Multivariate robust modeling 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.

Multi-objective robust design of helical milling hole quality on AISI H13 hardened steel by normalized normal constraint coupled with robust parameter design

“…Helical milling in the soft alloy Al 7075 was addressed considering robust multi-response optimisation [34] and considering multivariate robust optimisation [35]. In both cases the noise factor considered was the tool overhang length.…”

“…An important noise factor in mold and die machining is the tool overhang length. Tool overhang length is not defined considering the engineer preferences, but according to the workpiece geometry [35,38]. In cavities machining, it is necessary high tool overhang length to avoid collision between the tool holder and the workpiece.…”

“…However, for the decision maker, a mathematical criterion may be useful to define the best compromise Pareto optimal solution. Considering the Euclidian distance dj+ of each Pareto optimal solution * j f to the utopia point U f , j = 1, …, nsub, calculated according to the Equation35, the most compromise solution will be the one with lower dj+, i.e., Min(j ϵ nsub){dj+}[63]. the experimental procedure, describing equipment, material, tool, experimental design, method, and software.7 Experimental procedure Helical milling tests were carried out in workpieces of AISI H13 hardened steel using a CNC machining centre ROMI® Discovery 560 with numerical control Siemens® Sinumerik 810D in the machining laboratory of UFSJ.…”

Prediction of Thrust Force and Cutting Torque in Drilling Based on the Response Surface Methodology

“…Furthermore, its ability to be highly polished makes it suitable for the mold tool manufacturing industry. The aforementioned reasons have led a number of researchers to focus their studies on these factors [13][14][15]. In this study, an Al7075 plate (150 mm × 150 mm × 15 mm) was selected for performing the experimental work.…”

Multi-response optimization in cutting mild steels

“…Moreover, optimization/assessment of life cycle in turning of Ti-6Al-4V under N2 atmosphere, machinability of AISI 4140 by minimum quantity lubrication method, and optimization of cutting En-31 steel with Taguchi method were performed [18,19] . Apart from the hard-to-cut materials, effects of MQL and factors, on optimum roughness/tool wear/force in milling of Al alloys and SiCp composite [20][21][22][23][24][25] . Milling optimization, cutting condition, tool geometry effect, surface roughness on carbon steel by ceramic tool, cutting parameters on force/roughness and comparison of two tool's shapes were searched using Al alloy, alloyed steel, carbon steel of AISI 1045 and AISI 4140 steel [26][27][28][29][30][31] .…”