Discrete Element Method Simulation of Filling Level in Planetary
Ball Mill
MOHSEN MHADHBI1, BARIS AVAR2
1Laboratory of Useful Materials,
National Institute of Research and Physicochemical Analysis,
Technopole Sidi Thabet 2020 Ariana,
TUNISIA
2Department of Metallurgical and Materials Engineering,
Zonguldak Bülent Ecevit University,
Incivez 67100 Zonguldak,
TURKEY
Abstract: - In this study, DEM (discrete element method) was used to improve our understanding of the
fundamental processes involved in the ball milling process, with a particular emphasis on the effect of the many
different filling levels in planetary ball mills. This DEM methodology facilitates the simulation of the behavior
of balls and powder particles inside the vials, enabling an understanding of the nature of the material milling
and the structure of the flow. The major benefit of the DEM technique is the ability to incorporate
interrelationships among different milling parameters. The simulations indicate that changing the filling level
has a significant effect on the ball milling process.
Key-Words: - planetary ball mill, simulation, discrete element method, modeling, filling level, milling
parameters.
Received: March 27, 2024. Revised: September 1, 2024. Accepted: October 3, 2024. Published: November 25, 2024.
1 Introduction
Planetary ball mills have emerged as a tool, in
materials science, for efficiently breaking down a
wide variety of materials. These high-energy mills
are used in working with very sensitive powder
applications e.g. pharmaceuticals and fine chemicals
to nanomaterials, where the purity and stability of
the material are of vital importance. As the vials
used in this work have a larger size than
the common scale used, such one is able to be
inserted into a planetary ball mill for milling that is
rotated with respect to their own axes, and
simultaneously around the central axis in opposite
directions. This provides a relatively complex
centrifugal pseudo-acceleration, which in turn
impacts the movements and collisions with the
milling media inside of the vials. In order to obtain
the intrinsic mechanisms involved in planetary ball
milling, researchers used the Discrete Element
Method (DEM) simulations. Through these
simulations, valuable insights regarding the velocity
distributions of particles, the character of the applied
stress conditions, as well as the on overall filling
level inside milling vials have been obtained, [1].
DEM has been used to model planetary ball
mills which have not only shed light on particle
dynamics but also offered the facility of choosing
the right milling condition for targeted material
properties. DEM, by simulating motion and
interaction of milling media, can thus help
researchers understand how the operational
variables (rotational speed, vial geometry, and
media size) control the milling process. Therefore,
predictive models were designed to predict results
including particle size distribution, milling
efficiency, and material breakage type. In addition,
DEM simulations have been used to investigate how
the wear rate for both media and milling vials is
affected by milling media material and shape, giving
rise to more wear-resistant and efficient designs.
These are essential properties to scale up laboratory
results in industrial applications and for consistency
in product quality and process efficiency. With the
promises held by these simulation techniques in
tuning milling processes for peculiar material needs,
including novel nanomaterials production, fine-
tuning of pharmaceutical powders, and development
of new chemical compounds.
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Mohsen Mhadhbi, Baris Avar
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The Discrete Element Method (DEM)
represents a numerical method often adopted in the
modeling and optimization of ball mills, [2]. DEM
relies on computational techniques to analyze
particle movement and collisions based on Newton's
laws of motion. In previous research, [3], [4], we
used DEM modeling to analyze the simulations of a
planetary ball mill. The simulation of varying ball
mills is a significant area of research utilizing DEM
in numerous studies. The authors of the study [5]
revealed that the impact energy of the balls greatly
affected the effectiveness of the milling process.
During the comparative analysis in [6], steel balls
and alumina balls were evaluated for their
effectiveness in grinding the cement clinker using a
population balance model (PBM) and DEM, which
concluded that energy savings of up to thirty-five
percent could be achieved in milling when alumina
balls were used to replace steel balls. In addition to
the aforementioned considerations, a computational
fluid dynamics (CFD) analysis was conducted to
examine the influence of milling circumstances on
the particle size, [7]. In [8], it was used DEM
simulations to study the thermal transfer properties
of the ball-milling components. They found that the
simulations corresponded to an experimental
investigation, thereby validating that the simulations
represented a realistic approximation of the
phenomena being modeled. Similarly, the study [9]
used a DEM approach to simulate ball motion in
planetary ball mills. A strong correlation between
the experimental and simulation results was found
across different test conditions. Separately, the study
[10] compared the results of simulating the charging
behaviour in a centrifugal grinding device to their
experimental results. The simulation results were
also found to correspond closely with the
experimental data. In [11], it was used DEM
simulations to investigate the mechanisms
responsible for high-energy planetary ball milling
processes. These results lead to the conclusion that
using DEM simulation can enhance our
understanding of how operational variables affect
the dynamics of the system. Additionally, the study
[12] developed a new technique to model DEM
balls in considering slurry within a tumbling mill.
The simulations indicated that specific impact
energy directly correlated with the milling rate
within the sample material. Furthermore, the authors
suggested that the energy input was an important
variable within the milling process. The study [13]
developed a new mechanistic Universidade Federal
do Rio de Janeiro (UFRJ) mill to model particle size
distribution using a dry laboratory planetary mill.
Their simulations indicated that the proposed model
gave accurate predictions for the model. The study
[14] presented a new method that models the three-
dimensional profile of an end-milled floor surface
using various variables including tool setting error,
tool workpiece vibration, tool path overlap, and
cutting motion. The results demonstrated good
agreement between observed and predicted three-
dimensional topography.
The primary purpose of this study is to achieve
a better understanding of the phenomena occurring
during rotating dynamics in a laboratory-scale
planetary ball mill through DEM simulations at
different fill levels.
2 Used Equipment
Planetary ball milling is a commonly used
technology in materials science and engineering,
primarily in the production of advanced materials
and the size reduction of powders. The technique
utilizes the rotation of a grinding vial around its own
axes simultaneously with the turntable (or sun
wheel) spinning in the opposite direction, creating a
complex dynamic motion. The combination of dual
rotation creates a high-energy environment to which
impact and shear forces are applied to the milling
media which maximizes particle size reduction,
mixing, and mechanical alloying, making planetary
ball milling a staple method in the development of
nanomaterials and fine powder processing.
The milling capacity of a planetary ball mill is a
result of several interactions of important
mechanisms. First, it relies on the impact force
generated as the milling media strikes the material
being milled, resulting in fracture and size reduction
of the milled material. Shear force is also important,
which occurs when particles become entrapped
between colliding balls or between the balls and the
vial walls. This force is important to facilitate the
plastic deformation of particles, re-shaping
the workability of the particles, and blending the
milled material. Impact and shear forces can result
in not only a reduced particle size but also play a
vital role in solid-state reactions, phase changes, or
in some cases the formation of amorphous phases,
which is a key step in the synthesis of new
materials. Moreover, the intense localized energy
dissipation within vials contributes to the activation
of chemical reactions, enabling the formation of
new compounds and alloys that might be
challenging to achieve using conventional methods.
The energy transfer in a planetary ball mill is
significant and is characterized by the high kinetic
energy imparted to the powder by the colliding
milling media. However, accurately quantifying the
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energy transferred during milling is challenging
because of the intricate nature of the milling
process, which involves variable factors, such as
milling speed, media size, and milling duration.
In this study, a high-energy planetary ball mill
(manufactured by Fritsch, model Pulverisette
7, Germany) was employed, which is equipped with
two vials that rotate around a single axis while the
turn disc rotates in the opposite direction (Figure 1).
Steel balls 15 mm in diameter were used as milling
media. The planetary motion is simulated through a
rotary motion of the vial around its axis,
accompanied by the introduction of a rotating
centrifugal pseudo-acceleration affecting the
particles.
Fig. 1: a) P7-planetary ball mill apparatus, b)
Schematic depicting the motion of the ball inside the
vials
3 Simulation Procedure
The DEM simulations were conducted utilizing the
commercially available EDEM 2021 software [15],
which assumes that the particles are spheres and that
minor overlap occurs during collisions. The model
that has been employed in the analysis of the
collision between two particles is predicated upon
the linear spring-dashpot contact model, [16]. Figure
2 provides an overview of the configuration of the
"Particle Shape Editor", which includes a number of
commands (shapes, 3D model, properties,
the format of template, etc). The following section
outlines the steps required to create and organize an
EDEM Material Model database. The following
steps are required to create an EDEM material
model database:
- Creating material categories
- Creating equipment materials
- Creating a bulk material and assigning shapes
- Defining material size distribution
- Defining the material interactions
- Saving an EDEM material model database
- Using EDEM material models in simulation
The use of CAD templates is useful for creating
multi-spherical shapes.
In addition to the usual approaches for creating
the EDEM material model database, careful
calibration and validation were conducted on the
simulation parameters to accurately replicate the
actual milling process behavior. This involved
modifying the input parameters (e.g. particle
density, friction coefficients, and restitution) to
match experimental data acquired from physical
milling operations. The iterative process is vital for
refining the DEM model and predicting the particle
dynamics and energy transfer in the planetary ball
mill precisely. To assess the validity of the
simulations, anticipated results were compared
against empirical data from earlier literature (e.g.
particle size distribution and milling performance).
Moreover, it is fundamental to ensure that model
particles' shapes and dimensions are appropriate
representations of manufactured particles to
generate simulation results that are reliable and
reproducible both scientifically and practically. The
importance of demonstrating this congruence of
particle shape is amplified when accurately
modeling particle interactions associated with a
milling process. The development of multispherical
shapes in Computer-Aided Design (CAD) templates
results in a substantially more faithful representation
of nonspherical shapes compared to simple spheres,
which enhances the level of realism of the model. In
the simulations, to mimic the planetary motion of
the mill as effectively as possible, both the vial's
rotation around its own axis and the turn disc's
rotation in the opposite direction produce the
centrifugal acceleration needed for accurate
modeling. The abovementioned process has been
enhanced and integrated in order to create a strong
and viable method for evaluating the influence of
the combination of specific mill parameters on the
comminution mechanism, which will lead to a better
understanding of the interactions occurring in
planetary ball mills.
Fig. 2: The appearance of the particle shape editor.
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4 Results and Discussion
The filling of milling media is an important
parameter in characterizing particle wear and/or
compression frequencies [17], and it determines
milling quality [18]. In this work, we conducted
simulations with varying media filling values of 40,
50, 60, and 70 percent. In the simulations, 25 mm
diameter balls were employed, along with fine
particle size distributions having a diameter of 3
mm.
Figure 3 illustrates the snapshots of DEM
simulations, which demonstrate the impact of
varying media filling values (40, 50, 60, and 70
%). The particles are colored in different colors
based on their velocities as they are blue (lowest
velocity) and red (highest velocity). As can be seen
from the figure, the degree of mixing rises as the
voids are filled, with segregation becoming a
significant phenomenon at low filling levels. This
phenomenon is due to the fact that there are not
enough particles available to fill the cavities in the
bottle, causing particles to trickle down into the ball
charge, [19]. Similarly, the study [20] reported that
the milling media concentration is directly
proportional to the total filling level. According to
the study [21], the motion of particles even changes
from cataracts to cascading movement as the filling
level increases from 10 to 30 %.
Fig. 3: Snapshots of DEM simulations showing
different values of media filling:(a) 40 %, (b) 50 %,
(c) 60 %, and (d) 70 %
A snapshot of the DEM simulation of the
milling media at elevated milling speeds is shown in
Figure 4. It can be observed that the acceleration of
milling velocity results in an accumulation of
particles in the vicinity of the vial's wall.
Additionally, it can be seen that the particles are
launched higher than the balls due to their higher
mobility inside the vial. The results indicate a
comparable pattern between the observed
experimental and the simulated data.
Fig. 4: Snapshot of DEM simulation of milling
media at elevated milling speed
Increasing the milling speed may affect the
particulate or ball movement within the vial. With
this proposed model, it can clearly explain the
phenomenon that occurred during the ball milling
process.
The trends in particle behavior, as a function of
the media filling level and the milling speed,
provide further insight into optimizing the milling
conditions for different material systems. As the
media filling level is increased, the rate of particle-
particle interactions and collisions increases, thus
improving comminution efficiency and decreasing
the risk of particle agglomeration. At higher filling
levels, the free space available for particle motion
becomes scarce, thus limiting their ability to move
freely and decreasing the effective energy for
milling particles. In contrast, at low filling levels,
the available free space would lead to the free
movement of particles, which can increase the
chance of segregation and product inconsistency.
The DEM simulations also illustrated that when
the milling speed was increased, the net centrifugal
forces acting on the particles were larger, resulting
in higher particle velocities and faster mixing
efficiency. Additionally, it would appear as
conditions improved, the energy reached a chaotic
state where added speed resulted in a greater
discrepancy in velocities together with higher
impact, higher kinetic energy transfer, and increased
overall efficiency. Indeed, whilst this energy
contribution led to improved performance in terms
of rapid size reduction, it also increased the risk of
early degradation of the milling media and vial.
Conditions can be maintained in a positive and
productive milling process once the disadvantages
are controlled around process efficiency and product
quality. These findings provide valuable insights
into the important relationships between the filling
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level and milling speed that positively influence mill
performance. It is particularly important to key strict
attention to these relationships to ensure the desired
material properties have been obtained in the
processed material while reduced to a minimum
where disruptions can disrupt the milling process
efficiency.
5 Conclusion
In this research, a discrete element method (DEM)
model was utilized for investigating the feed level in
planetary ball mills, reporting a correlation between
simulation results and experimental results. The
results confirm the degree of filling is a key
operational parameter related to the extent and
degree of milling. Furthermore, it also shows that
varying the milling speed has a real influence on the
movement of the milling media (particles and balls)
inside the vial. The DEM model that has been
developed shows the capacity for describing much
complexity with the ball milling processes and acts
as a real advance for understanding what will
happen as ball milling takes place. By exploring the
effect of filling levels and milling speeds in a
structured way, we have been able to provide unique
insights into particle dynamics, energy transfer, and
milling efficiency in general. These results highlight
the significance of having improved operational
parameters or variables in order to obtain the
material properties that are intended, whilst limiting
the less desirable consequences. The validated
model thus serves as a powerful tool for enhancing
the design and optimization of planetary ball milling
processes, contributing to improved process
efficiency and product quality.
Acknowledgement:
The authors would like to thank the National
Institute of Research and Physicochemical Analysis
(Tunisia) for supporting this work. The authors
would also like to thank the Altair academic team
for providing academic licenses used in this
research.
Declaration of Generative AI and AI-assisted
Technologies in the Writing Process
During the preparation of this work the authors used
Altair software in order to simulate filling level in a
planetary ball mill. After using this tool/service, the
authors reviewed and edited the content as needed
and take full responsibility for the content of the
publication.
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following: study conception and design, data
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Sources of Funding for Research Presented in a
Scientific Article or Scientific Article Itself
No funding was received for conducting this study.
Conflict of Interest
The authors declare that there are no conflicts of
interest.
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