3770 XXXI International Mineral Processing Congress 2024 Proceedings/Washington, DC/Sep 29–Oct 3
is dependent on size, flaw structure, composition and
accrual damage). This paper explores the effect of ball size
and mill diameter on collision environment, which argu-
ably has an effect on the probability of fracture of different
particle sizes, the size distribution of progeny generated and
the mechanism of ball wear. Ansys ROCKY ®, a commercial
software package, was used to carry out the simulations for
the investigation undertaken.
Simulation Set Up
In an operating mill, balls do not exist as a mono size form,
but they generate an equilibrium size distribution, which
depends on the make-up ball size(s) and the ball wear rate.
Therefore, to investigate the effect of ball size on the mill
collision environment, the simulations were set up using
seasoned load of balls. A seasoned load mimicked an equi-
librium size distribution in a mill that is periodically topped
up with a mono size batch of balls. The mono size batch of
top-up balls used were 60 mm, 50 mm, 40 mm, 30 mm,
and 20 mm balls. The calculation of the seasoned loads was
based on Eq. (1), assuming that the wear is driven by abra-
sion. Table 1 shows the seasoned loads of balls used in the
simulations. Within a size interval, the distribution of mass
followed the relationship described by Eq. (2).
*log^sizeh Mass A B =+(2)
Table 2 shows the dimensions of the batch mills simu-
lated and the operating conditions. The mill are at Mintek,
and are used for routine test-work for generating data for
mill sizing and simulations (ball mills and AG/SAG mills).
To investigate the effect of mill diameter on collision envi-
ronment, simulations were set up using seasoned loads of
the following mono size batch of top-up balls: 60 mm,
50 mm, 40 mm, 30 mm and 20 mm (shown in Table 1).
Mill Geometry
Figure 2 shows the 1.2 m diameter mill (left) and 0.6 m
diameter mill (right). The material property of the all mill
geometries constructed was defined by three parameters,
which were the density =7850 kg·m–3, Young’s modulus
=1×1011 N·m−2 and Poisson’s ratio =0.3. The geometries
of the 1.8 m mill and 0.3 m mill were similar to the ones
shown in Figure 2.
Material Contact Parameters
The Hertzian spring-dashpot law was chosen to model nor-
mal contact force, and the Mindlin-Deresiewicz law was
chosen to model the tangential contact force. These con-
tact force laws have been used widely in simulation stud-
ies that had energy dissipation as a parameter of interest
(Weerasekara et al., 2016 Bbosa et al., 2016 Carvalho,
2013 Sarracino et al., 2004). Various combinations of
coefficient of friction and restitution were used, but on this
paper the data presented is from simulations that used a
coefficient of restitution =0.3 and coefficient of friction of
0.2 for steel-steel collisions.
Collision Environment
The primary source of energy dissipation during a col-
lision is related to the inelastic nature of the contact force
Fc. The dissipation work done by this force (Wdiss) and
power (Pdiss) are calculated using Eq. (3) and (4). The inte-
gral is defined over the entire collision interval (loading and
unloading):
W v dt diss
c c
rel $8F =-(3)
P tout
W
diss k
k diss
1 ==
/^h
(4)
Table 1. Seasoned load of balls used in the simulations
Size (mm)
60 mm
Ball Top-Up Size
50 mm
Ball Top-Up Size
40 mm
Ball Top-Up Size
30 mm
Ball Top-Up Size
20 mm
Ball Top-Up Size
–75+53 38.95 0.00 0.00 0.00 0.00
–53 +37.5 44.86 66.56 18.57 0.00 0.00
–37.5 +26.5 12.16 25.12 61.16 35.27 0.00
–26.5 +19 3.20 6.60 16.08 51.35 22.33
–19 +13.2 0.83 1.72 4.18 13.36 77.59
Table 2. Simulation set up
Mill dimensions
(D×L)
0.3 m × 0.3 m
0.3 m × 0.6 m
0.6 m × 0.3 m
0.6 m × 1.1 m
1.2 m × 0.3 m
1.2 m × 2.0 m
1.8 m × 0.3 m
1.8 m × 3.3 m
Mill speed 75% of critical
Charge filling 30%
is dependent on size, flaw structure, composition and
accrual damage). This paper explores the effect of ball size
and mill diameter on collision environment, which argu-
ably has an effect on the probability of fracture of different
particle sizes, the size distribution of progeny generated and
the mechanism of ball wear. Ansys ROCKY ®, a commercial
software package, was used to carry out the simulations for
the investigation undertaken.
Simulation Set Up
In an operating mill, balls do not exist as a mono size form,
but they generate an equilibrium size distribution, which
depends on the make-up ball size(s) and the ball wear rate.
Therefore, to investigate the effect of ball size on the mill
collision environment, the simulations were set up using
seasoned load of balls. A seasoned load mimicked an equi-
librium size distribution in a mill that is periodically topped
up with a mono size batch of balls. The mono size batch of
top-up balls used were 60 mm, 50 mm, 40 mm, 30 mm,
and 20 mm balls. The calculation of the seasoned loads was
based on Eq. (1), assuming that the wear is driven by abra-
sion. Table 1 shows the seasoned loads of balls used in the
simulations. Within a size interval, the distribution of mass
followed the relationship described by Eq. (2).
*log^sizeh Mass A B =+(2)
Table 2 shows the dimensions of the batch mills simu-
lated and the operating conditions. The mill are at Mintek,
and are used for routine test-work for generating data for
mill sizing and simulations (ball mills and AG/SAG mills).
To investigate the effect of mill diameter on collision envi-
ronment, simulations were set up using seasoned loads of
the following mono size batch of top-up balls: 60 mm,
50 mm, 40 mm, 30 mm and 20 mm (shown in Table 1).
Mill Geometry
Figure 2 shows the 1.2 m diameter mill (left) and 0.6 m
diameter mill (right). The material property of the all mill
geometries constructed was defined by three parameters,
which were the density =7850 kg·m–3, Young’s modulus
=1×1011 N·m−2 and Poisson’s ratio =0.3. The geometries
of the 1.8 m mill and 0.3 m mill were similar to the ones
shown in Figure 2.
Material Contact Parameters
The Hertzian spring-dashpot law was chosen to model nor-
mal contact force, and the Mindlin-Deresiewicz law was
chosen to model the tangential contact force. These con-
tact force laws have been used widely in simulation stud-
ies that had energy dissipation as a parameter of interest
(Weerasekara et al., 2016 Bbosa et al., 2016 Carvalho,
2013 Sarracino et al., 2004). Various combinations of
coefficient of friction and restitution were used, but on this
paper the data presented is from simulations that used a
coefficient of restitution =0.3 and coefficient of friction of
0.2 for steel-steel collisions.
Collision Environment
The primary source of energy dissipation during a col-
lision is related to the inelastic nature of the contact force
Fc. The dissipation work done by this force (Wdiss) and
power (Pdiss) are calculated using Eq. (3) and (4). The inte-
gral is defined over the entire collision interval (loading and
unloading):
W v dt diss
c c
rel $8F =-(3)
P tout
W
diss k
k diss
1 ==
/^h
(4)
Table 1. Seasoned load of balls used in the simulations
Size (mm)
60 mm
Ball Top-Up Size
50 mm
Ball Top-Up Size
40 mm
Ball Top-Up Size
30 mm
Ball Top-Up Size
20 mm
Ball Top-Up Size
–75+53 38.95 0.00 0.00 0.00 0.00
–53 +37.5 44.86 66.56 18.57 0.00 0.00
–37.5 +26.5 12.16 25.12 61.16 35.27 0.00
–26.5 +19 3.20 6.60 16.08 51.35 22.33
–19 +13.2 0.83 1.72 4.18 13.36 77.59
Table 2. Simulation set up
Mill dimensions
(D×L)
0.3 m × 0.3 m
0.3 m × 0.6 m
0.6 m × 0.3 m
0.6 m × 1.1 m
1.2 m × 0.3 m
1.2 m × 2.0 m
1.8 m × 0.3 m
1.8 m × 3.3 m
Mill speed 75% of critical
Charge filling 30%