3876 XXXI International Mineral Processing Congress 2024 Proceedings/Washington, DC/Sep 29–Oct 3
lacking proper algorithms in the commercial DEM package
to handle those obstacles.
After years of exploration, the authors have developed
a new algorithm, which successfully overcomes these obsta-
cles. In the new algorithm, (i) a parametric model is used
to cover the liner surface geometry from new to worn state,
(ii) a least square method is used to smooth shear work
done on the entire Vertimill screw liner worn surface, and
(iii) the liner volume loss due to wear can be translated into
the changes of geometric parameters ensuring the quality
of re-mesh. We show the practicality of the DEM model
for Vertimill liner wear prediction with a sample numerical
case for the Metso Vertimill (VTM ®).
A PARAMETRIC MODEL FOR VTM LINER
SURFACE MESH
As shown in Figure 1, the VTM liner surface mesh con-
sists of n+1 sections. At each sectional profile, there are
m uniformly distributed nodal points, of which the point
Oi remain intact during wearing process, and thus can be
taken as a reference point for the section. The n+1 points Oi
(i=0,1,2,…,n) fall in one helix curve described by
xi0 =r0 cos qi, yi0=r0 sin qi, zi0=h0 qi (i=0,1,2,…,n)
and the m nodal points in the ith section profile have the
following coordinates
xij =(r0+D rij) cos qi,
yij= (r0+D rij) sin qi,
zij =h0 qi +Dzij (j=0,1,2,…,m–1)
Since all the nodal points at the ith sectional profile share
the same angle qi, the section can also be called qi-section.
The locations of starting and ending sections are
defined by two angles q0 and qn (Figure 1). Between q0 and
qn, qi (i=1, 2,…, n–1) are uniformly distributed. At each
section profile, the m nodal points are also uniformly dis-
tributed (Figure 1). Thus, the liner surface can be meshed
by all of the sectional nodal points into n × m grids. The
parameters qi, D rij and Dzij, will vary as the liner surface
evolves from new to worn state throughout the wearing
process, and correspondingly the mesh will be conformed
with the surface wear.
EMBEDDED ARCHARD’S WEAR MODEL
Following the same algorithm as in (Qiu et al., 2001), we
embedded the following Archard’s wear model in the DEM
program:
dV A dh C dW ==
Figure 1. VTM liner sections
lacking proper algorithms in the commercial DEM package
to handle those obstacles.
After years of exploration, the authors have developed
a new algorithm, which successfully overcomes these obsta-
cles. In the new algorithm, (i) a parametric model is used
to cover the liner surface geometry from new to worn state,
(ii) a least square method is used to smooth shear work
done on the entire Vertimill screw liner worn surface, and
(iii) the liner volume loss due to wear can be translated into
the changes of geometric parameters ensuring the quality
of re-mesh. We show the practicality of the DEM model
for Vertimill liner wear prediction with a sample numerical
case for the Metso Vertimill (VTM ®).
A PARAMETRIC MODEL FOR VTM LINER
SURFACE MESH
As shown in Figure 1, the VTM liner surface mesh con-
sists of n+1 sections. At each sectional profile, there are
m uniformly distributed nodal points, of which the point
Oi remain intact during wearing process, and thus can be
taken as a reference point for the section. The n+1 points Oi
(i=0,1,2,…,n) fall in one helix curve described by
xi0 =r0 cos qi, yi0=r0 sin qi, zi0=h0 qi (i=0,1,2,…,n)
and the m nodal points in the ith section profile have the
following coordinates
xij =(r0+D rij) cos qi,
yij= (r0+D rij) sin qi,
zij =h0 qi +Dzij (j=0,1,2,…,m–1)
Since all the nodal points at the ith sectional profile share
the same angle qi, the section can also be called qi-section.
The locations of starting and ending sections are
defined by two angles q0 and qn (Figure 1). Between q0 and
qn, qi (i=1, 2,…, n–1) are uniformly distributed. At each
section profile, the m nodal points are also uniformly dis-
tributed (Figure 1). Thus, the liner surface can be meshed
by all of the sectional nodal points into n × m grids. The
parameters qi, D rij and Dzij, will vary as the liner surface
evolves from new to worn state throughout the wearing
process, and correspondingly the mesh will be conformed
with the surface wear.
EMBEDDED ARCHARD’S WEAR MODEL
Following the same algorithm as in (Qiu et al., 2001), we
embedded the following Archard’s wear model in the DEM
program:
dV A dh C dW ==
Figure 1. VTM liner sections