XXXI International Mineral Processing Congress 2024 Proceedings/Washington, DC/Sep 29–Oct 3 3769
In Eq. (1), m is the mass of the ball, t is the time, D is the
diameter of the grinding ball, k is the proportionality con-
stant and n is an exponential constant.
The choice of ball size is known to be a trade-off
between wear (which affects the costs of replenishing) and
throughput for a specific product size (Cho et al., 2013
Concha et al. 1992). Figure 1 shows a trade-off between
ball media wear and throughput capacity for a ball mill-
ing circuit treating a copper ore to achieve a given grind
size over a range of make-up ball sizes. The plots suggest
that continuous improvements on the understanding of the
ball size-mill performance and ball size-ball wear relation-
ships are crucial in making mills operation efficient and
profitable.
The distribution of energy into shear and impact com-
ponents of collisions (which essentially defines the mill
collision environment) determines the relative strengths of
attrition breakage and impact breakage, and the mechanism
of media wear. In the published literature, the ball size-mill
performance relationship and ball size-ball wear relation-
ship are not explained in terms of changes in the collision
environment as the ball size is changed. This paper explores
the effect of ball size on the mill collision environment, and
its implications on the ball size-mill performance and ball
size-ball wear relationships.
Sizing and optimisation of grinding mills using the
population balance modelling approach (Herbst et al.,
1980) has thrived over the last three decades. The approach
relies on bench-scale testing using mills of diameters rang-
ing from 0.2 m to 0.6 m. The prediction of the impact
of oversized feed to a ball mill using this approach is not
straightforward given the difficulty associated to obtaining
reliable results from the use of large ball sizes in labora-
tory mills, where the largest ball size recommended is one
eighth of the mill diameter. Although the approach has
been largely successful, it does take into account the mill
collision environment. This paper explores the effect of mill
diameter on collision environment, and its implication on
grinding performance predictions.
Discrete Element Method (DEM) was used to inves-
tigate the effects of ball size and mill diameter on collision
environment.
DEM SIMULATIONS
Overview
For a mill of a given size, speed and charge filling, the rate
of size reduction of particles depends on (i) the collision
frequency of balls (ii) the probability of capture of particles
between the colliding balls and (iii) the probability of frac-
ture of the captured particles. The probability of fracture
is dependent on the amount of energy dissipated on a col-
lision, the amount of energy a particle absorbs during a
stressing event, and the fracture energy of a particle (which
Figure 1. Relationship between steel consumption and circuit throughput
In Eq. (1), m is the mass of the ball, t is the time, D is the
diameter of the grinding ball, k is the proportionality con-
stant and n is an exponential constant.
The choice of ball size is known to be a trade-off
between wear (which affects the costs of replenishing) and
throughput for a specific product size (Cho et al., 2013
Concha et al. 1992). Figure 1 shows a trade-off between
ball media wear and throughput capacity for a ball mill-
ing circuit treating a copper ore to achieve a given grind
size over a range of make-up ball sizes. The plots suggest
that continuous improvements on the understanding of the
ball size-mill performance and ball size-ball wear relation-
ships are crucial in making mills operation efficient and
profitable.
The distribution of energy into shear and impact com-
ponents of collisions (which essentially defines the mill
collision environment) determines the relative strengths of
attrition breakage and impact breakage, and the mechanism
of media wear. In the published literature, the ball size-mill
performance relationship and ball size-ball wear relation-
ship are not explained in terms of changes in the collision
environment as the ball size is changed. This paper explores
the effect of ball size on the mill collision environment, and
its implications on the ball size-mill performance and ball
size-ball wear relationships.
Sizing and optimisation of grinding mills using the
population balance modelling approach (Herbst et al.,
1980) has thrived over the last three decades. The approach
relies on bench-scale testing using mills of diameters rang-
ing from 0.2 m to 0.6 m. The prediction of the impact
of oversized feed to a ball mill using this approach is not
straightforward given the difficulty associated to obtaining
reliable results from the use of large ball sizes in labora-
tory mills, where the largest ball size recommended is one
eighth of the mill diameter. Although the approach has
been largely successful, it does take into account the mill
collision environment. This paper explores the effect of mill
diameter on collision environment, and its implication on
grinding performance predictions.
Discrete Element Method (DEM) was used to inves-
tigate the effects of ball size and mill diameter on collision
environment.
DEM SIMULATIONS
Overview
For a mill of a given size, speed and charge filling, the rate
of size reduction of particles depends on (i) the collision
frequency of balls (ii) the probability of capture of particles
between the colliding balls and (iii) the probability of frac-
ture of the captured particles. The probability of fracture
is dependent on the amount of energy dissipated on a col-
lision, the amount of energy a particle absorbs during a
stressing event, and the fracture energy of a particle (which
Figure 1. Relationship between steel consumption and circuit throughput