XXXI International Mineral Processing Congress 2024 Proceedings/Washington, DC/Sep 29–Oct 3 3877
where dV is the lost volume of material in a grid due to
wear, A is the grid surface area, dh is the related thickness
loss, C is the material wear resistant coefficient, and dW is
the differential shear work done on the grid surface.
To speed up the wear process, we follow the two crite-
ria mentioned in the above section to choose an artificial
wear resistant coefficient Cmodel to replace C, as discussed
in (Qiu et al., 2001), which enables faster wear simulations
without losing wear characteristics.
SHEAR WORK AVERAGING ALGORITHM
The side effect of speed-up of wear simulation is that the
collected shear work done on the liner surface within each
incremental time is very rough. Thus, a special averaging
algorithm is needed to smooth the shear work. For this pur-
pose, firstly we average the grid shear work across VTM
liner flights (usually two). Secondly, we use least square
method to enforce the roughly distributed shear work over
the liner surface to fit a polynomial equation so that the
shear work become continuous over the liner surface. This
ensures the smoothness of wear surface.
WEAR SIMULATION ALGORITHM
The wear simulation can be described as the following steps.
1. Set up the VTM model with new liner and run the
simulation to reach steady state.
2. At each time increment, collect the shear work
done on each grid.
3. Apply the least square model to smooth the shear
work over the entire liner surface.
4. Apply Archard’s wear model to each grid and cal-
culate the volume loss due to wear.
5. Translate the grid volume losses into grid nodal
displacements.
6. Update the parameters of D rij and Dzij, and q0
and qn and then reorganize locations of qi-sections
by enforcing uniform distribution of qi (i=1,2,…
,n–1) between q0 and qn.
7. Reorganize nodal points for each sectional profile
by enforcing uniformity, and
8. Go back to the above step 2.
BALL ADDITION MECHANISM
As liner wear progresses, the effective outer radius of each
qi-sections will be reduced, and consequently the Vertimill
power draw will drop. In mill operations, the operator will
periodically add more ball media to the mill to try to main-
tain a constant power. Thus, in the DEM model, a ball
addition mechanism is introduced by adding balls from the
mill top at every incremental time when the liner geometry
is updated.
LINER LIFE TERMINATION CONDITION
In the field, it is observed, for some specific designs, as the
life of a liner approaches to the end, a cavity will appear at
the liner surface near the edge, which will expand and then
later cause the loss of the edge piece (Figure 2). To account
for the pattern, we introduced a cavity formation mecha-
nism in the DEM model, which is activated as the liner
localized thickness decreases to zero.
Figure 2. Formation of a cavity on the liner surface near the
edge
where dV is the lost volume of material in a grid due to
wear, A is the grid surface area, dh is the related thickness
loss, C is the material wear resistant coefficient, and dW is
the differential shear work done on the grid surface.
To speed up the wear process, we follow the two crite-
ria mentioned in the above section to choose an artificial
wear resistant coefficient Cmodel to replace C, as discussed
in (Qiu et al., 2001), which enables faster wear simulations
without losing wear characteristics.
SHEAR WORK AVERAGING ALGORITHM
The side effect of speed-up of wear simulation is that the
collected shear work done on the liner surface within each
incremental time is very rough. Thus, a special averaging
algorithm is needed to smooth the shear work. For this pur-
pose, firstly we average the grid shear work across VTM
liner flights (usually two). Secondly, we use least square
method to enforce the roughly distributed shear work over
the liner surface to fit a polynomial equation so that the
shear work become continuous over the liner surface. This
ensures the smoothness of wear surface.
WEAR SIMULATION ALGORITHM
The wear simulation can be described as the following steps.
1. Set up the VTM model with new liner and run the
simulation to reach steady state.
2. At each time increment, collect the shear work
done on each grid.
3. Apply the least square model to smooth the shear
work over the entire liner surface.
4. Apply Archard’s wear model to each grid and cal-
culate the volume loss due to wear.
5. Translate the grid volume losses into grid nodal
displacements.
6. Update the parameters of D rij and Dzij, and q0
and qn and then reorganize locations of qi-sections
by enforcing uniform distribution of qi (i=1,2,…
,n–1) between q0 and qn.
7. Reorganize nodal points for each sectional profile
by enforcing uniformity, and
8. Go back to the above step 2.
BALL ADDITION MECHANISM
As liner wear progresses, the effective outer radius of each
qi-sections will be reduced, and consequently the Vertimill
power draw will drop. In mill operations, the operator will
periodically add more ball media to the mill to try to main-
tain a constant power. Thus, in the DEM model, a ball
addition mechanism is introduced by adding balls from the
mill top at every incremental time when the liner geometry
is updated.
LINER LIFE TERMINATION CONDITION
In the field, it is observed, for some specific designs, as the
life of a liner approaches to the end, a cavity will appear at
the liner surface near the edge, which will expand and then
later cause the loss of the edge piece (Figure 2). To account
for the pattern, we introduced a cavity formation mecha-
nism in the DEM model, which is activated as the liner
localized thickness decreases to zero.
Figure 2. Formation of a cavity on the liner surface near the
edge