Experimental Determination of Grinding Parameters using a Ball Mill
with Innovative Lifters
MIGLENA PANEVA, PETER PANEV, NIKOLAY STOIMENOV
Institute of Information and Communication Technologies,
Bulgarian Academy of Sciences,
Acad. G. Bonchev St., Block 2, 1113-Sofia,
BULGARIA
Abstract: - In the developed work, experiments were made with a laboratory ball mill with a liner with
symmetrical displaced eight innovative lifters with a spheroidal tetrahedron type. Based on experiments done in
a previous study, the number of lifters with innovative shapes, as well as their sizes, were determined. The
additive material used for grinding media is PLA material and for grinding bodies PLA, SteelFill (based on
PLA), and CarbonFilTM (based on PETG) are used which are printed on a 3D printer. The mill’s critical speed
(CS), the angle of separation (shoulder angle), and the toe angle in the cataract mode of operation were
determined experimentally. Experiments were carried out with different mill filling percentages - 20% and
30%. The required speed of the ball mill with grinding media with innovative lifters at cataract mode of
operation for the three types of materials is almost the same - with an average value of 45% of CS. The best
energy efficiency and grinding efficiency material at 20% filling of the mill is obtained with a SteelFill
filament, and at 30% - with a PLA filament.
Key-Words: - ball mill, innovative lifter, additive material, critical speed, angle
Received: February 27, 2023. Revised: July 25, 2023. Accepted: August 28, 2023. Published: September 25, 2023.
1 Introduction
The essential factors for competition in the industry
are low cost, high quality, and fast production. For
this reason, to investigate the milling processes, it is
necessary to work in laboratory conditions. The use
of a laboratory mill, whose grinding media and
bodies are made of 3D materials, allows for
analyzing the excavation and grinding processes.
Investigating the following key factors is performed:
the mill shoulder and toe angles, the influence of the
coefficients of friction, rolling friction, and
restitution, conducting experiments with different
sizes, shapes of grinding bodies, and grinding
environments, including testing of the yield point of
different materials with acoustic emission methods.
In, [1], [2], [3], is ascertained that the different sizes,
shapes of grinding bodies, and grinding environment
influence the mill shoulder and toe angles as well as
the coefficients of sliding friction, rolling friction,
and restitution. When the fill percentage of the ball
mill is changed, including the shape, size, and
composition of the grinding bodies, the required
power is also changed through their effect on the
shear strength of the charge, [4]. The shape and
profiles of the liners are used for shield plates and
milling, and the lifters have a significant influence
on the productivity and effective grinding of the
output product, [5]. In, [6], a type of lifter for the
experiments is presented and shows a cataract mode
of operation in a laboratory ball mill with clockwise
rotation at which regime the grinding results are
better. The mill shell inside the mill which has 8
innovative lifters with a spheroidal tetrahedron form
and displaced symmetrically, protects the grinding
bodies and the drum from rapid wear, [7], [8].
Another possible solution to determine and
optimize processes in the ball mills is the DEM
simulations, [9]. The simulations can reduce time
for investigations, as well as ball consumables and
environment such as grinding bodies, lifters, drums,
etc.
The investigation aims to determine the
parameters of grinding a laboratory ball – the
critical speed, the separation angle, and the toe angle
at the cataract regime of operation. The liner with
lifters is produced from PLA material and the
charge of a ball mill is at 20% and 30% made from
3 types of material – PLA, SteelFill, and
CarbonFilTM, by using a 3D printer. The
experiments are performed without the presence of
grinding material.
WSEAS TRANSACTIONS on APPLIED and THEORETICAL MECHANICS
DOI: 10.37394/232011.2023.18.16
Miglena Paneva, Peter Panev,
Nikolay Stoimenov
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2 Apparatus and Materials
The laboratory ball mill used throughout this study
has an outer diameter of the chamber of 0,269 m, an
inner diameter of 0,228 m, and a length of the mill
of 0,013 m. The length of the mill is constructed to
work with one row of balls. There are 2 transparent
plexiglass covers allowing us to investigate the
interaction of the grinding ball. The motor has 1.1
kW power, controllable speed, and intelligent
control. The PLA filament is used for 3D printing of
the drum and mill shell with lifters due to its good
mechanical properties and the high aesthetic quality
of the surface. By unscrewing the bolts holding the
two covers, the grinding media (lifters) can be easily
replaced with ones of different materials, shapes,
and lengths. The parameter of the innovative lifters
can be seen in, [6]. The direction of rotation of the
ball mill is clockwise. The speed of the ball mill is
determined with an electronic tachometer.
According to the volume of the innovative lifters,
the volume of the free inner space of a ball mill is
V- 5,195.10-4 m3.
The grinding bodies in the shape of spheres are
3D printed with three types of filament: PLA,
SteelFill, and CarbonFilTM according to the
producer’s recommendations and according to
performed experiments, [10], with 100% infill after
which their weight was measured, [3], [11].
Each mill charge is determined experimentally,
specifying the number and mass of spheres required.
For 20% filling of a ball mill, the required number
of spheres is 142, and for 30% filling- 210 pieces.
The coefficients of sliding friction, rolling, and
restitution for the pair PLA-PLA, PLA-SteelFil, and
PLA-Carbon can be seen in, [12], [13], [14], [15].
A high-speed camera NAC MEMRECAM HX-6 is
used to record the moment of critical speed,
separation, and incidence. The camera parameters
allow for recording frames with different resolutions
per second (fps) where the maximum is up to
360000, [16]. The analyses of the recorded videos
are carried out using the Vicasso 2009 software.
3 Experimental Results and
Discussion
Firstly, the critical speed of the mill with 20 % filling
is determined using spheres made of three types of
materials- PLA, SteelFill, and CarbonFilTM. The
critical speed is reached when all the spheres fit
evenly around the circumference. By means of the
buttons positioned in the electronic dashboard, the
speed is increased until the desired state is reached.
The achieved velocity is measured with an electronic
tachometer in rpm, positioned stationary on a stand,
and a marker is placed in the ball mill. The marker is
needed for the tachometer for counting the rpm’s.
With the help of the high-speed camera, the moment
of the critical speed is recorded at 1000 fps. The
video is checked for discrepancies and a photo is
taken by snapshot application. From the snapshots,
the shoulder and toe angles are measured. Figure 1
shows a view from the critical speed at 20% filling
of the ball mill.
Fig. 1: Critical speed at 20% filling of the ball mill
The next searched mode of operation is the
cataract mode. It is determined by using the data
from the video, recorded with the high-speed
camera. The determination of the shoulder angle is
established in 3 points. The first point is the moment
of separation angle (shoulder angle) of the grinding
bodies, point two is the mill center and point three is
the end point of the mill, placed horizontally from
the center. Figure 2 shows the detected speed of the
ball mill using different materials.
a) b)
c)
Fig. 2: Shoulder angle at 20% filling of the ball mill:
a) PLA, b) SteelFill, c) CarbonFilTM
From the same video, the toe angle is determined.
The measurement of the toe angle is performed also
in 3 points. The starting point is the moment of
incident of the grinding bodies with the chamber, the
second point is the center of the mill, and the third
point is the end of the mill horizontally from the
center, shown in Figure 3.
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The same procedure of measurements of the
parameters at 30% filling of the ball mill is made.
The determined critical speed is measured with a
tachometer. The experimental setup is presented in
Figure 4.
The determined shoulder angle and toe angle are
presented respectively in Figure 5 and Figure 6 for
the three materials. The results of all experiments are
presented in Table 1.
a) b)
c)
Fig. 3: Toe angle at 20% filling of the ball mill: a)
PLA, b) SteelFill, c) CarbonFilTM
Fig. 4: Critical speed at 30% filling of the ball mill
a) b)
c)
Fig. 5: Shoulder angle at 30% filling: a) PLA, b)
SteelFill, c) CarbonFilTM
Of the base of measured values, a percentage of
the critical speed at 20% and 30% filling of the mill
at cataract mode of operation is calculated,
according to eq. (1). The values are shown in Table
1.
% Vcr = 𝑩𝒂𝒍𝒍 𝒎𝒊𝒍𝒍 𝒔𝒑𝒆𝒆𝒅
𝑪𝒓𝒊𝒕𝒊𝒄𝒂𝒍 𝒔𝒑𝒆𝒆𝒅 x 100, rpm (1)
It’s seen that the calculated % of critical speeds
in which the mill operates in a cataract mode is
almost equal at the different filling. The average
value is 46 % of the CS and only for the SteelFill
material at 20% filling and CarbonFilTM at 30%
filling with an average value of 44 %.
At 20% of the mill fill capacity, the SteelFill
material has the largest separation angle and the
smallest toe angle. This material is measured with
the largest weight. The percentage of Vcr in the
cataract mode of operation is also the least
compared to the other materials. That is why it is the
material where the least energy is used. This leads to
a reduction in the revolutions of the mill, which will
increase energy efficiency.
a) b)
c)
Fig. 6: Toe angle at 30% filling: a) PLA, b) SteelFill,
c) CarbonFilTM
At 30% fill of the ball mill, the data differ
significantly compared to those at 20% fill of the
mill. In this case, the PLA material has the largest
separation angle and the smallest toe angle. At this
charge, the weight of the material has the greatest
influence and the rolling friction coefficient is the
smallest – 0,060. The lighter the material and the
lower the coefficient of rolling friction, the more
energy-efficient the mill's operation.
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4 Conclusion
In the present work, the parameters of work of a
laboratory ball mill with 8 innovative lifters,
produced from PLA material interacting with
grinding bodies produced from three different
materials- PLA, SteelFill, and CabronFilTM are
determined at two different charges- 20% and 30%
filling of the ball mill.
Table 1. Experimental Results
% of Filling
Material
Critical speed,
[rpm]
Toe
angle,[ ]
Ball mill
speed, [rpm]
% of Critical
speed, Vcr
20% filling
PLA
131
27,62
59,8
45,6
CarbonFilTM
124
42,27
57
46
SteelFill
123,4
39,36
54
43,8
30% filling
PLA
134,3
35
61,6
45,9
CarbonFilTM
128,6
41,58
56,2
43,7
SteelFill
125,5
37,17
57,3
45,66
The critical speeds, shoulder angles, and toe
angles are experimentally determined at the two
levels of filling. Due to the use of the high-speed
camera, the exact moments for determining the
parameters were recorded. The data are reported
with Vicasso 2009 software. The ball mill rotates in
a clockwise direction, the critical speed at which the
particles start to centrifuge differs for each material
and with the different % filling of the ball mill.
The results show that the required speed of the
ball mill with grinding media with innovative lifters,
made by PLA material to reach the cataract mode of
operation are almost the same for the three types of
materials- on average 45% of CS.
From the observed materials, the best energy
efficiency and grinding efficiency at 20% filling of
the mill is obtained with the SteelFill filament,
which is the heaviest of the observed ones. At 30%
charge of the mill, the lighter material and with the
lower coefficient of rolling friction – the PLA
filament has the best grinding parameters, according
to investigated materials.
The contribution of this work is the proving of
the influence of the characteristics of the grinding
media and the grinding bodies. When studying the
movement and interaction between grinding bodies,
it is extremely important to consider side factors
such as the weight of grinding bodies, coefficients
of friction, restitution, shape, lifter size, etc. When
the milling process with the aforementioned factors
is better understood, it will lead to process
optimization, reduction of production costs, and
improvement of energy efficiency.
5 Future Steps
In future work, it is planned to conduct experiments
on the interaction of the same number and material
of the liner but through lifters with different shapes
and with grinding bodies made of the same additive
materials- PLA, CarbonFilTM, and Steelfill. The data
will be compared to that of a mill without lifters.
Simulations with software working on the discrete
element method will be made with the same
parameters, used in this publication aiming to
compare the real experiment to the simulation
modeling experiment.
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Nikolay Stoimenov
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DOI: 10.37394/232011.2023.18.16
Miglena Paneva, Peter Panev,
Nikolay Stoimenov
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Contribution of Individual Authors to the
Creation of a Scientific Article (Ghostwriting
Policy)
- Nikolay Stoimenov carried out for determining a
critical speed.
- Miglena Paneva is responsible for determining a
cataract mode and calculation of a % of a critical
speed.
- Peter Panev carried out a determination of a
shoulder angle and toe angle.
Sources of Funding for Research Presented in a
Scientific Article or Scientific Article Itself
This work was partially supported by project No KP-
06-H47/5 “Research and optimization of the
interaction between grinding bodies and media with
an innovative shape”, financed by the Bulgarian
National Science Fund.
Conflict of Interest
The authors have no conflicts of interest to declare.
Creative Commons Attribution License 4.0
(Attribution 4.0 International, CC BY 4.0)
This article is published under the terms of the
Creative Commons Attribution License 4.0
https://creativecommons.org/licenses/by/4.0/deed.en
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WSEAS TRANSACTIONS on APPLIED and THEORETICAL MECHANICS
DOI: 10.37394/232011.2023.18.16
Miglena Paneva, Peter Panev,
Nikolay Stoimenov
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177
Volume 18, 2023