Prediction and visualization of charge shape and ball trajectory in tumbling mills: a python-based tool for liner design and operational optimizations

Tumbling mills are critical in mineral processing due to their high energy consumption and impact on downstream processes. The mining industry accounts for 1.7% of global energy consumption, with comminution responsible for approximately 25% of this usage. Mill performance is largely governed by charge shape and media trajectory, which are significantly influenced by liner design and wear conditions. However, existing tools provide limited capabilities for combined analysis of these critical parameters. This study introduces a Python-based tool that integrates the Morrell C model for charge shape prediction with Powell's model for media trajectory calculation, offering comprehensive visualization of mill dynamics. The tool's effectiveness was demonstrated through two case studies on an 8-meter SAG mill: first optimizing initial liner design parameters and then adapting operating parameters to compensate for liner wear over a six-month period. Results show how the tool enables proactive operational adjustments based on visualized trajectory changes, helping maintain optimal grinding efficiency throughout the liner lifecycle. This integrated approach to design and operational optimization contributes to improved energy efficiency, extended liner life, and more sustainable mineral processing practices.