DEM Modeling and Optimization of the High Energy Ball Milling
MOHSEN MHADHBI
Laboratory of Useful Materials
National Institute of Research and Physicochemical Analysis
Technopole Sidi Thabet 2020 Ariana
TUNISIA
Abstract: - The Discrete Element Method (DEM) is a numerical method for simulating the dynamics of
particles processes. This present work focuses on DEM simulations of a scale laboratory planetary ball mill
through DEM Altair 2021.2 software to optimize and modulate the milling parameters. The simulation results
show a good agreement with the experiments. The numerical model is shown to be a promising tool for the
knowledge of dry milling in a planetary ball mill.
Key-Words: - High-energy ball milling, Simulation, Optimization, Parameters, Modeling.
Received: August 5, 2021. Revised: May 12, 2022. Accepted: June 8, 2022. Published: July 5, 2022.
1 Introduction
The discrete (or distinct) element method (DEM)
was first developed by Cundal and Strack [1] to
simulate granular soil. Xie et al. [2] investigated the
influence of filling level on the wear of liner and
vibration of a semi-autogenous grinding (SAG) mill
by using DEM approach. They concluded that the
high-energy collision between liner and milling
media was the principal cause for mill vibration and
liner wear. Xie and Zhao [3] applied DEM to study
the influence of fluid, friction coefficient, and
milling speed on the wear rate in a planetary ball
mill. The results showed that drag force and torque
from fluid could decrease the particle wear and that
the rotation revolution radius affected the mill
speed. Therefore, the impact energy of the particles,
in ball mills, under various operating conditions was
analyzed by DEM simulations [4]. It was showed
that the impact energy was influenced by the
operating conditions of milling. Zeng et al. [5] used
DEM approach to investigate the influences of
rotation speed and particle shape on flow behaviors
in a vertical rice mill. They revealed that effects of
ratio on the milling rely on rotation speed and that
mean collision rate increase with increasing ratio for
a lower rotation speed. Zeng et al. [6] used a
numerical discrete element method (DEM) and
particle replacement model (PRM) to simulate grain
breakage in a vertical rice mill. The simulation
results showed that the proposed method was an
effective and efficient guidance to explain the
mechanisms occurring in rice mill. Xie et al. [7]
applied DEM for modeling a SAG mill with
spherical and polyhedral media. They revealed that
the charging of particles in the polyhedron-sphere
milling system was blocked by polyhedral particles
and that the energy collision between liner and
material has increased remarkably. A combined
physical and DEM approach was used to investigate
cubical and spherical particles behavior in tumbling
mills [8]. It was showed that changing spherical to
cubical particles increased the simulation time by 35
folds. Pedrayes et al. [9] used DEM to characterize
the load torque of tumbling ball mills in the
frequency domain. They concluded that load torque
signal contains sufficient information to characterize
the load level of the ball mill. Similarly, the effects
of filling level on the rice milling accuracy of rice in
the friction rice mill were studied using DEM
approach [10]. The obtained results showed that
with increase of filling level, additional particles
penetrate outside ring subsequently principally inner
ring.
Powell et al. [11] used DEM modeling to
simulate the dynamics of ball movement in an
industrial scale ball mill.
Some researchers [12] have validated the DEM
simulations using Positron Emission Particle
Tracking (PEPT) experiments in rotating
drums. They concluded a strong statistical
agreement between the tuned DEM and PEPT
data. Other researchers [13] studied the influence of
contact parameters on charge motion and power
draw by DEM modeling of a scale laboratory ball
mill. They demonstrate agreement between
simulations and experiment.
This paper aims to study the effects of mill speed
on the load behavior during milling process. The
simulations of the milling media were conducted by
Altair 2021.2 software.
2 Materials and Methods
In this section, we provide the software used for the
simulation, the instrument used for milling, and the
input parameters for DEM simulation.
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2.1 Discrete Element Model
The simulations were performed by Altair 2021.2
Software [14] that is designed for the simulation and
analysis of bulk particle handling and processing
operations. Therefore, the Hertz Mindlin is the
contact model used in DEM because of its accurate
and efficient. The normal and tangential contact
forces are calculated based on the Hertz theory [15]
and Mindlin and Deresiewicz theory [16],
respectively. The tangential force uses the
Coulomb’s law of dry friction. The coefficient of
restitution is a function of the normal and tangential
components. This section was detailed in a previous
work [17].
2.2 Instrument
The high-energy planetary ball mill [18] fabricated
by German Fritsch Company (type Pulversiette 7)
was used in the simulation. This mill consists of a
rotating support disk (called turn table) and two
milling vials, as presented in Fig. 1.
Fig.1. Pulverisette 7 planetary ball mill and vials
used in experiment.
Fig. 2 shows the operating principle of the planetary
ball mill. The supporting disk and the vials,
containing the balls and powder, rotate in opposite
directions.
Fig.2. The operating principle of the planetary ball
mill.
2.3 Simulation Parameters
The parameters of the materials used in the DEM
simulations are shown in Table 1. These DEM
parameters were determined from experimental and
references [19]. The diameter of the milling balls
was fixed as 15 mm.
During simulation, the powder particles are
considered as spheres in order to reduce the required
computation time. The volume of a powder particle
was assumed equal the volume of a sphere with a
diameter of 1.2 mm.
Table 1. The parameters for DEM simulations [19].
Parameter
Value
Revolution speed (rpm)
350
Rotational speed (rpm)
700
Density of vial and balls (kg/m3)
7700
Density of powder (kg/m3)
4000
Poisson’s ratio of vial and balls
0.27
Poisson’s ratio of powder
0.3
Young’s modulus of vial and balls (Pa)
1.8×1011
Young’s modulus of powder (Pa)
1×107
Restitution coefficient of ball-ball and
ball-vial
0.75
Restitution coefficient of powder-
powder
0.3
Restitution coefficient of powder-ball
and powder-vial
0.5
Static friction coefficient of ball-ball
and ball-vial
0.5
Static friction coefficient of powder-
powder
0.7
Static friction coefficient of powder-ball
and powder-vial
0.7
Rolling friction coefficient of ball-ball
and ball-vial
0.01
Rolling friction coefficient of powder-
powder
0.15
Rolling friction coefficient of powder-
ball and powder-vial
0.15
Time step (s)
1.01×10-4
3 Results and Discussion
Fig. 3 shows the ball charge motion inside the mill
in different characteristics zones and positions: (1)
the head represents the highest point of the liner that
is still in contact with the particles (also called the
apex of charge trajectory); (2) the shoulder
represents the region where the cascading material
flows down; (3) the dead zone which is colored
blue; (4) the bulk toe represents the point of
intersection of tumbling charge with mill shell; (5)
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Mohsen Mhadhbi
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Volume 2, 2022
the impact toe (crushing toe) represents the region
where cataracting charge impacts shell or bulk
charge; and (6) the cascading charge which is
colored red.
Fig.3. The ball charge motion in characteristics
zones and positions.
Fig. 4 shows the snapshots of particles and balls
motion during the ball milling process. Thus, the
color indicates the particles velocity from blue
(slow) to red (fast). By analyzing the trajectory of
the milling media during the simulation of milling,
the following conclusions can be drawn : at the
begining (Fig. 4a), it can be seen that the milling
media going up to a lower height. After that, with
increasing the milling time (Fig. 4b), it can be seen
that that the milling media going up to a great height
due to the increase of kinetic energy. Furthermore,
when the milling time is increased (Fig. 4c), the
milling media were thrown towards the center of
vial, which is caused by the centrifugal acceleration
created by the planetary motion. Finally, for
prolonged milling time (Fig. 4d), it can be observed
that the milling media were located at toe and
shoulder regions. The motion patterns observed in
the simulation were also reported in several studies
[20-22].
Fig.4. Snapshots of milling media during the ball
milling.
In general, it can be seen from the simulation
results that the DEM model is able to predict the
milling media of the laboratory ball mill for
different characteristics zones and positions.
Therefore, additional DEM simulations are required
to fully understand the milling mechanism.
4 Conclusion
In conclusion, DEM simulations were employed to
optimizing and modeling the milling media in a
planetary ball mill. DEM simulations can be used to
calculate collision rates of balls and powder
particles in a laboratory scale ball mill. More work
would be complemented in our future research.
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Author Contributions:
Mohsen Mhadhbi carried out the simulation and
wrote the paper throughout.
Sources of funding for research
presented in a scientific article or
scientific article itself
No funding to declare.
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International, CC BY 4.0)
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