Vibrating Screen (Metso): Difference between revisions

From Met Dynamics
Jump to navigation Jump to search
m (1 revision imported)
imported>Scott.Munro
(8 intermediate revisions by 3 users not shown)
Line 1: Line 1:
== Description ==
== Description ==


This article describes an implementation of the vibrating screen sizing methodology described by '''Metso''' (Viilo, 2011), coupled with the classification methods of Whiten and White (1977), Dehghani et al. (2002) and Firth and Hart (2008).{{Viilo (2011)}}{{Whiten and White (1977)}}{{Dehghani et al. (2002)}}{{Firth and Hart (2008)}}
This article describes an implementation of the vibrating screen sizing methodology described by '''Metso''' (Viilo, 2011), coupled with the classification methods of Whiten and White (1977), Dehghani et al. (2002), and Firth and Hart (2008).{{Viilo (2011)}}{{Whiten and White (1977)}}{{Dehghani et al. (2002)}}{{Firth and Hart (2008)}}


== Model theory ==
== Model theory ==
{{Restricted content}}


{{Under construction|section}}
<hide>
This model estimates the undersize transmission capacity of a given vibrating screen, from which the load and efficiency may be determined. The efficiency value is subsequently used to determine the classification performance of the screen, as outlined below.
 
</hide><div class="user-show">
=== Screen capacity ===
</div><hide>
 
{| style="float:right; margin-left: 10px;"
|-
|
| [[File:VibratingScreenMetso1.png|thumb|425px|Figure 1. Specific screen capacity (after Viilo, 2011).{{Viilo (2011)}}]]
|-
|
| [[File:VibratingScreenMetso2.png|thumb|425px|Figure 2. Retained material factor, B (after Viilo, 2011).{{Viilo (2011)}}]]
|-
|
| [[File:VibratingScreenMetso3.png|thumb|425px|Figure 3. Half-size factor, C (after Viilo, 2011).{{Viilo (2011)}}.]]
|-
|
| [[File:VibratingScreenMetso4.png|thumb|425px|Figure 4. Wet screening factor, E (after Viilo, 2011).{{Viilo (2011)}}]]
|-
|
| [[File:VibratingScreenMetso5.png|thumb|425px|Figure 5. Moisture factor, L, (after Viilo, 2011).{{Viilo (2011)}}]]
|-
|
| [[File:VibratingScreenMetso6.png|thumb|425px|Figure 6. Screen load-efficiency relationship (after Viilo, 2011).{{Viilo (2011)}}]]
|-
|colspan="2" |
{| style="margin-left: auto; margin-right: 0px;"
|- style="vertical-align:top;"
| style="padding: 5px" |
{| class="wikitable"
|+ Table 1. Deck position (D)
|-
! Deck position !! Factor (D)
|-
| First|| 1.0
|-
| Second|| 0.9
|-
| Third|| 0.8
|-
| Fourth|| 0.7
|}
| style="padding: 5px" |
{| class="wikitable"
|+ Table 2. Shape of surface opening (H)
|-
! Opening !! Factor (H)
|-
| Round || 0.9
|-
| Square || 1.0
|-
| Rectangular || 1.05
|}
| style="padding: 5px" |
{| class="wikitable"
|+ Table 3. Particle shape (I)
|-
! Shape !! Factor (I)
|-
| Rounded || 1.2
|-
| Cubical || 1.0
|-
| Flaky|| 0.9
|}
 
|}
|-
|
| <div style="float: right; margin-left: 0px;">
{| class="wikitable"
|+ Table 4. Screen type (K)
|-
! Slope !! Deck !! Vibration !! Factor (K)
|-
|rowspan="2" | Horizontal
| Straight || Linear|| 0.9
|-
| Straight || Constant elliptical|| 1.1
|-
|rowspan="3" | Inclined
| Straight || Circular || 1.0
|-
| Straight || Variable elliptical|| 1.1
|-
| Straight || Linear|| 1.0
|-
|rowspan="4" | Multislope
| Multislope|| Linear || 1.3
|-
| Triple slope  || Variable elliptical|| 1.4
|-
| Dual slope|| Linear || 1.1
|-
| Dual slope|| Variable elliptical|| 1.3
|}
|}
 
[[File:VibratingScreenWhiten1.png|thumb|550px|Figure 7. Example panel layout for a vibrating screen deck.]]
 
[[File:VibratingScreenWhiten2.png|thumb|500px|Figure 8. Schematic diagram of three screens in series.]]
 
[[File:VibratingScreenWhiten3.png|thumb|500px|Figure 9. Schematic diagram of three panel rows in series, analogous to the three screens in series of Figure 8.]]
 
Viilo (2011) outlines a method for the sizing of vibrating screens for a given feed duty and desired separation.{{Viilo (2011)}}
 
The screen sizing method may be reversed for already existing screens and used to determine the nominal throughput capacity. The nominal capacity may be compared to the actual feed duty to generate a screen ''load'' performance parameter, from which the screen ''efficiency'' may be determined.
 
The ''specific screening capacity'', <math>Q_{\rm {spec}}</math> (t/h/m<sup>2</sup>) is defined as:
 
:<math>Q_{\rm {spec}} = A \cdot B \cdot C \cdot D \cdot E \cdot F \cdot G \cdot  H \cdot I \cdot J \cdot K \cdot L</math>
 
where:
* <math>A</math> is the specific screening capacity (t/h/m<sup>2)</sup>
* <math>B</math> is the retained (oversize) factor (-)
* <math>C</math> is the halfsize factor (-)
* <math>D</math> is the deck position factor (-)
* <math>E</math> is the wet screening factor (-)
* <math>F</math> is the material weight factor (-)
* <math>G</math> is the surface open area factor (-)
* <math>H</math> is the shape of the surface opening factor (-)
* <math>I</math> is the particle shape factor (-)
* <math>J</math> is the efficiency factor, which equals 1.0 for the reverse screening calculation (-)
* <math>K</math> is the screen type factor (-)
* <math>L</math> is the moisture factor (-)
 
The values of the factors <math>A</math>, <math>B</math>, <math>C</math>, <math>E</math>, and <math>L</math> are determined from the charts provided in Figures 1 - 5.
 
Note that Factor <math>E</math> is only applied during wet screening, where water is added to the feed or screen deck, and assumes a value of 1.0 otherwise. Similarly, the moisture factor <math>L</math> is only applied during dry screening and adopts a value for 1.0 for wet screening applications.
 
Factors <math>D</math>, <math>H</math>, <math>I</math> and <math>K</math> are determined by consulting Tables 1 - 4.
 
Factor <math>F</math> is defined as:
 
:<math>F = \dfrac{\rho_{\rm S}}{2.7}</math>
 
where <math>\rho_{\rm S}</math> is the solid density (t/m<sup>3</sup>), and Factor <math>G</math> is:
 
:<math>G = \dfrac{\rm {OAF}}{0.5}</math>
 
where <math>\rm {OAF}</math> is the open area fraction of the screen deck (m<sup>2</sup>/m<sup>2</sup>).
 
The screen '''load''' (frac) is then defined as the "ratio of the flow rate of sub-aperture particles in the feed to the undersize transmission capacity of the screen", i.e.:
 
:<math>{\rm {Load}} = \dfrac{(Q_{\rm M, F}).P_{\rm Aperture}.S}{Q_{\rm {spec}}.l.w}</math>
 
where:
* <math>Q_{\rm {M,F}}</math> is the mass flow rate of particles in the feed stream (t/h)
* <math>P_{\rm {Aperture}}</math> is the mass fraction of particles in the feed which are smaller than the aperture size (w/w)
* <math>l</math> is the screen length in the direction of flow (m)
* <math>w</math> is the screen width in the transverse  direction to flow (m)
* <math>S</math> is the screen safety factor (-)
 
The safety factor, <math>S</math>, is typically 1.0, but may be adjusted to match performance data where some aspects of the screen design are unknown.
 
The target screen '''efficiency''' of undersize removal, <math>(E_{\rm US})_{\rm T}</math> (frac), may then be determined from the screen load via Figure 6.
 
A classification-by-size relationship is subsequently applied to the screen feed to yield the estimated screen efficiency.
 
</hide><div class="user-show">
=== Classification ===
</div><hide>
 
This model applies a modified version of the Whiten and White (1977) expression for classification of particles to oversize:{{Whiten and White (1977)}}
 
{{Model theory (Text, Whiten and White Partition Curve)}}
 
</hide><div class="user-show">
==== Particle aspect ratio ====
</div><hide>
 
{{Model theory (Text, Dehghani Particle Aspect Ratio)}}
 
</hide><div class="user-show">
==== Partition averaging ====
</div><hide>
 
{{Model theory (Text, Whiten Partition Averaging)}}
 
</hide><div class="user-show">
==== Particle entrainment ====
</div><hide>
 
{{Model theory (Text, Firth Particle Entrainment)}}
 
</hide><div class="user-show">
 
=== Multi-row screening ===
</div><hide>
 
{{Model theory (Text, Screen Multi-row)|Figure1=7|Figure2=8|Figure3=9}}
 
Note: For the purposes of screen capacity and efficiency calculations:
* The length of the screen (<math>l</math>) is the sum of the length of all defined rows.
* The aperture of the screen is defined as the smallest aperture dimension of all defined rows.
* The open area fraction of the screen is the row length-weighted average of the fraction open areas (<math>f_{\rm o}</math>) of all defined rows.
 
</hide><div class="user-show">
=== Aperture size ===
</div><hide>
 
The ''nominal'' aperture size of a screen deck with multiple aperture sizes is defined as the "largest size of the smallest dimension of each aperture on the deck", i.e.
 
:<math>\text{Aperture} = \max \big \{ \min (D_1, D_2)_1 \dots \min (D_1, D_2)_p \big \}</math>
 
This value of <math>\text{Aperture}</math> therefore represents the size of the largest spherical/cubical particle which can appear in the underflow stream, and is used in the [[Vibrating Screen (Metso)#Screen_capacity|screen capacity]]  estimation described above and [[Vibrating Screen (Metso)#Screen_efficiency|screen efficiency]] calculation defined below.
 
</hide><div class="user-show">
=== Screen efficiency ===
</div><hide>
 
{{Model theory (Text, Screen Efficiency)}}
 
The screen model automatically adjusts the <math>n_L</math> classification parameter to match <math>E_{\rm US}</math> to the target efficiency value, <math>(E_{\rm US})_{\rm T}</math>, determined by the screen capacity relationships above.
 
</hide><div class="user-show">
=== Multiple decks ===
</div><hide>
 
{{Model theory (Text, Screen Multiple Decks)}}
</hide>


== Excel ==
== Excel ==
{{Under construction|section}}


The Metso vibrating screen model may be invoked from the Excel formula bar with the following function call:
The Metso vibrating screen model may be invoked from the Excel formula bar with the following function call:
Line 16: Line 238:


{{Excel (Text, Help, No Arguments)}}
{{Excel (Text, Help, No Arguments)}}
=== Inputs ===
{{Excel (Text, Inputs)}}
:<math>Parameters=
\begin{bmatrix}
\text{Moisture (}%\text{ w/w)}\\
\text{Screen type}\\
\text{Deck position}\\
\text{Wet screening (True/False)}\\
w\text{ (m)}\\
S\text{ (-)}\\
d_{\rm AR} \text{ (mm/mm)}\\
R_{\rm f} \text{ (frac)}\\
\lambda\\
\end{bmatrix},\;\;\;\;\;\;
Size = \begin{bmatrix}
s_{1}\text{ (mm)}\\
\vdots\\
s_n\text{ (mm)}\\
\end{bmatrix},\;\;\;\;\;\;
Feed= \begin{bmatrix}
(Q_{\rm M,F})_{11}\text{ (t/h)} & \dots & (Q_{\rm M,F})_{1m}\text{ (t/h)}\\
\vdots & \ddots & \vdots\\
(Q_{\rm M,F})_{n1}\text{ (t/h)} & \dots & (Q_{\rm M,F})_{nm}\text{ (t/h)}\\
\end{bmatrix},\;\;\;\;\;\;
</math>
:<math>
OreSG= \begin{bmatrix}
(\rho_{\rm s})_1\text{ (t/m}^\text{3}\text{)} & \dots & (\rho_{\rm s})_m\text{ (t/m}^\text{3}\text{)}\\
\end{bmatrix},\;\;\;\;\;\;
Rows= \begin{bmatrix}
L_1\text{ (m)} & (D_1)_1\text{ (mm)} & (D_2)_1\text{ (mm)} & (f_{\rm o})_1\text{ (m}^2\text{/m}^2\text{)}\\
\vdots & \vdots & \vdots & \vdots\\
L_p\text{ (m)} & (D_1)_p\text{ (mm)} & (D_2)_p\text{ (mm)} & (f_{\rm o})_p\text{ (m}^2\text{/m}^2\text{)}\\
\end{bmatrix}\;\;\;\;\;\;
</math>
where:
* <math>\text{Moisture}</math> is the mass fraction of moisture in the screen feed (% w/w)
* <math>\text{Screen type}</math> is the deck slope and motion characteristic of the screen:
** ''0 = Horizontal, Straight, Linear''
** ''1 = Horizontal, Straight, Const. Elliptical''
** ''2 = Inclined, Straight, Circular''
** ''3 = Inclined, Straight, Variable Elliptical''
** ''4 = Inclined, Straight, Linear''
** ''5 = Multislope, Linear''
** ''6 = Multislope, Triple slope, Variable Elliptical''
** ''7 = Multislope, Dual slope, Linear''
** ''8 = Multislope, Dual slope, Variable Elliptical''
** ''9 = Ignore''
* <math>\text{Deck position}</math> is the location of the deck (''1 = first, 2 = second, 3 = third, 4 = fourth'')
* <math>\text{Wet screening}</math> indicates whether the wet screening factor, <math>E</math>, should be applied (''True/False'')
* <math>d_i</math> is the size of the square mesh interval that feed mass is retained on (mm)
* <math>m</math> is the number of ore types
* <math>Q_{\rm M,F}</math> is feed solids mass flow rate by size and ore type (t/h)
=== Results ===
The results are displayed in Excel as an array corresponding to the matrix notation below:
:<math>
mdUnit\_Screen\_Metso =
\begin{bmatrix}
\begin{bmatrix}
l\text{ (m)}\\
\text{Aperture (mm)}\\
\text{OAF (m}^2\text{/m}^2\text{)}\\
\text{Opening shape}\\
\text{Particle shape}\\
\rho_{\rm S}\text{ (t/m}^3\text{)}\\
\text{Oversize fraction (frac)}\\
\text{Half-size fraction (frac)}\\
A\text{ (t/h/m}^2\text{)}\\
B\text{ (-)}\\
C\text{ (-)}\\
F\text{ (-)}\\
E\text{ (-)}\\
F\text{ (-)}\\
G\text{ (-)}\\
H\text{ (-)}\\
I\text{ (-)}\\
J\text{ (-)}\\
K\text{ (-)}\\
L\text{ (-)}\\
Q_{\rm spec}\text{ (-)}\\
Q_{\rm U}\text{ (-)}\\
\text{Screen area (m}^2\text{)}\\
\text{Required area (m}^2\text{)}\\
\text{Load (frac)}\\
(E_{\rm US})_{\rm T}\\
(E_{\rm US})_{\rm A}\\
n_{\rm L} \text{ (/m)}\\
\end{bmatrix}
\begin{array}{cccc}
\begin{bmatrix}
\bar d_1\text{ (mm)}\\
\vdots\\
\bar d_n\text{ (mm)}
\end{bmatrix}
&
\begin{bmatrix}
(Q_{\rm M,OS})_{11}\text{ (t/h)} & \dots & (Q_{\rm M,OS})_{1m}\text{ (t/h)}\\
\vdots & \ddots & \vdots\\
(Q_{\rm M,OS})_{n1}\text{ (t/h)} & \dots & (Q_{\rm M,OS})_{nm}\text{ (t/h)}\\
\end{bmatrix}
&
\begin{bmatrix}
(Q_{\rm M,US})_{11}\text{ (t/h)} & \dots & (Q_{\rm M,US})_{1m}\text{ (t/h)}\\
\vdots & \ddots & \vdots\\
(Q_{\rm M,US})_{n1}\text{ (t/h)} & \dots & (Q_{\rm M,US})_{nm}\text{ (t/h)}\\
\end{bmatrix}
&
\begin{bmatrix}
(E_{\rm oa})_1\text{ (frac)}\\
\vdots\\
(E_{\rm oa})_n\text{ (frac)}
\end{bmatrix}
\\
\\
\\
\\
\\
\\
\\
\\
\\
\\
\\
\\
\\
\\
\\
\\
\\
\\
\\
\\
\\
\\
\\
\\
\\
\\
\\
\end{array}
\end{bmatrix}
</math>
where:
* <math>\text{Opening shape}</math> is the shape of the apertures (''= 0 if all defined rows have square apertures, = 1 otherwise'')
* <math>\text{Particle shape}</math> is the shape of the feed particles based on the aspect ratio (''= 1 if <math>d_{\rm AR}=1</math>, = 2 otherwise'')
* <math>\text{Oversize fraction}</math> is the fraction of feed particles larger than the aperture size, i.e. <math>1-P_{\rm Aperture}</math> (frac)
* <math>\text{Half-size fraction}</math> is the fraction of feed particles smaller than the half the aperture size, i.e. <math>P_{0.5\rm Aperture}</math> (frac)
* <math>Q_{\rm U}</math> is the mass flow rate of particles in the feed smaller than the aperture size, i.e. <math>Q_{\rm M,F}.P_{\rm Aperture}</math> (frac)
* <math>\text{Screen area}</math> is the total area of all defined rows, i.e. <math>l \times w</math> (m<sup>2</sup>)
* <math>\text{Required area}</math> is the area required to screen the given feed at 100% load, i.e. <math>Q_{\rm U}.S \big/ Q_{\rm spec}</math> (m<sup>2</sup>)
* <math>(E_{\rm US})_{\rm T}</math> is the target efficiency of undersize removal required by the screen capacity calculations (frac)
* <math>(E_{\rm US})_{\rm A}</math> is the actual efficiency of undersize removal achieved by the screen (frac)
* <math>n_{\rm L}</math> is number of trials parameter (/m) required to achieve the target efficiency (/m)
* <math>Q_{\rm M,OS}</math> is mass flow rate of solids to the oversize stream (t/h)
* <math>Q_{\rm M,US}</math> is mass flow rate of solids to the undersize stream (t/h)
=== Example ===
The images below show the selection of input arrays and output results in the Excel interface.
{|
|- style="vertical-align:top;"
|
[[File:VibratingScreenMetso7.png|left|frame|Figure 4. Example showing the selection of the '''Parameters''' (blue frame) array in Excel.]]
[[File:VibratingScreenMetso9.png|left|frame|Figure 5. Example showing the selection of the '''Rows''' (pink frame) array in Excel.]]
| [[File:VibratingScreenMetso8.png|left|frame|Figure 6. Example showing the selection of the '''Size''' (red frame), '''Feed''' (purple frame), and '''OreSG''' (green frame) arrays in Excel.]] 
| [[File:VibratingScreenMetso10.png|left|frame|Figure 7. Example showing the outline of the '''Results''' (light blue frame) array in Excel.]]
|}


== SysCAD ==
== SysCAD ==


{{Under construction|section}}
The sections and variable names used in the SysCAD interface are described in detail in the following tables.
 
Note that both a '''Deck''' page and a '''Partition''' page are provided for each connected oversize discharge stream.
 
{{SysCAD (Page, Screen, DLL*Screen)}}
 
==== Deck page ====
 
The Deck page is used to specify the required model method and associated input parameters.
 
{{SysCAD (Text, Table Header)}}
 
{{SysCAD (Text, Screen, Deck)}}
 
{{SysCAD (Text, Help Link)}}
 
|-
! colspan="3" style="text-align:left;" |''Parameters''
|- style="vertical-align:top;"
| rowspan="10" | ScreenType
|Ignore
|The screen type factor (K) is ignored
|- style="vertical-align:top;"
|Horizontal, Straight, Linear
| rowspan="9" | The screen deck slope and motion configuration selected from Table 4.
|- style="vertical-align:top;"
|Horizontal, Straight, Const. Ellip.
|- style="vertical-align:top;"
|Inclined, Straight, Circular
|- style="vertical-align:top;"
|Inclined, Straight, Var. Ellip.
|- style="vertical-align:top;"
|Inclined, Straight, Linear
|- style="vertical-align:top;"
|Multislope, Linear
|- style="vertical-align:top;"
|Multislope, Triple slope, Var. Ellip.
|- style="vertical-align:top;"
|Multislope, Dual slope, Linear
|- style="vertical-align:top;"
|Multislope, Dual slope, Var. Ellip.
|-
|WetScreening
|True/False
|Indicates if the deck is wet screening (sprays, slurry etc).
|-
|DeckPosition
|Input
|Position of the deck, 1 = First, 2 = Second etc.
|-
|ScreenWidth / W
|Input
|Width of the screen.
|-
|SafetyFactor / S
|Input
|Value of the safety factor S.
|-
|ParticleAspectRatio / ParticleAR
|Input
|Value of the particle aspect ratio, i.e. (second longest dimension):(longest dimension).
|-
|Rf
|Input
|Fines recovery parameter, fraction of the finest particles or liquids split to oversize stream.
|-
|Lambda
|Input
|Fines recovery parameter, shape factor.
|-
|UseGeoMeanSize
|CheckBox
|Indicates whether to use the geometric mean size method for partitioning rather than interval averaging.
|-
! colspan="3" style="text-align:left;" |''Rows''
|-
|NumRows
|Input
|Number of screen panel rows.
|-
|L
|Input
|Length of the row in the direction of travel.
|-
|ApertureL / D1
|Input
|Aperture length.
|-
|ApertureW / D2
|Input
|Aperture width.
|-
|OpenArea / fo
|Input
|Open area fraction of the row.
 
{{SysCAD (Text, Screen, Liquids)|method=1}}
 
|-
! colspan="3" style="text-align:left;" |''Results''
|-
|ScreenLength
|style="background: #eaecf0" | Display
|Total length of all defined rows.
|-
|Aperture
|style="background: #eaecf0" | Display
|Smallest aperture dimension of all defined rows.
|-
|OpenAreaFraction / OAF
|style="background: #eaecf0" | Display
|Average open area fraction of all defined rows.
|- style="vertical-align:top;"
|rowspan="3" | OpeningShape
|style="background: #eaecf0" | Round
|Aperture shape is round.
|-
|style="background: #eaecf0" | Square
|Aperture shape is square based on aperture dimensions of all rows.
|-
|style="background: #eaecf0" | Rectangular
|Aperture shape is rectangular based on aperture dimensions of all rows.
|- style="vertical-align:top;"
|rowspan="3" | ParticleShape
|style="background: #eaecf0" | Rounded
|Particle shape is rounded.
|-
|style="background: #eaecf0" | Cubical
|Particle shape is cubical based on particle aspect ratio.
|-
|style="background: #eaecf0" | Flaky
|Particle shape is flaky based on particle aspect ratio.
|-
|SolidsDensity / SRho
|style="background: #eaecf0" | Display
|Combined density of all solids with a particle size distribution property.
|-
|Oversize
|style="background: #eaecf0" | Display
|Fraction of oversize particles in deck feed.
|-
|Halfsize
|style="background: #eaecf0" | Display
|Fraction of half-size particles in deck feed.
|-
! colspan="3" style="text-align:left;" |''Factor''
|-
|BasicCapacity / A
|style="background: #eaecf0" | Display
|Basic capacity of the screen.
|-
|OversizeFactor / B
|style="background: #eaecf0" | Display
|Particle oversize factor.
|-
|HalfSizeFactor / C
|style="background: #eaecf0" | Display
|Particle half-size factor.
|-
|DeckPosition / D
|style="background: #eaecf0" | Display
|Deck location factor.
|-
|WetScreening / E
|style="background: #eaecf0" | Display
|Wet screening factor.
|-
|MaterialWeight / F
|style="background: #eaecf0" | Display
|Material weight (density) factor.
|-
|SurfaceOpenArea / G
|style="background: #eaecf0" | Display
|Open area factor.
|-
|OpeningShape / H
|style="background: #eaecf0" | Display
|Opening shape factor.
|-
|ParticleShape / I
|style="background: #eaecf0" | Display
|Particle shape factor.
|-
|Efficiency / J
|style="background: #eaecf0" | Display
|Efficiency factor.
|-
|ScreenType/ K
|style="background: #eaecf0" | Display
|Screen type factor.
|-
|Moisture / L
|style="background: #eaecf0" | Display
|Feed moisture factor.
|-
! colspan="3" style="text-align:left;" |''Load-Efficiency''
|-
|AvailableArea
|style="background: #eaecf0" | Display
|Area available for screening, i.e. ''total screen length x width''.
|-
|RequiredArea
|style="background: #eaecf0" | Display
|Screening area required to treat feed stream at 100% loading.
|-
|Load
|style="background: #eaecf0" | Display
|Ratio of the flow rate of sub-aperture particles in the deck feed to the undersize transmission capacity of the deck.
|-
|Efficiency
|style="background: #eaecf0" | Display
|Fraction of total sub-aperture sized material in deck feed that is actually recovered to the deck undersize stream.
|}
 
{{SysCAD (Page, Hydrocyclone, Partition)|ActionU=Partition|ActionL=partition|DestinationU=Oversize|DestinationL=oversize|UnitL=screen}}
 
{{SysCAD (Page, About)}}
 
==== Additional notes ====
 
{{SysCAD (Text, No PSD Splits)|gasstream=undersize}}
 
== See also ==
 
* [[Vibrating Screen (Whiten)]]
 
== External links ==
 
* [https://help.syscad.net/Met_Dynamics_-_Screen Met Dynamics - Screen (help.syscad.net)]
* [https://help.syscad.net/Example_-_09_Met_Dynamics_Projects#Crushing_and_Grinding_Example Crushing and Grinding Example project (help.syscad.net)]
* [https://help.syscad.net/Example_-_09_Met_Dynamics_Projects#Crushing,_Grinding_and_Flotation_Example Crushing, Grinding and Flotation Example project (help.syscad.net)]
* [https://help.syscad.net/Example_-_09_Met_Dynamics_Projects#Gravity,_Dense_Medium_and_Magnetic_Separation_Example Gravity, Dense Medium, and Magnetic Separation Example project (help.syscad.net)]


== References ==
== References ==

Revision as of 14:20, 1 May 2025

Description

This article describes an implementation of the vibrating screen sizing methodology described by Metso (Viilo, 2011), coupled with the classification methods of Whiten and White (1977), Dehghani et al. (2002), and Firth and Hart (2008).[1][2][3][4]

Model theory

Nuvola apps important blue.svg.png This content is available to registered users. Please log in to view.

Screen capacity

Classification

Particle aspect ratio

Partition averaging

Particle entrainment

Multi-row screening

Aperture size

Screen efficiency

Multiple decks

Excel

The Metso vibrating screen model may be invoked from the Excel formula bar with the following function call: 

=mdUnit_Screen_Metso(Parameters as Range, Size as Range, Feed as Range, OreSG as Range, Rows as Range)

Invoking the function with no arguments will print Help text associated with the model, including a link to this page.

Inputs

The required inputs are defined below in matrix notation with elements corresponding to cells in Excel row () x column () format:


where:

  • is the mass fraction of moisture in the screen feed (% w/w)
  • is the deck slope and motion characteristic of the screen:
    • 0 = Horizontal, Straight, Linear
    • 1 = Horizontal, Straight, Const. Elliptical
    • 2 = Inclined, Straight, Circular
    • 3 = Inclined, Straight, Variable Elliptical
    • 4 = Inclined, Straight, Linear
    • 5 = Multislope, Linear
    • 6 = Multislope, Triple slope, Variable Elliptical
    • 7 = Multislope, Dual slope, Linear
    • 8 = Multislope, Dual slope, Variable Elliptical
    • 9 = Ignore
  • is the location of the deck (1 = first, 2 = second, 3 = third, 4 = fourth)
  • indicates whether the wet screening factor, , should be applied (True/False)
  • is the size of the square mesh interval that feed mass is retained on (mm)
  • is the number of ore types
  • is feed solids mass flow rate by size and ore type (t/h)

Results

The results are displayed in Excel as an array corresponding to the matrix notation below:


where:

  • is the shape of the apertures (= 0 if all defined rows have square apertures, = 1 otherwise)
  • is the shape of the feed particles based on the aspect ratio (= 1 if , = 2 otherwise)
  • is the fraction of feed particles larger than the aperture size, i.e. (frac)
  • is the fraction of feed particles smaller than the half the aperture size, i.e. (frac)
  • is the mass flow rate of particles in the feed smaller than the aperture size, i.e. (frac)
  • is the total area of all defined rows, i.e. (m2)
  • is the area required to screen the given feed at 100% load, i.e. (m2)
  • is the target efficiency of undersize removal required by the screen capacity calculations (frac)
  • is the actual efficiency of undersize removal achieved by the screen (frac)
  • is number of trials parameter (/m) required to achieve the target efficiency (/m)
  • is mass flow rate of solids to the oversize stream (t/h)
  • is mass flow rate of solids to the undersize stream (t/h)

Example

The images below show the selection of input arrays and output results in the Excel interface.

Figure 4. Example showing the selection of the Parameters (blue frame) array in Excel.
Figure 5. Example showing the selection of the Rows (pink frame) array in Excel.
Figure 6. Example showing the selection of the Size (red frame), Feed (purple frame), and OreSG (green frame) arrays in Excel.
Figure 7. Example showing the outline of the Results (light blue frame) array in Excel.

SysCAD

The sections and variable names used in the SysCAD interface are described in detail in the following tables.

Note that both a Deck page and a Partition page are provided for each connected oversize discharge stream.

MD_Screen page

The first tab page in the access window will have this name.

Tag (Long/Short) Input / Display Description/Calculated Variables/Options
Tag Display This name tag may be modified with the change tag option.
Condition Display OK if no errors/warnings, otherwise lists errors/warnings.
ConditionCount Display The current number of errors/warnings. If condition is OK, returns 0.
GeneralDescription / GenDesc Display This is an automatically generated description for the unit. If the user has entered text in the 'EqpDesc' field on the Info tab (see below), this will be displayed here.

If this field is blank, then SysCAD will display the unit class ID.

Requirements
On CheckBox This enables the unit. If this box is not checked, then the MassFracToOS option appears below.
MassFracToOS Input Only appears if the On field above is not checked. Specifies the fraction of feed mass that reports to the overflow stream when the model is off.
NumParallelUnits Input The number of parallel, identical units to simulate:
  • Feed is divided by the number of parallel units before being sent to the unit model.
  • Unit model products are multiplied back by the same value and returned to the SysCAD product streams.
  • All unit model result values are shown per parallel unit.
Options
ShowQFeed CheckBox QFeed and associated tab pages (eg Sp) will become visible, showing the properties of the combined feed stream.
SizeForPassingFracCalc Input Size fraction for % Passing calculation. The size fraction input here will be shown in the Stream Summary section.
FracForPassingSizeCalc Input Fraction passing for Size calculation. The fraction input here will be shown in the Stream Summary section.
Stream Summary
MassFlow / Qm Display The total mass flow in each stream.
SolidMassFlow / SQm Display The Solids mass flow in each stream.
LiquidMassFlow / LQm Display The Liquid mass flow in each stream.
VolFlow / Qv Display The total Volume flow in each stream.
Temperature / T Display The Temperature of each stream.
Density / Rho Display The Density of each stream.
SolidFrac / Sf Display The Solid Fraction in each stream.
LiquidFrac / Lf Display The Liquid Fraction in each stream.
Passing Display The mass fraction passing the user-specified size (in the field SizeForPassingFracCalc) in each stream.
Passes Display The user-specified (in the field FracForPassesSizeCalc) fraction of material in each stream will pass this size fraction.

Deck page

The Deck page is used to specify the required model method and associated input parameters.

Tag (Long/Short) Input / Display Description/Calculated Variables/Options
Deck
On Checkbox This enables the deck. If off, the feed to this deck passes directly to the next deck (or undersize) without partition.
Method Partition (User) The partition to oversize for each size interval is defined by the user. Different values can be used for different solids.
Partition (Reid-Plitt) The partition to oversize for each size interval is defined by a Reid-Plitt efficiency curve. Different parameters can be used for different solids.
Partition (Whiten-Beta) The partition to oversize for each size interval is defined by a Whiten-Beta efficiency curve. Different parameters can be used for different solids.
Vibrating (Karra) The Karra vibrating screen model is used to determine the partition of solids to oversize and undersize for each size interval.
Vibrating (Whiten) The Whiten vibrating screen model is used to determine the partition of solids to oversize and undersize for each size interval.
Vibrating (Metso) The Metso vibrating screen model is used to determine the partition of solids to oversize and undersize for each size interval.
Fine Wet (Mwale) The Mwale fine wet screen model is used to determine the partition of solids to oversize and undersize for each size interval.
Dewatering (Ng) The Ng dewatering screen model is used to determine the moisture content of oversize material, and the partition of solids to oversize and undersize for each size interval.
HelpLink ButtonModelHelp.png Opens a link to this page using the system default web browser. Note: Internet access is required.
Parameters
ScreenType Ignore The screen type factor (K) is ignored
Horizontal, Straight, Linear The screen deck slope and motion configuration selected from Table 4.
Horizontal, Straight, Const. Ellip.
Inclined, Straight, Circular
Inclined, Straight, Var. Ellip.
Inclined, Straight, Linear
Multislope, Linear
Multislope, Triple slope, Var. Ellip.
Multislope, Dual slope, Linear
Multislope, Dual slope, Var. Ellip.
WetScreening True/False Indicates if the deck is wet screening (sprays, slurry etc).
DeckPosition Input Position of the deck, 1 = First, 2 = Second etc.
ScreenWidth / W Input Width of the screen.
SafetyFactor / S Input Value of the safety factor S.
ParticleAspectRatio / ParticleAR Input Value of the particle aspect ratio, i.e. (second longest dimension):(longest dimension).
Rf Input Fines recovery parameter, fraction of the finest particles or liquids split to oversize stream.
Lambda Input Fines recovery parameter, shape factor.
UseGeoMeanSize CheckBox Indicates whether to use the geometric mean size method for partitioning rather than interval averaging.
Rows
NumRows Input Number of screen panel rows.
L Input Length of the row in the direction of travel.
ApertureL / D1 Input Aperture length.
ApertureW / D2 Input Aperture width.
OpenArea / fo Input Open area fraction of the row.
Liquids
LiquidsSeparMethod Split To OS (User) Liquids are split to oversize by a user-defined fraction of liquids in the feed.
Split To OS (Rf) Liquids are split to oversize by the Rf fraction specified for the screen model.
OS Solids Fraction Sufficient liquids mass is recovered to the oversize stream to yield the user-defined oversize solids mass fraction value (if possible).
OS Liquids Fraction Sufficient liquids mass is recovered to the oversize stream to yield the user-defined oversize liquids mass fraction value (if possible).
OSSolidsFracReqd / OS.SfReqd Input Required value of the mass fraction of solids in the oversize stream. Only visible if OS Solids Fraction is selected.
OSLiquidsFracReqd / OS.LfReqd Input Required value of the mass fraction of liquids in the oversize stream. Only visible if OS Liquids Fraction is selected.
LiqSplitToOS / OS.LiqSplit Input/Display The fraction of feed liquids recovered to the oversize stream.
Results
ScreenLength Display Total length of all defined rows.
Aperture Display Smallest aperture dimension of all defined rows.
OpenAreaFraction / OAF Display Average open area fraction of all defined rows.
OpeningShape Round Aperture shape is round.
Square Aperture shape is square based on aperture dimensions of all rows.
Rectangular Aperture shape is rectangular based on aperture dimensions of all rows.
ParticleShape Rounded Particle shape is rounded.
Cubical Particle shape is cubical based on particle aspect ratio.
Flaky Particle shape is flaky based on particle aspect ratio.
SolidsDensity / SRho Display Combined density of all solids with a particle size distribution property.
Oversize Display Fraction of oversize particles in deck feed.
Halfsize Display Fraction of half-size particles in deck feed.
Factor
BasicCapacity / A Display Basic capacity of the screen.
OversizeFactor / B Display Particle oversize factor.
HalfSizeFactor / C Display Particle half-size factor.
DeckPosition / D Display Deck location factor.
WetScreening / E Display Wet screening factor.
MaterialWeight / F Display Material weight (density) factor.
SurfaceOpenArea / G Display Open area factor.
OpeningShape / H Display Opening shape factor.
ParticleShape / I Display Particle shape factor.
Efficiency / J Display Efficiency factor.
ScreenType/ K Display Screen type factor.
Moisture / L Display Feed moisture factor.
Load-Efficiency
AvailableArea Display Area available for screening, i.e. total screen length x width.
RequiredArea Display Screening area required to treat feed stream at 100% loading.
Load Display Ratio of the flow rate of sub-aperture particles in the deck feed to the undersize transmission capacity of the deck.
Efficiency Display Fraction of total sub-aperture sized material in deck feed that is actually recovered to the deck undersize stream.

Partition page

The Partition page is used to display (or specify) the partition by species/component/element/individual phase and size values.

Tag (Long/Short) Input / Display Description/Calculated Variables/Options
Distribution
Name Display Shows the name of the SysCAD Size Distribution (PSD) quality associated with the feed stream.
IntervalCount Display Shows the number of size intervals in the SysCAD Size Distribution (PSD) quality associated with the feed stream.
SpWithPSDCount Display Shows the number of species in the feed stream assigned with the SysCAD Size Distribution (PSD) quality.
Partition
Method Model / User Select model-calculated or user-defined partition to separate each solids species type.
Density Display Density of each solid species.
Size Display Size of each interval in mesh series.
MeanSize Display Geometric mean size of each interval in mesh series.


All (All column) Display
  • Actual overall partition to oversize of all solid species, for each size interval.
  • Excludes solid species not present in the screen feed.
Partition Display
  • Partition to oversize for each size interval, in each solid species, as determined by the selected model or user defined value.
  • Note: These values are displayed regardless of whether the solid species is present in the screen feed or not.
All (All row, All column) Display
  • Displays the actual, total, partition of all solids with a particle size distribution property in the feed to oversize.
  • Excludes solid species not present in the screen feed.
All (All row, per species) Display
  • Actual overall partition to oversize for each solid species, for all size intervals in that species.
  • Excludes solid species not present in the screen feed.
CmpPartition
Components
ButtonHideComponents.png
ButtonShowComponents.png
 Hides or shows component partition table.
Size Display Size of each interval in mesh series.
MeanSize Display Geometric mean size of each interval in mesh series.
All (All column) Display
  • Actual overall partition to oversize of all solid components, for each size interval.
  • Excludes solid components not present in the screen feed.
CmpPartition Display
  • Partition to oversize for each size interval, in each solid component, as determined by the selected model or user defined value.
  • Excludes solid components not present in the screen feed.
All (All row, All column) Display
  • Displays the actual, total, partition of all solid components with a particle size distribution property in the feed to oversize.
  • Excludes solid components not present in the screen feed.
All (All row, per component) Display
  • Actual overall partition to oversize for each solid component, for all size intervals in that component.
  • Excludes solid components not present in the screen feed.
ElePartition
Elements
ButtonHideElements.png
ButtonShowElements.png
 Hides or shows element partition table.
Size Display Size of each interval in mesh series.
MeanSize Display Geometric mean size of each interval in mesh series.
All (All column) Display
  • Actual overall partition to oversize of all solid elements, for each size interval.
  • Excludes solid elements not present in the screen feed.
ElePartition Display
  • Partition to oversize for each size interval, in each solid element, as determined by the selected model or user defined value.
  • Excludes solid elements not present in the screen feed.
All (All row, All column) Display
  • Displays the actual, total, partition of all solid elements with a particle size distribution property in the feed to oversize.
  • Excludes solid elements not present in the screen feed.
All (All row, per element) Display
  • Actual overall partition to oversize for each solid element, for all size intervals in that component.
  • Excludes solid elements not present in the screen feed.
IPhPartition
IPhases
ButtonHideIPhases.png
ButtonShowIPhases.png
 Hides or shows individual phases partition table.
Size Display Size of each interval in mesh series.
MeanSize Display Geometric mean size of each interval in mesh series.
All (All column) Display
  • Actual overall partition to oversize of all solid individual phases, for each size interval.
  • Excludes solid individual phases not present in the screen feed.
IPhPartition Display
  • Partition to oversize for each size interval, in each solid individual phase, as determined by the selected model or user defined value.
  • Excludes solid individual phases not present in the screen feed.
All (All row, All column) Display
  • Displays the actual, total, partition of all solid individual phases with a particle size distribution property in the feed to oversize.
  • Excludes solid individual phases not present in the screen feed.
All (All row, per individual phase) Display
  • Actual overall partition to oversize for each solid individual phase, for all size intervals in that component.
  • Excludes solid individual phases not present in the screen feed.

About page

This page is provides product and licensing information about the Met Dynamics Models SysCAD Add-On.

Tag (Long/Short) Input / Display Description/Calculated Variables/Options
About
HelpLink ButtonLicensingHelp.png Opens a link to the Installation and Licensing page using the system default web browser. Note: Internet access is required.
Information ButtonCopyToClipboard.png Copies Product and License information to the Windows clipboard.
Product
Name Display Met Dynamics software product name
Version Display Met Dynamics software product version number.
BuildDate Display Build date and time of the Met Dynamics Models SysCAD Add-On.
License
File ButtonBrowse.png This is used to locate a Met Dynamics software license file.
Location Display Type of Met Dynamics software license or file name and path of license file.
SiteCode Display Unique machine identifier for license authorisation.
ReqdAuth Display Authorisation level required, MD-SysCAD Full or MD-SysCAD Runtime.
Status Display License status, LICENSE_OK indicates a valid license, other messages report licensing errors.
IssuedTo Display Only visible if Met Dynamics license file is used. Name of organisation/seat the license is authorised to.
ExpiryDate Display Only visible if Met Dynamics license file is used. License expiry date.
DaysLeft Display Only visible if Met Dynamics license file is used. Days left before the license expires.

Additional notes

  • Solid species that do not possess a particle size distribution property are split according to the overall mass split of the default particle size distribution species selected in the SysCAD Project Configuration.
  • If the default particle size distribution species is not present in the unit feed, the overall split of all other species with particle size distributions combined is used, as determined by the model.
  • Gas phase species report directly to the undersize stream without split.

See also

External links

References

  1. ↑ Viilo, K. (ed), 2011. Crushing and Screening Handbook, 5th Edition. Metso.
  2. ↑ Whiten, W.J. and White, M.E., 1977. Modelling and simulation of high tonnage crushing plants. In: Proceedings of the 12th International Mineral Processing Congress, vol. II. Sao Paulo, pp. 148–158.
  3. ↑ Dehghani, A., Monhemius, A.J. and Gochin, R.J., 2002. Evaluating the Nakajima et al. model for rectangular-aperture screens. Minerals engineering, 15(12), pp.1089-1094.
  4. ↑ Firth, B. and Hart, G., 2008. Some aspects of modeling partition curves for size classification. International journal of coal preparation and utilization, 28(3), pp.174-187.
Retrieved from "https://wiki.metdynamics.com.au/index.php?title=Vibrating_Screen_(Metso)&oldid=2709"