A multivariate mean square error optimization of AISI 52100 hardened steel turning

Hardened steel turning has received special attention in recent years due to its many applications in modern industries. The characteristics that define its machinability—expressed in terms of multiple response problems—are usually represented by experimental model building strategies like response surface methodology (RSM). Such strategies, however, have a particular drawback when multiple correlated regression functions are present. The optimization of multiple process characteristics without considering the variance–covariance structure among the responses may lead to an inadequate optimum. To deal with this constraint, this paper presents a novel multiobjective optimization method; it correctly focuses the multiple correlated characteristics of the AISI 52100 hardened steel, based on the concept of multivariate mean square error. This novel approach combines principal component analysis with RSM focusing a multidimensional nominal-the-best problem. In this kind of optimization, all the characteristics (tool life, cutting time, cost, material removal rate, and surface roughness) have a specific target while maintaining a strong correlation structure. Transforming the original responses and respective targets to the plane of a multivariate principal component scores, an optimization routine is capable of finding out a compromise solution that attends all the established targets. The following AISI 52100 turning process variables were considered in this study: cutting speed, feed rate, and depth of cut. Theoretical and experimental results were convergent and confirmed in a case study.