The sizing of ball mills and ball milling circuits from laboratory grinding tests is largely a question of applying empirical equations or factors based on accumulated experience. Different manufacturers use different methods, and it is difficult to check the validity of the sizing estimates when estimates from different sources are widely divergent. It is especially difficult to teach mill sizing and circuit design to engineering students because of the apparent lack of a logical engineering foundation for the empirical equations. It is the purpose of this communication to demonstrate this logical foundation and to show the inter-relations between treatments using the concepts of specific rate-of-breakage/breakage distribution parameters and the more empirical methods.
A) Total Apparent Volumetric Charge Filling – including balls and excess slurry on top of the ball charge, plus the interstitial voids in between the balls – expressed as a percentage of the net internal mill volume (inside liners).
B) Overflow Discharge Mills operating at low ball fillings – slurry may accumulate on top of the ball charge; causing, the Total Charge Filling Level to be higher than the Ball Filling Level. Grate Discharge mills will not face this issue.
C) This value represents the Volumetric Fractional Filling of the Voids in between the balls by the retained slurry in the mill charge. As defined, this value should never exceed 100%, but in some cases – particularly in Grate Discharge Mills – it could be lower than 100%. Note that this interstitial slurry does not include the overfilling slurry derived from the difference between the Charge and Ball Mill Filling.
D) Represents the so-called Dynamic Angle of Repose (or Lift Angle) adopted during steady operation by the top surface of the mill charge (“the kidney”) with respect to the horizontal. A reasonable default value for this angle is 32°, but may be easily “tuned” to specific applications against any available actual power data.