Model:Bond RMBM Model - Revision history

Alex Doll at 18:48, 6 March 2022

2022-03-06T18:48:12Z

Alex Doll: /* Formulae */

2021-11-23T16:31:29Z

Formulae

Alex Doll: /* Optional parameters */

2020-03-22T17:49:12Z

Optional parameters

Alex Doll: /* Formulae */

2016-06-22T17:37:25Z

Formulae

Alex Doll: /* Formulae */

2016-06-22T17:35:30Z

Formulae

Alex Doll: /* Bond/Rowland rod mill ball mill model */

2016-06-22T17:13:41Z

Bond/Rowland rod mill ball mill model

Alex Doll: /* Secondary and tertiary crushers */

2015-04-26T17:12:54Z

Secondary and tertiary crushers

Alex Doll: Created page with "category:Models category:Specific Energy Models Category:Bond rod mill ball mill Model == Bond/Rowland rod mill ball mill model == This is a rod mill feeding a bal..."

2015-04-26T16:52:42Z

Created page with "category:Models category:Specific Energy Models Category:Bond rod mill ball mill Model == Bond/Rowland rod mill ball mill model == This is a rod mill feeding a bal..."

New page

[[category:Models]]
[[category:Specific Energy Models]]
[[Category:Bond rod mill ball mill Model]]
== Bond/Rowland rod mill ball mill model ==
This is a rod mill feeding a ball mill model that estimates the specific energy consumption (ERM and EBM) using the Rowland interpretation of the classical Bond work index equation including Rowland efficiency factors.

===Testwork Required===
* [[Testwork: Bond ball mill work index|Bond ball mill work index]]
* [[Testwork: Bond rod mill work index|Bond rod mill work index]]

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

<math> E_{total} = E_{RM} + E_{BM} </math>

The rod mill oversize feed factor (EF4RM) is calculated using the greater of the sample's rod mill or crushing work index (which is usually the WiRM). The optimal feed size and EF4 are both calculated using whichever is greater.

<math>
EF_4^{RM} =\left [ 1 + \left( \frac{ (0.907 \times Wi_{RM} - 7) }{ \left (\frac{F_{80} }{ T_{80}} \right )} \right) \left ( {\frac{F_{80} }{ { 16 000 \left(\frac{14.33}{Wi_{RM} } \right )^{0.5}}} }-1 \right ) \right ]
</math>

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

<math>
EF_4^{BM} =\left [ 1 + \left( \frac{(0.907 \times Wi_{BM} - 7) }{ \left (\frac{T_{80} }{ P_{80}} \right )} \right) \left ( {\frac{T_{80} }{ { 4000 \left(\frac{14.33}{Wi_{RM} } \right )^{0.5}}} }-1 \right ) \right ]
</math>

where:
* F80, µm is the specified circuit feed size (crushing plant product)
* T80, µm is the transfer size that balances the power draw in rod & ball mill stages.
* P80, µm is the specified product size (hydrocyclone overflow)

== Secondary and tertiary crushers ==

The model assumes any secondary and/or tertiary crushing happens upstream of the rod mill. Crusher specific energy is not included in this model.

The choice of crushers and arrangement is normally based on volumetric flow and not on power draw. Use a crusher catalogue or another tool, like Metso's Bruno software, to determine the size and arrangement of the crushers ahead of the ball mill(s).

← Older revision		Revision as of 16:31, 23 November 2021
Line 46:		Line 46:


−	~~The~~ ball mill ~~oversize~~ ~~feed~~ ~~factor~~ (EF<sub>4</sub><sup>BM</sup>) is ~~always calculated with the~~ ball mill work index. ~~The~~ ~~optimal~~ feed ~~size~~ ~~for~~ the ~~EF<sub>4</sub><sup>BM</sup>~~ is ~~always~~ ~~calculated~~ ~~using~~ the ~~rod~~ ~~mill~~ ~~work~~ ~~index~~.	+	Both the ball mill and rod mill work index values are used to compute EF<sub>4</sub><sup>BM</sup>: The ball mill work index in the oversize feed factor component and the rod mill work index in the optimal feed size component.

	<math>		<math>

@@ Line 69: / Line 69: @@
 * '''T<sub>80</sub> min''' and '''T<sub>80</sub> min''' override the transfer size restrictions built into the model
 * [[Ball mill work index adjustment]] used to adjust Wi<sub>BM</sub> for different P<sub>80</sub> sizes.
-** '''coefficient (a)''', the fitted coefficient to the adjustment equation
+** '''coefficient (a)''', the fitted Hukki coefficient to the adjustment equation (enter as a positive number)
 === Secondary and tertiary crushers ===

@@ Line 18: / Line 18: @@
 <math>
-E_{BM} = Wi_{BM} \times \left ( \tfrac {10}{\sqrt{ P_{80} }} - \tfrac {10}{\sqrt{ F_{80} }} \right ) \times EF_4^{BM} \times EF_5</math>
+E_{BM} = Wi_{BM} \times \left ( \tfrac {10}{\sqrt{ P_{80} }} - \tfrac {10}{\sqrt{ T_{80} }} \right ) \times EF_4^{BM} \times EF_5</math>
 <sup>[[Bibliography:_Specific_energy_consumption_models|Rowland, 2006]]</sup>

@@ Line 15: / Line 15: @@
 === Formulae ===
 <math>
-E_{RM} = Wi_{RM} \times \left ( \tfrac {10}{\sqrt{ T_{80} }} - \tfrac {10}{\sqrt{ F_{80} }} \right )\times EF_4^{RM} </math>
+E_{RM} = Wi_{RM} \times \left ( \tfrac {10}{\sqrt{ T_{80} }} - \tfrac {10}{\sqrt{ F_{80} }} \right )\times EF_4^{RM} \times EF_6 \times EF_8 </math>
 <math>
 E_{BM} = Wi_{BM} \times \left ( \tfrac {10}{\sqrt{ P_{80} }} - \tfrac {10}{\sqrt{ F_{80} }} \right ) \times EF_4^{BM} \times EF_5</math>
@@ Line 27: / Line 28: @@
 EF_4^{RM} =\left [ 1 +  \left( \frac{ (0.907 \times Wi_{RM}  - 7) }{ \left (\frac{F_{80} }{ T_{80}} \right )}  \right) \left ( {\frac{F_{80} }{ { 16 000 \left(\frac{14.33}{Wi_{RM} } \right )^{0.5}}} }-1 \right ) \right ]
 </math>
 The ball mill oversize feed factor (EF<sub>4</sub><sup>BM</sup>) is always calculated with the ball mill work index.  The optimal feed size for the EF<sub>4</sub><sup>BM</sup> is always calculated using the rod mill work index.
@@ Line 39: / Line 57: @@
 * P<sub>80</sub>, &micro;m is the specified product size (hydrocyclone overflow)
 ===Required parameters===

← Older revision		Revision as of 17:12, 26 April 2015
Line 36:		Line 36:


		+	===Required parameters===
⚫	== Secondary and tertiary crushers ==
		+	* '''F<sub>80</sub>, µm''' is the 80% passing size of the fresh feed to the circuit (expected to be a Bond-compatible size distribution).
		+	* '''P<sub>80</sub>, 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.
		+
		+	===Optional parameters===
		+	* '''Description''' and '''Comment''' are optional text fields
		+	* '''Maximum t/h limit''' is a t/h throughput above which a warning message is displayed (but does not actually limit the throughput).
		+	* '''T<sub>80</sub> min''' and '''T<sub>80</sub> min''' override the transfer size restrictions built into the model
		+	* [[Ball mill work index adjustment]] used to adjust Wi<sub>BM</sub> for different P<sub>80</sub> sizes.
		+	** '''coefficient (a)''', the fitted coefficient to the adjustment equation
		+	** '''exponent (b)''', the fitted exponent to the adjustment equation
		+
		+
		⚫	=== Secondary and tertiary crushers ===

	The model assumes any secondary and/or tertiary crushing happens upstream of the rod mill. Crusher specific energy is not included in this model.		The model assumes any secondary and/or tertiary crushing happens upstream of the rod mill. Crusher specific energy is not included in this model.

@@ Line 1: / Line 1: @@
 [[category:Models]]
 [[category:Specific Energy Models]]
-[[Category:Bond rod mill ball mill Model]]
+[[Category:P80 adjustment]]
 == Bond/Rowland rod mill ball mill model ==
 This is a rod mill feeding a ball mill model that estimates the specific energy consumption (E<sub>RM</sub> and E<sub>BM</sub>) using the Rowland interpretation of the classical Bond work index equation including Rowland efficiency factors.