XXXI International Mineral Processing Congress 2024 Proceedings/Washington, DC/Sep 29–Oct 3 3771
where vcrel is the instantaneous relative velocity at the con-
tact point, k is the number of collisions occurring within
the time interval Δtout. The total contact force is given by
Eq. (5):
F F n F
c n c t $=+(5
where Fn and Ft are, respectively, the normal and tangential
components of the contact force. Additionally, n
c is the
normal unit vector of the contact.
The shear work (Wshear) is calculated using Eq. (6):
W ds shear
t t $8F =-(6)
where dst is the sliding distance, i.e., the displacement paral-
lel to the tangential plane of the contact. The difference of
Eq. (3) and (6) gives the impact work.
RESULTS AND DISCUSSION
Effect of Ball Size on Collision Environment
Figure 3 show the effect of ball size on the distribution of
power between shear and impact components of collisions.
For each mill, it is evident from Figure 3 that of the power
dissipated, the proportion that is taken by the shear com-
ponent of collisions increases as a smaller ball top-up size is
used. E.g., in a 1.2 m Ø mill changing from 60 mm top-up
Figure 2. Mill geometries used in the simulations
Figure 3. Effect of ball size on the distribution of collision power
where vcrel is the instantaneous relative velocity at the con-
tact point, k is the number of collisions occurring within
the time interval Δtout. The total contact force is given by
Eq. (5):
F F n F
c n c t $=+(5
where Fn and Ft are, respectively, the normal and tangential
components of the contact force. Additionally, n
c is the
normal unit vector of the contact.
The shear work (Wshear) is calculated using Eq. (6):
W ds shear
t t $8F =-(6)
where dst is the sliding distance, i.e., the displacement paral-
lel to the tangential plane of the contact. The difference of
Eq. (3) and (6) gives the impact work.
RESULTS AND DISCUSSION
Effect of Ball Size on Collision Environment
Figure 3 show the effect of ball size on the distribution of
power between shear and impact components of collisions.
For each mill, it is evident from Figure 3 that of the power
dissipated, the proportion that is taken by the shear com-
ponent of collisions increases as a smaller ball top-up size is
used. E.g., in a 1.2 m Ø mill changing from 60 mm top-up
Figure 2. Mill geometries used in the simulations
Figure 3. Effect of ball size on the distribution of collision power