Multivariate robust modelling and optimization of cutting forces of the helical milling process of the aluminum alloy Al 7075

Abstract

Helical milling is an advanced hole-making process and different approaches considering controllable variables have been presented addressing modelling and optimization of machining forces in helical milling. None of them considers the importance of the noise variables and the fact that machining forces components are usually correlated. Exploring this issue, this paper presents a multivariate robust modelling and optimization of cutting forces of the helical milling of the aluminum alloy Al 7075. For the study, the tool overhang length was defined as noise variable since in cavities machining there are specific workpiece geometries that constrain this variable; the controllable variables were axial feed per tooth, tangential feed per tooth and cutting speed. The cutting forces in the workpiece coordinate system were measured and the components in the tool coordinate system, i.e., the axial and radial forces, were evaluated. Since these two outcomes are correlated, the weighted principal component analysis was performed together with the robust parameter design to allow the multivariate robust modelling of the mean and variance equations. The normal boundary intersection method was used to obtain a set of Pareto robust optimal solutions related to the mean and variance equations of the weighted principal component. The optimization of the weighted principal component through the normal boundary intersection method was performed and the results evaluated in the axial and radial cutting forces components. Confirmation runs were carried out and it was possible to conclude that the models presented good fit with experimental data and that the Pareto optimal point chosen for performing the confirmation runs is robust to the tool overhang length variation. Finally, the cutting force models were also presented for mean and variance in the workpiece coordinate system in the time domain, presenting low error regarding the experimental test, endorsing the results.