Multivariate global index and multivariate mean square error optimization of AISI 1045 end milling

Surface roughness is used as a product quality index and technical requirement of machined parts. Consequently, it is important to know the relationship between process parameters and roughness outcomes. Considering that there are different outcomes for measuring roughness, the present works aim the modelling and optimization of surface roughness based on principal component analysis using the multivariate mean square error and the multivariate global index methods. This paper presents a sequential methodology on roughness surface multivariate modelling and optimization. Initially, a complete factorial design was used with centre points, and the hardness of machined surfaces as a covariate was taken into account. On the second part, the axial points were supplied to complete the central composite design and fit a second-order model. Principal component analysis was applied to represent the set of roughness responses and fit a unique response surface regression model in terms of cutting data. The different non-linear programming methods were applied and compared through the global percentage error criteria, considering the outcomes targets. Confirmation runs on multivariate global index optimal point achieved original responses means within the confidence interval of optimal point and very near to the fitted value.