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

Abstract

Helical milling is a hole-making process which has been applied in hardened materials. Due to the difficulties on achieving high-quality boreholes in these materials, the influence of noise factors, and multi-quality performance outcomes, this work aims the multi-objective robust design of hole quality on AISI H13 hardened steel. Experiments were carried out through a central composite design considering process and noise factors. The process factors were the axial and tangential feed per tooth of the helix, and the cutting velocity. The noise factors considered were the tool overhang length, the material hardness and the borehole height of measurement. Response models were obtained through response surface methodology for roughness and roundness outcomes. The models presented good explanation of data variability and good prediction capability. Mean and variance models were derived through robust parameter design for all responses. Similarity analysis through cluster analysis was realised, and average surface roughness and total roundness were selected to multi-objective optimisation. Mean square error optimisation was performed to achieve bias and variance minimization. Multi-objective optimisation through normalized normal constraint was performed to achieve a robust Pareto set for the hole quality outcomes. The normalized normal constraint optimisation results outperformed the results of other methods in terms of evenness of the Pareto solutions and number of Pareto optimal solutions. The most compromise solution was selected considering the lowest Euclidian distance to the utopia point in the normalized space. Individual and moving range control charts were used to confirm the robustness achievement with regard to noise factors in the most compromise Pareto optimal solution. The methodology applied for robust modelling and optimisation of helical milling of AISI H13 hardened steel was confirmed and may be applied to other manufacturing processes. KeywordsHelical milling; AISI H13 hardened steel; Multi-objective robust optimization; Robust parameter design; Normalized normal constraint method. R 2 coefficient of determinationRadj 2 adjusted coefficient of determination Radj 2 prediction coefficient of determination

Multivariate GR&R through factor analysis

“…However, concerning roughness, P7 presents low roughness, while P8 presents high roughness. Some parts with low roughness may present high roundness [35]. The plots confirm the homogeneity among operators, for both factors PA1 and PA2, since for each part all means are close and the confidence intervals intersect.…”

“…The present MSA study was conducted previously to the modeling and optimization of helical milling of AISI H13 hardened steel study, to guarantee the capability of the measurement system. However, the latter results were published before, see Pereira, et al [35].…”

“…It must be stressed that the complete product characterization is necessary for process modeling [35],…”

Investigation of the effects of skewness Rsk and kurtosis Rku on tribological behavior in a pin-on-disc test of surfaces machined by conventional milling and turning processes

“…The roughness manipulation affects the quality of the mechanical and structural components, not only in the visual aspect, but also in the wear and lubrication behavior, friction coefficient, corrosion and fatigue resistance, heat transfer, load transmission, adhesion of coatings and light reflection [7][8][9] . Many tribological studies are being carried out to understand the influence of the machining process parameters, and if possible, manipulate them to obtain surfaces with satisfactory characteristics 10,11 .…”

“…Mathematically, the R a parameter represents the absolute average of all heights measured along the evaluation length. All valleys must be converted to peaks 8,14 . This is a justification by which many authors claim that this parameter does not differentiate peaks and valleys.…”