Tumbling mills, consisting of large rotating cylinders, are extensively used in various industries for the crushing and grinding of a wide range of granular materials. Of critical importance for such communition devices are the particle size reduction efficiency, the total energy consumed, and the wear on the internal liner surface.
To gain confidence in the numerical simulation capabilities for this application, a validation study of the ball charge in a laboratory-scale ball mill has been undertaken. The mill has a diameter of 800 mm and a length of 400 mm. A total of 19,116 spherical steel balls of 15 mm diameter were considered.
Three-dimensional DEM simulations have been performed to account for interaction of the balls with the end walls. Rotational speeds of 70% and 80% of the critical speed (at which centrifuging occurs) have been considered.
The images below provide a comparison between the numerical results and experimental data for a speed of 70% critical. Good qualitative agreement for the shape of the ball charge can be observed.
courtesy Magotteaux SA
Animations of the charge motion for the two rotational speeds considered indicate a greater number of cataracting particles at the higher speed, and an associated increase in the dispersion of the balls near the free surface. For both speeds, there is no evidence of cataracting particles colliding dirctly with the liner.
70% of critical speed
80% of critical speed
A more quantitative comparison can been made by comparing the power draw of the mill, resulting from collisional interaction of the ball charge with the liner and end walls. The plot below shows the temporal dependence of the total force amplitude and the power draw for a rotational speed of 70% critical. After the initial transient phase of about 2 ms, an excellent agreement between the computed and experimental values of the power draw is observed.
Finally, numerical simulations can provide a wealth of physical quantities that are difficult or impossible to measure experimentally. As an example, the plot below shows the angular dependence of the average components of force (total, normal and tangential) on the liner. The collisional intensity (time average of the number of balls in contact with the liner surface) is also shown.