Analyzing the Effect of Process Parameters on the Shape of 3D Profiles

This paper investigates the effect of process parameters on the shape of three-dimensional (3D) curves. Compared with recent literature on profile modeling (generally used for process monitoring applications), the main novelty consists of dealing with curves that do not lie in a plane but in space. In particular, a generalization of principal component analysis (PCA), based on the appropriate use of complex rather than real numbers (complex PCA), is used as a modeling tool. Scores of the significant components obtained via complex PCA are then used as data input for the analysis of variance to investigate the effect of process parameters on the machined shape. The first advantage of complex PCA is its insensitivity to rotation about the origin of the complex plane, a property that produces a significant simplification of the preliminary step of profile registration. Second, complex PCA outperforms alternative PCA-based approaches in terms of the power of detecting the effect of controllable factors on the profile shape. The proposed procedure is particularly useful when the quality characteristic of interest is related to geometric tolerances, as shown in a real case study of the axial straightness of lathe-turned items.