Máxima verossimilhança restrita e propagação de erro na modelagem de média-variância da vida de ferramenta de corte em processos de usinagem

Abstract

Tool life constitutes a fundamental criterion for decision-making aimed at excellence in machining processes, as it directly impacts production costs, final product quality, operational efficiency, sustainability indicators, and energy consumption. However, in most experimental trials, the tool is not continuously monitored, and only the effective cutting time or the machined length until the specified wear limit is reached is recorded. Thus, each observation represents only a fraction of the tool life, inducing a pattern of non-constant variance (heteroscedasticity), which violates the assumptions of Ordinary Least Squares and requires modeling approaches capable of simultaneously representing the mean and the variance of the response variable. This thesis proposes an integrated methodological approach for the simultaneous modeling of the mean and variance of tool life, based on Propagation of Error (POE) and Restricted Maximum Likelihood. The methodology was applied to a dataset obtained from a Central Composite Design, derived from experiments conducted with seven Sandvik Coromant inserts, including five ceramic grades and two PCBN grades, used in the hard turning of AISI H13 steel. The results demonstrated the superiority of the proposed approaches compared to Ordinary Least Squares, both in terms of goodness of fit and predictive performance. Among the evaluated algorithms, the methods based on POE exhibited the best performance, showing a greater ability to adequately represent both the mean and the variance of tool life. In the optimization stage, a mean–variance multiobjective optimization was performed using the Normal Boundary Intersection method. The selection of the optimal solution was conducted using a decision criterion based on the Mahalanobis distance, and the results were subsequently validated through confirmation experiments. Overall, the findings demonstrate that the joint modeling of mean and variance provides a more robust methodological framework for predicting tool life and defining machining parameters under uncertainty, contributing to increased reliability, operational efficiency, and sustainability in manufacturing processes.