Minerals Engineering 139 (2019) 105699
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Minerals Engineering
journal homepage: www.elsevier.com/locate/mineng
Effects of screen decks’ aperture shapes and materials on screening
efficiency
T
⁎
A. Davoodi ,a, M. Bengtssonb, E. Hulthéna, C.M. Evertssona
a
b
Chalmers University of Technology, S-412 96 Gothenburg, Sweden
University of Borås, S-506 30 Borås, Sweden
A R T I C LE I N FO
A B S T R A C T
Keywords:
Screen
DEM
Discrete Element Method
Classification efficiency
Separation
Screening is a key unit operation for the large-scale separation of materials. There are certain different machine
parameters and variables that affect the process of screening. The Discrete Element Method (DEM) is a suitable
method to analyze parameters and variables. The main benefit of using the DEM for simulating the screening
process is that, as a contact model, it provides the possibility of tracking each particle in the material flow and all
collisions between particles and between particles and boundaries.
There are different types of materials used for screening media, such as rubber and polyurethane, which are
used in modular systems as a panel, and such as steel, which are used as a wire in the mesh. This paper presents
how different materials used in screen decks affect the screening process. The materials’ strength and elasticity
have been examined in order to study how the aperture will change in different materials and how different
shapes of the aperture and material of screening media affect the screening performance by analyzing the effect
on material flow.
1. Introduction
One of the main stages in the processing of granular material is the
separation of materials based on the particle shape and size. Screening
has been used as the main separation process in the mineral processing
industry (Delaney et al., 2012). There are several primary factors that
affect the screening process, such as feed rate, aperture ratio, shape of
the particle, particle size distribution (PSD) and type of vibratory motion (Subasinghe et al., 1989), (Soldinger, 2000).
The bulk of the behavior of particles in the screening process is
dependent on interactions between individual particles and between
particles and the screen deck. This behavior is even affected by other
factors, which make the optimization process more difficult when using
experimental techniques. Simulation has become a common tool in the
design and optimization of processing granular materials (Cleary,
2009). One of the simulation methods that has been used recently is the
Discrete Element Method (DEM). DEM is a discontinuous simulation
method, which is a requirement for granular material simulation based
on their highly discontinuous nature (Chen and Tong, 2009).
There are three main phases in a typical DEM algorithm; in the first
one, a search grid is used to periodically build a near-neighbor interaction list that contains all of the particle pairs and object–particle pairs
that are likely to experience collisions in the short term. In the second
stage, the forces on each pair of colliding particles and boundary objects
⁎
are evaluated in their local reference frame using a suitable contact
force model and then transformed into the simulation frame of reference. Finally, in the third stage, all of the forces and torques on each
particle and object are summed, and the resulting equations of motion
are integrated to obtain the resulting motion of these bodies (Quist and
Evertsson, 2010). According to Cleary (2009), DEM simulations may
involve particle collisions with other particles and geometry. It is
therefore highly difficult to truly validate DEM simulations due to
factors, such as the shape of the particles. Simulated particles are made
up of spheres, and the experimental particles are non-spherical.
The material on the screen deck builds different layers that contain
many different sizes. In previous research, a layer model has been defined by assuming the minimum effect of shape and density, which is an
important factor in the screening process (Soldinger, 2000). The stratification process occurring during the screening process is expected to
be in a vertical direction. In the stratification process, one mass flow of
the same fraction changes places with another mass flow with a different fraction during the time interval (Soldinger, 1999). The next step
is a passage process, which is dependent on the mass flow of the particles on the bottom layer that are in contact with the screen deck
(Soldinger Stafhammar, 1999). The effect of certain material layers in
the screening process is more difficult to study by use of mathematical
models due to different parameters and variables, such as particle shape
and the effect of particle collision.
Corresponding author.
https://doi.org/10.1016/j.mineng.2019.01.026
Received 31 May 2018; Received in revised form 25 January 2019; Accepted 28 January 2019
Available online 04 March 2019
0892-6875/ © 2019 Elsevier Ltd. All rights reserved.
Minerals Engineering 139 (2019) 105699
A. Davoodi, et al.
Nomenclature
ṁ i
k
Δt
v
α
f
R
amax
mass flow of the material, Eq. (1), (kg/h)
passage parameter, Eq. (1), (–)
time taken for the material passing through the aperture in
the screen surface, Eq. (1), (s)
velocity, Eq. (2), (m/s)
slope of the screen deck, Eq. (2), (Angle)
frequency, Eq. (2), (Hz)
function of stroke, Eq. (2), (mm)
deck acceleration, Eq. (3), (m/s2)
0.5
In early research work on screen models, most published information has been empirical. Finding an advanced mathematical and experimental model is highly difficult because of the complex nature of
particles and, for example, how the different shape of particles affects
the collisions between them.
Previous research shows that particle movement on a rubber deck
with a low feed rate results in larger bounces, that means that the
chance of a connection between each particle and the screen deck is
reduced and screen efficiency is low. However, with a higher feed rate,
there are more collisions between particles, which cause smaller
bounces and a higher screen efficiency. For each screening process, it is
therefore very important to find the optimum feed rate, dependent on
the particle size distribution (PSD), in order to increase screen efficiency.
The purpose of this paper is to model the effect of the loading ratio
to observe the impact on bed thickness and screening performance on
decks with different aperture shapes and with different material properties in the screen media.
kj = ka, j (amax / g − 0.4)0.6e−kb, j (amax / g − 0.4)
{amax ⩾ 0.4g }
(3)
3
ka, j = 11.5e−5.1(dj / acap)
(4)
15
kb, j = 1.5(dj / acap) e (dj / acap)
The basic principle for modeling material flow in a screen is to use a
mass balance equation as shown in Eq. (1). The screen model presented
by Soldinger Stafhammar (2002) uses a mass balance model that handles both the internal mass flow inside the material bed and the mass
flow passing the screen deck. In this paper, the material flow through
the screen deck will be analyzed since it is affected by the geometrical
and material properties of the screen cloth (Soldinger Stafhammar,
2002).
The mass balance at a given point on the screen deck can be expressed as
γ′ =
(b cos α − c sin α ) f
(a + b)(a + f ) cos α
′ =
γsteel
η=
(6)
(bsteel cos α − csteel sin α ) f
(asteel + bsteel )(asteel + fsteel ) cos α
γ ′ (b2 + f 2 )
γ ′steel (bsteel 2 + bsteel 2)
(8)
(9)
3. Experimental setup using DEM
(1)
DEM simulations have been used recently to study screen efficiency.
Several studies have been conducted using DEM simulations to analyze
the separation performance by studying different parameters and behavior of the particles during screening performance. For example, the
effect of different levels of acceleration has been studied by Cleary et al.
(2009). Additionally, the effect of particle size distribution has been
studied by Jahani et al. (2015). The methodology of this paper is based
(a)
mi
(c)
mi +1
v = (0.064α + 0.2)(380R − 0.18)
+ 0.018α − 0.38)
(7)
acap = ηaap
where ṁ i is a mass flow rate (kg/h) of the material, k is passage
parameter and Δt is the time taken for the material passing through the
aperture in the screen surface.
The mass balance equation in Eq. (1) is presented visually in Fig. 1.
In research by Soldinger Stafhammar (2002), an empirical model for
the transport velocity of the material along the screen deck has been
presented.
The velocity model shown in Eq. (2) is a function of stroke R and
frequency f and the slope of the screen deck α . The model is valid for
steel screen cloths. Eq. (2) is based on circular motion and the direction
is a mass flow direction.
(0.095fα (−0.5)
(5)
where the passage parameter k is a function of particle size dj , aperture
diameter acap can be calculated by Eq. (9). The estimate of η can be
calculated as a function of the slope of the screen deck, deck acceleration a max and the gravitational acceleration g . Fig. 3 shows the rate
of passage is low at very low acceleration. By increasing the acceleration, the particles start to move and the process of stratification will
appear which means the particles will presented to the aperture and the
passage process starts.
In research by (Asbjörnsson, 2016), a correction factor was introduced to compensate for the change in screen cloth geometry. The
correction factor is calculated using Eqs. (6)–(8). The correction factor
is then multiplied with the original aperture size, as shown in Eq. (9).
Fig. 4 shows a schematic drawing of an aperture shape including the
different parameters.
2. Modeling mass flow through a screen deck
ṁ i + 1 = ṁ i − kṁ i Δt
particle size, Eqs. (4) and (5), (mm)
aperture diameter, Eqs. (4) and (5), (mm)
the original aperture size, Eq. (9), (mm)
normal force, Eq. (11), (N)
stiffness of the spring, Eq. (11), (–)
the relative velocities, Eq. (11), (m/s)
viscoelastic damping constant, Eq. (11), (–)
tangential force, Eq. (12), (N)
stiffness of the spring, Eq. (12), (–)
viscoelastic damping constant, Eq. (12), (–)
the relative velocities, Eq. (12), (m/s)
dj
aap
acap
Fn
Kn
Vn
Cn
Ft
Kt
Ct
Vt
kmi Δt
(2)
As Fig. 2, shows the transport velocity of the material on a screen
increases by increasing the stroke and frequency.
The mass flow passing through the screen deck is governed by the
passage parameter k shown in Eq. (3):
(b)
Fig. 1. Mass balance equation, (a) the initial mass flow on deck at time i, (b) the
mass flow passing the deck at time i, (c) the updated mass flow at time i + 1.
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Minerals Engineering 139 (2019) 105699
A. Davoodi, et al.
Fig. 2. The transport velocity as a function of stroke and frequency, β = 15∘ .
Fig. 4. Schematic drawing of an aperture shape where a, b, c and f represents
the geometrical parameters of the screen media.
In this simulation, the length of the screen is 1500 mm; the width is
600 mm. A schematic view of the screen deck and the shape of the
aperture in both steel and rubber/polyurethane are shown in Fig. 7.
The next step is to set up the simulation. Particles with user-defined
diameters were employed to match the planned simulations. All
Fig. 3. Passage parameter k depends on acceleration and relative size of the
particles in a fraction.
on DEM simulations and has been done in four steps, which are shown
in Fig. 5. There is some difference between the previous research with
DEM simulations and this paper, one of the most important one is how
to define the particle shape for having more realistic result as possible
which will present later in this chapter.
The test plan is based on a research question, which is how different
material and aperture shape of the screen deck affect screening efficiency by altering the feed rate. Ten simulations have been run in total:
five simulations for panel screen deck and five simulations for steel wire
mesh screen deck. As Table 2 shows, the parameter that changes in the
simulation is the feed rate, which starts at 20 ton/h and increases by 5
ton/h up to 40 ton/h.
The particles are generated in different coordinate systems in the
particle factory to create a random orientation in each simulation. The
particle factory is shown in Fig. 6. The use of randomized particle orientation will result in different material segregation in all simulations.
The rationale for using this approach is to mimic a variation that would
occur during a physical experiment.
The next step is to build the geometry for each simulation. The simulation uses two screen decks with different materials and aperture
shapes. The steel screen deck is built with wire, which is thinner
compared to the rubber screen deck that is cubically shaped. Therefore,
the number of holes are greater on the steel deck. The length of the
screen will affect the efficiency of the screen since it is important to
allow sufficient time for the stratification process to continue. Fig. 6
shows a schematic setup for the DEM simulation.
Test plan
Build geometry
of screen
Set up
Simulation
Analysing data
Fig. 5. Four steps that have been applied as a methodology for this paper.
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A. Davoodi, et al.
Particle factory
generated by ton/h which are 20 ton/h, 25 ton/h, 30 ton/h, 35 ton/h
and 40 ton/h in five different simulations.
The polyurethane/rubber deck consists of a flat surface uniformly
perforated with square apertures with a size of 13 × 13 mm spaced
8.0 mm apart. The wire mesh apertures have a size of 13 × 13 mm
spaced 5.0 mm apart. Table 2 lists the operating conditions used in the
present work.
The simulations are carried out under the conditions shown in
Table 2. To be able to track the particles during the screening process,
some geometrical bins have been used. Geometrical bins placed under
the screen make it possible to see the number of particles passing
through the screen deck in that particular section. The length of the
screen surface was divided into five parts to analyze the relationship
between screen length and screening efficiency. Fig. 9 shows a snapshot
of the simulation and geometrical bins.
For each simulation in DEM, before extracting the data, the simulation should achieve a steady-state, which means the total number of
particles in the system is stable after a given period. The average time
for the overflow particles to travel along the entire deck from the feed
end to the discharge end is 2.4 s in the simulations and simulations are
steady-state after 3.2 s.
To better understand the screening behavior, particle flow on the
screen is first analyzed. Such dynamic information is readily obtained
from the present DEM simulations. In the screening process based on
the feed rate, increasing the length of the screen surface can allow the
screening efficiency to reach 100%, theoretically.
In this paper, materials are fed over the screen with five different
mass flow rates, as shown in Table 2. Next, the materials fall onto and
flow along the screen surface in the gravitational field. At the beginning
of the process, the free-flowing particles may interact with each other
before reaching the screen surface and will be impacted with the screen
deck or other particles on the surface.
It is, however, important to note the effect of segregation on the
screening process especially at the feeding point. As mentioned earlier,
the particles are generated in different positions, which means that the
segregation will appear slightly differently during the simulations.
Therefore, the proportion of fine particles in the first layer of the material bed that has contact with the screen surface has a big influence on
the screening process. With a higher proportion of coarse particles in
the first layer, the open area will be blocked, and the material bed
builds up faster, and the passage rate will decrease.
Overflow
Underflow
Fig. 6. Schematic of setup for DEM simulation.
a) Panel deck
b) Wire mesh
deck
Fig. 7. Snapshot of screen surface of a screen deck in (a) rubber/polyurethane
(b) screen deck in steel.
particles are non-spherical in shape, with an average particle diameter
of 8 mm. The consequences of using one sphere particle in the simulations compare to multisphere particles are very different. Multisphere
particle gives more realistic result based on closer shape to real particles
(Quist and Evertsson, 2010). Fig. 8 shows the shape of the particles that
have been used for the simulations. The material is a rock with a solid
density of 2900 kg/m3. The separation of these particles may represent
the essential sorting operation seen in a typical screening process. More
generally, this model features the main characteristics of many industrial screening applications.
Fig. 8 shows the two types of particles that have been generated.
The shape and mass of density of particles have an effect on the segregation and stratification process which means that during the
screening the particles with the largest size, move to the top; for this
reason, having various particle shapes in the simulations makes the
output more comparable to the real screening process. It would be
useful to consider a wider range of shapes, since it is always possible
that certain shapes, not considered here, may show different behavior
in simulations. The reason to not having more particle shape in this
simulation is to decreasing the computation time. The cons of having
more particle shape is that simulation time will be increase but the
advantage is the segregation will be more realistic compare to real
screening process. Particle 1 has been defined by three different sizes,
which are shown in Table 1. The diameter of particle 1 is 20 mm, which
was generated on a different scale to get the reasonable particle size
distribution (PSD) for the simulations. A different size of particles and
their proportions can be seen in Table 2.
The number of particles that have been generated for particle 2 is
fixed. The reason for this is to track the same amount of particles with
the same fraction of different material flow. The total number of particle 2 is 10,000, and the diameter is 6 mm. The amount of particle 1 is
3.1. Contact model theory of DEM
There are various different contact models, such as the linear elastic
model and Hertz–Mindlin's contact model. The linear contact model
may not be precise enough when the shape of the particles is considered
as spherical however. Hertz–Mindlin's contact model is developed to
Particle 1
Particle 2
Fig. 8. Particle 1 with five spheres and particle 2 with four spheres.
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Minerals Engineering 139 (2019) 105699
A. Davoodi, et al.
Table 1
Diameter of particle one generated for simulation.
Particle 1
Diameter (mm)
% of mass
5.2
9.1
15.6
50
30
20
solve the contact behavior for spherical shapes (Maw et al., 1976).
Hertz–Mindlin's contact model is a no-slip model that uses a linear
spring-dashpot model (Just et al., 2013). Fig. 10 shows the interaction
between two particles with frictional elements between normal force
and tangential force.
The contact force between impacting particles is split into a normal
force Fn and a tangential force Ft which is
Fn = −Kn Δx + Cn Vn
(11)
Ft = −Kt Δx + Ct Vt
(12)
Bin5
Bin4
Bin3
Bin1
Fig. 9. Snapshot of the simulation after 14 s. Particles colored by mass, darker
particles have more mass.
where Δx is particle displacements in the normal and tangential directions, Vn and Vt are the relative velocities. K is the stiffness of the
spring and C is the viscoelastic damping constant. If Ft exceeds the
limiting frictional force, then the particles will slide over each other,
and the tangential force is calculated using the frictional coefficient f :
Ft = −fFn
Bin2
Ft
XB,local
ZB,local
Ct
Kt
(13)
Particle B
4. Results and discussion
YB,local
ZA,local
This section is divided into two subsections where one is the effect
of the aperture on screening efficiency along screen length, and the
other section is the effect of screen deck material on screening efficiency along screen length.
Particle A
XA,local
Kn
μ
Cn
Fn
4.1. Effect of the aperture on screening efficiency along screen length
YA,local
Further analysis has been carried out to examine the number of
particles passing through the screen at different sections along the
whole screen length during a period. This has been done by using
geometrical bins and by recording particle coordinates when they pass
through the bins in the model. Fig. 11 shows the relative number of
particles passing through at different sections of the screen, at a longer
interval of 1500 mm, for a period of 15-s simulations.
The amount of the particles passing through bin 1 is higher in the
screening process with wire mesh when the feeding rate is 20 ton/h and
25 ton/h. By increasing the feed rate to 30 ton/h, the number of particles in both the panel and wire mesh deck in bin 1 is almost the same.
Once the feed rate increases to 35 ton/h and 40 ton/h the panel deck is
more efficient. The reason for this is that the number of holes in the
wire mesh deck is higher compared to the panel deck because of the
Fig. 10. Graphic illustration of Hertz–Mindlin's contact model.
thinner wire, which means that the particles have more chances of
passing through the deck before building up on the material bed. As
more materials are fed onto the screen, the accumulation of particles
spreads onto the whole feeding region and material heap forms, as seen
in Fig. 12 for low and high feeding rate.
When the material bed has built up, then the stratification process
will affect the screening, which means that small particles still have
chances to travel across the interstitial gaps between large particles
near the screen and thus pass through the apertures in the feeding region. The reason that more particles pass through bin 1 in the panel
deck compared to the wire mesh in higher feed rate is that particle
Table 2
Summary of modeling conditions.
Material properties
Poisson’s ratio
Shear modulus
Density
Particles
Screen (steel)
Screen (rubber)
0.3
0.2
0.4
24 MPa
79 GPa
0.0006 GPa
2900 kg/m3
7800 kg/m3
1200 kg/m3
Collision properties
Coefficient of restitution
The coefficient of static friction
The coefficient of rolling friction
Particle-particle
Particle-screen (rubber)
Particle-screen (steel)
0.2
0.3
0.6
0.6
0.4
0.45
0.01
0.01
0.01
Particle diameter
User defined
Particle generate rate
For particle 1:20 t/h, 25 t/h, 30 t/h, 35 t/h, 40 t/h
Screen aperture
Screen declination
13 mm × 13 mm
16°
Particle generate position
Screen vibration
In particle, factory positioned randomly
Sinusoidal translation, amplitude 4 mm, frequency 16 Hz
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Minerals Engineering 139 (2019) 105699
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4
x 10
4
8
20 ton/h (Steel deck)
20 ton/h (Rubber deck)
7
Total Numbers of particles
Total Numbers of particles
8
6
5
4
3
2
1
0
1
2
3
4
Bin number
(a)
x 10
25 ton/h (Steel deck)
25 ton/h (Rubber deck)
7
6
5
4
3
2
1
0
1
5
2
3
Bin number
4
5
(b)
4
x 10
4
8
30 ton/h (Steel deck)
30 ton/h (Rubber deck)
7
Total Numbers of particles
Total Numbers of particles
8
6
5
4
3
2
1
0
1
2
3
4
Bin number
(c)
x 10
35 ton/h (Steel deck)
35 ton/h (Rubber deck)
7
6
5
4
3
2
1
0
1
5
2
3
4
5
Bin number
(d )
4
Total Numbers of particles
8
x 10
40 ton/h (Steel deck)
40 ton/h (Rubber deck)
7
6
5
4
3
2
1
0
1
2
3
4
5
Bin number
(e)
Fig. 11. Analysis of screening performance along the screen length.
collisions between the particles increases due to more material on
screen deck.
As seen in Fig. 11 for bin 2, the scenario is the same as bin 1, which
means the material bed still has the same effect on screening in this
section. By decreasing the thickness of the material, layer particles have
more of a chance to reach the screen deck and pass through. As particles
travel along the screen surface, more and more undersized particles
velocity along the screen deck is less by using the panel deck. Therefore,
the stratification process takes more time, and the particles have more
chance to reach the screen deck. The average velocity for particles
along the panel deck is 0.56 m/s, whereas in the steel deck it is 0.68 m/s
in the simulations. Fig. 13 shows the average particle velocity in both
the panel and steel deck at different feed rates. By increasing the feed
rate, the particle velocity will decrease because of the number of
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A. Davoodi, et al.
process. It was shown in Table 1 that the proportion of fine particles is
high in the simulations. A large number of fine particles will slow down
the material transfer during the stratification; this can be seen in
Fig. 12a and b. When the proportion of fine particles is low, the interaction with other particles is less, which means that it is easier for
small particles to pass through space between larger particles. Since the
feed rate is low, the undersize material will be included in the bottom
layer, which has a higher probability of passage. As Fig. 11c–e shows,
by increasing the feed rate, the total numbers of particles that pass
through bin 1 increase in both the panel and wire mesh deck. This is
because more fine material feeds to the screen. However, in the process,
it causes a thicker layer of material, which will result in more time
needed for the undersized material to stratify in the space between the
oversized materials.
The passage process depends on the number of fine particles that
have contact with the screen surface, i.e., the more particles coming in
contact with the screen surface, then the higher the probability of
passage.
The rate of passage will decrease when the smallest particles have
passed through the screen deck in the first two sections. In the simulation with 20 and 25 ton/h feed rates, the number of particles that pass
through bin 4 and bin 5 is almost zero. Next, by increasing the feed rate,
more fine particles travel along the screen deck as the probability that
they have contact with the screen deck lessens due to a thicker material
bed layer building up. They continue therefore to move along the
screen deck passing through in bin 4 and 5, which can be seen in
Fig. 11(d) and (e).
The mathematical model from Soldinger (1999) shows the relationship between numbers of material layers and passage probability,
which proves that the probability of passage will increase when the
screen surface is covered by one layer of fine particles. The rate of
passage for fine particles through the apertures is calculated by the
mass of a single-particle layer of fine material that covers the entire
screen surface and the parameters that determine the rate of passage.
To track the fine particles in different screen deck materials, one
particle with the same size and same amount has been generated.
Fig. 14 shows that the amount of particle 2 that passes through bin 1 in
the wire mesh deck is higher compared to the panel deck because of a
higher number of holes in the wire mesh screen deck compared to the
panel deck. This causes more material to pass through screen deck by
free fall in the feeding point. In the other sections of the screen, the
material bed has been generated, and the number of type two particles
that pass the screen deck is almost the same because the stratification
process has occurred.
Fig. 12. Figure (a) shows the particle bed in 20 ton/h feeding and figure (b)
show 40 ton/h feeding.
7000
20
20
25
25
30
30
35
35
40
40
Total Numbers of particles
6000
Fig. 13. Average of particle velocity at different feed rates.
pass through the apertures.
The stratification process depends on the difference in the particle
size, which means that when increasing the difference in particle size
then stratification will increase (Soldinger Stafhammar, 1999). The
particle size distribution (PSD) in all of the simulations is the same; this
is because the simulation conditions are the same for the stratification
5000
4000
3000
ton/h (Steel deck)
ton/h (Rubber deck)
ton/h (Steel deck)
ton/h (Rubber deck)
ton/h (Steel deck)
ton/h (Rubber deck)
ton/h (Steel deck)
ton/h (Rubber deck)
ton/h (Steel deck)
ton/h (Rubber deck)
2000
1000
0
1
2
3
4
5
Bin number
Fig. 14. Tracking the passage of particle type two along the screen deck.
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4.2. Effect of screen deck material on screening efficiency along screen
length
material. In the case of the DEM model, this is covered by
Hertz–Mindlin's contact model.
To be able to fully analyzing different type of screen decks the effect
of material should be studied as well. Beside the shape of the aperture
the material is also different, for wire mesh the material is steel and for
the panel is rubber or polyurethane. Both steel and polyurethane are
hard materials which means the aperture size is not affected by the load
of material. On the other hand, the rubber has different elastic behavior, when calculating the maximum load from simulation in one area
of the screen deck the bending of that area has been calculated which is
very small and does not affect the aperture size.
Furthermore, the effect of different materials on the number of
bounces for one single particle has been analyzed. The reason for this
analysis is that increasing the number of particle bounces increases the
number of interactions with the screen deck, which in turn increases the
probability of passage. This has been done by running the simulations
with one single particle; the particle is big enough to not pass through
the apertures. The study has been done in two different ways. First, the
total number of particle contact with the screen deck by time step has
been analyzed. For each screen deck material type, three simulations
have been done with the same particle but different starting positions
based on the position of creating the particle. Fig. 15 shows the number
of particle bounces in different screen deck material. The number of
contacts on the steel screen deck was marginally lower compared to the
rubber and polyurethane decks. The reason for this is that the damping
ratio is greater on the steel deck compared to the rubber and polyurethane decks.
However, this analysis is for a single particle and can be compared
to a single particle layer. However, when the material bed builds up, the
interaction between particles will appear, which affects the number of
bounces and time required for particles travelling along the screen
deck.
5. Conclusions
A number of main conclusion can be drawn:
1. DEM modeling has provided an understanding of the particle separation process at a discrete particle level. This modeling displays
advantages as a tool for the study of different screening processes.
DEM modeling can increase the resolution to be able to understand
different physical characteristics, e.g., the usage of different screen
media revealed that the tangential particle velocity is lower for
panel deck media compared to the steel media. The increased resolution suggests alternatives to laborious physical testing in the
initial stages when designing a screen. The screening process is affected mostly by the interaction between the particles; DEM has the
advantage of covering different contact models that can be used for
simulations and this can be validated by different models that are
based on experiments.
2. The simulation results show that the number of particles that pass
through the screen deck varies depending on the configuration of
the screen media. The number of holes in a wire screen deck is more
than the rubber and polyurethane decks and thus has a larger effect,
especially in feeding point before building up the particle bed. When
the feed rate is low, there will be a difference in the screening
performance. By increasing the feed rate, the material bed will start
building up, and the stratification process starts, which affects the
efficiency of screening.
3. The number of particles that bounce on the steel screen deck is less
compared to values for the rubber and polyurethane decks, but the
difference is not excessively more and only affects the single layer
particles.
4. The simulation shows that the effect of aperture shape on screening
efficiency is not significant, but different sections on the screen deck
have different passage rates base on the aperture shape.
5. The use of the DEM simulations enables optimization of the feed rate
since the effect of varying the loading conditions can be simulated
and analyzed. One layer of particles is not always efficient, because
the particles travel faster along the screen deck with fewer bounces
due to fewer interactions with other particles.
4.3. Model comparison
As mentioned earlier in this paper, there are a number of models
that define screening performance in different process conditions. In
this paper, the mass balance model presented by Soldinger (2002) has
been analyzed by using MATLAB to study the passage rate along the
screen deck.
A comparison is made between steel and panel deck media. The feed
rate and size distributions are fixed. The model presented by Soldinger
(2002) allows a wider size distribution since it is designed to simulate a
population of particles subjected to screening. The size distribution is
chosen to be in the same size range as for the DEM simulation. In Fig. 16
the simulation result shows that the steel deck is more efficient compared to the panel deck in the feeding point; this result is very similar to
the DEM model presented in Fig. 14.
In work by Asbjörnsson et al. (2015), the theoretical model for the
geometry was introduced that could be used for modeling the panel
decks. However, the model used the same velocity for different types of
screening material. The equation for determining particle velocity,
shown in Eq. (1), consists of many empirical parameters that suggests
the velocity function can be modified to handle more process variables
in the future. The empirical model does not cover the effect of, the
particle size distribution or different feed rates to calculate the passage
rate. The DEM model can cover this. The main reason for analyzing
different feed rates and particle size distributions is that the interaction
between the particles will change and it is affects the particle velocity
along the screen deck. Lower particle velocity in the screening process
gives the particle a higher chance for stratifying earlier in the process
and thus passing through screening deck.
One other parameter that is not covered by the empirical model is
friction. Friction between particles and between particles and the screen
deck is different based on different rock materials used and screen deck
6. Future work
One future study that may be possible to achieve by DEM simulations is the analysis of the effect of particles characteristics, such as
shape and density in combination with different aperture shapes on the
12
Steel deck
Rubber deck
Polyurthane deck
Total Numbers of contact
with screen deck
11
10
9
8
7
6
5
1
1.5
2
Start position
2.5
3
Fig. 15. Number of bounces on different screen deck materials.
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Minerals Engineering 139 (2019) 105699
A. Davoodi, et al.
0.5
The mass passing through
screen deck [ton]
for robust performance. Miner. Eng.
Asbjörnsson, G., Bengtsson, M., Hulthén, Evertsson, 2016. Model of banana screen for
robust performance. Miner. Eng. 91, 66–73.
Chen, Y.-H., Tong, X., 2009. Application of the DEM to screening process: a 3D simulation. Min. Sci. Technol. (China) 19, 493–497.
Cleary, P.W., 2009. Ball motion, axial segregation and power consumption in a full scale
two chamber cement mill. Miner. Eng. 22, 809–820.
Cleary, P.W., Sinnott, M.D., Morrison, R.D., 2009. Separation performance of double deck
banana screens – Part 1: Flow and separation for different accelerations. Miner. Eng.
22, 1218–1229.
Delaney, G.W., Cleary, P.W., Hilden, M., Morrison, R.D., 2012. Testing the validity of the
spherical DEM model in simulating real granular screening processes. Chem. Eng. Sci.
68, 215–226.
Jahani, M., Farzanegan, A., Noaparast, M., 2015. Investigation of screening performance
of banana screens using LIGGGHTS DEM solver. Powder Technol. 283, 32–47.
Just, S., Toschkoff, G., Funke, A., Djuric, D., Scharrer, G., Khinast, J., Knop, K.,
Kleinebudde, P., 2013. Experimental analysis of tablet properties for discrete element
modeling of an active coating process. AAPS PharmSciTech 14, 402–411.
Maw, N., Barber, J.R., Fawcett, J.N., 1976. The oblique impact of elastic spheres. Wear
38, 101–114.
Quist, J., Evertsson, C., 2010. Application of discrete element method for simulating
feeding conditions and size reduction in cone crushers, XXV International Mineral
Processing Congress 2010, IMPC 2010, pp. 3337–3347.
Soldinger, M., 1999. Interrelation of stratification and passage in the screening process.
Miner. Eng. 12, 497–516.
Soldinger, M., 2000. Influence of particle size and bed thickness on the screening process.
Miner. Eng. 13, 297–312.
Soldinger, M., 2002. Transport velocity of a crushed rock material bed on a screen. Miner.
Eng. 15, 7–17.
Soldinger Stafhammar, M., 1999. Stratification and passage processes in rock material
screening.
Soldinger Stafhammar, M., 2002. Screening of Crushed Rock Material. Institutionen för
maskin- och fordonssystem, Chalmers tekniska högskola.
Subasinghe, G.K.N.S., Schaap, W., Kelly, E.G., 1989. Modelling the screening process: a
probabilistic approach. Powder Technol. 59, 37–44.
Steel deck
0.45
Rubber deck
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Screen length [M]
Fig. 16. Total mass is passing through screen deck.
screen deck.
Particle size distribution (PSD) is one of the most important factors
in the screening process; it affects both the stratification and passage
rate, and it would be interesting to study the effect of PSD on different
aperture shapes. This research may show how different proportions of
fine material influence the efficiency of the screening process.
References
Asbjörnsson, G., Bengtsson, M., Hulthén, E., Evertsson, M., 2015. Model of banana screen
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