Multi-Objective Optimization of the Grinding Process in a Spring-Rotor Mill Using Regression-Based Modeling

This study addresses the problem of improving the efficiency of fine grinding of bulk materials in a spring-rotor mill. The objective is to determine technologically sound operating parameters based on mathematical modeling, design of experiments, and multi-objective optimization. The methodology relies on a full-factorial experimental design according to the Hartley plan, with five control factors: rotor rotational speed, material loading ratio, overlap of the working zones, grinding chamber clearance, and grinding duration. The analyzed responses include grinding fineness, throughput, power consumption, specific energy consumption, and specific metal intensity. Based on experimental data, adequate second-order polynomial regression models were obtained for all response variables using the least-squares method. Statistical analysis showed that grinding time and rotational speed had the most significant influence on the process. Multi-objective optimization using the weighted-sum method enabled the identification of optimal operating conditions that balance product quality, throughput, and energy consumption. Verification experiments confirmed the adequacy of the developed models. Practical implementation of the optimized regimes increases throughput by 15–20% while simultaneously reducing energy consumption by 8–12% compared with empirically selected operating conditions. The proposed models and recommendations provide a quantitative basis for tuning and controlling grinding equipment in processing industries.