SAGMILLING.COM - User contributions [en]

User:Alex Doll

2026-05-17T13:19:40Z

Alex Doll: /* Test suite before deploying new code */

==Alex's to-do lists==
Stuff that Alex needs to not forget.

===Setting up a new project===
# Click the Administration button
# Create a new Client
## Assign the new administrator
## The database structure, including default data, will populate.
## Check that indexing of table index fields is active
# Switch to the new Client and check that the database is populated correctly
# Email the new administrator with credentials and URL.

===Test suite before deploying new code===
On the development server
# create a new project
## add a member to this new project
# create a new test result
## Add the 3 work index values
## check these appear in the Testwork Summary listing
## check these appear in the testwork comparison charts
# delete a test result. delete a whole sample.
# create a new optimized Bond SABC circuit
## create new mill for the new circuit from templates or from blanks
## check tent diagram
## change to raw Bond circuit
# create a new SSBM circuit
## create new mill for the new circuit from templates or from blanks
# create a new SSSAG circuit
## create new mill for the new circuit from templates or from blanks
# create a new template mill for a SAG mill, a pebble crusher and a ball mill.

Compare the '''Example''' project on development server versus main server
# View model output table of a circuit
## Pull up some summary charts
## Check some SAG-limited samples
## Check some ball-limited samples
## Run the PDF report, confirm percentile samples against the HTML list.
# Check the result table totals are the same
# Edit a SAG mill; change the model on a SAG mill
## check a tent diagram
## change speed or filling on tent diagram
# Edit a ball mill; change the model on a ball mill
## check a tent diagram
## change speed or filling on tent diagram
# Manually override the test results and the F80, P80 sizes (use the data entry fields on the flowsheet page)
# Edit a crusher

Conversions between test types

2026-05-15T13:20:16Z

Alex Doll: /* Medium size class */

[[category:testwork]]
==Converting between comminution test types==
Different tests are used in different grindability models for substantially the same purposes. Certain grindability tests are compatible with other tests, and an approximate conversion can be established by comparing to a database of testwork.

The determination of which tests are compatible with other tests is largely a function of the particle size of the specimens subjected to testing.[[Bibliography:_Testwork_programs|Doll & Barratt, 2011]] Ore properties also play a role because some tests are sensitive to changes in ore density and other tests operate with a biased sample consisting only of competent pieces.

===Medium size class===
The three tests in the medium size class are:
* Bond rod mill work index (WiRM)
* SAG Grindability index (SGI) or SAG Power index (SPI™)
* Drop weight test, both JK and SMC (A×b, DWI, Mia, etc)

{|
|-
| '''Bond rod mill work index versus A×b''' Only considering rod mill work index tests performed in laboratory mills equipped with wave liners. This is the standard specified by F. Bond and is typical of laboratories in North and South America. Non-standard (Australian type) rod mill results also shown for comparison.

A Non-standard rod mill result can be converted to a Bond rod mill work index by:

Bond WiRM = 0.565 × (Winonstandard)1.12

Source: Dec 2025 Public Grindability Database

|| [[File:ExampleDB-WiRMvAxb-comparison.png|500px]]
|-
| '''A×b versus Bond rod mill Wi''' The regression above is not reversible, it is better to re-run the regression swapping the axes to generate a synthetic A×b value from a rod mill work index.
|| [[File:A×b_v_WiRM2.png|500px|Published A×b and WiRM results]]
|-
| '''Bond rod mill work index versus SGI & SPI''' Only considering rod mill work index tests performed in laboratory mills equipped with wave liners. SGI does not contain a density correction, and this relationship is probably only valid for ore density in the range of 2.50 to 2.80 t/m3 Only considers SGI values less than 150 as greater values are meaningless.
|| [[File:WiRM_v_SGI.svg]]
|-
| '''SGI & SPI versus Bond rod mill work index''' Only considering rod mill work index tests performed in laboratory mills equipped with wave liners. SGI does not contain a density correction, and this relationship is probably only valid for ore density in the range of 2.50 to 2.80 t/m3 Only considers SGI values less than 150 as greater values are meaningless.
|| [[File:SGI_v_WiRM.svg]]
|-
| '''SGI & SPI''' versus '''A×b''' Only considering SGI values below 150 minutes. SGI does not contain a density correction, and this relationship is probably only valid for ore density in the range of 2.50 to 2.80 t/m3
|| [[File:SGI vs A×b.png]]
|}

===Extra parameters for Drop Weight Tests (DWT)===
A drop weight test is usually interpreted using a plot of the %passing 10% of the original particle size (t10) versus the energy of the weight that impacted the specimen (Ecs). These are plotted at fit to an exponential relationship with fitting parameters "A" (coefficient) and "b" (exponent).

There are several derived parameters that are commonly used in modelling that can be calculated using these A and b values, usually based on the slope of the curve at the origin of the plot. This is commonly referred to as the (A×b) value.

* DWI = 100 × (density, kg/L) / (A×b)
* Mia = 379.40 × (A×b)-0.80
* Mih = 577.37 × (A×b)-1.00
* Mic = 296.81 × (A×b)-1.00
[[File:DWI_Axb.png]]

[[File:Mia_Axb.png]]

[[File:Mih_Axb.png]]

[[File:Mic_Axb.png]]

File:SGI v WiRM.svg

2026-05-15T13:18:27Z

Alex Doll: Public Grindability Database regression of the SAG Grindability Index versus the Bond-type rod mill work index. Only considers SGI values below 150 minutes.

== Summary ==
Public Grindability Database regression of the SAG Grindability Index versus the Bond-type rod mill work index. Only considers SGI values below 150 minutes.

File:WiRM v SGI.svg

2026-05-15T13:17:09Z

Alex Doll: Public Grindability Database regression between Bond-type rod mill work index and the SAG Grindability Index (SGI), only considering SGI values below 150 minutes.

== Summary ==
Public Grindability Database regression between Bond-type rod mill work index and the SAG Grindability Index (SGI), only considering SGI values below 150 minutes.

File:ExampleDB-WiRMvSGI-comparison.png

2026-05-15T13:12:36Z

Alex Doll: Alex Doll reverted File:ExampleDB-WiRMvSGI-comparison.png to an old version

Example database comparison of Bond rod mill work index (wave-liner machines) against the SAG grindability index or SAG Power Index (SGI or SPI™).

File:ExampleDB-WiRMvSGI-comparison.png

2026-05-15T13:11:17Z

Alex Doll: Alex Doll uploaded a new version of File:ExampleDB-WiRMvSGI-comparison.png

Example database comparison of Bond rod mill work index (wave-liner machines) against the SAG grindability index or SAG Power Index (SGI or SPI™).

Conversions between test types

2026-05-15T13:10:25Z

Alex Doll: /* Medium size class */

[[category:testwork]]
==Converting between comminution test types==
Different tests are used in different grindability models for substantially the same purposes. Certain grindability tests are compatible with other tests, and an approximate conversion can be established by comparing to a database of testwork.

The determination of which tests are compatible with other tests is largely a function of the particle size of the specimens subjected to testing.[[Bibliography:_Testwork_programs|Doll & Barratt, 2011]] Ore properties also play a role because some tests are sensitive to changes in ore density and other tests operate with a biased sample consisting only of competent pieces.

===Medium size class===
The three tests in the medium size class are:
* Bond rod mill work index (WiRM)
* SAG Grindability index (SGI) or SAG Power index (SPI™)
* Drop weight test, both JK and SMC (A×b, DWI, Mia, etc)

{|
|-
| '''Bond rod mill work index versus A×b''' Only considering rod mill work index tests performed in laboratory mills equipped with wave liners. This is the standard specified by F. Bond and is typical of laboratories in North and South America. Non-standard (Australian type) rod mill results also shown for comparison.

A Non-standard rod mill result can be converted to a Bond rod mill work index by:

Bond WiRM = 0.565 × (Winonstandard)1.12

Source: Dec 2025 Public Grindability Database

|| [[File:ExampleDB-WiRMvAxb-comparison.png|500px]]
|-
| '''A×b versus Bond rod mill Wi''' The regression above is not reversible, it is better to re-run the regression swapping the axes to generate a synthetic A×b value from a rod mill work index.
|| [[File:A×b_v_WiRM2.png|500px|Published A×b and WiRM results]]
|-
| '''Bond rod mill work index versus SGI & SPI''' Only considering rod mill work index tests performed in laboratory mills equipped with wave liners. SGI does not contain a density correction, and this relationship is probably only valid for ore density in the range of 2.50 to 2.80 t/m3 Only considers SGI values less than 150 as greater values are meaningless.
|| [[File:ExampleDB-WiRMvSGI-comparison.png]]
|-
| '''SGI & SPI versus Bond rod mill work index''' Only considering rod mill work index tests performed in laboratory mills equipped with wave liners. SGI does not contain a density correction, and this relationship is probably only valid for ore density in the range of 2.50 to 2.80 t/m3 Only considers SGI values less than 150 as greater values are meaningless.
|| [[File:ExampleDB-WiRMvSGI-comparison.png]]
|-
| '''SGI & SPI''' versus '''A×b''' Only considering SGI values below 150 minutes. SGI does not contain a density correction, and this relationship is probably only valid for ore density in the range of 2.50 to 2.80 t/m3
|| [[File:SGI vs A×b.png]]
|}

===Extra parameters for Drop Weight Tests (DWT)===
A drop weight test is usually interpreted using a plot of the %passing 10% of the original particle size (t10) versus the energy of the weight that impacted the specimen (Ecs). These are plotted at fit to an exponential relationship with fitting parameters "A" (coefficient) and "b" (exponent).

There are several derived parameters that are commonly used in modelling that can be calculated using these A and b values, usually based on the slope of the curve at the origin of the plot. This is commonly referred to as the (A×b) value.

* DWI = 100 × (density, kg/L) / (A×b)
* Mia = 379.40 × (A×b)-0.80
* Mih = 577.37 × (A×b)-1.00
* Mic = 296.81 × (A×b)-1.00
[[File:DWI_Axb.png]]

[[File:Mia_Axb.png]]

[[File:Mih_Axb.png]]

[[File:Mic_Axb.png]]

Measurement of power

2026-04-20T15:24:54Z

Alex Doll: /* Measurement of power */

[[Category: Specific Energy Models]]
[[Category: Benchmarking]]
==Measurement of power==
[[file:MotorPower-Rev5.png|thumb|Typical mill drive electrical network showing loses]]
Each piece of an electrical network introduces electrical loses such as voltage drop (resistance and heat) and alternating current phase misalignment (power factor). Mechanical loses occur between a motor output shaft and driven equipment, such as heat losses in gearboxes and pinion gears. Because of these cumulative power losses, the actual amount of power declines as it travels through an electrical and/or mechanical network.

Power measurements are made relative to a certain position in an electrical network. The location where a measurement is made is often different to where a power model is valid, and a conversion between the power relative to the two locations in the network is needed.

The software considers two efficiency factors when performing the conversion, one mechanical efficiency and one electrical efficiency.

* The '''mechanical efficiency''' is the drive efficiency from the motor output shaft to the mill shell and includes the pinion losses and any gearboxes. (gearless: the motor output is at the mill shell, so this efficiency is always "1.0"). The efficiency is expressed as a decimal, so a pinion gear with 98.5% efficiency is expressed as 0.985.

* The '''electrical efficiency''' is the efficiency measured from the DCS measurement position to the motor output shaft and includes the motor efficiency (which you can read from the name-plate) and possibly drive system and conductor losses. Many mines read the electrical power at the motor leads so the electrical efficiency is just the motor losses. Note that some modern drive systems (e.g. ABB ACS6000 and any gearless drive) will provide the control system with the motor's output power corrected to be mechanical. For these systems (especially gearless), set the electrical efficiency to 1.0; otherwise express the effienciency as a decimal (e.g. 0.96 for 96%).

===Power at the Mill Shell===

Power models in SAGMILLING.COM are all expressed ''relative to the mill shell'' for both specific energy consumption (eg. Esag, kWh/t) and for mill power draw models (eg. Nordberg ball mill power prediction for a mill geometry). This ''relative to the mill shell'' definition roughly corresponds to the amount of energy that ore consumes given an efficient set of mill bearings, liners, etc.

===Power at the DCS===

A Distributed Control System (DCS) consists of a set of sensors in the plant that send information back to a central processing computer that turns the sensor information into actual measurements. For example, given a single-pinion synchronous motor system where:
* A voltage sensor sits on the medium voltage bus feeding the LCI unit in the motor drive.
* A current sensor in the MCC panel is connected to the LCI output ahead of the conductor leading to the motor input.
* These two measurements are combined in the DCS computer resulting in a power measurement relative to "somewhere in the network". There is a voltage loss in the LCI (so the voltage can only be relative to LCI input), but the current will be similar at the LCI input and output. Therefore, the combination of Volts & Amps in the computer actually corresponds to the measurement of power at the LCI input (corresponds to the input to the CCV position on the diagram as LCI is an alternative technology that does the same overall job).

===Calculating the Conversion===
Losses of power are combined by multiplication.

Continuing the example above, if the DCS indicates a 5100 kW power, the corresponding power at the mill shell would be calculated as follows:
* The electrical system for a synchronous motor with pinion corresponds to the blue set of values on [[Media:MotorPower-Rev5.png|the diagram]].
* The LCI input corresponds to the "CCV/Transformer Input" block on [[Media:MotorPower-Rev5.png|the diagram]]. The LCI does the same job as a CCV (cycloconverter); they are different technologies to achieve variable speed in synchronous motors.
* The losses for a variable speed drive between the "CCV/Transformer Input" block and the "Motor Input" block is 0.98.
* The losses for synchronous motor "Motor Input" block and "Motor Output" block is 0.96.
* The losses for a medium-speed pinion (no gearbox) "Motor Output" block and the "Mill Shell" block is 0.985.
* The total losses is calculated as ''0.980 × 0.960 × 0.985 = 0.927''.
* The power at the mill shell (the pinion output) is 5100 kW × 0.927 = 4726 kW.
** The missing 374 kW are lost to heat in the electrical network and the gears, and a little bit to the power factor of the system.

'''Warning:''' This approach generally neglects significant power factor loses. If a mill drive system is being used for power factor correction at the minesite, then a site-specific network diagram with the actual loses including power factor must be created.

Testwork: Bond ball mill work index

2026-03-04T08:45:12Z

Alex Doll:

[[category:Testwork]]
[[category:Bond/Barratt Model]]
[[category:SMC Model]]
[[Category:Amelunxen SGI Model]]
==Testwork: Bond Ball Mill Work Index==
{{Test|name=Bond Ball Mill Work Index|Abrev=WiBM|Alt=BWI|F80=2440 µm|P80=75-300 µm|Models=Bond models, SGI, Morrell Mi}}
The Bond ball mill work index is one of the most commonly used grindability tests in mining, and is often referred to as ''the Bond work index''.

The test is a 'locked-cycle' test where ground product is removed from test cycles and replaced by fresh feed. The test much achieve a steady-state before completion.

===Sample Requirements===

The test requires about 8 kg of material. Although it can work on feed as fine as 2.5 mm, it is best to send material to the testing laboratory that is nominally at least 8 mm (including the natural fines that are part of the sample). The laboratories have a standard way of reducing the coarse material to the (roughly) 2.5 mm size used to feed the test that will not introduce excessive fines.

===Test Inputs===

It is necessary for the engineer to specify the desired product size of the test so that the laboratory can choose the appropriate closing mesh screen for conducting the test. This product size is typically the feed size to flotation or leaching. Example product sizes are 200 µm for copper porphyries (select a 212 µm screen), 100 µm for gold cyanidation (select a 150 µm or 125 µm closing screen) or 75 µm for complex sulphides (select a 105 µm screen).

===Test Outputs===

The laboratory will report the following information:
* umClosing: The closing mesh size the test was run at, also called P100 or P1. Convert to µm, if needed, before entering into the database.
* F80: Sample feed size in µm (and usually will provide a particle size distribution)
* P80: Sample finished product size in µm (and usually will provide a particle size distribution)
* gpr: The average grams per revolution of the last three cycles (sometimes is labelled ''GPB'')
* fdpassing: The percentage (0-100) of the feed that already passes the closing screen size
* WiBM: The calculated work index (SAGMILLING.COM uses only metric units; if the laboratory reported work index in "short ton" units, multiply that value by 1.1023 and enter the result).

When entering results into the SAGMILLING.COM database table, the following extra fields are available:
* ModBWI: is this test modified from the original Bond protocol? An open-circuit Minnovex ModBWI test or a SAGDesign ball mill work index with non-standard feed would be entered as "true" (or "1" in a [[Testwork: Batch entry|batch upload]] of test results).
* synthetic indicates whether this is a real test result, or just a synthetic one that should only be used for modelling. If this column contains a value of '1' (boolean=true) for a test, then that test is understood to not be a real test result and is therefore not shown on the testwork comparison charts. Synthetic values are available when running circuit model simulations and do show up in the list of model results.

The computation of a Bond ball mill work index was empirically calibrated by Fred Bond using a short ton basis. The modern (metric tonne) basis is the following equation:

Wi_{BM} = \frac{1.1023 \times 44.5}{P_{100}^{0.23} \times gpr^{0.82} \times (\frac{10}{\sqrt{P_{80}}} - \frac{10}{\sqrt{F_{80}}})}

===Derived values composed from WiBM results===
* Morrell ''Mib'' value is calculated for a sample if the following are available: '''umClosing''', '''F80''', '''P80''', '''gpr'''.
** Units are kWh/t based on Morrell's empirical calibration.
** This value is used in the [[:Category:SMC Model|Morrell Mi models]].
** \Mib = \frac{18.18}{P_{100}^{0.295} × (gpr) \left [ P_{80}^{f(P_{80})} - F_{80}^{f(F_{80})} \right ]} kWh/t
** where: f(''x'') = -0.293 - ''x''/10⁶
* ''Levin B'' parameter is calculated for a sample if the following are available: '''umClosing''', '''F80''', '''P80''', '''gpr''', '''fdpassing'''.
** Units of the Levin B are mWh per revolution of a standard Bond grindability ball mill (mWh/rev). Watch out, as this metric is also given as kWh/rev in literature.
** This value is not used in any computations, but can be used in external calculation such as [https://sagmilling.com/articles/37/view/2020%20CMP%20-%20Alex%20Doll.pdf?s=1 Functional Performance].
** B = \frac{4900 × (gpr)^{0.18}}{P_{100}^{0.23} (100 - Fd%passing)} mWh/rev

=== Modelling ===
Ball mill work index is used in several SAGMILLING.COM circuit models, including:
* [[Model:BondModel|Bond/Barratt specific energy consumption circuit model]].
* [[Model:Bond RMBM Model|Bond/Rowland rod mill & ball mill specific energy consumption circuit model]].
* [[Model:Amelunxen SGI|Amelunxen SGI SAG and ball mill circuit model]].
* [[Model:Morrell SMC SAG|Morrell SMC (Mib) SAG and ball mill circuit model]] (uses the ''umclosing'', ''F80'', ''P80'', and ''gpr'' values to calculate ''Mib'').

It is also used in the CEET2 model (distributed by [http://www.sgs.ca/en/Mining/Metallurgy-and-Process-Design.aspx SGS]) and is commonly used by people running the JK SimMet population balance model (distributed by [http://www.jktech.com.au JK Tech]).

The work index is used to calculate the energy requirement to grind rocks in the fine size range, below 2.5 mm into the range of a few hundreds of micrometres. Heterogeneous ore types typically are sensitive to the product size of the test, and the work index value changes if the test is performed to a coarser or finer product. Always specify the desired product size of the test to the laboratory, or conduct a [[Ball mill work index adjustment]] procedure to determine the effect of changing the product size on work index.

=== Corrections and adjustments ===

'''Estimate of P80 when P100 is known'''

(Source https://www.linkedin.com/posts/alex-doll-66b57465_workindex-comminution-grinding-activity-6873690907527532544-u6DD)

The P80 of a ball mill work index test can be estimated if the P100 is know based on this equation:
P_{80}=0.92 × (P_{100})^{0.96}

[[File:P80_P100-powermodel.png]]

'''Estimate grams per revolution when only P100 is known'''

NI43-101 reports often provide P100 and the work index. To estimate the other parameters, you can assume:
* the P80 is 0.92 × (P100, µm)0.96
* assume the F80 is 2440 µm (see [[https://www.researchgate.net/publication/363350623_A_new_methodology_to_obtain_a_corrected_Bond_ball_mill_work_index_valid_with_non-standard_feed_size Nikolić, Doll, & Trumić (2022)]])

The grams per revolution can be computed by rearranging Bond's laboratory equation:

gpr = \left[ \frac{1.1023 \times 44.5}{P_{100}^{0.23} \times Wi_{BM} \times (\frac{10}{\sqrt{P_{80}}} - \frac{10}{\sqrt{F_{80}}})} \right]^\frac{1}{0.82}

To adjust a ball mill grindability test work index or Mib value to a different P80 basis, use the [[Ball mill work index adjustment]] method of Josefin & Doll.

'''Correct for 'non standard' feed size'''

If the ball mill test feed material was too small for the stage crushing to make a normal F80, then the correction from ''Nikolić, Doll, & Trumić (2022)'' [[https://www.researchgate.net/publication/363350623_A_new_methodology_to_obtain_a_corrected_Bond_ball_mill_work_index_valid_with_non-standard_feed_size A new methodology to obtain a corrected Bond ball mill work index valid with non-standard feed size]] may be applied. The method is also described in Procemin 2022 paper [[https://www.researchgate.net/publication/372393426_Secrets_of_the_Bond_Ball_mill_grindability_test Secrets of the Bond Ball Mill Grindability Test]]

=== Computing Mib from incomplete Ball Mill Work Index data ===
Use this nomograph to compute an Mib from a ball mill work index if you know the P100 size that the test should be run at.

[[File:MibFromWiBM byP100.png]]

Benchmarking: Specific Energy Consumption Models

2026-02-11T12:52:40Z

Alex Doll: /* Benchmarking: Private surveys */

[[category:Bibliography]]
[[category:Models]]
[[category:Benchmarking]]
==Benchmarking: Amelunxen SGI - Agnico Eagle Laronde==
''Starkey, J., Robitaille, J., Cousin, P., Jordan, J. and Kosick, G.'', '''Design of the Agnico-Eagle Laronde Division SAG mill'''. Proceedings of SAG 2001, pages III-165 to III-178.

* Survey conducted for six months after start-up
* Specific energy values corrected to "mill shell" basis (motor input basis given in the reference)

Result for default Amelunxen SGI SAB model conditions:
{| class="wikitable" border="1"
|-
!
!Esag
!Epeb
!Ebm
!Etotal
!t/h
|-
| Predicted
| 6.5
| -
| 6.9
| 13.4
| 196
|-
| Survey
| 6.1
| -
| 6.4
| 12.5
| 210
|-
| Difference
| 0.4
| -
| 0.5
| 0.9
| 14
|-
| Difference
| model 7% high
| -
| model 8% high
| model 7% high
| model 7% low
|}

[[Benchmarking: Amelunxen SGI - Agnico Eagle|Show details of benchmarking]]

==Benchmarking: Bond/Barratt - Cadia East (underground)==
''Engelhardt, D., Robertson, J., Lane, G., Powwel, M.S. and Griffin, P.'', '''Cadia Expansion - From open pit to block cave and beyond'''. Proceedings of MetSoc 2012.

* Design criteria and plant trial of underground Cadia East ore
* Ore was blasted underground and had F80 = 80 mm on surface
* Work index appears to have been determined on a non-standard rod mill apparatus. The rod mill Wi is probably invalid.
* This ore breaks the Bond/Barratt models, the combination of work index values is not a good fit for Barratt's original calibration of his model.

Result for default Optimized Bond/Barratt SABC model conditions:
{| class="wikitable" border="1"
|-
!
! ESAG
! Eball
! Etotal
! t/h
|-
| Model
| 12.2 kWh/t
| 15.1 kWh/t
| 27.7 kWh/t
| 1294 t/h
|-
| Measured
| 10.6 kWh/t
| 13.2 kWh/t
| 23.8 kWh/t
| 1482 t/h
|-
| Difference
| 1.6 kWh/t
| 1.9 kWh/t
| 3.9 kWh/t
| -188 t/h
|-
| Difference
| 15%
| 14%
| 16%
| -13%
|}

[[Benchmarking: Bond - Cadia East|Show details of benchmarking]]

==Benchmarking: Bond/Barratt - Cadia==
''Dunne, R., Morrell, S., Lane, G., Valery, W. and Hart, S.'', '''Design of the 40 foot diameter SAG mill installed at the Cadia gold copper mine'''. Proceedings of SAG 2001, pages I-43 to I-58.

''Lane, G., Foggiatto, B. and Bueno, M'', '''Power-based comminution calculations using Ausgrind'''. Proceedings of Procemin 2013, Chapter 2, paper 2.

* Survey conducted shortly after start-up

Result for default Optimized Bond/Barratt SABC model conditions:
{| class="wikitable" border="1"
|-
!
!Esag
!Epeb
!Ebm
!Etotal
!t/h
|-
| Predicted
| 8.6
| 0.3
| 8.5
| 17.4
| 2000
|-
| Survey
| 8.6
| -
| 8
| 16.6
| 2065
|-
| Difference
| 0
| 0.3
| 0.5
| 0.8
| -65
|-
| Difference
| 0%
| -
| 6%
| 5%
| -3%
|}

[[Benchmarking: Bond - Cadia|Show details of benchmarking]]

==Benchmarking: Bond/Barratt SABC Circuit Specific Energy Consumption - Copper Mountain==

* ''Morrison, R.'', '''Current Plant Conditions at Copper Mountain'''. Presentation to the BC/Yukon Branch Canadian Mineral Processors, November 29, 2012; Vancouver, Canada.
* ''van de Vijfeijken, M.'', ''Filidore, A.'', ''Walbert, M.'' and ''Marks, A.'', '''Copper Mountain: Overview on the Grinding Mills and their Dual Pinion Mill Drives.''' Proceedings of the SAG 2011 Conference, September 25-28, 2011; Vancouver, Canada.
* ''Marks, A., Sams, C. and Major, K.'', '''Grinding Circuit Design for Similco Mines'''. Proceedings of the SAG 2011 Conference, September 25-28, 2011; Vancouver, Canada.

Result for default Optimized Bond/Barratt model conditions:
{| class="wikitable" border="1"
|-
!
! Tonnage
|-
| Model
| 1455 t/h
|-
| Measured
| 1600 t/h
|-
| Difference
| 145 t/h
|-
| Difference
| 9.5%
|}

[[Benchmarking: Bond - Copper Mountain|Show details of benchmarking]]

==Benchmarking: Bond/Barratt SAG Mill Specific Energy Consumption - Detour Lake ==
* ''J. Torrealba-Vargas, J.-F. Dupont, J. McMullen, A. Allaire and R. Welyhorsky'', '''The successful development of the detour lake grinding circuit: from testwork to production'''. Proceedings of the SAG 2015 Conference, September 2015, Vancouver, Canada, Paper 38.

The mill is in the final stages of ramp-up, and has not reached its ultimate capacity. If we use the April/May 2015 values from Figure 5, the results look like:

* Etotal : model 7% low
* t/h : model 13% high

The throughput is likely to continue to increase as the ramp-up continues, so the difference between the model and the actual plant is likely to reduce.

[[Benchmarking: BondBarratt - Detour Lake|Show details of benchmarking]]

==Benchmarking: Bond/Barratt SAG Mill Specific Energy Consumption - Esperanza ==
* ''Villanueva, F. and Soto, L.'', '''SEC and the impact on a mills selection for DMC project'''. Proceedings of the XXVII International Mineral Processing Congress, October 2014, Santiago, Chile. C14-23.

Paper describes modelling of two expansion cases (Esperanza Sur and Encuentro). Some operating data for the current Esperanza pit & plant are provided as they were used to tune the comminution models used for the expansion cases.

{|class="wikitable" border="1"
! !! Average ore
|-
| Measured SAG specific energy consumption, kWh/t
| style="text-align:center"| 5.5
|-
| Predicted SAG specific energy consumption, kWh/t
| style='text-align:center' | 5.9
|-
| Difference, kWh/t
| style='text-align:center'| 0.4
|-
| Difference, %
| style='text-align:center'| model predicts 7% high
|}

[[Benchmarking: Bond - Esperanza|Show details of benchmarking]]

==Benchmarking: Bond/Barratt SABC Circuit Specific Energy Consumption - Fort Knox==
* ''Magnuson, R.; Hallow, J.; Mosher, J.; Major, K.'', '''The Fort Knox Mill: Design, Commissioning and Operation'''. Proceedings of the SAG 2001 Conference, Vancouver, Canada.

Optimized Bond/Barratt SABC circuit (10% Essbm calibration factor).

Result for default model conditions:
{| class="wikitable" border="1"
|-
!
! Etotal
! WiO
!
! Tonnage
!
|-
| Model
| 11.43
| 15.90
| kWh/t
| 1,607
| t/h
|-
| Measured
| 10.50
| 14.61
| kWh/t
| 1,733
| t/h
|-
| Difference
| 0.93
| 1.29
| kWh/t
| 126
| t/h
|-
| Difference
| 8.9%
| 8.8%
|
| 7.3%
|
|}

Model predicts 8.9% harder than survey resulting in predicted throughput 7.3% lower than survey.

[[Benchmarking: Bond - Fort Knox|Show details of benchmarking]]

==Benchmarking: Bond/Barratt SABC Circuit Specific Energy Consumption - Kanowna Belle ==

''Lunt, D.J., Thompson, A. and Ritchie, I.'' '''The Design and Operation of the Kanowna Belle Milling Circuit''', SAG 1996, Pages 81-96.

{| class="wikitable"
|-
! !! Survey !! Optimized Model !! Difference
|-
| ESAG || 12.55 kWh/t || 13.27 kWh/t || +5.7%
|-
| Eball || 9.70 kWh/t || 10.24 kWh/t || +5.6%
|-
| Epeb || 0.99 kWh/t || 1.04 kWh/t || +5.2%
|-
| '''Etotal''' || '''23.24 kWh/t''' || '''24.55 kWh/t''' || '''+5.6%'''
|}

Two possible circuit models were tested, and the ''Optimized Bond/Barratt SABC model'' better matches the survey than the'' Raw Bond/Barratt model''.

[[Benchmarking: Bond - Kanowna Belle|Show details of benchmarking]]

==Benchmarking: Bond/Barratt SABC Circuit Specific Energy Consumption - Meadowbank==

* ''Muteb, P. & Allaire, J.'', '''Meadowbank Mine Process Plant Throughput Increase''', Proceedings of the Canadian Mineral Processors Annual General Meeting, Ottawa, Canada, January 2013.

Paper describes a "sick" SAG mill and the changes made to "bring it to health". The "healthy" mill conditions benchmark as follows:

* Actual SAG/ball motor powers (at shell): 3,168 kW / 4,105 kW
* Actual daily average throughput: 500 tonnes/hour
* Predicted SAG/ball motor powers (at shell): 3,096 kW / 4,182 kW
* Predicted nominal throughput: 500 tonnes/hour (0% difference)

{|class="wikitable" border="1"
! !!SAG!!Ball Mill!!total
|-
| Measured specific energy consumption, kWh/t||6.34||8.21||14.55
|-
| Predicted specific energy consumption, kWh/t||6.19||8.36||14.55
|-
| Difference, kWh/t||-0.15||0.15||0.00
|-
| Difference, %||-2.3%||1.8%||0.0%
|}

[[Benchmarking: Bond - Meadowbank|Show details of benchmarking]]

==Benchmarking: Amelunxen SGI SABC Circuit Specific Energy Consumption - Macraes==

''Barns, K., Lane, G., Osten, K. & Scagliotta, N.'', '''Benchmarking Energy Efficiency - A Case Study at Macraes Gold Mine''', Proceedings of the AusIMM MetPlant conference, Perth, Australia, September 2004.

{| class="wikitable"
|-
! !! !! Survey 5 !! Survey 4 !! Survey 3 !! Survey 2 !! Survey 1 !! Overall Average
|-
| SAG specific power || ||7.1% || 7.6% || 23.4% || 5.0% || 9.4% || 10.5%
|-
| ball mill specific power || ||7.1% || 7.7% || 16.6% || 4.9% || 11.4% || 9.6%
|-
| total specific power || ||7.1% || 7.7% || 19.0% || 5.0% || 10.8% || 9.9%
|-
| CFball || ||-17.5% || 16.9% || 0.5% || 10.6% || 8.3% || 3.8%
|}

The overall specific energy consumption predictions of the model are conservative by about 10%. The CFball predictions are within 4% overall, but can be wildly different on any particular sample.
Circuit feed sizes were varied during the surveys, ranging between 51 and 107 mm; the SGI equation doesn't have a explicit F80 term, so feed sizes may be confusing the method.

[[Benchmarking: SGI - Macraes|Show details of benchmarking]]

==Benchmarking: Bond/Barratt SABC Circuit Specific Energy Consumption - Macraes==

''Barns, K., Lane, G., Osten, K. & Scagliotta, N.'', '''Benchmarking Energy Efficiency - A Case Study at Macraes Gold Mine''', Proceedings of the AusIMM MetPlant conference, Perth, Australia, September 2004.

Difference between model results and plant surveys:
{| class="wikitable"
|-
! !! !! Survey 5 !! Survey 4 !! Survey 3 !! Survey 2 !! Survey 1 !! Overall Average
|-
| SAG specific power || ||-5.3% ||-5.0% || 6.3% || 0.5% || 2.2% || -0.2%
|-
| ball mill specific power || ||-6.3% ||-4.7% || 3.6% || 1.9% || 3.2% || -0.5%
|-
| total specific power || ||-6.8% ||-3.8% || 5.4% || 1.4% || 2.9% || -0.2%
|}

[[Benchmarking: Bond - Macraes|Show details of benchmarking]]

==Benchmarking: Bond/Barratt ABC Circuit Specific Energy Consumption - Santa Rita==

''Latchireddi, S. & Faria, E.'', '''Achievement of High Energy Efficiency in Grinding Mills at Santa Rita''', Proceedings of the Canadian Mineral Processors Annual General Meeting, Ottawa, Canada, January 2013.

''Faria, E. & Latchireddi, S.'', '''Commissioning and Operation of Milling Circuit at Santa Rita Nickel Operation''', Paper #137: Proceedings of the International Autogenous Grinding, Semiautogenous Grinding and High Pressure Grinding Roll Technology Conference, Vancouver, Canada, September 2011.

{|class="wikitable" border="1"
! !!FAG!!BM!!Pebble Crusher!!total
|-
| Measured specific energy consumption, kWh/t||9.55||7.28||0.34||17.18
|-
| Predicted specific energy consumption, kWh/t||9.78||8.33||0.39||18.50
|-
| Difference, kWh/t||0.23||1.05||0.05||1.32
|-
| Difference, %||2.4%||14.4%||14.7%||7.7%
|}

[[Benchmarking: Bond - Santa Rita|Show details of benchmarking]]

==Benchmarking: Bond/Barratt SAB Circuit Specific Energy Consumption - Selbaie==

''Duval, L. and Wood, K.'', '''Testing, Design and Operation of SAG Circuit at Les Mines Selbaie''', Proceedings of the SAG 1989 Conference, Vancouver, Canada, September 1989.

''Wood, K. and Duval, L.'', '''Mill Expansion at Les Mines Selbaie''', Proceedings of the 25th Anniversary Issue of the Canadian Mineral Processors, Ottawa, Canada (Paper № 8), January 1987.

* SAB circuit
* SAG feed F80 = 117 mm
* cyclone overflow, P80 = 45 µm

{|class="wikitable" border="1"
! !!SAG!!BM!!total
|-
| Predicted specific energy consumption, kWh/t|| 11.99 || 12.37 || 24.37
|-
| Predicted operating work index, metric|| 20.3|| 14.2 || 16.7
|-
| Measured operating work index, metric|| 20.0 || 13.8 || 16.0
|-
| Difference, metric Wi units|| 0.3 || 0.4 || 0.6
|-
| Difference, %|| 2%|| 3%|| 4%
|}

[[Benchmarking: Bond/Barratt - Selbaie|Show details of benchmarking]]

==Benchmarking: Bond/Rowland SSBM Circuit Specific Energy Consumption - Boddington ==

The Bond/Rowland SSBM model was fit to the observed operation of the Boddington HPGR circuit. The fitting parameters are:
* Essbm calibration factor: (-0.13)
* Mechanical efficiency of HPGR crushers: 0.28.

Because the model is specifically fit to the Boddington data, it doesn't make any meaningful throughput predictions, but the following predictions are available:
* Ball mill operating work index reduction versus laboratory: 5% (microcracking/phantom cyclone effect)
* Secondary crusher WiO is 18.1 kWh/tonne (versus laboratory determination 27.7 kWh/t).

[[Benchmarking: Bond - Boddington|Show details of benchmarking]]

==Benchmarking: Bond/Rowland SSBM Circuit Specific Energy Consumption - Tropicana ==

The Bond/Rowland SSBM model was fit to the observed operation of the Tropicana HPGR circuit. The fitting parameters are:
* Essbm calibration factor: (0%)
* Mechanical efficiency of HPGR crushers: 0.44.

[[Benchmarking: Bond - Tropicana|Show details of benchmarking]]

==Benchmarking: Morrell Mih model Circuit Specific Energy Consumption - Tropicana ==

The Morrell Mi model (SMC test & recalibrated ball mill work index) was compared to the observed operation of the Tropicana HPGR circuit:

{| class="wikitable"
|-
! !! Model Prediction !! Survey Actual !! Difference
|-
| EsecCr || 0.52 kWh/t || 0.40 kWh/t || model 30% high
|-
| Ehpgr || 2.83 kWh/t || 2.60 kWh/t || model 9% high
|-
| Eball || 18.36 kWh/t || 16.77 kWh/t || model 9% high
|-
| Etotal || 21.70 kWh/t || 19.77 kWh/t || model 10% high
|}

The Morrell model is about 10% conservative versus the survey results.

The throughput determined by the ball mill treatment rate is 710 t/h, versus observed 734 t/h (model is 3% conservative).

[[Benchmarking: Morrell Mih - Tropicana|Show details of benchmarking]]

==Benchmarking: Bond/Barratt Single Stage SAG model Circuit Specific Energy Consumption - Yanacocha ==

Two surveys were published, the first survey was noted that "the circuit was not operating efficiently", so the model predictions are expected to be optimistic.

{| class="wikitable"
|-
! !! Survey Actual !! Model Prediction !! Difference !! Comment
|-
| Survey 1 EASAG || 19.8 kWh/t || 16.4 kWh/t || model 20% low || Ignore survey, mill operating poorly
|-
| Survey 2 EASAG || 18.0 kWh/t || 16.3 kWh/t || model 10% low || Survey probably OK
|}

The first survey has significantly higher energy consumption than the model predicts. The author of the reference paper says that the mill was not operating well, so it is reasonable to ignore this survey and not use it as a valid "benchmark" as we are only interested in benchmarking against circuits that are operating "well".

The second survey is operating better, and can be assumed valid basis for benchmarking.

[[Benchmarking: Yanacocha Single-stage SAG Mill|Show details of benchmarking]]

==Benchmarking: Morrell Mi Single Stage SAG model Circuit Specific Energy Consumption - Yanacocha ==

The same two surveys as the Bond/Barratt model (above) give the following:
{| class="wikitable"
|-
! !! Survey Actual !! Model Prediction !! Difference !! Comment
|-
| Survey 1 EASAG || 19.8 kWh/t || 12.7 kWh/t || model 56% low || Ignore survey, mill operating poorly
|-
| Survey 2 EASAG || 18.0 kWh/t || 12.5 kWh/t || model 43% low || Significant difference
|}

Both these predictions are significantly different from the surveys. Either the circuit is performing much worse than the Bond/Barratt model predicts or else there is something in Yanacocha that is confusing the Mi method.

[[Benchmarking: Yanacocha Single-stage SAG Mill|Show details of benchmarking]]

==Benchmarking: More Single-stage SAG surveys==
* See the Procemin 2017 paper '''Power-based modelling of single-stage AG and SAG mill circuits''', A. Doll & M. Becerra [https://www.sagmilling.com/articles/33/view/17PRM-GMT_DollBecerra-SingleStageSAG.pdf?s=1 PDF download]
{| style="border-spacing:0;margin:auto;width:17.59cm;"
|- style="border-top:0.05pt solid #000000;border-bottom:0.05pt solid #000000;border-left:none;border-right:none;padding:0.097cm;"
| align=center|
| align=center| '''Barratt model'''
| align=center| '''Morrell model'''
| align=center| '''Amelunxen model '''
| align=center| '''El Soldado model '''
|- style="border-top:none;border-bottom:0.05pt solid #000000;border-left:none;border-right:none;padding:0.097cm;"
| align=center| Qty of parameters:
| align=center| 3
| align=center| 2
| align=center| 2
| align=center| 1
|- style="border:none;padding:0.097cm;"
|| El Soldado
| align=center style="color:#008000;" | 5%
| align=center style="color:#008000;" | -1%
| align=center style="color:#008000;" | -4%
| align=center style="color:#008000;" | -5%
|- style="border:none;padding:0.097cm;"
|| Palabora
| align=center style="color:#008000;" | 3%
| align=center style="color:#800000;" | -28%
| align=center style="color:#800000;" | -21%
| align=center style="color:#800000;" | -34%
|- style="border:none;padding:0.097cm;"
|| Tarkwa
| align=center style="color:#008000;" | -1%
| align=center style="color:#008000;" | 6%
| align=center style="color:#808000;" | 11%
| align=center style="color:#800000;" | 125%
|- style="border:none;padding:0.097cm;"
|| Degrussa
| align=center| ESAG: 28%
Etotal: 17%
| align=center| ESAG: 4%
Etotal: 2%
| align=center| ESAG: 7%
Etotal: 15%
| align=center| ESAG: 13%
|- style="border:none;padding:0.097cm;"
|| Yanacocha
| align=center style="color:#808000;" | -18%
| align=center style="color:#800000;" | -33%
| align=center style="color:#800000;" | -25%
| align=center style="color:#800000;" | -40%
|-
|}

==Benchmarking: Private surveys==

Private surveys that do not include details, but the difference between plant performance and model predictions are provided below:

* Project 0082, using Optimized Bond-Barratt model.
# SAB survey: Etotal: actual = 6.72 kWh/t, predicted = 6.78 kWh/t, difference 0.9%
# ABC survey: Etotal: actual = 7.75 kWh/t, predicted = 8.14 kWh/t, difference 4.8%

* Project 0104, SABC-A survey
# Optimized Bond-Barratt model : Etotal: actual = 20.8 kWh/t, predicted = 20.7 kWh/t, difference 0.0%
# Morrell Mi (SMC) model : Etotal: actual = 20.8 kWh/t, predicted = 20.2 kWh/t, difference 2.9%

* Project 0149, SAB survey (BC Cu porphyry, without Josefin correction)
# Optimized Bond-Barratt model : Etotal: actual = 6.42 kWh/t, predicted = 7.04 kWh/t, difference 9.7%
# Morrell Mi (SMC) model : Etotal: actual = 6.42 kWh/t, predicted = 7.27 kWh/t, difference 13.2%

* Project 0203, SAB (Andean porphyry, all kWh/t at mill shell)
# SAB survey: Etotal = 11.3 kWh/t, ESAG = 4.8 kWh/t, Eball = 6.5 kWh/t, WiO = 16.1
# Optimized Bond/Barratt model: Etotal = 10.2 kWh/t (-11%), ESAG = 4.1 kWh/t (-17%), Eball = 6.1 kWh/t (-6.7%), WiO = 14.9 (-7.5%)
# Morrell Mi model: Etotal = 12.0 kWh/t (+5.6%), ESAG = 4.8 kWh/t (-0.5%), Eball = 6.5 kWh/t (+9.7%), WiO = 17.5 (+8.7%)

Testwork: Bond rod mill work index

2026-02-06T11:54:45Z

Alex Doll: /* Laboratory Apparatus */

[[category:Testwork]]
[[category:Bond work index]]
==Testwork: Bond Rod Mill Work Index==
{{Test|name=Bond Rod Mill Work Index|Abrev=WiRM|Alt=RWI|F80=11 000 µm|P80=900 µm|Models=Bond models}}

The test is a 'locked-cycle' test where ground product is removed from test cycles and replaced by fresh feed. The test must achieve a steady-state before completion. The Bond rod mill work index is not as common as the [[Testwork: Bond ball mill work index|Bond ball mill work index]], but the laboratory procedures are quite similar.

Warning: There are two different variations on the mill apparatus. The SAGMILLING.COM models expect a mill with a "wave liner", and is not compatible with mills using "smooth liners". Most laboratories outside of Australia use the wave liner style of machine – these results can safely be used in the models. Bond rod mill work index results from Australian laboratories with smooth liners should not be used in the SAGMILLING.COM models without corrections, see the ''apparatus'' section, below.

===Sample Requirements===

The test requires about 15 kg of material. Although it can work on feed as fine as 10 mm, it is best to send material to the testing laboratory that is nominally at least 25 mm (including the natural fines that are part of the sample). The laboratories have a standard way of reducing the coarse material to the (roughly) 10 mm size used to feed the test that will not introduce excessive fines.

===Test Inputs===

When WiRM is used to size SAG mills, the Bond/Barratt model assumes a 14# Tyler (1180 µm) closing mesh size — the engineer should specify this closing mesh size to the laboratory performing the tests. When used to size rod mills, the engineer should specify the target product size for the industrial plant (the laboratory will choose an appropriate closing screen mesh size to achieve that product size).

===Test Outputs===

The laboratory will report the following information:
* umclosing: The aperture size on the screen used to close the test, µm. (or the P100 size)
* F80: Sample feed size in µm (and usually will provide a particle size distribution)
* P80: Sample finished product size in µm (and usually will provide a particle size distribution)
* gpr: The average grams per revolution of the last three cycles (sometimes is labelled ''GPB'')
* WiRM: The calculated work index (SAGMILLING.COM uses only metric units; if the laboratory reported work index in "short ton" units, multiply that value by 1.1023 and enter the result).

Extra field available for modelling
* synthetic indicates whether this is a real test result, or just a synthetic one that should only be used for modelling. If this column contains a value of '1' (boolean=true) for a test, then that test is understood to not be a real test result and is therefore not shown on the testwork comparison charts. Synthetic values are available when running circuit model simulations and do show up in the list of model results.

<math> Wi_{RM} = \frac{1.1023 \times 62}{P_{100}^{0.23} \times gpr^{0.625} \times (\frac{10}{\sqrt{P_{80}}} - \frac{10}{\sqrt{F_{80}}})}</math>

=== Laboratory Apparatus ===
Rod mill work index results are only valid if the laboratory apparatus has the following features:
* a wave liner
* the mill is rocked 5° backward and forward every 10 revolutions

Several laboratories (mostly in Australia) do not have the proper apparatus and their "rod mill work index" results will be incompatible with a "Bond rod mill work index".

A Non-standard rod mill result can be converted to a Bond rod mill work index by:

Bond WiRM = 0.565 × (Winonstandard)1.12

Source: Dec 2025 Public Grindability Database

[[File:ExampleDB-WiRMvAxb-comparison.png|600px|Published A×b and WiRM results]]

=== Modelling ===
Rod mill work index is used in the SAGMILLING.COM [[Model:BondModel|Bond/Barratt specific energy consumption model]].

The work index is used to calculate the energy requirement to grind rocks in the medium size range, from 10 mm - 20 mm down to about 2 mm.

Conversions between test types

2026-02-06T11:54:35Z

Alex Doll: /* Medium size class */

[[category:testwork]]
==Converting between comminution test types==
Different tests are used in different grindability models for substantially the same purposes. Certain grindability tests are compatible with other tests, and an approximate conversion can be established by comparing to a database of testwork.

The determination of which tests are compatible with other tests is largely a function of the particle size of the specimens subjected to testing.[[Bibliography:_Testwork_programs|Doll & Barratt, 2011]] Ore properties also play a role because some tests are sensitive to changes in ore density and other tests operate with a biased sample consisting only of competent pieces.

===Medium size class===
The three tests in the medium size class are:
* Bond rod mill work index (WiRM)
* SAG Grindability index (SGI) or SAG Power index (SPI™)
* Drop weight test, both JK and SMC (A×b, DWI, Mia, etc)

{|
|-
| '''Bond rod mill work index versus A×b''' Only considering rod mill work index tests performed in laboratory mills equipped with wave liners. This is the standard specified by F. Bond and is typical of laboratories in North and South America. Non-standard (Australian type) rod mill results also shown for comparison.

A Non-standard rod mill result can be converted to a Bond rod mill work index by:

Bond WiRM = 0.565 × (Winonstandard)1.12

Source: Dec 2025 Public Grindability Database

|| [[File:ExampleDB-WiRMvAxb-comparison.png|500px]]
|-
| '''A×b versus Bond rod mill Wi''' The regression above is not reversible, it is better to re-run the regression swapping the axes to generate a synthetic A×b value from a rod mill work index.
|| [[File:A×b_v_WiRM2.png|500px|Published A×b and WiRM results]]
|-
| '''Bond rod mill work index versus SGI & SPI''' Only considering rod mill work index tests performed in laboratory mills equipped with wave liners. SGI does not contain a density correction, and this relationship is probably only valid for ore density in the range of 2.50 to 2.80 t/m3 Only considers SGI values less than 150 as greater values are meaningless.
|| [[File:ExampleDB-WiRMvSGI-comparison.png]]
|-
| '''Bond rod mill work index versus SGI & SPI''' Only considering rod mill work index tests performed in laboratory mills equipped with wave liners. SGI does not contain a density correction, and this relationship is probably only valid for ore density in the range of 2.50 to 2.80 t/m3 Only considers SGI values less than 150 as greater values are meaningless.
|| [[File:ExampleDB-WiRMvSGI-comparison.png]]
|-
| '''SGI & SPI''' versus '''A×b''' Only considering SGI values below 150 minutes. SGI does not contain a density correction, and this relationship is probably only valid for ore density in the range of 2.50 to 2.80 t/m3
|| [[File:SGI vs A×b.png]]
|}

===Extra parameters for Drop Weight Tests (DWT)===
A drop weight test is usually interpreted using a plot of the %passing 10% of the original particle size (t10) versus the energy of the weight that impacted the specimen (Ecs). These are plotted at fit to an exponential relationship with fitting parameters "A" (coefficient) and "b" (exponent).

There are several derived parameters that are commonly used in modelling that can be calculated using these A and b values, usually based on the slope of the curve at the origin of the plot. This is commonly referred to as the (A×b) value.

* DWI = 100 × (density, kg/L) / (A×b)
* Mia = 379.40 × (A×b)-0.80
* Mih = 577.37 × (A×b)-1.00
* Mic = 296.81 × (A×b)-1.00
[[File:DWI_Axb.png]]

[[File:Mia_Axb.png]]

[[File:Mih_Axb.png]]

[[File:Mic_Axb.png]]

Conversions between test types

2026-02-06T11:54:11Z

Alex Doll: /* Medium size class */

[[category:testwork]]
==Converting between comminution test types==
Different tests are used in different grindability models for substantially the same purposes. Certain grindability tests are compatible with other tests, and an approximate conversion can be established by comparing to a database of testwork.

The determination of which tests are compatible with other tests is largely a function of the particle size of the specimens subjected to testing.[[Bibliography:_Testwork_programs|Doll & Barratt, 2011]] Ore properties also play a role because some tests are sensitive to changes in ore density and other tests operate with a biased sample consisting only of competent pieces.

===Medium size class===
The three tests in the medium size class are:
* Bond rod mill work index (WiRM)
* SAG Grindability index (SGI) or SAG Power index (SPI™)
* Drop weight test, both JK and SMC (A×b, DWI, Mia, etc)

{|
|-
| '''Bond rod mill work index versus A×b''' Only considering rod mill work index tests performed in laboratory mills equipped with wave liners. This is the standard specified by F. Bond and is typical of laboratories in North and South America. Non-standard (Australian type) rod mill results also shown for comparison.

A Non-standard rod mill result can be converted to a Bond rod mill work index by:

Bond WiRM = 0.565 × (Winonstandard)^1.12

Source: Dec 2025 Public Grindability Database

|| [[File:ExampleDB-WiRMvAxb-comparison.png|500px]]
|-
| '''A×b versus Bond rod mill Wi''' The regression above is not reversible, it is better to re-run the regression swapping the axes to generate a synthetic A×b value from a rod mill work index.
|| [[File:A×b_v_WiRM2.png|500px|Published A×b and WiRM results]]
|-
| '''Bond rod mill work index versus SGI & SPI''' Only considering rod mill work index tests performed in laboratory mills equipped with wave liners. SGI does not contain a density correction, and this relationship is probably only valid for ore density in the range of 2.50 to 2.80 t/m3 Only considers SGI values less than 150 as greater values are meaningless.
|| [[File:ExampleDB-WiRMvSGI-comparison.png]]
|-
| '''Bond rod mill work index versus SGI & SPI''' Only considering rod mill work index tests performed in laboratory mills equipped with wave liners. SGI does not contain a density correction, and this relationship is probably only valid for ore density in the range of 2.50 to 2.80 t/m3 Only considers SGI values less than 150 as greater values are meaningless.
|| [[File:ExampleDB-WiRMvSGI-comparison.png]]
|-
| '''SGI & SPI''' versus '''A×b''' Only considering SGI values below 150 minutes. SGI does not contain a density correction, and this relationship is probably only valid for ore density in the range of 2.50 to 2.80 t/m3
|| [[File:SGI vs A×b.png]]
|}

===Extra parameters for Drop Weight Tests (DWT)===
A drop weight test is usually interpreted using a plot of the %passing 10% of the original particle size (t10) versus the energy of the weight that impacted the specimen (Ecs). These are plotted at fit to an exponential relationship with fitting parameters "A" (coefficient) and "b" (exponent).

There are several derived parameters that are commonly used in modelling that can be calculated using these A and b values, usually based on the slope of the curve at the origin of the plot. This is commonly referred to as the (A×b) value.

* DWI = 100 × (density, kg/L) / (A×b)
* Mia = 379.40 × (A×b)-0.80
* Mih = 577.37 × (A×b)-1.00
* Mic = 296.81 × (A×b)-1.00
[[File:DWI_Axb.png]]

[[File:Mia_Axb.png]]

[[File:Mih_Axb.png]]

[[File:Mic_Axb.png]]

Testwork: Bond rod mill work index

2026-02-06T11:53:52Z

Alex Doll: /* Laboratory Apparatus */

[[category:Testwork]]
[[category:Bond work index]]
==Testwork: Bond Rod Mill Work Index==
{{Test|name=Bond Rod Mill Work Index|Abrev=WiRM|Alt=RWI|F80=11 000 µm|P80=900 µm|Models=Bond models}}

The test is a 'locked-cycle' test where ground product is removed from test cycles and replaced by fresh feed. The test must achieve a steady-state before completion. The Bond rod mill work index is not as common as the [[Testwork: Bond ball mill work index|Bond ball mill work index]], but the laboratory procedures are quite similar.

Warning: There are two different variations on the mill apparatus. The SAGMILLING.COM models expect a mill with a "wave liner", and is not compatible with mills using "smooth liners". Most laboratories outside of Australia use the wave liner style of machine – these results can safely be used in the models. Bond rod mill work index results from Australian laboratories with smooth liners should not be used in the SAGMILLING.COM models without corrections, see the ''apparatus'' section, below.

===Sample Requirements===

The test requires about 15 kg of material. Although it can work on feed as fine as 10 mm, it is best to send material to the testing laboratory that is nominally at least 25 mm (including the natural fines that are part of the sample). The laboratories have a standard way of reducing the coarse material to the (roughly) 10 mm size used to feed the test that will not introduce excessive fines.

===Test Inputs===

When WiRM is used to size SAG mills, the Bond/Barratt model assumes a 14# Tyler (1180 µm) closing mesh size — the engineer should specify this closing mesh size to the laboratory performing the tests. When used to size rod mills, the engineer should specify the target product size for the industrial plant (the laboratory will choose an appropriate closing screen mesh size to achieve that product size).

===Test Outputs===

The laboratory will report the following information:
* umclosing: The aperture size on the screen used to close the test, µm. (or the P100 size)
* F80: Sample feed size in µm (and usually will provide a particle size distribution)
* P80: Sample finished product size in µm (and usually will provide a particle size distribution)
* gpr: The average grams per revolution of the last three cycles (sometimes is labelled ''GPB'')
* WiRM: The calculated work index (SAGMILLING.COM uses only metric units; if the laboratory reported work index in "short ton" units, multiply that value by 1.1023 and enter the result).

Extra field available for modelling
* synthetic indicates whether this is a real test result, or just a synthetic one that should only be used for modelling. If this column contains a value of '1' (boolean=true) for a test, then that test is understood to not be a real test result and is therefore not shown on the testwork comparison charts. Synthetic values are available when running circuit model simulations and do show up in the list of model results.

<math> Wi_{RM} = \frac{1.1023 \times 62}{P_{100}^{0.23} \times gpr^{0.625} \times (\frac{10}{\sqrt{P_{80}}} - \frac{10}{\sqrt{F_{80}}})}</math>

=== Laboratory Apparatus ===
Rod mill work index results are only valid if the laboratory apparatus has the following features:
* a wave liner
* the mill is rocked 5° backward and forward every 10 revolutions

Several laboratories (mostly in Australia) do not have the proper apparatus and their "rod mill work index" results will be incompatible with a "Bond rod mill work index".

A Non-standard rod mill result can be converted to a Bond rod mill work index by:

Bond WiRM = 0.565 × (Winonstandard)^1.12

Source: Dec 2025 Public Grindability Database

[[File:ExampleDB-WiRMvAxb-comparison.png|600px|Published A×b and WiRM results]]

=== Modelling ===
Rod mill work index is used in the SAGMILLING.COM [[Model:BondModel|Bond/Barratt specific energy consumption model]].

The work index is used to calculate the energy requirement to grind rocks in the medium size range, from 10 mm - 20 mm down to about 2 mm.

Testwork: Bond rod mill work index

2026-02-06T11:34:33Z

Alex Doll: /* Laboratory Apparatus */

[[category:Testwork]]
[[category:Bond work index]]
==Testwork: Bond Rod Mill Work Index==
{{Test|name=Bond Rod Mill Work Index|Abrev=WiRM|Alt=RWI|F80=11 000 µm|P80=900 µm|Models=Bond models}}

The test is a 'locked-cycle' test where ground product is removed from test cycles and replaced by fresh feed. The test must achieve a steady-state before completion. The Bond rod mill work index is not as common as the [[Testwork: Bond ball mill work index|Bond ball mill work index]], but the laboratory procedures are quite similar.

Warning: There are two different variations on the mill apparatus. The SAGMILLING.COM models expect a mill with a "wave liner", and is not compatible with mills using "smooth liners". Most laboratories outside of Australia use the wave liner style of machine – these results can safely be used in the models. Bond rod mill work index results from Australian laboratories with smooth liners should not be used in the SAGMILLING.COM models without corrections, see the ''apparatus'' section, below.

===Sample Requirements===

The test requires about 15 kg of material. Although it can work on feed as fine as 10 mm, it is best to send material to the testing laboratory that is nominally at least 25 mm (including the natural fines that are part of the sample). The laboratories have a standard way of reducing the coarse material to the (roughly) 10 mm size used to feed the test that will not introduce excessive fines.

===Test Inputs===

When WiRM is used to size SAG mills, the Bond/Barratt model assumes a 14# Tyler (1180 µm) closing mesh size — the engineer should specify this closing mesh size to the laboratory performing the tests. When used to size rod mills, the engineer should specify the target product size for the industrial plant (the laboratory will choose an appropriate closing screen mesh size to achieve that product size).

===Test Outputs===

The laboratory will report the following information:
* umclosing: The aperture size on the screen used to close the test, µm. (or the P100 size)
* F80: Sample feed size in µm (and usually will provide a particle size distribution)
* P80: Sample finished product size in µm (and usually will provide a particle size distribution)
* gpr: The average grams per revolution of the last three cycles (sometimes is labelled ''GPB'')
* WiRM: The calculated work index (SAGMILLING.COM uses only metric units; if the laboratory reported work index in "short ton" units, multiply that value by 1.1023 and enter the result).

Extra field available for modelling
* synthetic indicates whether this is a real test result, or just a synthetic one that should only be used for modelling. If this column contains a value of '1' (boolean=true) for a test, then that test is understood to not be a real test result and is therefore not shown on the testwork comparison charts. Synthetic values are available when running circuit model simulations and do show up in the list of model results.

<math> Wi_{RM} = \frac{1.1023 \times 62}{P_{100}^{0.23} \times gpr^{0.625} \times (\frac{10}{\sqrt{P_{80}}} - \frac{10}{\sqrt{F_{80}}})}</math>

=== Laboratory Apparatus ===
Rod mill work index results are only valid if the laboratory apparatus has the following features:
* a wave liner
* the mill is rocked 5° backward and forward every 10 revolutions

Several laboratories (mostly in Australia) do not have the proper apparatus and their "rod mill work index" results will be incompatible with a "Bond rod mill work index".

A Non-standard rod mill result can be converted to a Bond rod mill work index by:

Bond WiRM = 0.42 × (Winonstandard)^1.22

Source: Dec 2023 Public Grindability Database

[[File:ExampleDB-WiRMvAxb-comparison.png|600px|Published A×b and WiRM results]]

=== Modelling ===
Rod mill work index is used in the SAGMILLING.COM [[Model:BondModel|Bond/Barratt specific energy consumption model]].

The work index is used to calculate the energy requirement to grind rocks in the medium size range, from 10 mm - 20 mm down to about 2 mm.

Benchmarking: Morrell Mih - Tropicana

2026-01-30T11:32:00Z

Alex Doll: /* Modelling */

[[category: Benchmarking]]
[[category: HPGR]]
[[category: Bibliography]]
==Benchmarking: Morrell SMC and ball mill model - Tropicana HPGR circuit==

===Sources, SAG 2015 conference===
''Koch, F., Siddall, L., Lovatt, I., Giddy, M. and DiTrento, M.'' '''RAPID RAMP-UP OF THE TROPICANA HPGR CIRCUIT''', SAG 2015 paper number 70.

''Gardula, A., Das, D., DiTrento, M. and Joubert, S.'' '''FIRST YEAR OF OPERATION OF HPGR AT TROPICANA GOLD MINE – CASE STUDY''', SAG 2015 paper number 69

* Primary crusher product (model F80) approximately 150 mm
* Secondary crushing circuit 1 × XL900 crusher
* Tertiary crushing circuit 1 × 2.0 m by 1.85 m HPGR, with two 2.2 MW drives
* Fine screen aperture 4 mm, 57% passing 3 mm.
* Ball mill 24 ft diam by 43 ft long with twin-pinion 7 MW SER v/s drives

Average Primary Ore sample tested at ALS Ammtec gave following determinations:
* UCS 76.7 MPa
* WiC 16.1 (metric)
* WiRM 19.4 (metric, but based on non-standard liner geometry)
* WiBM 17.6 (metric)
* JKDWT: A×b 36.1, ta 0.40
* SMC test™ A×b 41.4, DWi 7.21
* Bond Ai 0.291

Plant design criteria:
* primary crusher product (circuit F80) = 150 mm
* hydrocyclone overflow (circuit P80) = 75 mm
* ball mill using WRIM with Slip Energy Recovery and gearbox, assume 0.95 × 0.97 efficiency = 0.9215 conversion DCS power to shell.

Plant DCS data Jan 2014 to Mar 2015:
* secondary crusher specific energy consumption 0.4 kWh/t
** assume product size 35 mm
** power draw back-calculates to 763 t/h × 0.4 = 305 kW (45% of available power)
* ball mill throughput 734 t/h (use this as overall throughput at 91.2% availability)
* HPGR specific energy consumption, EHPGR = 2.60 kWh/t
** power draw back-calculates to 763 t/h × 2.60 = 1984 kW (45% of available power)
* energy associated to auxiliary equipment in sec crushing & HPGR = 0.70 + 1.08 = 1.78 kWh/t
* HPGR circuit product size assumed (T80) 3.5 mm
* ball mill drawing about 14 MW (assumed DCS, works out to 13.0 MW at mill shell)
* Eball = 16.77 kWh/t at shell (18.2 kWh/t at DCS)

==Modelling==
Use the '''Morrell SMC HPGR and ball mill''' circuit model with the '''HPGR-BM''' flowsheet. The relationship between a drop weight test A×b and the Mia, Mic and Mih factors (fitted to Doll, 2016 published information) is:
* Mia = 390.89× (A×b)-0.81
* Mih = 577.0 × (A×b)-1.00
* Mic = 303.48 × (A×b)-1.00

[[File:Benchmarking-Tropicana-Mih.png|thumb|alt=Screenshot showing model output screen|Model screenshot]]

Using the average A×b = 38.75 for the Primary-Average ore type gives '''Mia = 20.21 kWh/t, Mic = 7.75 kWh/t''' and '''Mih = 14.89 kWh/t'''.
(using an arithmetic average of A×b values is not recommended generally, but won't make a difference to the precision of this survey data).

Convert the ball mill work index to an Mib value of 25.39 kWh/t by assuming the test conditions suitable for a Wi of 17.6 metric units:
* BM test F80: 2300 µm
* BM test P80: 75 µm (assume same as the circuit design)
* BM test grams per revolution: 1.01 (calculated based on above)

The model predictions are:
* Secondary crushing, '''EsecCr''' = 0.63 × MiEquation(Mic = 7.75, F80 = 35000 µm, P80 = 3500 µm) × 1.0 = '''0.52 kWh/t'''
* HPGR, '''Ehpgr''' = 0.84 × MiEquation(Mih = 14.89, F80 = 35000 µm, P80 = 6000 µm) × 1.0 = '''2.81 kWh/t'''
* Ball mill, '''Eball''' = MiEquation(20.21, 750.0, 3500.0) × 1.000 + MiEquation(25.390, 75.0, 750.0) = '''18.41 kWh/t'''

'''Ball mill model:'''
* Use the '''Nordberg wet overflow ball mill''' model
* Quantity 1
* Mill dimensions, diameter 24 ft, EGL 43 ft
* motor mechanical efficiency 0.97; motor efficiency to DCS 0.95
* motor power, 7000 kW, twin-pinion drives
* Assume 6 inch liner thickness, 7.80 t/m3 ball density.
* Assume speed is 75% of critical and load is 32% v/v

'''Secondary crusher model:'''
* Quantity 1.
* XL900 crushers, use 900 HP motor.
* set mechanical efficiency to 0.6 so that sec crushing isn't limiting the throughput (would be 0.45 to match plant kW draw).

'''HPGR model:'''
* Quantity 1.
* HPGR motor 4400 kW (actually 2 × 2200 kW).
* set mechanical efficiency to 0.50 to avoid limiting the throughput (would be 0.45 to match plant kW draw).

'''Morrell SMC HPGR and Ball Mill Circuit model:'''
* Set the crusher product size to 35 000 µm and the transfer size to 3500 µm.
* Circuit feed size 150 000 µm and product size 75 µm
* (optional) Set the conveyor lift height to 30 m
* Result is 745 t/h circuit throughput with Etotal of 20.5 kWh/t (excluding auxiliary equipment)
* Predicts 6% increase in ball mill operating work index (18.7) versus laboratory Wi (17.5).

==Discussion==

The comparison of predicted specific energy consumption versus actual observed in the surveys is given below:

{| class="wikitable"
|-
! !! Model Prediction !! Survey Actual !! Difference
|-
| EsecCr || 0.52 kWh/t || 0.40 kWh/t || model 30% high
|-
| Ehpgr || 2.81 kWh/t || 2.60 kWh/t || model 8% high
|-
| Eball || 18.41 kWh/t || 16.77 kWh/t || model 10% high
|-
| Etotal || 21.74 kWh/t || 19.77 kWh/t || model 10% high
|}

The Morrell model results using SMC and ball mill laboratory tests is about 10% conservative versus the survey results. This is not a bad result considering the variation in laboratory result (A×b) observed and how neither the SMC test nor the ball mill test were originally created to deal with HPGR technology.

The throughput determined by the ball mill treatment rate is 708 t/h, versus observed 734 t/h (model is 4% conservative, an excellent prediction).

===Microcracking/phantom cyclone/ball mill performance===
The predicted 6% increase in WiO fits nicely with the observation at Tropicana that "The range over five field tests was 0% to 8% higher power consumption when compared to the theoretical prediction."

Conversions between test types

2026-01-09T13:06:27Z

Alex Doll: /* Medium size class */

[[category:testwork]]
==Converting between comminution test types==
Different tests are used in different grindability models for substantially the same purposes. Certain grindability tests are compatible with other tests, and an approximate conversion can be established by comparing to a database of testwork.

The determination of which tests are compatible with other tests is largely a function of the particle size of the specimens subjected to testing.[[Bibliography:_Testwork_programs|Doll & Barratt, 2011]] Ore properties also play a role because some tests are sensitive to changes in ore density and other tests operate with a biased sample consisting only of competent pieces.

===Medium size class===
The three tests in the medium size class are:
* Bond rod mill work index (WiRM)
* SAG Grindability index (SGI) or SAG Power index (SPI™)
* Drop weight test, both JK and SMC (A×b, DWI, Mia, etc)

{|
|-
| '''Bond rod mill work index versus A×b''' Only considering rod mill work index tests performed in laboratory mills equipped with wave liners. This is the standard specified by F. Bond and is typical of laboratories in North and South America. Non-standard (Australian type) rod mill results also shown for comparison.

A Non-standard rod mill result can be converted to a Bond rod mill work index by:

Bond WiRM = 0.903 × (Winonstandard)0.902

Source: Dec 2025 Public Grindability Database

|| [[File:ExampleDB-WiRMvAxb-comparison.png|500px]]
|-
| '''A×b versus Bond rod mill Wi''' The regression above is not reversible, it is better to re-run the regression swapping the axes to generate a synthetic A×b value from a rod mill work index.
|| [[File:A×b_v_WiRM2.png|500px|Published A×b and WiRM results]]
|-
| '''Bond rod mill work index versus SGI & SPI''' Only considering rod mill work index tests performed in laboratory mills equipped with wave liners. SGI does not contain a density correction, and this relationship is probably only valid for ore density in the range of 2.50 to 2.80 t/m3 Only considers SGI values less than 150 as greater values are meaningless.
|| [[File:ExampleDB-WiRMvSGI-comparison.png]]
|-
| '''Bond rod mill work index versus SGI & SPI''' Only considering rod mill work index tests performed in laboratory mills equipped with wave liners. SGI does not contain a density correction, and this relationship is probably only valid for ore density in the range of 2.50 to 2.80 t/m3 Only considers SGI values less than 150 as greater values are meaningless.
|| [[File:ExampleDB-WiRMvSGI-comparison.png]]
|-
| '''SGI & SPI''' versus '''A×b''' Only considering SGI values below 150 minutes. SGI does not contain a density correction, and this relationship is probably only valid for ore density in the range of 2.50 to 2.80 t/m3
|| [[File:SGI vs A×b.png]]
|}

===Extra parameters for Drop Weight Tests (DWT)===
A drop weight test is usually interpreted using a plot of the %passing 10% of the original particle size (t10) versus the energy of the weight that impacted the specimen (Ecs). These are plotted at fit to an exponential relationship with fitting parameters "A" (coefficient) and "b" (exponent).

There are several derived parameters that are commonly used in modelling that can be calculated using these A and b values, usually based on the slope of the curve at the origin of the plot. This is commonly referred to as the (A×b) value.

* DWI = 100 × (density, kg/L) / (A×b)
* Mia = 379.40 × (A×b)-0.80
* Mih = 577.37 × (A×b)-1.00
* Mic = 296.81 × (A×b)-1.00
[[File:DWI_Axb.png]]

[[File:Mia_Axb.png]]

[[File:Mih_Axb.png]]

[[File:Mic_Axb.png]]

File:A×b v WiRM2.png

2026-01-09T13:04:51Z

Alex Doll: 2025 version of the Public Grindabilty Database

== Summary ==
2025 version of the Public Grindabilty Database

Conversions between test types

2026-01-09T13:04:22Z

Alex Doll: /* Medium size class */

[[category:testwork]]
==Converting between comminution test types==
Different tests are used in different grindability models for substantially the same purposes. Certain grindability tests are compatible with other tests, and an approximate conversion can be established by comparing to a database of testwork.

The determination of which tests are compatible with other tests is largely a function of the particle size of the specimens subjected to testing.[[Bibliography:_Testwork_programs|Doll & Barratt, 2011]] Ore properties also play a role because some tests are sensitive to changes in ore density and other tests operate with a biased sample consisting only of competent pieces.

===Medium size class===
The three tests in the medium size class are:
* Bond rod mill work index (WiRM)
* SAG Grindability index (SGI) or SAG Power index (SPI™)
* Drop weight test, both JK and SMC (A×b, DWI, Mia, etc)

{|
|-
| '''Bond rod mill work index versus A×b''' Only considering rod mill work index tests performed in laboratory mills equipped with wave liners. This is the standard specified by F. Bond and is typical of laboratories in North and South America. Non-standard (Australian type) rod mill results also shown for comparison.

A Non-standard rod mill result can be converted to a Bond rod mill work index by:

Bond WiRM = 0.903 × (Winonstandard)0.902

Source: Dec 2025 Public Grindability Database

|| [[File:ExampleDB-WiRMvAxb-comparison.png|500px]]
|-
| '''A×b versus Bond rod mill Wi''' The regression above is not reversible, it is better to re-run the regression swapping the axes to generate a synthetic A×b value from a rod mill work index.
|| [[File:A×b_v_WiRM2.png|Published A×b and WiRM results]]
|-
| '''Bond rod mill work index versus SGI & SPI''' Only considering rod mill work index tests performed in laboratory mills equipped with wave liners. SGI does not contain a density correction, and this relationship is probably only valid for ore density in the range of 2.50 to 2.80 t/m3 Only considers SGI values less than 150 as greater values are meaningless.
|| [[File:ExampleDB-WiRMvSGI-comparison.png]]
|-
| '''Bond rod mill work index versus SGI & SPI''' Only considering rod mill work index tests performed in laboratory mills equipped with wave liners. SGI does not contain a density correction, and this relationship is probably only valid for ore density in the range of 2.50 to 2.80 t/m3 Only considers SGI values less than 150 as greater values are meaningless.
|| [[File:ExampleDB-WiRMvSGI-comparison.png]]
|-
| '''SGI & SPI''' versus '''A×b''' Only considering SGI values below 150 minutes. SGI does not contain a density correction, and this relationship is probably only valid for ore density in the range of 2.50 to 2.80 t/m3
|| [[File:SGI vs A×b.png]]
|}

===Extra parameters for Drop Weight Tests (DWT)===
A drop weight test is usually interpreted using a plot of the %passing 10% of the original particle size (t10) versus the energy of the weight that impacted the specimen (Ecs). These are plotted at fit to an exponential relationship with fitting parameters "A" (coefficient) and "b" (exponent).

There are several derived parameters that are commonly used in modelling that can be calculated using these A and b values, usually based on the slope of the curve at the origin of the plot. This is commonly referred to as the (A×b) value.

* DWI = 100 × (density, kg/L) / (A×b)
* Mia = 379.40 × (A×b)-0.80
* Mih = 577.37 × (A×b)-1.00
* Mic = 296.81 × (A×b)-1.00
[[File:DWI_Axb.png]]

[[File:Mia_Axb.png]]

[[File:Mih_Axb.png]]

[[File:Mic_Axb.png]]

Conversions between test types

2026-01-09T12:59:08Z

Alex Doll: /* Medium size class */

[[category:testwork]]
==Converting between comminution test types==
Different tests are used in different grindability models for substantially the same purposes. Certain grindability tests are compatible with other tests, and an approximate conversion can be established by comparing to a database of testwork.

The determination of which tests are compatible with other tests is largely a function of the particle size of the specimens subjected to testing.[[Bibliography:_Testwork_programs|Doll & Barratt, 2011]] Ore properties also play a role because some tests are sensitive to changes in ore density and other tests operate with a biased sample consisting only of competent pieces.

===Medium size class===
The three tests in the medium size class are:
* Bond rod mill work index (WiRM)
* SAG Grindability index (SGI) or SAG Power index (SPI™)
* Drop weight test, both JK and SMC (A×b, DWI, Mia, etc)

{|
|-
| '''Bond rod mill work index versus A×b''' Only considering rod mill work index tests performed in laboratory mills equipped with wave liners. This is the standard specified by F. Bond and is typical of laboratories in North and South America. Non-standard (Australian type) rod mill results also shown for comparison.

A Non-standard rod mill result can be converted to a Bond rod mill work index by:

Bond WiRM = 0.903 × (Winonstandard)0.902

Source: Dec 2025 Public Grindability Database

|| [[File:ExampleDB-WiRMvAxb-comparison.png|500px]]
|-
| '''Bond rod mill Wi versus A×b for copper porphyries''' A slightly better relationship can be determined if the database is limited to projects of a similar lithology. Limiting to only the Andean copper porphyry projects results in a slightly better correlation.
|| [[File:Twcompare_axb_vs_wirm.svg‎|Published A×b and WiRM results for Andean porphyries]]
|-
| '''Bond rod mill work index versus SGI & SPI''' Only considering rod mill work index tests performed in laboratory mills equipped with wave liners. SGI does not contain a density correction, and this relationship is probably only valid for ore density in the range of 2.50 to 2.80 t/m3 Only considers SGI values less than 150 as greater values are meaningless.
|| [[File:ExampleDB-WiRMvSGI-comparison.png]]
|-
| '''SGI & SPI''' versus '''A×b''' Only considering SGI values below 150 minutes. SGI does not contain a density correction, and this relationship is probably only valid for ore density in the range of 2.50 to 2.80 t/m3
|| [[File:SGI vs A×b.png]]
|}

===Extra parameters for Drop Weight Tests (DWT)===
A drop weight test is usually interpreted using a plot of the %passing 10% of the original particle size (t10) versus the energy of the weight that impacted the specimen (Ecs). These are plotted at fit to an exponential relationship with fitting parameters "A" (coefficient) and "b" (exponent).

There are several derived parameters that are commonly used in modelling that can be calculated using these A and b values, usually based on the slope of the curve at the origin of the plot. This is commonly referred to as the (A×b) value.

* DWI = 100 × (density, kg/L) / (A×b)
* Mia = 379.40 × (A×b)-0.80
* Mih = 577.37 × (A×b)-1.00
* Mic = 296.81 × (A×b)-1.00
[[File:DWI_Axb.png]]

[[File:Mia_Axb.png]]

[[File:Mih_Axb.png]]

[[File:Mic_Axb.png]]

File:ExampleDB-WiRMvAxb-comparison.png

2026-01-09T12:35:05Z

Alex Doll: Alex Doll uploaded a new version of File:ExampleDB-WiRMvAxb-comparison.png

Comparison of rod mill work index (only laboratories using wave liners) to the A×b values of both JK DWT and SMC tests.

Work Index

2025-10-08T13:27:09Z

Alex Doll: /* Bond Work Index */

[[category:Testwork]]
[[category:Work Index]]
==Bond Work Index==
The Bond Work Index is an empirical calibration of comminution equipment specific energy consumption at different size classes. Three types of work index are ore hardness laboratory tests that can be used to design industrial grinding equipment.

There are five types of Work Index, per the following subsections.

===Ball mill work index===
This is a laboratory measurement used to determine the ore grindability in the particle size range typically encountered by ball mills.
[[Testwork:_Bond_ball_mill_work_index]]

===Rod mill work index===
This is a laboratory measurement used to determine the ore grindability in the particle size range typically encountered by rod mills, which were common grinding equipment in the mid twentieth century.
[[Testwork:_Bond_rod_mill_work_index]]

===Crushing work index===
Also called the '''Low Energy Impact Test''' (LEIT), this is a laboratory measurement used to determine the ore crusability in the particle size range typically encountered by cone crushers.
[[Testwork:_Bond_crushing_work_index]]

===Operating work index===
This is a generic work index measured on an arbitrary piece of comminution equipment. Computing the operating work index requires the following measurements for the equipment:
* the fresh feed rate in dry tonnes per hour (excluding any circulating load), '''t/h'''
* the mechanical power consumed by the equipment at the equipment input (kW at the mill shell or pinion), '''kW'''
* the fresh feed 80% passing size in µm, F80
* the classified product 80% passing size in µm, P80

The Operating Work Index (WiO) is calculated as follows:

<math>Wi_{O} = \frac{kW / (t/h)}{10 \times \left(P_{80}^{-0.5} - F_{80}^{-0.5} \right)}</math>

===Work Index (generic)===
The most generic definition of Work Index is that it is one-tenth of the coefficient of the special case of the [[Bibliography:_Specific_energy_consumption_models|Hukki Conjecture ]] where the exponent is fixed at –½. The Hukki Conjecture is a continuum of grindability models that link the Work Index to other models like the SGI model, Rittinger, Kick, and Signature Plots.

==The Units of Work Index==
The modern units of work index are '''kW·h·µm½·tonne-1''' and are distinct from Specific Energy Consumption (kWh/t).

=== Basis ===

The Third Theory equation is:
<math>E = \frac{kW}{(t/h)} =10 \times Wi \times \left(P_{80}^{-0.5} - F_{80}^{-0.5} \right)</math>

The modern interpretation of work index is as follows:

* the ''10'' is a unitless scaling factor
* the Work Index be treated as a coefficient related to the ''derivative of Specific Energy Consumption'' with particle size.

In this interpretation, the units of work index become '''kW·h·µm½·t-1''' and the units of work index are distinct from Specific Energy Consumption. The values obtained will be relative to the type of ton/tonne measured; the original work by Bond was performed in US short tons (907 kg) or US long tons (1016 kg), but all modern work uses the basis of metric tonnes (1000 kg).

=== History ===
The unfortunate common practice in the industry is to give Work Index the same units as specific energy consumption, specifically ''kWh/t''. This is due to how the Third Theory equation was empirically calibrated and does not reflect any underlying physics.

* If the ''10'' in the Third Theory is interpreted as the square-root of 100 µm, a "typical product size" of ball milling operations,
* then the units of the size term (P₈₀-½-F₈₀-½) cancel the units of the coefficient (10).

This has the unwanted suggestion that Work Index is additive with Specific Energy Consumption, which it is not. Errors in technical documents have been caused by inexperienced engineers making this mistake.

SAGMILLING.COM:Privacy policy

2025-10-08T13:02:22Z

Alex Doll:

We don't store anything beyond the typical Apache logs, which rarely get viewed by a human. You are pretty anonymous here.

The typical MediaWiki cookies are used to store your preferences, blah blah. We won't waste your time with an annoying pop-up message telling you this every time you visit the site.

SAGMILLING.COM:Privacy policy

2025-10-08T13:01:55Z

Alex Doll: Created page with "We don't store anything beyond the typical Apache logs, which rarely get viewed by a human. You are pretty anonymous here. The typical MediaWiki cookies are used to store yo..."

Model:Bond/Barratt SAB Model

2025-07-18T14:48:30Z

Alex Doll: /* Model defaults */

Software change log

2025-07-04T12:02:08Z

Alex Doll: /* 2024-09-23: Fixed bug with Pc_ssbm */

==Change Log==

=== 2025-07-04: Formatting change on some subscripts ===
* Changed from HTML subscripts to unicode subscripts in certain applications, like P₈₀, on output sheets and graphs.

=== 2024-09-23: Fixed bug with Pc_ssbm ===
* Bond model calibration value "Pc_ssbm" wasn't being properly assigned to the SSBM calculations. Was stuck at 9400, now the entered value is used. See [[Model:Bond/Barratt_SABC_Models]]

=== 2024-04-13: Text changes describing power ===
* Tweaked the text to synchronize the way power is described between the flowsheet, tent diagrams, and mill details.
* "Usable" label has been replaced with either "drawn" or "available"

=== 2023-08-03: Monte Carlo simulation model, Bond/Barratt Single-Stage SAG models ===
* Monte Carlo now available for Bond single-stage SAG model, see [[:Category:Monte_Carlo]].

=== 2023-06-08: Monte Carlo simulation model, Bond/Barratt SABC/SAB models ===
* New capability to run Monte Carlo models, see [[:Category:Monte_Carlo]].

=== 2023-02-12: New feature, filenames of downloadable report & spreasheet ===
* The downloadable documents related to running a model now have much more useful filenames, including the date that the document was generated and for which project.

=== 2023-01-31: Bugfix, administrators now see all projects ===
* Fixed a bug where people with Admin level access could not see projects in their client area unless the Admin who actually created the project manually adds the other admins to the access control list. Only people with User level access should be unable to view projects unless explicitly granted access.

=== 2022-06-10: Mih model fix for no result table ===
* Fixed a bug where the Morrell Mi models for HPGR circuits were failing to provide a table of model outputs (for all samples).

=== 2022-05-26: SABC Mi models use peb cr CSS for Epeb ===
* The Morrell Mi models for SABC circuits now read the CSS the user has set for the pebble crusher to compute Epeb. Before a fixed CSS of 12,500 µm was used.

=== 2022-03-28: added VaryP80 and VarySpeed functionality to Mi BM models ===
* The Morrell Mi models for tertiary crushing & single stage ball milling and HPGR & ball milling down have the same functionality as the SAG models where a maximum circuit throughput can be specified and the mills will either overgrind or vary the BM speed to compensate.

=== 2022-01-01: Minor back-end SQL change ===
* Minor change in the SQL code that generates a list of model results. The latest MariaDB added a new reserved word "offset" that was used as a local column in a subquery; this was failing on the backup server (but never affected the main server).

=== 2021-09-20: Changed operation of SSBM contingency ===
* SSBM contingency now operates in the same way as CFsag and CFball, where Etotal now equals (Essbm×contingency). So 1.0 is Etotal=Essbm, and 1.1 is Etotal=1.1×Essbm. Old behaviour had a hidden +1, so old behaviour was Etotal=Essbm×(1+contingency).

=== 2021-03-26: Added Josefin equation to Morrell SSBM model ===
* Mib is now computed using a Hukki exponent if one is entered in the circuit configuration. Users should note that the Hukki exponent for Mi models has a different value to Hukki exponents for Bond models.

=== 2020-12-23: Bug fixes, laboratory listing ===
* Fixed a bug where laboratory data entry would crash without meaningful feedback if a 'short name' is invalid. Added error msgs for 'duplicate' and 'too long' conditions when creating or modifying a laboratory record.

=== 2020-10-05: Added ball wear estimate to ball mills ===
* Added an Improved Benevente equation to the ball mill summary pages. Requires the sample have a Bond Ai (abrasion index) value in order to display. This value is not picked up in the report tables, so you need to look at the ball mill summary pop-up on each simulation to find this value. A future update will include this estimate on the report output tables.

=== 2020-05-15: Changed units of Levin B ===
* Switched the output units of Levin B to mWh/rev (was kWh/rev previously, which made unusably small numbers)

=== 2020-05-08: Bugfix for testwork program names ===
* Fixed a bug preventing the renaming of an existing testwork program

=== 2020-04-08: Added new Nordberg ball mill model for dry grate discharge ===
* Mill power draw model for dry grinding. Add an Essbm contingency of 1.30 when using a Bond-Rowland model (this is for the EF1 factor, 1.3 for dry grinding)

=== 2020-03-23: Tent diagram, sample density(SG) ===
* Fixed current sample density not passing through to tent diagram when manual entry field is empty.

=== 2020-03-21: Server upgrade, SSSAG refactoring ===
* Server operating system and Debian base packages updated.
* Single-stage SAG mill models changed, removed open circuit SAG and replaced with two closed circuit SAG options, one with other without pebble crushing.
* Mill model detail pages now include an extra line of model detail showing values for key model sub-components.

=== 2020-02-20: Crusher and WiBM table refactoring ===
* Refactored the crusher class into two distinct classes, one for cone crusher and other for HPGR.
* Refactored the ball mill work index testwork database table to include percentage of test feed passing the closing size.
* Added calculation of the Levin-B value to WiBM detail calculation.

=== 2019-12-05: SSBM Mi model ===
* Added Morrell Mi model for secondary, tertiary cone crushers and single stage ball milling
* changed icon on manual override submit buttons on circuit flowsheet panel.
* Fixed Morrell Mi models not honouring manually entered F80 and P80 overrides

=== 2019-05-03: Tent diagram caption ===
* Fixed a bug in the density displayed in the caption of a tent diagram.

=== 2019-02-20: Raw Bond Model ===
* Fixed a bug in the transfer size computation.

=== 2018-06-26: Upgraded Mpdf library ===
* June 2018 server upgrade broke the ability to create PDF reports. The Mpdf library was upgraded to the latest version minor code tweaks were done to connect it into the code base.

=== 2018-05-30: Circuit t/h limits, sample density ===
* Circuit t/h limits are now enforced when running models, and the model predicts one possible outcome where mill charges and speeds change to accommodate a reduced throughput (there are infinitely many mathematically valid possibilities).
* Determination of the sample density in the situation where there is no WiC density and multiple DWT densities has changed. Old behaviour is to pick the last DWT test density, new behaviour is to arithmetically average all DWT densities for the sample.

=== 2018-04-15: Austin SAG model default cone angle, E_SSBM for SGI & Mi models ===
* Calculations involving the Austin SAG model were not using the default 15 degree cone angle, defaulting to zero (flat-ended mill). Fixed so that no cone angle entry now is interpreted as 15 degrees.
* SSBM calculation corrected for SGI and Mi models (EF4 value now uses Bond methodology)

=== 2017-09-10: Feed and product (F80, P80) sizes manually adjustable, El Soldado SGI model ===
* Temporary changes to the F80 and P80 sizes can now be entered on the flowsheet display page (just as you can manually adjust test results on a flowsheet page). These changes are not saved, but allow users to see the effect of F80 & P80 changes without changing the stored circuit settings.
* The Single Stage SAG mill model using SGI values has been changed to the El Soldado basis (Becerra and Jorquera, Procemin 2016).

=== 2017-09-05: Minor cleanup, Mih model ===
* Forced the Mih model (Morrell HPGR model) to check that Sc is not greater than 1. This requirement is explained in the GMSG Morrell standard (2015-08-21).
* Discontinued the 'particle size plotting' tool. Modern browsers won't run java applets anymore, so the tool won't function. :'(

=== 2017-08-15: SSL certificates changed ===
* Switched the main site SSL certificate to LetsEncrypt. Added certificate to the wiki.

=== 2017-03-21: Bond models can configure internal transfer sizes ===
* The various Bond models now have the ability to modify the calibration internal transfer sizes. Rare that you would want to do this, but Alex encountered a project that needed this capability.
* Tent diagrams can now have non-integer ball charges and filling volumes.

=== 2017-03-11: Changed Mia, Mic estimate from A×b for SMC model ===
* Updated the prediction of Mia and Mic used in the Morrell SMC circuit model for the case where A×b is given, but Mia and/or Mic are not. The new estimate is based on the calibration in Doll, Procemin 2016 (paper № 35).
* Removed some unnecessary messages from tent diagram display.

=== 2016-11-03: Fixed bug with SGI single-stage SAG model ===
* The P80 wasn't being used correctly with the SS SAG model using SGI. Corrected and now appears to be working properly (thanks to Anglo American El Soldado for their Procemin paper that enabled this bug to be diagnosed).

=== 2016-10-25: New single-stage SAG circuit models ===
* Added two new models for single-stage SAG mill circuits, one based on Morrell Mi and other on Amelunxen SGI. Be careful with the SGI model as the calibration might be suspect if you are grinding below 500 µm (it should work for iron ore AG, not so sure about porphyry copper).
* Changed the listing of model results so that only the columns that matter for a particular circuit flowsheet are showing. The "ball mill" specific energy consumption doesn't show in single-stage SAG mill circuits, for example. The exported (.ODS) spreadsheets still show all columns and in their SABC column names, so E_hpgr is actually listed as E_asag (to be fixed later).

=== 2016-07-29: Mib where two WiBM records exist ===
* The way Mib is treated has changed in the case of two WiBM records exist for the same sample (duplicate ball mill Wi tests). The old method would draw the parameters (F80, P80, gpr, closing mesh) and calculate the Mib. The new method calculates the Mib in the database and then accumulates Mib values. The new method works better in the situation where one of the duplicate WiBM records has omitted the Mib parameters (accumulating NULL values works better).

=== 2016-07-20: Rudimentary calculations without entering test results is now possible ===
* Circuit calculations may now be done even if no samples are present. This is usually done for quick prototyping or checking the expected power draw of a mill without all the fuss of entering test results.
* The manual entry testwork fields are pre-populated with some bogus data (work index values of 10, for example) that you can change and re-run the calculations. These changes are not stored and you'll need to re-enter any testwork changes each time a mill or a circuit setting is modified.

=== 2016-07-20: Added last update date to projects view ===
* The listing of projects now shows the date and UTC time of the last time a complete set of "results" was generated. This date is not affected by changes to the mills or circuit settings, only the creation of a set of list of results for all samples will trigger the date to update.

=== 2016-07-20: Database index and keys ===
* Added more table indexes to speed up complicated queries such as parameter-versus-parameter plots.
* Added foreign key constraints to improve back-end database maintenance. Should not affect end users.

=== 2016-06-22: Rod Mill & Ball Mill circuit fixes, GMSG calculation ===
* Fixes to borked RMBM circuit calculations.
* Added RMBM circuit fed from open circuit crushing.
* Added GMSG Bond Standard calculation to samples with Bond series of test results.

=== 2016-04-22: Added Morrell SMC & ball mill based HPGR model ===
* Uses Morrell's Mic, Mih, Mia and Mib values to predict specific energy consumption of an HPGR circuit
* Changed summary output "proportion of power draw" for crusher classes to be based on denominator of motor output power.

=== 2016-02-26: Added %solids warning to Austin model ===
* Added a warning to Austin SAG model if %solids is outside the range of 60% to 80% solids.

=== 2016-01-15: Bug fix and more translations ===
* Fixed a long-standing bug where the liner thickness for newly created mills reverts to the default liner thickness the second time the mill is edited.
* Made mill model names translatable strings.

=== 2016-01-10: Testwork comparison chart ===
* Added the Morrell '''Mib''' value to the list of available tests to view.
* Changed the behaviour of plots where the same test is being plotted on both axis. The single determination is used as the index key (JOIN ON `id`) instead of all permutations of the sample (JOIN ON `sampleid`).

=== 2016-01-06: Articles list now has topic filters ===
* Added the ability to filter the list of articles so that only articles pertaining to a particular topic are shown. Easier to browse these shorter lists.

=== 2016-01-01: Server move ===
* Moved to an upgraded virtual server box with the latest PHP and MySQL implementation (using current stable Debian repository).

===2015-11-17: Morrell SMC model ===
* Fixed a bug where Morrell SMC model gave an error message and zero throughput. (Also related to the 2015-11-08 fix to the Raw Bond model)

===2015-11-11: Bond Single Stage SAG model ===
* Fixed a bug where Bond SSSAG model gave an error message and zero throughput. (The 2015-11-08 fix to the Raw Bond model broke the Bond SSSAG model)

===2015-11-08: SGI model Epeb handling ===
* Fixed a bug where the pebble crusher specific energy consumption was not be included in the Amelunxen SGI model Etotal value

===2015-10-05: Ball mill default cone angle ===
* Changed the default cone angle for ball mills to 15 degrees.

===2015-10-05: Report changes ===
* Allow the user to define which percentiles should appear on a report. The 'PDF export' button now opens a small text field where a space-delimited list of percentiles may be entered. If this field is blank, then no "flowsheets" will appear in the report.
* Added some more information to mill & PDF output pages, such as the mechanical & electrical efficiency of drives.

===2015-07-24: Synthetic Testwork results ===
* Added a new column to several testwork tables called 'synthetic'. If this column contains a value of '1' (boolean=true) for a test, then that test is understood to not be a real test result and is therefore not shown on the testwork comparison charts. It is available when running circuit model simulations and does show up in the list of model results.

* Fixed a bug where the motor torque for mills with qty>2 was showing the sum of the torque for all mills rather than the torque for a single mill.

===2015-06-12: Test result summary===
* A testwork summary listing now shows the '''Mia''' and '''Mib''' values needed for the Morrell SMC model. The '''DWI''' value was removed from the summary as it is not used directly in any of the models.

* Minor changes to the PDF report showing specific energy model names rather than their ID number.

===2015-06-02: Tent Diagram===
* A Tent diagram can now show just power, just torque, or overlay both.

===2015-05-13: Drive torque===
* Modified the tent diagram to show the process torque demand (at the mill shell) across the range of mill speed
* Added the torque (at the mill shell) to the list of properties in the mill detail listing.

===2015-05-07: Tent diagram===
* Modified range of tent diagram up to 85% of critical speed.
* Fixed bug where operating speed determined the torque of the tent diagram peak.

===2015-04-25: Added Morrell SMC (Mia, Mib) SAB & SABC circuit model===
* New specific energy model for SAG & ball mill circuits that uses Mia (from SMC™ test) and Mib (from a Bond WiBM) values.
* '''Must''' enter the following information for the Bond ball mill work index to permit Mib calculation in order to run this model:
** Test P100 (closing screen) size, µm
** Test P80 size, µm
** Test F80 size, µm
** Test grams per revolution (GPR)

===2015-04-21: Added rod mill-ball mill circuit model===
* New specific energy model using Bond/Rowland method for rod mills and ball mills.
* Fixed a problem with default values not appearing in drop-down select fields.
* Tweaked behaviour of SGI model under SAG-limited and ball-limited conditions.

===2015-04-10: Added Amelunxen SGI model===
* New specific energy model for SAG & ball mill circuits that uses SGI (or SPI™) values instead of Bond work index for rod mill and crushing.
* Mandatory to set the CFsag and CFball configuration factors, see the [[Model:Amelunxen SGI|documentation]].

==Bug list==
Known bugs that are scheduled for fixing:

* SGI model PDF output does not show the CFsag and CFball values [mostly cosmetic, low priority]
* The exported (.ODS) spreadsheets of circuit model results show columns with their SABC column names, so E_hpgr is actually listed as E_asag. Some meaningless columns (such as E_bm in a Single-Stage SAG circuit) also show. [Mostly cosmetic, just know to change E_asag to whatever is appropriate for your flowsheet.]

SAGMILLING.COM:General disclaimer

2024-12-03T12:51:13Z

Alex Doll: Use this information at your own risk

The "Wiki" website is the online documentation for the SAGMILLING.COM software. The documentation contained herein is derived from public sources or has been generated by the website operator, Alex G Doll Consulting Limited of Cork, Ireland.

'''Use this information at your own risk'''. The author makes no guarantee that the information presented in this website is suitable for any purpose and it is your responsibility, as the audience, to use sound judgement and external validation before relying on the concepts and equations provided herein.

'''All models are wrong, but some are useful'''. A model is a simplified representation of reality that humans can use to perform calculations and make predictions. Because models are simplified, they are wrong; they are not a one-for-one representation of reality and models are only valid within the calibration space for which they have been configured. The audience is cautioned that all of the models presented in this website have their own calibration spaces and may or may not be suitable for any given situation.

Software change log

2024-09-23T14:08:17Z

Alex Doll: /* 2024-09-23: Fixed bug with Pc_ssbm */

==Change Log==

=== 2024-09-23: Fixed bug with Pc_ssbm ===
* Bond model calibration value "Pc_ssbm" wasn't being properly assigned to the SSBM calculations. Was stuck at 9400, now the entered value is used. See [[Model:Bond/Barratt_SABC_Models]]

=== 2024-04-13: Text changes describing power ===
* Tweaked the text to synchronize the way power is described between the flowsheet, tent diagrams, and mill details.
* "Usable" label has been replaced with either "drawn" or "available"

=== 2023-08-03: Monte Carlo simulation model, Bond/Barratt Single-Stage SAG models ===
* Monte Carlo now available for Bond single-stage SAG model, see [[:Category:Monte_Carlo]].

=== 2023-06-08: Monte Carlo simulation model, Bond/Barratt SABC/SAB models ===
* New capability to run Monte Carlo models, see [[:Category:Monte_Carlo]].

=== 2023-02-12: New feature, filenames of downloadable report & spreasheet ===
* The downloadable documents related to running a model now have much more useful filenames, including the date that the document was generated and for which project.

=== 2023-01-31: Bugfix, administrators now see all projects ===
* Fixed a bug where people with Admin level access could not see projects in their client area unless the Admin who actually created the project manually adds the other admins to the access control list. Only people with User level access should be unable to view projects unless explicitly granted access.

=== 2022-06-10: Mih model fix for no result table ===
* Fixed a bug where the Morrell Mi models for HPGR circuits were failing to provide a table of model outputs (for all samples).

=== 2022-05-26: SABC Mi models use peb cr CSS for Epeb ===
* The Morrell Mi models for SABC circuits now read the CSS the user has set for the pebble crusher to compute Epeb. Before a fixed CSS of 12,500 µm was used.

=== 2022-03-28: added VaryP80 and VarySpeed functionality to Mi BM models ===
* The Morrell Mi models for tertiary crushing & single stage ball milling and HPGR & ball milling down have the same functionality as the SAG models where a maximum circuit throughput can be specified and the mills will either overgrind or vary the BM speed to compensate.

=== 2022-01-01: Minor back-end SQL change ===
* Minor change in the SQL code that generates a list of model results. The latest MariaDB added a new reserved word "offset" that was used as a local column in a subquery; this was failing on the backup server (but never affected the main server).

=== 2021-09-20: Changed operation of SSBM contingency ===
* SSBM contingency now operates in the same way as CFsag and CFball, where Etotal now equals (Essbm×contingency). So 1.0 is Etotal=Essbm, and 1.1 is Etotal=1.1×Essbm. Old behaviour had a hidden +1, so old behaviour was Etotal=Essbm×(1+contingency).

=== 2021-03-26: Added Josefin equation to Morrell SSBM model ===
* Mib is now computed using a Hukki exponent if one is entered in the circuit configuration. Users should note that the Hukki exponent for Mi models has a different value to Hukki exponents for Bond models.

=== 2020-12-23: Bug fixes, laboratory listing ===
* Fixed a bug where laboratory data entry would crash without meaningful feedback if a 'short name' is invalid. Added error msgs for 'duplicate' and 'too long' conditions when creating or modifying a laboratory record.

=== 2020-10-05: Added ball wear estimate to ball mills ===
* Added an Improved Benevente equation to the ball mill summary pages. Requires the sample have a Bond Ai (abrasion index) value in order to display. This value is not picked up in the report tables, so you need to look at the ball mill summary pop-up on each simulation to find this value. A future update will include this estimate on the report output tables.

=== 2020-05-15: Changed units of Levin B ===
* Switched the output units of Levin B to mWh/rev (was kWh/rev previously, which made unusably small numbers)

=== 2020-05-08: Bugfix for testwork program names ===
* Fixed a bug preventing the renaming of an existing testwork program

=== 2020-04-08: Added new Nordberg ball mill model for dry grate discharge ===
* Mill power draw model for dry grinding. Add an Essbm contingency of 1.30 when using a Bond-Rowland model (this is for the EF1 factor, 1.3 for dry grinding)

=== 2020-03-23: Tent diagram, sample density(SG) ===
* Fixed current sample density not passing through to tent diagram when manual entry field is empty.

=== 2020-03-21: Server upgrade, SSSAG refactoring ===
* Server operating system and Debian base packages updated.
* Single-stage SAG mill models changed, removed open circuit SAG and replaced with two closed circuit SAG options, one with other without pebble crushing.
* Mill model detail pages now include an extra line of model detail showing values for key model sub-components.

=== 2020-02-20: Crusher and WiBM table refactoring ===
* Refactored the crusher class into two distinct classes, one for cone crusher and other for HPGR.
* Refactored the ball mill work index testwork database table to include percentage of test feed passing the closing size.
* Added calculation of the Levin-B value to WiBM detail calculation.

=== 2019-12-05: SSBM Mi model ===
* Added Morrell Mi model for secondary, tertiary cone crushers and single stage ball milling
* changed icon on manual override submit buttons on circuit flowsheet panel.
* Fixed Morrell Mi models not honouring manually entered F80 and P80 overrides

=== 2019-05-03: Tent diagram caption ===
* Fixed a bug in the density displayed in the caption of a tent diagram.

=== 2019-02-20: Raw Bond Model ===
* Fixed a bug in the transfer size computation.

=== 2018-06-26: Upgraded Mpdf library ===
* June 2018 server upgrade broke the ability to create PDF reports. The Mpdf library was upgraded to the latest version minor code tweaks were done to connect it into the code base.

=== 2018-05-30: Circuit t/h limits, sample density ===
* Circuit t/h limits are now enforced when running models, and the model predicts one possible outcome where mill charges and speeds change to accommodate a reduced throughput (there are infinitely many mathematically valid possibilities).
* Determination of the sample density in the situation where there is no WiC density and multiple DWT densities has changed. Old behaviour is to pick the last DWT test density, new behaviour is to arithmetically average all DWT densities for the sample.

=== 2018-04-15: Austin SAG model default cone angle, E_SSBM for SGI & Mi models ===
* Calculations involving the Austin SAG model were not using the default 15 degree cone angle, defaulting to zero (flat-ended mill). Fixed so that no cone angle entry now is interpreted as 15 degrees.
* SSBM calculation corrected for SGI and Mi models (EF4 value now uses Bond methodology)

=== 2017-09-10: Feed and product (F80, P80) sizes manually adjustable, El Soldado SGI model ===
* Temporary changes to the F80 and P80 sizes can now be entered on the flowsheet display page (just as you can manually adjust test results on a flowsheet page). These changes are not saved, but allow users to see the effect of F80 & P80 changes without changing the stored circuit settings.
* The Single Stage SAG mill model using SGI values has been changed to the El Soldado basis (Becerra and Jorquera, Procemin 2016).

=== 2017-09-05: Minor cleanup, Mih model ===
* Forced the Mih model (Morrell HPGR model) to check that Sc is not greater than 1. This requirement is explained in the GMSG Morrell standard (2015-08-21).
* Discontinued the 'particle size plotting' tool. Modern browsers won't run java applets anymore, so the tool won't function. :'(

=== 2017-08-15: SSL certificates changed ===
* Switched the main site SSL certificate to LetsEncrypt. Added certificate to the wiki.

=== 2017-03-21: Bond models can configure internal transfer sizes ===
* The various Bond models now have the ability to modify the calibration internal transfer sizes. Rare that you would want to do this, but Alex encountered a project that needed this capability.
* Tent diagrams can now have non-integer ball charges and filling volumes.

=== 2017-03-11: Changed Mia, Mic estimate from A×b for SMC model ===
* Updated the prediction of Mia and Mic used in the Morrell SMC circuit model for the case where A×b is given, but Mia and/or Mic are not. The new estimate is based on the calibration in Doll, Procemin 2016 (paper № 35).
* Removed some unnecessary messages from tent diagram display.

=== 2016-11-03: Fixed bug with SGI single-stage SAG model ===
* The P80 wasn't being used correctly with the SS SAG model using SGI. Corrected and now appears to be working properly (thanks to Anglo American El Soldado for their Procemin paper that enabled this bug to be diagnosed).

=== 2016-10-25: New single-stage SAG circuit models ===
* Added two new models for single-stage SAG mill circuits, one based on Morrell Mi and other on Amelunxen SGI. Be careful with the SGI model as the calibration might be suspect if you are grinding below 500 µm (it should work for iron ore AG, not so sure about porphyry copper).
* Changed the listing of model results so that only the columns that matter for a particular circuit flowsheet are showing. The "ball mill" specific energy consumption doesn't show in single-stage SAG mill circuits, for example. The exported (.ODS) spreadsheets still show all columns and in their SABC column names, so E_hpgr is actually listed as E_asag (to be fixed later).

=== 2016-07-29: Mib where two WiBM records exist ===
* The way Mib is treated has changed in the case of two WiBM records exist for the same sample (duplicate ball mill Wi tests). The old method would draw the parameters (F80, P80, gpr, closing mesh) and calculate the Mib. The new method calculates the Mib in the database and then accumulates Mib values. The new method works better in the situation where one of the duplicate WiBM records has omitted the Mib parameters (accumulating NULL values works better).

=== 2016-07-20: Rudimentary calculations without entering test results is now possible ===
* Circuit calculations may now be done even if no samples are present. This is usually done for quick prototyping or checking the expected power draw of a mill without all the fuss of entering test results.
* The manual entry testwork fields are pre-populated with some bogus data (work index values of 10, for example) that you can change and re-run the calculations. These changes are not stored and you'll need to re-enter any testwork changes each time a mill or a circuit setting is modified.

=== 2016-07-20: Added last update date to projects view ===
* The listing of projects now shows the date and UTC time of the last time a complete set of "results" was generated. This date is not affected by changes to the mills or circuit settings, only the creation of a set of list of results for all samples will trigger the date to update.

=== 2016-07-20: Database index and keys ===
* Added more table indexes to speed up complicated queries such as parameter-versus-parameter plots.
* Added foreign key constraints to improve back-end database maintenance. Should not affect end users.

=== 2016-06-22: Rod Mill & Ball Mill circuit fixes, GMSG calculation ===
* Fixes to borked RMBM circuit calculations.
* Added RMBM circuit fed from open circuit crushing.
* Added GMSG Bond Standard calculation to samples with Bond series of test results.

=== 2016-04-22: Added Morrell SMC & ball mill based HPGR model ===
* Uses Morrell's Mic, Mih, Mia and Mib values to predict specific energy consumption of an HPGR circuit
* Changed summary output "proportion of power draw" for crusher classes to be based on denominator of motor output power.

=== 2016-02-26: Added %solids warning to Austin model ===
* Added a warning to Austin SAG model if %solids is outside the range of 60% to 80% solids.

=== 2016-01-15: Bug fix and more translations ===
* Fixed a long-standing bug where the liner thickness for newly created mills reverts to the default liner thickness the second time the mill is edited.
* Made mill model names translatable strings.

=== 2016-01-10: Testwork comparison chart ===
* Added the Morrell '''Mib''' value to the list of available tests to view.
* Changed the behaviour of plots where the same test is being plotted on both axis. The single determination is used as the index key (JOIN ON `id`) instead of all permutations of the sample (JOIN ON `sampleid`).

=== 2016-01-06: Articles list now has topic filters ===
* Added the ability to filter the list of articles so that only articles pertaining to a particular topic are shown. Easier to browse these shorter lists.

=== 2016-01-01: Server move ===
* Moved to an upgraded virtual server box with the latest PHP and MySQL implementation (using current stable Debian repository).

===2015-11-17: Morrell SMC model ===
* Fixed a bug where Morrell SMC model gave an error message and zero throughput. (Also related to the 2015-11-08 fix to the Raw Bond model)

===2015-11-11: Bond Single Stage SAG model ===
* Fixed a bug where Bond SSSAG model gave an error message and zero throughput. (The 2015-11-08 fix to the Raw Bond model broke the Bond SSSAG model)

===2015-11-08: SGI model Epeb handling ===
* Fixed a bug where the pebble crusher specific energy consumption was not be included in the Amelunxen SGI model Etotal value

===2015-10-05: Ball mill default cone angle ===
* Changed the default cone angle for ball mills to 15 degrees.

===2015-10-05: Report changes ===
* Allow the user to define which percentiles should appear on a report. The 'PDF export' button now opens a small text field where a space-delimited list of percentiles may be entered. If this field is blank, then no "flowsheets" will appear in the report.
* Added some more information to mill & PDF output pages, such as the mechanical & electrical efficiency of drives.

===2015-07-24: Synthetic Testwork results ===
* Added a new column to several testwork tables called 'synthetic'. If this column contains a value of '1' (boolean=true) for a test, then that test is understood to not be a real test result and is therefore not shown on the testwork comparison charts. It is available when running circuit model simulations and does show up in the list of model results.

* Fixed a bug where the motor torque for mills with qty>2 was showing the sum of the torque for all mills rather than the torque for a single mill.

===2015-06-12: Test result summary===
* A testwork summary listing now shows the '''Mia''' and '''Mib''' values needed for the Morrell SMC model. The '''DWI''' value was removed from the summary as it is not used directly in any of the models.

* Minor changes to the PDF report showing specific energy model names rather than their ID number.

===2015-06-02: Tent Diagram===
* A Tent diagram can now show just power, just torque, or overlay both.

===2015-05-13: Drive torque===
* Modified the tent diagram to show the process torque demand (at the mill shell) across the range of mill speed
* Added the torque (at the mill shell) to the list of properties in the mill detail listing.

===2015-05-07: Tent diagram===
* Modified range of tent diagram up to 85% of critical speed.
* Fixed bug where operating speed determined the torque of the tent diagram peak.

===2015-04-25: Added Morrell SMC (Mia, Mib) SAB & SABC circuit model===
* New specific energy model for SAG & ball mill circuits that uses Mia (from SMC™ test) and Mib (from a Bond WiBM) values.
* '''Must''' enter the following information for the Bond ball mill work index to permit Mib calculation in order to run this model:
** Test P100 (closing screen) size, µm
** Test P80 size, µm
** Test F80 size, µm
** Test grams per revolution (GPR)

===2015-04-21: Added rod mill-ball mill circuit model===
* New specific energy model using Bond/Rowland method for rod mills and ball mills.
* Fixed a problem with default values not appearing in drop-down select fields.
* Tweaked behaviour of SGI model under SAG-limited and ball-limited conditions.

===2015-04-10: Added Amelunxen SGI model===
* New specific energy model for SAG & ball mill circuits that uses SGI (or SPI™) values instead of Bond work index for rod mill and crushing.
* Mandatory to set the CFsag and CFball configuration factors, see the [[Model:Amelunxen SGI|documentation]].

==Bug list==
Known bugs that are scheduled for fixing:

* SGI model PDF output does not show the CFsag and CFball values [mostly cosmetic, low priority]
* The exported (.ODS) spreadsheets of circuit model results show columns with their SABC column names, so E_hpgr is actually listed as E_asag. Some meaningless columns (such as E_bm in a Single-Stage SAG circuit) also show. [Mostly cosmetic, just know to change E_asag to whatever is appropriate for your flowsheet.]

Model:Bond/Barratt SABC Models

2024-09-23T14:05:25Z

Alex Doll: /* Optional parameters */

Model:Bond/Barratt SABC Models

2024-09-23T14:02:07Z

Alex Doll: /* Formulae */

[[Category:Models]]
[[Category:Specific Energy Models]]
[[Category: Bond/Barratt Model]]
[[Category: P80 adjustment]]
[[Category: Monte Carlo]]
== Bond/Barratt Specific Energy Consumption SABC Model ==

This is a SAG or AG mill plus ball mill model that estimates the overall circuit specific energy consumption using the classical Bond work index equation for multi-stage crushing and single-stage ball milling (Essbm) including Rowland efficiency factors. The circuit Etotal is equal to the Essbm plus an inefficiency factor (CF) related to the difference in grinding efficiency of the two types of circuits. The SAG mill specific energy consumption (ESAG) is calculated using the 1979 Barratt equation and the ball mill specific energy consumption (Ebm)

This model includes a [[phantom cyclone]] effect in the equations due to the ball mill being calculated by difference and not being calculated by the normal Bond equation. The resultant operating work index of the ball mill will vary according to the ratio of the ball mill, rod mill and crushing work index values and is in the range of 80% of the measured ball mill work index value.

===Testwork Required===
* [[Testwork: Bond ball mill work index|Bond ball mill work index]]
* [[Testwork: Bond rod mill work index|Bond rod mill work index]]
* [[Testwork: Bond crushing work index|Bond crushing (low-energy impact) work index]]

===Required parameters===
* '''F80, µm''' is the 80% passing size of the fresh feed to the circuit (expected to be a Bond-compatible size distribution).
* '''P80, µm''' is the 80% passing size of the circuit product (expected to be a Bond-compatible size distribution).
* '''Availability''', expressed as a decimal (0.90 = 90% availability) is used to convert t/h to t/d.
* Ball mill '''Operating strategy''' when circuit is SAG-limited (note, fixed speed can only be ''vary P80'')

===Optional parameters===
* '''Description''' and '''Comment''' are optional text fields
* '''Maximum t/h limit''' is a t/h throughput limit above which the mills will turn down by, for example, grinding out.
* '''T80 min''' and '''T80 min''' override the transfer size restrictions built into the model
* [[Ball mill work index adjustment]] used to adjust WiBM for different P80 sizes.
** '''exponent (a)''', the fitted Hukki exponent to the adjustment equation (enter as a positive number)
* '''Essbm calibration factor''' (CF), model tuning factor for Etotal

===Formulae===
<math>
E_{ssbm} = Wi_{C} \times \left ( \tfrac {10}{\sqrt{ Pc_{ssbm} }} - \tfrac {10}{\sqrt{ F_{80} }} \right ) + Wi_{RM} \times \left ( \tfrac {10}{\sqrt{ Prm }} - \tfrac {10}{\sqrt{ Pc_{ssbm} }} \right )\times EF_4^{RM} + Wi_{BM} \times \left ( \tfrac {10}{\sqrt{ P_{80} }} - \tfrac {10}{\sqrt{ Prm }} \right ) \times EF_4^{BM} \times EF_5</math>
[[Bibliography:_Specific_energy_consumption_models|Rowland, 2006]]

where
* Pcssbm is the calibration value entered for "Essbm crushing circuit product" (default: 9400)
* Prm is the calibration value entered for "Easag RM circuit product" (default: 2100)

<math> E_{total} = E_{ssbm} \times (CF) </math>

<math>\begin{align}
E_{SAG} = \Big[ & Wi_{C} \times \left ( \tfrac {10}{\sqrt{ P_{C} }} - \tfrac {10}{\sqrt{ F_{80} }} \right ) + Wi_{RM} \times \left ( \tfrac {10}{\sqrt{ P_{R} }} - \tfrac {10}{\sqrt{ P_{C} }} \right ) \times EF_4^{RM} \\
& + Wi_{BM} \times \left ( \tfrac {10}{\sqrt{110} } - \tfrac {10}{\sqrt{ P_{R} }} \right ) \times EF_4^{BM} \Big] \times 1.25 - Wi_{BM} \times \left ( \tfrac {10}{\sqrt{ {110} }} - \tfrac {10}{\sqrt{ T_{80} }} \right )
\end{align}
</math>
[[Bibliography:_Specific_energy_consumption_models|Barratt, 1989]]

where
* PC is the calibration value entered for "Easag crushing circuit product" (default: 18850)

<math> E_{bm}= E_{total} - E_{sag}</math>

As with most models, the power split between the SAG and ball mills is evaluated and the transfer size (T80) necessary to balance the power draw between the two stages is estimated. If that transfer size is within the specified limits, then the calculation proceeds to calculate the ESAG and Ebm using that transfer size. If the transfer size to balance the power is outside the specified limits, then the transfer size size is forced to the limit and the ESAG and Ebm values are then calculated. SAG-limited circuits (where the T80 hits the upper limit) will result in the ball mill over-grinding unless the ball mill speed is reduced to control the grind size (in the case of a variable speed mill). Ball-limited circuits (where the T80 hits the lower limit) will result in the charge level in the SAG mill dropping until its power draw matches the throughput limit dictated by the ball mill. It is important to realize that once the SAG mill charge level drops to be equal to the ball charge, the model will be operating "out of range" and the predictions will not be valid.

Circuits that operate at or near the transfer size limits should be less efficient than the default formulas will estimate. If you have a design that is consistently operating around the limits, then consider adding a contingency to inflate the specific energy consumption estimates to account for this poor grinding efficiency. Alternatively, if you are designing a new circuit then choose a different combination of SAG and ball mills that operates in a more reasonable transfer size range.

The optimum feed size for the rod mill oversize feed factor (EF4RM) in the Barratt ESAG equation is calculated using the greater of the sample's rod mill or crushing work index.

<math>F_{O}= 16000 \times \sqrt{\frac{13}{Max(Wi_{RM}, Wi_{C}) \div 1.1023} } </math>

The EF4RM is calculated greater of the crushing work index or the rod mill work index.

<math>EF_{4}^{RM} = \frac{RR+ \bigl(\frac{Max(Wi_C, Wi_{RM})}{1.1023} -7 \bigr) \times \frac {F_{80}-F_{O}}{F_{O}}}{RR}</math>

The ball mill oversize feed factor (EF4BM) is always calculated with the rod mill work index for the optimum feed size and the ball mill work index for EF4BM.

<math>F_{O}= 4000 \times \sqrt{\frac{13}{Wi_{RM} \div 1.1023} } </math>

<math>EF_{4}^{BM} = \frac{RR+ \bigl( \frac{Wi_{BM}}{1.1023} -7 \bigr) \times \frac {F_{80}-F_{O}}{F_{O}}}{RR}</math>

The model assumes that the calculated value of Essbm + the specified contingency is greater than the sum of Esag + Epeb; otherwise Ebm will be negative. The model does a check to see if Ebm calculated is negative (or close to zero) and, if so, will substitute the [[Model:RawBondModel|Raw Bond Model]] equation estimate for Ebm.

== Recommended Usage ==

This model should be the lower end-member of the range of Bond/Barratt style models. It is useful when interpreting pilot plant results to determine where the pilot plant results fall relative to the spectrum of models. It can be used as a realistic model for design work in softer ore types like copper porphyries. The Optimized Bond/Barratt model is best used for '''low competency ores''', such as those found in the Western Cordillera of North America or the Andes, where the impact crushing work index is similar to, or less than the rod mill and ball mill work index values. These ores tend to demonstrate a phantom cyclone effect.

[[file:WorkIndex-CompentIncompetent.png|alt=Diagram of work index by size|Work index by size examples of competent and incompetent ores]]

=== Discussion, pebble crushing ===
The pebble crusher is assumed to be part of the SAG mill for the purposes of this calculation. Epeb is calculated as the power drawn by the pebble crusher divided by the circuit throughput. This Epeb is then deducted from Esag.

The total circuit specific energy consumption is generally higher when no pebble crusher is present in a circuit. The rule of thumb is apply the CF value of 1.15 for SAB circuits (5% higher overall specific energy consumption) [[Bibliography:_Specific_energy_consumption_models#SPI.2FMinnovex_Method|Bennett, Dobby & Kosick, SAG 2001]]. Published data from Cadia confirms a 5% difference in throughput (and therefore, specific energy) when the pebble crusher is fully utilized.Hart, Valery, Clements, Reed, Song & Dunne, SAG 2001.

=== Discussion, Rowland EF factors ===
The model is only interested in the EF factors that are properties of the rock, namely the coarse feed EF4 factor and the fine product EF5 factor. The EF factors that correspond to machine characteristics are not included (EF1, EF2, EF3, EF6, EF7 and EF8) as they are intended to capture the inefficiency of certain types of milling circuits. The assumption in this model is that the Essbm is the "maximum efficiency" possible for a grinding circuit, to which we apply an empirical adjustment for SAG milling (''Cf'') which encapsulates any other EF factors in a form suitable for a SAG process.

=== Model defaults ===
* Maximum T80, µm = 6000
* Minimum T80, µm = 400
* PC for Essbm= 9400
* PC for Easag= 18850
* PR= 2100
* CF = 0.10

Software change log

2024-09-23T13:54:46Z

Alex Doll: /* 2024-04-13: Text changes describing power */

==Change Log==

=== 2024-09-23: Fixed bug with Pc_ssbm ===
* Bond model calibration value "Pc_ssbm" wasn't being properly assigned to the SSBM calculations. Was stuck at 9400, now the entered value is used.
=== 2024-04-13: Text changes describing power ===
* Tweaked the text to synchronize the way power is described between the flowsheet, tent diagrams, and mill details.
* "Usable" label has been replaced with either "drawn" or "available"

=== 2023-08-03: Monte Carlo simulation model, Bond/Barratt Single-Stage SAG models ===
* Monte Carlo now available for Bond single-stage SAG model, see [[:Category:Monte_Carlo]].

=== 2023-06-08: Monte Carlo simulation model, Bond/Barratt SABC/SAB models ===
* New capability to run Monte Carlo models, see [[:Category:Monte_Carlo]].

=== 2023-02-12: New feature, filenames of downloadable report & spreasheet ===
* The downloadable documents related to running a model now have much more useful filenames, including the date that the document was generated and for which project.

=== 2023-01-31: Bugfix, administrators now see all projects ===
* Fixed a bug where people with Admin level access could not see projects in their client area unless the Admin who actually created the project manually adds the other admins to the access control list. Only people with User level access should be unable to view projects unless explicitly granted access.

=== 2022-06-10: Mih model fix for no result table ===
* Fixed a bug where the Morrell Mi models for HPGR circuits were failing to provide a table of model outputs (for all samples).

=== 2022-05-26: SABC Mi models use peb cr CSS for Epeb ===
* The Morrell Mi models for SABC circuits now read the CSS the user has set for the pebble crusher to compute Epeb. Before a fixed CSS of 12,500 µm was used.

=== 2022-03-28: added VaryP80 and VarySpeed functionality to Mi BM models ===
* The Morrell Mi models for tertiary crushing & single stage ball milling and HPGR & ball milling down have the same functionality as the SAG models where a maximum circuit throughput can be specified and the mills will either overgrind or vary the BM speed to compensate.

=== 2022-01-01: Minor back-end SQL change ===
* Minor change in the SQL code that generates a list of model results. The latest MariaDB added a new reserved word "offset" that was used as a local column in a subquery; this was failing on the backup server (but never affected the main server).

=== 2021-09-20: Changed operation of SSBM contingency ===
* SSBM contingency now operates in the same way as CFsag and CFball, where Etotal now equals (Essbm×contingency). So 1.0 is Etotal=Essbm, and 1.1 is Etotal=1.1×Essbm. Old behaviour had a hidden +1, so old behaviour was Etotal=Essbm×(1+contingency).

=== 2021-03-26: Added Josefin equation to Morrell SSBM model ===
* Mib is now computed using a Hukki exponent if one is entered in the circuit configuration. Users should note that the Hukki exponent for Mi models has a different value to Hukki exponents for Bond models.

=== 2020-12-23: Bug fixes, laboratory listing ===
* Fixed a bug where laboratory data entry would crash without meaningful feedback if a 'short name' is invalid. Added error msgs for 'duplicate' and 'too long' conditions when creating or modifying a laboratory record.

=== 2020-10-05: Added ball wear estimate to ball mills ===
* Added an Improved Benevente equation to the ball mill summary pages. Requires the sample have a Bond Ai (abrasion index) value in order to display. This value is not picked up in the report tables, so you need to look at the ball mill summary pop-up on each simulation to find this value. A future update will include this estimate on the report output tables.

=== 2020-05-15: Changed units of Levin B ===
* Switched the output units of Levin B to mWh/rev (was kWh/rev previously, which made unusably small numbers)

=== 2020-05-08: Bugfix for testwork program names ===
* Fixed a bug preventing the renaming of an existing testwork program

=== 2020-04-08: Added new Nordberg ball mill model for dry grate discharge ===
* Mill power draw model for dry grinding. Add an Essbm contingency of 1.30 when using a Bond-Rowland model (this is for the EF1 factor, 1.3 for dry grinding)

=== 2020-03-23: Tent diagram, sample density(SG) ===
* Fixed current sample density not passing through to tent diagram when manual entry field is empty.

=== 2020-03-21: Server upgrade, SSSAG refactoring ===
* Server operating system and Debian base packages updated.
* Single-stage SAG mill models changed, removed open circuit SAG and replaced with two closed circuit SAG options, one with other without pebble crushing.
* Mill model detail pages now include an extra line of model detail showing values for key model sub-components.

=== 2020-02-20: Crusher and WiBM table refactoring ===
* Refactored the crusher class into two distinct classes, one for cone crusher and other for HPGR.
* Refactored the ball mill work index testwork database table to include percentage of test feed passing the closing size.
* Added calculation of the Levin-B value to WiBM detail calculation.

=== 2019-12-05: SSBM Mi model ===
* Added Morrell Mi model for secondary, tertiary cone crushers and single stage ball milling
* changed icon on manual override submit buttons on circuit flowsheet panel.
* Fixed Morrell Mi models not honouring manually entered F80 and P80 overrides

=== 2019-05-03: Tent diagram caption ===
* Fixed a bug in the density displayed in the caption of a tent diagram.

=== 2019-02-20: Raw Bond Model ===
* Fixed a bug in the transfer size computation.

=== 2018-06-26: Upgraded Mpdf library ===
* June 2018 server upgrade broke the ability to create PDF reports. The Mpdf library was upgraded to the latest version minor code tweaks were done to connect it into the code base.

=== 2018-05-30: Circuit t/h limits, sample density ===
* Circuit t/h limits are now enforced when running models, and the model predicts one possible outcome where mill charges and speeds change to accommodate a reduced throughput (there are infinitely many mathematically valid possibilities).
* Determination of the sample density in the situation where there is no WiC density and multiple DWT densities has changed. Old behaviour is to pick the last DWT test density, new behaviour is to arithmetically average all DWT densities for the sample.

=== 2018-04-15: Austin SAG model default cone angle, E_SSBM for SGI & Mi models ===
* Calculations involving the Austin SAG model were not using the default 15 degree cone angle, defaulting to zero (flat-ended mill). Fixed so that no cone angle entry now is interpreted as 15 degrees.
* SSBM calculation corrected for SGI and Mi models (EF4 value now uses Bond methodology)

=== 2017-09-10: Feed and product (F80, P80) sizes manually adjustable, El Soldado SGI model ===
* Temporary changes to the F80 and P80 sizes can now be entered on the flowsheet display page (just as you can manually adjust test results on a flowsheet page). These changes are not saved, but allow users to see the effect of F80 & P80 changes without changing the stored circuit settings.
* The Single Stage SAG mill model using SGI values has been changed to the El Soldado basis (Becerra and Jorquera, Procemin 2016).

=== 2017-09-05: Minor cleanup, Mih model ===
* Forced the Mih model (Morrell HPGR model) to check that Sc is not greater than 1. This requirement is explained in the GMSG Morrell standard (2015-08-21).
* Discontinued the 'particle size plotting' tool. Modern browsers won't run java applets anymore, so the tool won't function. :'(

=== 2017-08-15: SSL certificates changed ===
* Switched the main site SSL certificate to LetsEncrypt. Added certificate to the wiki.

=== 2017-03-21: Bond models can configure internal transfer sizes ===
* The various Bond models now have the ability to modify the calibration internal transfer sizes. Rare that you would want to do this, but Alex encountered a project that needed this capability.
* Tent diagrams can now have non-integer ball charges and filling volumes.

=== 2017-03-11: Changed Mia, Mic estimate from A×b for SMC model ===
* Updated the prediction of Mia and Mic used in the Morrell SMC circuit model for the case where A×b is given, but Mia and/or Mic are not. The new estimate is based on the calibration in Doll, Procemin 2016 (paper № 35).
* Removed some unnecessary messages from tent diagram display.

=== 2016-11-03: Fixed bug with SGI single-stage SAG model ===
* The P80 wasn't being used correctly with the SS SAG model using SGI. Corrected and now appears to be working properly (thanks to Anglo American El Soldado for their Procemin paper that enabled this bug to be diagnosed).

=== 2016-10-25: New single-stage SAG circuit models ===
* Added two new models for single-stage SAG mill circuits, one based on Morrell Mi and other on Amelunxen SGI. Be careful with the SGI model as the calibration might be suspect if you are grinding below 500 µm (it should work for iron ore AG, not so sure about porphyry copper).
* Changed the listing of model results so that only the columns that matter for a particular circuit flowsheet are showing. The "ball mill" specific energy consumption doesn't show in single-stage SAG mill circuits, for example. The exported (.ODS) spreadsheets still show all columns and in their SABC column names, so E_hpgr is actually listed as E_asag (to be fixed later).

=== 2016-07-29: Mib where two WiBM records exist ===
* The way Mib is treated has changed in the case of two WiBM records exist for the same sample (duplicate ball mill Wi tests). The old method would draw the parameters (F80, P80, gpr, closing mesh) and calculate the Mib. The new method calculates the Mib in the database and then accumulates Mib values. The new method works better in the situation where one of the duplicate WiBM records has omitted the Mib parameters (accumulating NULL values works better).

=== 2016-07-20: Rudimentary calculations without entering test results is now possible ===
* Circuit calculations may now be done even if no samples are present. This is usually done for quick prototyping or checking the expected power draw of a mill without all the fuss of entering test results.
* The manual entry testwork fields are pre-populated with some bogus data (work index values of 10, for example) that you can change and re-run the calculations. These changes are not stored and you'll need to re-enter any testwork changes each time a mill or a circuit setting is modified.

=== 2016-07-20: Added last update date to projects view ===
* The listing of projects now shows the date and UTC time of the last time a complete set of "results" was generated. This date is not affected by changes to the mills or circuit settings, only the creation of a set of list of results for all samples will trigger the date to update.

=== 2016-07-20: Database index and keys ===
* Added more table indexes to speed up complicated queries such as parameter-versus-parameter plots.
* Added foreign key constraints to improve back-end database maintenance. Should not affect end users.

=== 2016-06-22: Rod Mill & Ball Mill circuit fixes, GMSG calculation ===
* Fixes to borked RMBM circuit calculations.
* Added RMBM circuit fed from open circuit crushing.
* Added GMSG Bond Standard calculation to samples with Bond series of test results.

=== 2016-04-22: Added Morrell SMC & ball mill based HPGR model ===
* Uses Morrell's Mic, Mih, Mia and Mib values to predict specific energy consumption of an HPGR circuit
* Changed summary output "proportion of power draw" for crusher classes to be based on denominator of motor output power.

=== 2016-02-26: Added %solids warning to Austin model ===
* Added a warning to Austin SAG model if %solids is outside the range of 60% to 80% solids.

=== 2016-01-15: Bug fix and more translations ===
* Fixed a long-standing bug where the liner thickness for newly created mills reverts to the default liner thickness the second time the mill is edited.
* Made mill model names translatable strings.

=== 2016-01-10: Testwork comparison chart ===
* Added the Morrell '''Mib''' value to the list of available tests to view.
* Changed the behaviour of plots where the same test is being plotted on both axis. The single determination is used as the index key (JOIN ON `id`) instead of all permutations of the sample (JOIN ON `sampleid`).

=== 2016-01-06: Articles list now has topic filters ===
* Added the ability to filter the list of articles so that only articles pertaining to a particular topic are shown. Easier to browse these shorter lists.

=== 2016-01-01: Server move ===
* Moved to an upgraded virtual server box with the latest PHP and MySQL implementation (using current stable Debian repository).

===2015-11-17: Morrell SMC model ===
* Fixed a bug where Morrell SMC model gave an error message and zero throughput. (Also related to the 2015-11-08 fix to the Raw Bond model)

===2015-11-11: Bond Single Stage SAG model ===
* Fixed a bug where Bond SSSAG model gave an error message and zero throughput. (The 2015-11-08 fix to the Raw Bond model broke the Bond SSSAG model)

===2015-11-08: SGI model Epeb handling ===
* Fixed a bug where the pebble crusher specific energy consumption was not be included in the Amelunxen SGI model Etotal value

===2015-10-05: Ball mill default cone angle ===
* Changed the default cone angle for ball mills to 15 degrees.

===2015-10-05: Report changes ===
* Allow the user to define which percentiles should appear on a report. The 'PDF export' button now opens a small text field where a space-delimited list of percentiles may be entered. If this field is blank, then no "flowsheets" will appear in the report.
* Added some more information to mill & PDF output pages, such as the mechanical & electrical efficiency of drives.

===2015-07-24: Synthetic Testwork results ===
* Added a new column to several testwork tables called 'synthetic'. If this column contains a value of '1' (boolean=true) for a test, then that test is understood to not be a real test result and is therefore not shown on the testwork comparison charts. It is available when running circuit model simulations and does show up in the list of model results.

* Fixed a bug where the motor torque for mills with qty>2 was showing the sum of the torque for all mills rather than the torque for a single mill.

===2015-06-12: Test result summary===
* A testwork summary listing now shows the '''Mia''' and '''Mib''' values needed for the Morrell SMC model. The '''DWI''' value was removed from the summary as it is not used directly in any of the models.

* Minor changes to the PDF report showing specific energy model names rather than their ID number.

===2015-06-02: Tent Diagram===
* A Tent diagram can now show just power, just torque, or overlay both.

===2015-05-13: Drive torque===
* Modified the tent diagram to show the process torque demand (at the mill shell) across the range of mill speed
* Added the torque (at the mill shell) to the list of properties in the mill detail listing.

===2015-05-07: Tent diagram===
* Modified range of tent diagram up to 85% of critical speed.
* Fixed bug where operating speed determined the torque of the tent diagram peak.

===2015-04-25: Added Morrell SMC (Mia, Mib) SAB & SABC circuit model===
* New specific energy model for SAG & ball mill circuits that uses Mia (from SMC™ test) and Mib (from a Bond WiBM) values.
* '''Must''' enter the following information for the Bond ball mill work index to permit Mib calculation in order to run this model:
** Test P100 (closing screen) size, µm
** Test P80 size, µm
** Test F80 size, µm
** Test grams per revolution (GPR)

===2015-04-21: Added rod mill-ball mill circuit model===
* New specific energy model using Bond/Rowland method for rod mills and ball mills.
* Fixed a problem with default values not appearing in drop-down select fields.
* Tweaked behaviour of SGI model under SAG-limited and ball-limited conditions.

===2015-04-10: Added Amelunxen SGI model===
* New specific energy model for SAG & ball mill circuits that uses SGI (or SPI™) values instead of Bond work index for rod mill and crushing.
* Mandatory to set the CFsag and CFball configuration factors, see the [[Model:Amelunxen SGI|documentation]].

==Bug list==
Known bugs that are scheduled for fixing:

* SGI model PDF output does not show the CFsag and CFball values [mostly cosmetic, low priority]
* The exported (.ODS) spreadsheets of circuit model results show columns with their SABC column names, so E_hpgr is actually listed as E_asag. Some meaningless columns (such as E_bm in a Single-Stage SAG circuit) also show. [Mostly cosmetic, just know to change E_asag to whatever is appropriate for your flowsheet.]

File:ExampleDB-WiRMvAxb-comparison.png

2024-07-19T22:50:26Z

Alex Doll: Alex Doll uploaded a new version of File:ExampleDB-WiRMvAxb-comparison.png

Comparison of rod mill work index (only laboratories using wave liners) to the A×b values of both JK DWT and SMC tests.

Testwork: Bond ball mill work index

2024-07-03T13:31:52Z

Alex Doll: /* Testwork: Bond Ball Mill Work Index */

[[category:Testwork]]
[[category:Bond/Barratt Model]]
[[category:SMC Model]]
[[Category:Amelunxen SGI Model]]
==Testwork: Bond Ball Mill Work Index==
{{Test|name=Bond Ball Mill Work Index|Abrev=WiBM|Alt=BWI|F80=2440 µm|P80=75-300 µm|Models=Bond models, SGI, Morrell Mi}}
The Bond ball mill work index is one of the most commonly used grindability tests in mining, and is often referred to as ''the Bond work index''.

The test is a 'locked-cycle' test where ground product is removed from test cycles and replaced by fresh feed. The test much achieve a steady-state before completion.

===Sample Requirements===

The test requires about 8 kg of material. Although it can work on feed as fine as 2.5 mm, it is best to send material to the testing laboratory that is nominally at least 8 mm (including the natural fines that are part of the sample). The laboratories have a standard way of reducing the coarse material to the (roughly) 2.5 mm size used to feed the test that will not introduce excessive fines.

===Test Inputs===

It is necessary for the engineer to specify the desired product size of the test so that the laboratory can choose the appropriate closing mesh screen for conducting the test. This product size is typically the feed size to flotation or leaching. Example product sizes are 200 µm for copper porphyries (select a 212 µm screen), 100 µm for gold cyanidation (select a 150 µm or 125 µm closing screen) or 75 µm for complex sulphides (select a 105 µm screen).

===Test Outputs===

The laboratory will report the following information:
* umClosing: The closing mesh size the test was run at, also called P100 or P1. Convert to µm, if needed, before entering into the database.
* F80: Sample feed size in µm (and usually will provide a particle size distribution)
* P80: Sample finished product size in µm (and usually will provide a particle size distribution)
* gpr: The average grams per revolution of the last three cycles (sometimes is labelled ''GPB'')
* fdpassing: The percentage (0-100) of the feed that already passes the closing screen size
* WiBM: The calculated work index (SAGMILLING.COM uses only metric units; if the laboratory reported work index in "short ton" units, multiply that value by 1.1023 and enter the result).

When entering results into the SAGMILLING.COM database table, the following extra fields are available:
* ModBWI: is this test modified from the original Bond protocol? An open-circuit Minnovex ModBWI test or a SAGDesign ball mill work index with non-standard feed would be entered as "true" (or "1" in a [[Testwork: Batch entry|batch upload]] of test results).
* synthetic indicates whether this is a real test result, or just a synthetic one that should only be used for modelling. If this column contains a value of '1' (boolean=true) for a test, then that test is understood to not be a real test result and is therefore not shown on the testwork comparison charts. Synthetic values are available when running circuit model simulations and do show up in the list of model results.

The computation of a Bond ball mill work index was empirically calibrated by Fred Bond using a short ton basis. The modern (metric tonne) basis is the following equation:

<math> Wi_{BM} = \frac{1.1023 \times 44.5}{P_{100}^{0.23} \times gpr^{0.82} \times (\frac{10}{\sqrt{P_{80}}} - \frac{10}{\sqrt{F_{80}}})}</math>

===Derived values composed from WiBM results===
* Morrell ''Mib'' value is calculated for a sample if the following are available: '''umClosing''', '''F80''', '''P80''', '''gpr'''.
** Units are kWh/t based on Morrell's empirical calibration.
** This value is used in the [[:Category:SMC Model|Morrell Mi models]].
** <math>Mib = \frac{18.18}{P_{100}^{0.295} × (gpr) \left [ P_{80}^{f(P_{80})} - F_{80}^{f(F_{80})} \right ]} </math> kWh/t
** where: f(''x'') = -0.293 - ''x''/10⁶
* ''Levin B'' parameter is calculated for a sample if the following are available: '''umClosing''', '''F80''', '''P80''', '''gpr''', '''fdpassing'''.
** Units of the Levin B are mWh per revolution of a standard Bond grindability ball mill (mWh/rev). Watch out, as this metric is also given as kWh/rev in literature.
** This value is not used in any computations, but can be used in external calculation such as [https://sagmilling.com/articles/37/view/2020%20CMP%20-%20Alex%20Doll.pdf?s=1 Functional Performance].
** <math>B = \frac{4900 × (gpr)^{0.18}}{P_{100}^{0.23} (100 - Fd%passing)}</math> mWh/rev

=== Modelling ===
Ball mill work index is used in several SAGMILLING.COM circuit models, including:
* [[Model:BondModel|Bond/Barratt specific energy consumption circuit model]].
* [[Model:Bond RMBM Model|Bond/Rowland rod mill & ball mill specific energy consumption circuit model]].
* [[Model:Amelunxen SGI|Amelunxen SGI SAG and ball mill circuit model]].
* [[Model:Morrell SMC SAG|Morrell SMC (Mib) SAG and ball mill circuit model]] (uses the ''umclosing'', ''F80'', ''P80'', and ''gpr'' values to calculate ''Mib'').

It is also used in the CEET2 model (distributed by [http://www.sgs.ca/en/Mining/Metallurgy-and-Process-Design.aspx SGS]) and is commonly used by people running the JK SimMet population balance model (distributed by [http://www.jktech.com.au JK Tech]).

The work index is used to calculate the energy requirement to grind rocks in the fine size range, below 2.5 mm into the range of a few hundreds of micrometres. Heterogeneous ore types typically are sensitive to the product size of the test, and the work index value changes if the test is performed to a coarser or finer product. Always specify the desired product size of the test to the laboratory, or conduct a [[Ball mill work index adjustment]] procedure to determine the effect of changing the product size on work index.

=== Corrections and adjustments ===

'''Estimate of P80 when P100 is known'''

(Source https://www.linkedin.com/posts/alex-doll-66b57465_workindex-comminution-grinding-activity-6873690907527532544-u6DD)

The P80 of a ball mill work index test can be estimated if the P100 is know based on this equation:
<math>P_{80}=0.92 × (P_{100})^{0.96}</math>

[[File:P80_P100-powermodel.png]]

'''Estimate grams per revolution when only P100 is known'''

NI43-101 reports often provide P100 and the work index. To estimate the other parameters, you can assume:
* the P80 is 0.92 × (P100, µm)0.96
* assume the F80 is 2440 µm (see [[https://www.researchgate.net/publication/363350623_A_new_methodology_to_obtain_a_corrected_Bond_ball_mill_work_index_valid_with_non-standard_feed_size Nikolić, Doll, & Trumić (2022)]])

The grams per revolution can be computed by rearranging Bond's laboratory equation:

<math> gpr = \left[ \frac{1.1023 \times 44.5}{P_{100}^{0.23} \times Wi_{BM} \times (\frac{10}{\sqrt{P_{80}}} - \frac{10}{\sqrt{F_{80}}})} \right]^\frac{1}{0.82} </math>

To adjust a ball mill grindability test work index or Mib value to a different P80 basis, use the [[Ball mill work index adjustment]] method of Josefin & Doll.

'''Correct for 'non standard' feed size'''

If the ball mill test feed material was too small for the stage crushing to make a normal F80, then the correction from ''Nikolić, Doll, & Trumić (2022)'' [[https://www.researchgate.net/publication/363350623_A_new_methodology_to_obtain_a_corrected_Bond_ball_mill_work_index_valid_with_non-standard_feed_size A new methodology to obtain a corrected Bond ball mill work index valid with non-standard feed size]] may be applied. The method is also described in Procemin 2022 paper [[https://www.researchgate.net/publication/372393426_Secrets_of_the_Bond_Ball_mill_grindability_test Secrets of the Bond Ball Mill Grindability Test]]

=== Computing Mib from incomplete Ball Mill Work Index data ===
Use this nomograph to compute an Mib from a ball mill work index if you know the P100 size that the test should be run at.

[[File:MibFromWiBM byP100.png]]

Conversions between test types

2024-07-02T14:06:59Z

Alex Doll: /* Medium size class */

[[category:testwork]]
==Converting between comminution test types==
Different tests are used in different grindability models for substantially the same purposes. Certain grindability tests are compatible with other tests, and an approximate conversion can be established by comparing to a database of testwork.

The determination of which tests are compatible with other tests is largely a function of the particle size of the specimens subjected to testing.[[Bibliography:_Testwork_programs|Doll & Barratt, 2011]] Ore properties also play a role because some tests are sensitive to changes in ore density and other tests operate with a biased sample consisting only of competent pieces.

===Medium size class===
The three tests in the medium size class are:
* Bond rod mill work index (WiRM)
* SAG Grindability index (SGI) or SAG Power index (SPI™)
* Drop weight test, both JK and SMC (A×b, DWI, Mia, etc)

{|
|-
| '''Bond rod mill work index versus A×b''' Only considering rod mill work index tests performed in laboratory mills equipped with wave liners. This is the standard specified by F. Bond and is typical of laboratories in North and South America. Non-standard (Australian type) rod mill results also shown for comparison.

A Non-standard rod mill result can be converted to a Bond rod mill work index by:

Bond WiRM = 0.42 × (Winonstandard)^1.22

Source: Dec 2023 Public Grindability Database

|| [[File:ExampleDB-WiRMvAxb-comparison.png]]
|-
| '''Bond rod mill Wi versus A×b for copper porphyries''' A slightly better relationship can be determined if the database is limited to projects of a similar lithology. Limiting to only the Andean copper porphyry projects results in a slightly better correlation.
|| [[File:Twcompare_axb_vs_wirm.svg‎|Published A×b and WiRM results for Andean porphyries]]
|-
| '''Bond rod mill work index versus SGI & SPI''' Only considering rod mill work index tests performed in laboratory mills equipped with wave liners. SGI does not contain a density correction, and this relationship is probably only valid for ore density in the range of 2.50 to 2.80 t/m3 Only considers SGI values less than 150 as greater values are meaningless.
|| [[File:ExampleDB-WiRMvSGI-comparison.png]]
|-
| '''SGI & SPI''' versus '''A×b''' Only considering SGI values below 150 minutes. SGI does not contain a density correction, and this relationship is probably only valid for ore density in the range of 2.50 to 2.80 t/m3
|| [[File:SGI vs A×b.png]]
|}

===Extra parameters for Drop Weight Tests (DWT)===
A drop weight test is usually interpreted using a plot of the %passing 10% of the original particle size (t10) versus the energy of the weight that impacted the specimen (Ecs). These are plotted at fit to an exponential relationship with fitting parameters "A" (coefficient) and "b" (exponent).

There are several derived parameters that are commonly used in modelling that can be calculated using these A and b values, usually based on the slope of the curve at the origin of the plot. This is commonly referred to as the (A×b) value.

* DWI = 100 × (density, kg/L) / (A×b)
* Mia = 379.40 × (A×b)-0.80
* Mih = 577.37 × (A×b)-1.00
* Mic = 296.81 × (A×b)-1.00
[[File:DWI_Axb.png]]

[[File:Mia_Axb.png]]

[[File:Mih_Axb.png]]

[[File:Mic_Axb.png]]

File:SGI vs A×b.png

2024-07-02T14:04:02Z

Alex Doll: Alex Doll uploaded a new version of File:SGI vs A×b.png

== Summary ==
Dec 2020 version of prediction equation for SGI from a drop weight A×b