Mathematical Model to Improve Energy Efficiency in Hammer Mills and Its Use in the Feed Industry: Analysis and Validation in a Case Study in Cuba

The feed industry is characterized by high energy consumption during the grinding stage, where hammer mills can account for up to 50% of total electricity usage; furthermore, efficiency analyses are based only on the classical equations reported in the literature. In this context, the present theoretical-applied research aimed to improve the efficiency of a plant operating below its nominal capacity. To achieve this, a comprehensive mathematical model was developed, integrating power and grain disintegration equations while overcoming the limitations of classical comminution theories. The model incorporates key factors such as feed rate, moisture content, absorbed power and hammer wear. Additionally, specific correction factors for temperature (Kt) and mechanical degradation (Kd) were introduced to accurately represent real operating conditions. The study was based on extensive measurements of electrical current, power factor, energy consumption, particle size distribution and thermal variations under different load conditions. The statistical analysis, which included ANOVA, ANCOVA and multiple regressions, demonstrated a predictive accuracy of 98% (R2) and a pseudo-R2 of 89%. This high correlation allowed for an 18% reduction in energy consumption equivalent to 4 kWh/t and up to a 30% improvement in particle size uniformity, surpassing typical factory performance. The findings highlight that integrating operational, thermodynamic and wear-related factors enhances the robustness of the model, promoting more reliable energy-management practices in hammer mills. Consequently, the results confirm that the developed model serves as a scientifically robust, efficient and applicable tool for improving energy efficiency and reducing environmental impacts in the agri-food industry.