Impact Crusher (Kojovic)

Description

This article describes an implementation of the Kojovic impact crusher model outlined by Kojovic et al. (1997).^[1]^[2]

The model is useful for simulating the product particle size distribution from vertical and horizontal shaft impact crushers, and similar equipment.

Model theory

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Vertical shaft impact crusher

Horizontal shaft impact crusher

Power draw

Multicomponent modelling

Excel

The Kojovic impact crusher model may be invoked from the Excel formula bar with the following function call:

=mdUnit_ImpactCrusher_Kojovic(Parameters as Range, Size as Range, CrusherFeed as Range, Appearance as Range, Ab 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 ( $i$ ) x column ( $j$ ) format:

Parameters={\begin{bmatrix}K_{1}{\text{ (mm)}}\\K_{2}{\text{ (mm)}}\\K_{3}{\text{ (-)}}\\E_{\rm {cs}}{\text{ (kWh/t)}}\\{\text{Internal mesh method}}^{*}\\\end{bmatrix}},\;\;\;\;\;\;Size={\begin{bmatrix}d_{1}{\text{ (mm)}}\\\vdots \\d_{n}{\text{ (mm)}}\\\end{bmatrix}},\;\;\;\;\;\;CrusherFeed={\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}}

Appearance={\begin{bmatrix}{\begin{bmatrix}(t_{75})_{10}{\text{ (}}\%{\text{)}}&(t_{50})_{10}{\text{ (}}\%{\text{)}}&(t_{25})_{10}{\text{ (}}\%{\text{)}}&(t_{4})_{10}{\text{ (}}\%{\text{)}}&(t_{2})_{10}{\text{ (}}\%{\text{)}}\\(t_{75})_{20}{\text{ (}}\%{\text{)}}&(t_{50})_{20}{\text{ (}}\%{\text{)}}&(t_{25})_{20}{\text{ (}}\%{\text{)}}&(t_{4})_{20}{\text{ (}}\%{\text{)}}&(t_{2})_{20}{\text{ (}}\%{\text{)}}\\(t_{75})_{30}{\text{ (}}\%{\text{)}}&(t_{50})_{30}{\text{ (}}\%{\text{)}}&(t_{25})_{30}{\text{ (}}\%{\text{)}}&(t_{4})_{30}{\text{ (}}\%{\text{)}}&(t_{2})_{30}{\text{ (}}\%{\text{)}}\\\end{bmatrix}}_{1}\\\vdots \\{\begin{bmatrix}(t_{75})_{10}{\text{ (}}\%{\text{)}}&(t_{50})_{10}{\text{ (}}\%{\text{)}}&(t_{25})_{10}{\text{ (}}\%{\text{)}}&(t_{4})_{10}{\text{ (}}\%{\text{)}}&(t_{2})_{10}{\text{ (}}\%{\text{)}}\\(t_{75})_{20}{\text{ (}}\%{\text{)}}&(t_{50})_{20}{\text{ (}}\%{\text{)}}&(t_{25})_{20}{\text{ (}}\%{\text{)}}&(t_{4})_{20}{\text{ (}}\%{\text{)}}&(t_{2})_{20}{\text{ (}}\%{\text{)}}\\(t_{75})_{30}{\text{ (}}\%{\text{)}}&(t_{50})_{30}{\text{ (}}\%{\text{)}}&(t_{25})_{30}{\text{ (}}\%{\text{)}}&(t_{4})_{30}{\text{ (}}\%{\text{)}}&(t_{2})_{30}{\text{ (}}\%{\text{)}}\\\end{bmatrix}}_{m}\\\end{bmatrix}},\;\;\;\;\;\;{\mathit {Ab}}={\begin{bmatrix}A_{1}{\text{ (}}\%{\text{)}}&\dots &A_{m}{\text{ (}}\%{\text{)}}\\b_{1}{\text{ (t/kWh)}}&\dots &b_{m}{\text{ (t/kWh)}}\\\end{bmatrix}}

where:

${\text{Internal mesh method}}^{*}$ is an optional input that determines the internal mesh series used by the model (0 = ${\sqrt {2}}$ mesh, 1 = External mesh, 2 = External + ${\sqrt {2}}$ mesh). If omitted, the default ${\sqrt {2}}$ mesh is used.
$n$ is the number of size intervals
$m$ is the number of ore types
$d_{i}$ is the size of the square mesh interval that mass is retained on (mm)
$d_{i+1}<d_{i}<d_{i-1}$ , i.e. descending size order from top size ( $d_{1}$ ) to sub mesh ( $d_{n}=0$ mm)
$Q_{\rm {M,F}}$ is the mass flow rate of particles in the crusher feed (t/h)
$(t_{y})_{x}$ is the fraction of mass passing one- $y$ th the size of a parent particle (%) when $x\%$ passes one-tenth the size of a parent particle (%), $y\in \{75,50,25,2\}$ , $x\in \{10,20,30\}$
$A$ and $b$ are the ore-specific drop weight test comminution hardness parameters (% and t/kWh, respectively).

Results

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

mdUnit\_ImpactCrusher\_Kojovic={\begin{bmatrix}{\begin{array}{c}{\begin{bmatrix}P{\text{ (kW)}}\\\end{bmatrix}}\\\\\\\end{array}}&{\begin{bmatrix}d_{1}{\text{ (mm)}}\\\vdots \\d_{n}{\text{ (mm)}}\end{bmatrix}}&{\begin{bmatrix}(Q_{\rm {M,P}})_{11}{\text{ (t/h)}}&\dots &(Q_{\rm {M,P}})_{1m}{\text{ (t/h)}}\\\vdots &\ddots &\vdots \\(Q_{\rm {M,P}})_{n1}{\text{ (t/h)}}&\dots &(Q_{\rm {M,P}})_{nm}{\text{ (t/h)}}\\\end{bmatrix}}\\\end{bmatrix}}

where $Q_{\rm {M,P}}$ is the mass flow rate of particles in the crusher product (t/h).

Example

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

Figure 1. Example showing the selection of the Parameters (blue frame) array in Excel.

Figure 2. Example showing the selection of the Size (red frame) and CrusherFeed (purple frame) arrays in Excel.

Figure 3. Example showing the selection of the Appearance' (green frame) and Ab (pink frame) arrays in Excel.

Figure 5. 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.

MD_Crusher 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 material will pass straight through the crusher with no change to the size distribution.
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 product is multiplied back by the same value and returned to the SysCAD product stream. All unit model result values are shown per parallel unit.
Method	Fixed Discharge	The discharge particle size distribution is user defined. Different distributions can be used for different solids.
	Whiten	The product size distribution and power draw are determined by the Whiten crusher model. Different parameters can be used for different solids.
	Impact (Kojovic)	The product size distribution and power draw are determined by the Kojovic impact crusher model. Different parameters can be used for different solids.
Options
ShowQFeed	CheckBox	QFeed and associated tab pages (eg Sp) will become visible, showing the properties of the combined feed stream.
ShowQProd	CheckBox	QProd and associated tab pages (eg Sp) will become visible, showing the properties of the products.
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.

Crusher page

The Crusher page is used to specify the input parameters for the crusher model.

Tag (Long/Short)	Input / Display	Description/Calculated Variables/Options
Whiten
HelpLink		Opens a link to this page using the system default web browser. Note: Internet access is required.
Requirements
EcsMethod	User Ecs	The specific comminution energy Ecs is specified by the user. Default option.
	VSI	The specific comminution energy Ecs is computed for a Vertical Shaft Impact (VSI) crusher.
	HSI	The specific comminution energy Ecs is computed for a Horizontal Shaft Impact (VSI) crusher.
InternalMesh	Root 2	A geometric mesh series at ${\sqrt {2}}$ intervals is applied. Default option.
	External	The particle size distribution mesh series present in the feed stream is used directly within the model.
	Root 2 + External	The ${\sqrt {2}}$ and External mesh intervals are combined and used internally by the model.
Parameters
K1	Input	Classification parameter, the size below which all particles are not selected for breakage and report directly to product.
K2	Input	Classification parameter, the size above which all particles are always selected for breakage.
K3	Input	Classification parameter, an exponent determining the shape of the classification function, usually a value of 2.3.
RotorSpeed / N	Input	Rotational speed of the rotor. Only visible if EcsMethod is set to VSI or HSI.
RotorRadius / r	Input	Radius of the rotor. Only visible if EcsMethod is set to VSI or HSI.
BarHeight / Hb	Input	Height of the crishing bar/anvil. Only visible if EcsMethod is set to HSI.
Ecs	Input / Display	The specific comminution energy imparted to the feed particles.
Power
GrossPower / P	Display	Estimated power required by a the machine to crush the feed into the given product size.

Ore page

This page is used to define the crusher comminution properties of SysCAD species with the size distribution quality in the project.

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.
View
ColumnView	CheckBox	Arranges the Appearance data in table format (default) or column view.

Appearance
OreSpecific	CheckBox	Ore-specific parameters, allows the Appearance data to be separately input for all species. Default is all species have the same set of single input properties. This option is only available if there is more than one species in the project with the size distribution property.
Appearance	Input	Appearance function data

Ecs
OreSpecific	CheckBox	Ore-specific parameters, allows the A and b data to be separately input for all species. Default is all species have the same set of single input properties.
A	Input	Comminution hardness A parameter.
b	Input	Comminution hardness b parameter.
t10	Input	Fraction of particle mass passing one-tenth of original particle size when broken by E_cs specific comminution energy.

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		Opens a link to the Installation and Licensing page using the system default web browser. Note: Internet access is required.
Information		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		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.

References

↑ Kojovic, T., Napier-Munn, Timothy J., and Andersen, J. S. (1997). Modelling cone and impact crushers using laboratory determined energy-breakage functions. Comminution Practices Symposium: SME Annual Meeting 1997, Denver, CO, USA, 24-27 February, 1997. Littleton, CO, USA: Society for Mining, Metallurgy and Exploration.
↑ Napier-Munn, T.J., Morrell, S., Morrison, R.D. and Kojovic, T., 1996. Mineral comminution circuits: their operation and optimisation. Julius Kruttschnitt Mineral Research Centre, Indooroopilly, QLD.

[Kojovic_al._(1997)-1] Kojovic, T., Napier-Munn, Timothy J., and Andersen, J. S. (1997). Modelling cone and impact crushers using laboratory determined energy-breakage functions. Comminution Practices Symposium: SME Annual Meeting 1997, Denver, CO, USA, 24-27 February, 1997. Littleton, CO, USA: Society for Mining, Metallurgy and Exploration.

[Napier-Munn_et_al._(1996)-2] Napier-Munn, T.J., Morrell, S., Morrison, R.D. and Kojovic, T., 1996. Mineral comminution circuits: their operation and optimisation. Julius Kruttschnitt Mineral Research Centre, Indooroopilly, QLD.

[1]

[2]

Impact Crusher (Kojovic)

Contents

Description

Model theory

Vertical shaft impact crusher

Horizontal shaft impact crusher

Power draw

Multicomponent modelling

Excel

Inputs

Results

Example

SysCAD

MD_Crusher page

Crusher page

Ore page

About page

See also

References

Navigation menu

Impact Crusher (Kojovic)

Description

Model theory

Vertical shaft impact crusher

Horizontal shaft impact crusher

Power draw

Multicomponent modelling

Excel

Inputs

Results

Example

SysCAD

MD_Crusher page

Crusher page

Ore page

About page

See also

References

Navigation menu

Search