The major difference between the upgraded ball mill model and
the prior-art population balance models is in the way the size
reduction is calculated. The upgraded model utilises a specific
energy-based equation (Eq. (11)) to calculate the particle breakage
index, t10. The product size distribution is then determined from
the t10–tn relationships. The specific energy term in Eq. (11) explicitly
takes into account the mill operational conditions, such as mill
geometry, ball charge volume and mill throughput, if the mill
power draw is calculated by Morrell’s power model or DEM; or
implicitly if the mill power is directly measured. The material factor
is also incorporated in Eq. (11), which can be independently
measured using the JKFBC. The mill is no longer treated as a ‘black
box’ in the upgraded ball mill model; instead both machine factor
and material factor have been mechanistically incorporated in the
size reduction model.