Crusher2
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Crusher2  Crusher 2 Model Theory 

Contents
 1 General Description
 2 Modelling Crushing and Comminution
 3 Inputs and Outputs
 4 Model Theory
 5 Data Sections
 6 Adding this Model to a Project
General Description
This model implements predictive comminution with a number of open literature correlations. The model can handle multiple ore streams with different selection and breakage functions and includes optional internal classification to model various closed circuit configurations.
 Partition Curves
 Whiten Crusher Model
 Selection/Breakage Models
 Test Data
The specific model is selected with the Method drop down list on the Crusher2 or Crusher tab.
Modelling Crushing and Comminution
If you are using these models you should be aware that getting useful results requires information about both the performance of the specific crusher type, and the mechanical properties of the ore. There are many different crusher and mill types, and each crusher type will perform differently for a given ore. At the same time, different ore characteristics will have a major impact on the performance of a specific crusher  the same unit may produce large quantities of fines with one ore and much coarser product with a different ore.
The recommended use for these models is to have existing data on the performance of a specific unit with a specific ore  and to tune the parameters of the model to match plant data. Changes in the ore flow or incoming size distribution should be modeled accurately. If a new ore has similar characteristics and mechanical testing is done to determine the new ore parameters, then the models should give a reasonable indication of how the new ore will behave in an existing plant.
Predictive crushing modelling is not an exact science and requires considerable background knowledge, as well as actual test data, to get useful results. The references below provide useful background information on modelling, as well as indicating the specific test data needed for the SysCAD model.
Diagram
The diagram shows the default drawing of the Crusher, with all of the streams that must be connected to the unit.
The physical location of the streams connecting to the Crusher is unimportant. The user may connect the streams to any position on the unit.
Inputs and Outputs
Label  Required Optional 
Input Output 
Number of Connections  Description  
Min  Max.  
Feed  1 Required  In  1  20  The feed to the Crusher 
Product  Required  Out  1  1  The product from the Crusher 
Model Theory
Crusher Methods available are:
Please see separate section for Crusher 2 Model Theory.
Data Sections
The default sections and variable names are described in detail in the following tables. The default Crusher access window consists of three sections. This number may increase or decrease, based on user configuration.
 Crusher2 tab  Contains general information relating to the unit.
 QFeed  Optional tab, only visible if ShowQFeed is enabled. This page shows the properties of the mixed stream as the feed to the Crusher2 model.
 Crusher tab will have different fields depending upon the Method selected by the user:
 Fixed Partition  The fields visible if the user selects the 'Fixed Partition' method.
 Whiten Crusher  The fields visible if the user selects the 'Whiten Crusher' method.
 Selection/Breakage  The fields visible if the user selects the 'Selection/Breakage' method.
 Test Data  The fields visible if the user selects the 'Test Data' method.
 Results  Only visible if Method is set to 'Whiten Crusher' and ShowResults is enabled.
 Selection/Breakage  Visible when method is set to Selection/Breakage.
 QProd  Optional tab, only visible if ShowQProd is selected. This page shows the properties of the final product stream from the Crusher2 model.
 Info tab  Contains general settings for the unit and allows the user to include documentation about the unit and create Hyperlinks to external documents.
 Links tab, contains a summary table for all the input and output streams.
 Audit tab  Contains summary information required for Mass and Energy balance. See Model Examples for enthalpy calculation Examples.
Crusher2 Page
Unit Type: Crusher2  The first tab page in the access window will have this name.
Tag (Long/Short)  Input / Calc  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. 
Method  Pass Through  The crusher will not change the feed (=product). This is an alternative to switching the model off and can be used when there is no PSD defined for the feed. 
Fixed Partition  The user defines a discharge partition curve from the Crusher. This can be one size distribution for all solids or one for each solid which can have its own size distribution.  
Whiten Crusher  The product size distribution will be determined using the Whiten empirical model which incorporates breakage and classification, based on a number of parameters. Different parameters can be used for different solids.  
Selection/Breakage  The user defines the Selection and Breakage criteria for the crusher. Different methods are available and different parameters can be used for different solids.  
Test Data  The user defines a Feed and Product size distribution. This can be one set of size distributions for all solids or one set for each solid which can have its own size distribution. These distributions are normally obtained from test work.  
Power Calculation  
BondWorkIndex / BondWI  Input  The Bond Work Index of the rock. This number will be used to calculate the power required to produce the final product. 
Options  
ShowQFeed  CheckBox  QFeed and associated tab pages (eg Sp) will become visible, showing the properties of the combined feed stream. See Material Flow Section. 
ShowQProd  CheckBox  QProd and associated tab pages (eg Sp) will become visible, showing the properties of the products. See Material Flow Section. 
SizeForPassingFracCalc  Input (global)  Size fraction for % Passing calculation. The size fraction input here will be shown in the results section. 
FracForPassingSizeCalc  Input (global)  Fraction passing for Size calculation. The fraction input here will be shown in the results section. 
Intervals  Toggle Button (Intervals_Ascending), the size distribution will be displayed with the largest sizes at the top of the list.  
Toggle Button (Intervals_decending) The size distribution will be displayed with the smallest sizes at the top of the list.  
Results  
Power  Calc  The calculated power to grind the product.

DistributionUsed  Result  The number of size distribution being used. If only one size distribution has been defined in the configuration file, then the distribution number used will be 0. The name of the distribution will be shown in brackets. 
Stream Result Summary The following fields are shown in a table for the Feed and Product streams.  
MassFlow / Qm  Calc  The mass flow rate of the Feed/Product streams. 
SolidMassFlow / SQm  Calc  The solid mass flow rate of the Feed/Product streams. 
LiquidMassFlow / LQm  Calc  The liquid mass flow rate of the Feed/Product streams. 
VolFlow / Qv  Calc  The volumetric flow rate of the Feed/Product streams. 
Temperature/ T  Calc  The temperature of the Feed/Product streams. 
Density / Rho  Calc  The density of the Feed/Product streams. 
SolidFrac / Sf  Calc  The solids fraction of the Feed/Product streams. 
LiquidFrac / Lf  Calc  The liquid fraction of the Feed/Product streams. 
Passing  Calc  Returns the % Passing of the user defined size (defined above) of the Feed/Product streams. 
Passes  Calc  Returns the size that has the user defined % Passing (defined above) of the Feed/Product streams. 
Crusher Page  Fixed Partition
The fields that will be visible when the Method selected is 'Fixed Partition'. See Model Theory  Fixed Partition Method for more information.
Crusher Page  Whiten Crusher
The fields that will be visible when the Method selected is 'Whiten Crusher'. See Model Theory  Whiten Crusher Method for more information.
Tag (Long/Short)  Input / Calc  Description/Calculated Variables / Options  
DisplayOre:  Input 
 
Requirements  
Method  Whiten Crusher  The product size distribution will be determined using the Whiten empirical model which incorporates breakage and classification, based on a number of parameters. Different parameters can be used for different solids.  
ShowResults  CheckBox  If this box is ticked, then the user will see a Results tab with the selection / breakage values displayed.  
Crusher Data (Ore Independent)  
CalcKs  CheckBox  If this box is ticked, then the user enters all the parameters required to calculate the K1 and K2 values. If the box is NOT ticked, then the user specifies the K values directly. Note that K3 is specified directly by the user in both cases.  
The fields shown below are only visible if the 'CalcKs' box is ticked (except for the K values).  
ClosedSideSetting/CSS  Input  The Closed Side Setting of the crusher. Also visible if the 'CalcT10' box is ticked.  
LLEN  Input  Liner Length  
LHR  Input  Liner age  
ET  Input  Eccentric Throw  
K1, K2, K3 are calculated via 6.56.7 in MCC K1 = A0+A1*CSSA2*TPH+A3*F80+A4*LLEN K2 = B0+B1*CSS+B2*TPH+B3*F80B4*LHR+B5*ET K3 = CO (Specified directly) These parameters should be found by data fitting View "All Fields" to see additional parameters  
A0 to A4  Input  Parameters required to calculate K1: K1 = A0 + A1*CSS  A2*TPH + A3*F80 + A4*LLEN  
B0 to B5  Input  Parameters required to calculate K2: K2 = B0 + B1*CSS + B2*TPH + B3*F80  B4*LHR + B5*ET  
K1  Input/Calc  Size below which all particles escape breakage. If CalcKs is ticked this is a result field, otherwise it is an input field.  
K2  Input/Calc  Size above which all particles are crushed. If CalcKs is ticked this is a result field, otherwise it is an input field. SysCAD will force K2 to always be greater than K1.  
K3  Input  Exponent. This is usually a fixed value of 2.3.  
CalcT10  CheckBox  If this box is ticked, then the user must enter all of the parameters required to calculate T10. If the box is NOT ticked, then the user specifies T10 directly.  
The fields shown below are only visible if the 'CalcT10' box is ticked (except for the T10 value).  
T10 is calculated from the correlation 6.8 in MCC T10 = D0D1*CSS+D2*TPHD3*F80 These parameters should be found by data fitting  
D0 to D3  Input  Parameters required to calculate T10: T10 = D0  D1*CSS + D2*TPH  D3*F80  
T10  Input/Calc  For a given feed particle, the percentage of product passing 10% of the original particle size after breakage. If CalcT10 is ticked this is a result field, otherwise it is an input field. The minimum value for T10 is 0.1.  
Calculated T_ values  
T75  Calc  The calculated T_75 value, the percentage of product passing 75% of the original particle size after breakage.  
T50  Calc  The calculated T_50 value, the percentage of product passing 50% of the original particle size after breakage.  
T25  Calc  The calculated T_25 value, the percentage of product passing 25% of the original particle size after breakage.  
T10  Calc  The calculated T_10 value, the percentage of product passing 10% of the original particle size after breakage.  
T4  Calc  The calculated T_4 value, the percentage of product passing 4% of the original particle size after breakage.  
T2  Calc  The calculated T_2 value, the percentage of product passing 2% of the original particle size after breakage.  
BreakageAtSize  Input  
Power parameters (Ore Independent)  
NoLoadPower/Pn  Input  The power draw of the Whiten Crusher with no feed.  
Scaling/A  Input  The dimensionless scaling factor for the actual crusher.  
TotalPendulmPower/Pp  Calc  The calculated Pendulum Power.  
CrusherPower/Pc  Calc  The crusher power draw with the feed load.  
Ore Specific Data  One set for each ore (These values are per solid ore type. Use the "DisplayOre:" scroll buttons (top of the tab page) to move between ore types.)  
Breakage parameters for SolidX  
SolidX...  
(The user enters the data for the General appearance function for the crusher model for each ore into the table. The table contains 3 rows, corresponding to T10 values of 10, 20 and 30. The columns are described below:)  
t75  Input  The required t75 value corresponding to the T10 value of 10, 20 or 30%.  
t50  Input  The required t50 value corresponding to the T10 value of 10, 20 or 30%.  
t25  Input  The required t25 value corresponding to the T10 value of 10, 20 or 30%.  
t4  Input  The required t4 value corresponding to the T10 value of 10, 20 or 30%.  
t2  Input  The required t2 value corresponding to the T10 value of 10, 20 or 30%.  
Power parameters for SolidX  
Pendulum ECS Data: kWh/ton  
(The user enters the Pendulum Ecs (specific comminution energy) data for each ore into the table. The table contains 3 columns, corresponding to 3 different pendulum tests. The rows are described below:)  
Init Size (mm)  Input  The initial material size for each of the 3 tests.  
T10=10  Input  The specific comminution energy (Ecs) value for each of the 3 tests when T10=10%.  
T10=20  Input  The specific comminution energy (Ecs) value for each of the 3 tests when T10=20%.  
T10=30  Input  The specific comminution energy (Ecs) value for each of the 3 tests when T10=30%. 
Results Page  Whiten Crusher
This tab will be visible when the Method selected is 'Whiten Crusher'. See Model Theory  Whiten Crusher Method for more information.
Tag (Long/Short)  Input / Calc  Description/Calculated Variables / Options  
DisplayOre:  Input 
 
MassFlow / Qm  Calc  The mass flow of the selected ore.  
Appearance Results for SolidX  
Selection  Calc  The calculated selection fraction of each size interval. Values can range from 0100%. Material selected will be redistributed to smaller size intervals as defined by the appearance function.  
Appearance  
(The following table is a triangular matrix showing the calculated appearance function. For each size interval, it shows how this is redistributed to other size fractions. The fractions must add to 1 (100%). Since it can not be redistributed to larger size fractions, the number of possible values decreases as the size interval reduces.)  
Additional Results for SolidX  
(The following table has one row for each size interval. The columns are explained below. IMPORTANT: this table is for Access window display of currently selected Ore only! Tags are not accessible for reporting.)  
Appearance  Calc  
Classification  Calc  The calculated fraction that is classified (selected for breakage) for the given size interval. Values can range from 0100%. Material classified (selected) will be redistributed to smaller size intervals as defined by the appearance function. This is the same as the Selection fractions shown at the top of the Results page.  
MassInBreakage  Calc  
PowerPerTon  Calc  The calculated specific comminution energy (Ecs) for the given size interval.  
Power  Calc  The calculated pendulum power (Pp) for the given size interval = MassInBreakage * PowerPerTon 
Crusher Page  Selection/Breakage
The fields that will be visible when the Method selected is 'Selection/Breakage'.
Tag (Long/Short)  Input / Calc  Description/Calculated Variables / Options 
Requirements  
Method  Selection/Breakage  The user defines the Selection and Breakage criteria for the crusher. Different methods are available and different parameters can be used for different solids. 
ShowRecalc  CheckBox  Tick this box to show when data arrays are recalculated. 
BreakageProbability  VogelPeukert  Uses the Vogel Selection Function to determine the Selection fraction for each size interval. The results are shown on the Selection/Breakage tab page. 
Austin  Uses the Austin Selection Function to determine the Selection fraction for each size interval. The results are shown on the Selection/Breakage tab page.  
User  The user specifies the Selection fraction for each size interval on the Selection/Breakage tab page.  
BreakageFunction  ReidStewart  Uses the ReidSteward Breakage Function. The results are shown on the Selection/Breakage tab page. 
Austin  Uses the Austin Breakage Function. The results are shown on the Selection/Breakage tab page.  
User  The user specifies the Breakage fractions for each size interval on the Selection/Breakage tab page.  
VogelPeukert  Uses the VogelPeukert Breakage Function. The results are shown on the Selection/Breakage tab page.  
Tavares  Uses the Tavares Breakage Function. The results are shown on the Selection/Breakage tab page.  
Logarithmic  Uses the Logarithmic Breakage Function. The results are shown on the Selection/Breakage tab page.  
Weibull  Uses the Weibull Breakage Function. The results are shown on the Selection/Breakage tab page.  
NStressEvents  Input  The number of Multiple Impact Events. See Multiple Impact Events. This may be an integer, or it may be a fractional value, such as 1.5. 
Impact Methods  
ImpactType  Hammer  The impact velocity is calculated from the rotation speed and rotor diameter. 
Impact  The user specifies the Impact velocity.  
RotorSpeed  Input  Only visible if ImpactType = Hammer. Rotational Speed for a Hammer Mill. 
RotorDiameter  Input  Only visible if ImpactType = Hammer. Rotor Diameter for a Hammer Mill. 
ImpactVelocity  Input/Calc  The impact velocity. This is used by some of the breakage probability (selection) and breakage function methods. If ImpactType = Hammer this is a result field, otherwise it is an input field. 
Classification  
Classification  Checkbox  If this box is ticked, then the unit will apply internal classification. 
(The following fields are only visible if Classification is ticked.)  
ClassificationType  NapierMunn  Uses the Napier Munn classification. 
Whiten  Uses the Whiten classification.  
User  The user enters their own classification data on the Selection/Breakage tab page.  
PostScreen  Checkbox  Transfer Model for closed loop classifier. 
K1  Input  Only visible if ClassificationType=NapierMunn. K1 parameter for Napier Munn classification model. 
K2  Input  Only visible if ClassificationType=NapierMunn. K2 parameter for Napier Munn classification model. 
K3  Input  Only visible if ClassificationType=NapierMunn. K3 parameter for Napier Munn classification model. 
Parameters...  
Breakage Probability Selection Methods  
Vogel Selection Function The user enters the following variables for each ore type.  
fMat is the material parameter, units kg/J/m xWm_min is the size independent threshold energy, units Jm/kg See VogelPeukert Mastercurve References  
fMat  Input  Material Parameter that characterises the resistance of particulate material against fracture in impact comminution. 
xWm_min  Input  Massspecific threshold energy for particle breakage, i.e. the specific energy which a particle can take up without fracture. 
k  Input  Number of impact events. 
Austin Selection Function The user enters the following variables for each ore type.  
S1  Input  Material Parameter. 0 <= S1 <= 1 
x1  Input  Minimum particle size. 0 <= x1 <= Maximum particle size in the feed stream. 
a  Input  Parameter. 0 <= a <= 1 
Breakage Functions  
ReidSteward Breakage Function The user enters the following variables for each ore type.  
Phi  Input  Experimentally determined material parameter. 
Gamma  Input  Experimentally determined material parameter. 
Beta  Input  Experimentally determined material parameter. 
Austin Breakage Function The user enters the following variables for each ore type.  
Phi  Input  Experimentally determined material parameter. 
Gamma  Input  Experimentally determined material parameter. 
Beta  Input  Experimentally determined material parameter. 
Vogel Breakage Function The user enters the following variables for each ore type.  
c  Input  Experimentally determined material parameter. 
d  Input  Experimentally determined material parameter. 
MinFragSize  Input  The minimum size to which the material can break. 
Tavares Breakage Function The user enters the following variables for each ore type.  
alpha  Input  Material Parameter based on experimental data. 
t10  Input  Material Parameter. 
Simple Log Breakage Function The user enters the following variable for each ore type.  
A  Input  Material Parameter. 
Weibull Breakage Function The user enters the following variables for each ore type.  
xu  Input  User Parameter. 
xStar  Input  User Parameter: xStar>xu 
n  Input  User Parameter: n>0 
Selection/Breakage Page
The selection, breakage fraction, cumulative breakage (and classification if enabled) data is available in tabular form. When User options are selected data may be entered manually.
Tag (Long/Short)  Input / Calc  Description/Calculated Variables / Options  
DisplayOre:  Input 
 
DisplayCumulative  CheckBox  Display Cumulative breakage.  
SolidX...  
MassFlow / Qm  Calc  The mass flow of the selected ore.  
Selection  Input/Calc  The specified/calculated selection fraction of each size interval. Values can range from 0100%. Material selected will be redistributed to smaller size intervals as defined by the breakage function.  
Breakage  
(The following table is a triangular matrix showing the specified/calculated breakage function. For each size interval, it shows how this is redistributed to other size fractions. The fractions must add to 1 (100%). Since it can not be redistributed to larger size fractions, the number of possible values decreases as the size interval reduces.)  
Cumlative Breakage for SolidX  
(Only visible if DisplayCumulative is ticked. The following table is a triangular matrix showing the calculated cumulative breakage. Since it can not be redistributed to larger size fractions, the number of possible values decreases as the size interval reduces.)  
Classification  
Retained  Input/Calc  Only visible if Classification is ticked on Crusher tab page. The specified/calculated fraction of each size interval to be retained. Values can range from 0100%.  
NOTE: If User options are selected, the parameters can be entered manually (or by user calculation in a PGM):  
See also PGM  Initialise to zero Example 
Crusher Page  Test Data
The fields that will be visible when the Method selected is 'Test Data'. See Model Theory  Test Data for more information.
Tag (Long/Short)  Input / Calc  Description/Calculated Variables / Options 
Requirements  
Method  Test Data  The user defines a Feed and Product size distribution. This can be one set of size distributions for all solids or one set for each solid which can have its own size distribution. These distributions are normally obtained from test work. 
IndividualCurves  CheckBox  If this is ticked, then the user enters Feed and Product size distributions for each individual solid. If the box is NOT ticked, then the user enters a single set of Feed and Product size distributions that is used for all of the solids. This is shown in the image below. 
SolidX  Input  The user enters the Feed size distribution based on test work. (see image below) 
Product  Input  The user enters the corresponding Product size distribution based on test work. (see image below) 
Extent  Calc  The calculated Extent of the size fraction that is retained. See Model Theory  Test Data for more information. 
Results  
SolidX(s).MassFlow / SolidX(s).Qm  Calc  The mass flow of the specified solid species. If it is the default solid species, then it will include the flow of any solids that were NOT specified to have an associated size distribution in the project cfg file. 
Adding this Model to a Project
Insert into Configuration file
Sort either by DLL or Group.
DLL:  Comminution.dll 
→  Units/Links  →  Size Alteration: Crusher2  
or  Group:  Size Distribution 
→  Units/Links  →  Size Alteration: Crusher2 
See Model Selection for more information on adding models to the configuration file.
Insert into Project
Insert Unit  →  Size Alteration  →  Crusher2 
See Insert Unit for general information on inserting units.