component scores, but the uncertainty in the original responses will be transferred and will influence the behavior of the regression function. This paper presents a model building strategy that consider the multivariate uncertainty as weighting matrix for the principal components. The main objective is to increase the value of R2 predicted to improve model's explanation and optimization results. A case study of AISI 52100 hardened steel turning with Wiper tools was performed in a Central Composite Design with three-factors (cutting speed, feed rate and depth of cut) for a set of five correlated metrics (Ra, Ry, Rz, Rq and Rt). Results indicate that different modeling methods conduct approximately to the same predicted responses, nevertheless the response surface to Weighted Principal Component - case b - (WPC1b) presented the highest predictability.