Stochastic Optimization of AISI 52100 Hard Turning With Six Sigma Capability Constraint

Abstract

Hard turning optimization problems are usually approached using response surface methodology. By running designed experiments, researchers build analytical models to represent the outputs under interest. However, most studies focus on the expected values of the outputs, and only a few consider the variances of the models, even though there are several stochastic programming (SP) techniques available in the literature. Such variances may have a significant impact on the problem solution. This paper aims to optimize the AISI 52100 hardened steel turning process using SP. The decision variables are cutting speed, feed rate, and depth of cut, outputs have cost per part and material removal rate, and average surface roughness six sigma capability is modeled as a stochastic constraint. The SP method is also compared with the conventional one, which did not include the variances into the problem. The results show that taking the variability of the models into account is necessary to obtain a satisfactory process capability and to analyze different scenarios. Finally, this paper shows that competitive results can be achieved by simplifying the problem formulation.INDEX TERMS Capability engineering optimization methods, response surface methodology, stochastic processes.

Multivariate Stochastic Optimization Approach Applied in a Flux-Cored Arc Welding Process

“…After the problem has been formulated, an algorithm is used to search for the optimal solution. The generalized reduced gradient (GRG) algorithm is often used when polynomial analytical models represent the responses of interest [4].…”

“…GRG reduces the number of variables by substituting the constraints of the objective functions. Therefore, the number of gradients is reduced [4].…”