Quantifying the contributions of powder mixing mechanisms using a combined proper orthogonal decomposition and analysis of variance approach

Abstract

In manufacturing, powder mixing processes are vital for ensuring product quality. The mixing progress and efficiency are determined based on the fundamental convection and diffusion mechanisms. While mixers are believed to have a unique primary mixing mechanism, recent findings from our group have verified that the main mechanism can change as the mixing progresses. The transitions were successfully captured using a new method incorporating proper orthogonal decomposition (POD) into the discrete element method simulation, proving POD as a valuable tool for mechanism identification. Nevertheless, the existing POD method cannot quantitatively evaluate these mechanisms, hindering a comprehensive analysis of their magnitudes and transitions. This study combines analysis of variance (ANOVA) with POD to solve the problem, establishing a POD-ANOVA framework to quantify the degree of contribution of the mechanisms. The capability of POD-ANOVA is assessed in the transverse mixing of a rolling drum. For a quantitative evaluation of the mechanism magnitudes, POD-ANOVA is performed over the entire mixing process (denoted as Standard POD-ANOVA). The convection and diffusion rates are then derived from the overall mixing rate. Validations show that the two rates corroborate well with common indicators of mechanism intensities. Furthermore, Standard POD-ANOVA is applied over sequential time domains to track mechanism transitions; however, it is found to be insufficiently precise. Thus, a new time-windowing POD is implemented, leading to Windowed POD-ANOVA. Over short time windows, the improved method can effectively quantify the transitions. Consequently, the proposed methods enable a quantitative evaluation of powder mixing mechanisms scientifically for the first time.