XXXI International Mineral Processing Congress 2024 Proceedings/Washington, DC/Sep 29–Oct 3 2039
was to develop a model that can predict the screening effi-
ciency, the throughput rate, and the material bed depth
along the screen deck from the feed end to the discharge
end of the screen. Also, the size distributions of undersize
and oversize material should be predicted. If the screening
efficiency, the throughput rate, and the material bed depth
along the screen deck can be predicted in advance, multiple
sized apertures can be reliably selected for the screen deck.
The third was to integrate the model with Microsoft Excel,
so that the model can be used to choose appropriately sized
apertures for the screens’ screening media.
METHODOLOGY
The Necessary Data for the Passing Probability Model
In the development of the passing probability model, cer-
tain factors must be known from the material to feed the
screen and from the screening machine itself before the data
can be entered into the model. The required data from the
screened material includes screen feed rate, feed material
cumulative size distribution, solid density of the screened
material, transport speed that material has while conveying
over the deck, and the special hit parameter for the screened
material that explains when the screened material hits the
deck compared to the material itself. Data from the screen-
ing machine include the width and length of the effective
screening area, the size of the aperture, the wire diameter of
the screening media, the screen rotation speed, the length
and angle of the stroke, the shape of the stroke and the
inclination of the screen deck.
Results from the tests made in 1998 at Metso’s Tampere
factory (Viilo, 1998), were used for the model development
because the throughput rate was measured from several sec-
tors of the screen deck and the tests were made on an indus-
trial scale.
Design and Preparation for the Passing
Probability Model
The screen simulation model was based on the passing
probability of the particles on the screen deck, which has
several sized apertures. The model is based on probabil-
ity mathematics, and it was initially presented by Metsälä
(2008) based in Whiten (1972). The basic function of the
model is to calculate the amount of material from the mate-
rial bed along the screen that has a certain probability of
passing through the apertures. The model was developed
and tested further with 1998s industrial sized screen tests
of the Nordberg-Lokomo company (now part of Metso).
Some simplifications were made to facilitate the use of the
model and to make it. The purpose was first to study the
initial model, then test it and recognize the possible errors
and fix them. After that, the model was tested in more
complex conditions to gain more knowledge of the uni-
versality of the model, and its possible weaknesses. With
new results, the initial model was further developed to give
more precise performance in different cases to obtain the
final shape. However, the new model will require fine tun-
ing and correction.
Challenges with VSMA Theory
Currently, the VSMA (1998) screen sizing theory is widely
utilized for screen sizing and simulation in the mining and
aggregate industries. For simulation purposes, the theory
can be inverted so that it calculates the amount of undersize
in t/h from the available screening area. The main prob-
lem with the theory is that it only calculates the under-
flow of the screen deck with a certain screening area from
Equation (1),
· SA A B·C·D·E·F·G·H·J
Q
USFeed =
where SA is the screening area [m2], QUSFeed is the amount
of undersize material in the feed [t/h], A is the basic capac-
ity [t/h/m2], B is the oversize factor, C is the half size factor,
D is the deck location factor, E is the wet screening factor,
F is the bulk density, G is the screening element open area
factor, H is the shape of the aperture and J is the screening
efficiency (Viilo, 2020).
Other simple calculations, such as the calculation of
the overflow of the screen in t/h and the screening efficiency
for each deck of the screen can be calculated when the feed
flow and the underflow and their gradations are known.
The issue is that the VSMA theory is unable to predict the
efficiency and throughput rate of the screened material at
the points between the feed end and the discharge end of
the screen deck. Also, the calculation can only be done with
one aperture size per deck, which is not the case in most
situations because there are usually several aperture sizes on
the same screen deck, especially in the aggregate industry.
The passing probability simulation model for these prob-
lems was developed to have a more accurate prediction of
the screening process with realistic input.
TESTS AND MODELLING
The Principle of the Passing Probability Model
Figure 1 illustrates the basic principles of the passing prob-
ability model. The solid black arrow represents the feed
stream [t/h], solid red arrows represent the amount of
undersize material US [t/h] from each of the brown cal-
culation elements (CE) and solid blue arrows represent the
was to develop a model that can predict the screening effi-
ciency, the throughput rate, and the material bed depth
along the screen deck from the feed end to the discharge
end of the screen. Also, the size distributions of undersize
and oversize material should be predicted. If the screening
efficiency, the throughput rate, and the material bed depth
along the screen deck can be predicted in advance, multiple
sized apertures can be reliably selected for the screen deck.
The third was to integrate the model with Microsoft Excel,
so that the model can be used to choose appropriately sized
apertures for the screens’ screening media.
METHODOLOGY
The Necessary Data for the Passing Probability Model
In the development of the passing probability model, cer-
tain factors must be known from the material to feed the
screen and from the screening machine itself before the data
can be entered into the model. The required data from the
screened material includes screen feed rate, feed material
cumulative size distribution, solid density of the screened
material, transport speed that material has while conveying
over the deck, and the special hit parameter for the screened
material that explains when the screened material hits the
deck compared to the material itself. Data from the screen-
ing machine include the width and length of the effective
screening area, the size of the aperture, the wire diameter of
the screening media, the screen rotation speed, the length
and angle of the stroke, the shape of the stroke and the
inclination of the screen deck.
Results from the tests made in 1998 at Metso’s Tampere
factory (Viilo, 1998), were used for the model development
because the throughput rate was measured from several sec-
tors of the screen deck and the tests were made on an indus-
trial scale.
Design and Preparation for the Passing
Probability Model
The screen simulation model was based on the passing
probability of the particles on the screen deck, which has
several sized apertures. The model is based on probabil-
ity mathematics, and it was initially presented by Metsälä
(2008) based in Whiten (1972). The basic function of the
model is to calculate the amount of material from the mate-
rial bed along the screen that has a certain probability of
passing through the apertures. The model was developed
and tested further with 1998s industrial sized screen tests
of the Nordberg-Lokomo company (now part of Metso).
Some simplifications were made to facilitate the use of the
model and to make it. The purpose was first to study the
initial model, then test it and recognize the possible errors
and fix them. After that, the model was tested in more
complex conditions to gain more knowledge of the uni-
versality of the model, and its possible weaknesses. With
new results, the initial model was further developed to give
more precise performance in different cases to obtain the
final shape. However, the new model will require fine tun-
ing and correction.
Challenges with VSMA Theory
Currently, the VSMA (1998) screen sizing theory is widely
utilized for screen sizing and simulation in the mining and
aggregate industries. For simulation purposes, the theory
can be inverted so that it calculates the amount of undersize
in t/h from the available screening area. The main prob-
lem with the theory is that it only calculates the under-
flow of the screen deck with a certain screening area from
Equation (1),
· SA A B·C·D·E·F·G·H·J
Q
USFeed =
where SA is the screening area [m2], QUSFeed is the amount
of undersize material in the feed [t/h], A is the basic capac-
ity [t/h/m2], B is the oversize factor, C is the half size factor,
D is the deck location factor, E is the wet screening factor,
F is the bulk density, G is the screening element open area
factor, H is the shape of the aperture and J is the screening
efficiency (Viilo, 2020).
Other simple calculations, such as the calculation of
the overflow of the screen in t/h and the screening efficiency
for each deck of the screen can be calculated when the feed
flow and the underflow and their gradations are known.
The issue is that the VSMA theory is unable to predict the
efficiency and throughput rate of the screened material at
the points between the feed end and the discharge end of
the screen deck. Also, the calculation can only be done with
one aperture size per deck, which is not the case in most
situations because there are usually several aperture sizes on
the same screen deck, especially in the aggregate industry.
The passing probability simulation model for these prob-
lems was developed to have a more accurate prediction of
the screening process with realistic input.
TESTS AND MODELLING
The Principle of the Passing Probability Model
Figure 1 illustrates the basic principles of the passing prob-
ability model. The solid black arrow represents the feed
stream [t/h], solid red arrows represent the amount of
undersize material US [t/h] from each of the brown cal-
culation elements (CE) and solid blue arrows represent the