Austin SAG model - Revision history

Alex Doll: /* Model Inputs */

2025-09-15T13:44:13Z

Model Inputs

← Older revision		Revision as of 13:44, 15 September 2025
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	* Motor rated speed, in units of mill RPM (not motor RPM, must multiply by gear ratios).		* Motor rated speed, in units of mill RPM (not motor RPM, must multiply by gear ratios).
	* Quantity of pinions (and motors)		* Quantity of pinions (and motors)

			==Model output==
			The Austin model outputs the mechanical power of the cylindrical section of a tumbling mill. The software adds an extra 5% for cone ends for situations where the mill has a cone angle greater than 1%. The default mill cone angle is 15%, so entering an angle of 0° will trigger the default of 15% (so use a fake cone angle of 0.5° for flat-ended mills).

			==Model calibration==
			Alex Doll did a model calibration check of several SAG mill power draw models (including the Austin model) in Procemin 2013 and IMPC 2016. The model deviation from measurements has a standard deviation of 9% and average/median of 1.1%/1.5% (meaning there is a minor bias high).

			These works are available from:
			<li>[https://www.sagmilling.com/articles/20/view/Procemin2013-AlexDoll-SAGPowerModels.pdf?s=1 Technical paper for Procemin 2013]
			<li>[https://www.sagmilling.com/articles/29/view/IMPC2016-AlexDoll-SAG%20data%20set.pdf?s=1 Technical paper for IMPC 2016] (supersedes the Procemin 2013 paper)
			<li>[https://www.sagmilling.com/articles/25/view/SurveyTabulation-IMPC2016-v6.ods?s=1 Data set for IMPC 2016]

Alex Doll: /* Model Inputs */

2016-06-17T23:02:13Z

Model Inputs

@@ Line 31: / Line 31: @@
 == Model Inputs==
 <b>Motor characteristics</b> are also requested:
@@ Line 38: / Line 49: @@
 * Motor efficiency and any other efficiency factors to the DCS measurement position in the network.
 * Motor rated speed, in units of mill RPM (not motor RPM, must multiply by gear ratios).

Alex Doll at 22:57, 17 June 2016

2016-06-17T22:57:34Z

← Older revision		Revision as of 22:57, 17 June 2016
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	=== Percent solids ===		=== Percent solids ===
	The model is run with a fixed 80% solids by weight <sup>[[Bibliography:_Mill_power_draw_models\|Doll, 2013]]</sup>. This is because the form of the equation proposed by Austin appears to have the %solids term in the wrong place (denominator of the expression rather than the numerator where other models put it). The calibration presented at IMPC 2016 suggests the fixed %solids term is reasonably valid over the range of 60% to 80% solids.		The model is run with a fixed 80% solids by weight <sup>[[Bibliography:_Mill_power_draw_models\|Doll, 2013]]</sup>. This is because the form of the equation proposed by Austin appears to have the %solids term in the wrong place (denominator of the expression rather than the numerator where other models put it). The calibration presented at IMPC 2016 suggests the fixed %solids term is reasonably valid over the range of 60% to 80% solids.

			== Model Inputs==


			<b>Motor characteristics</b> are also requested:

			* Motor rated power (output shaft)
			* Mechanical efficiency of downstream drive (pinions, gearboxes)
			* Motor efficiency and any other efficiency factors to the DCS measurement position in the network.
			* Motor rated speed, in units of mill RPM (not motor RPM, must multiply by gear ratios).

Alex Doll: /* Percent solids */

2016-02-26T20:10:40Z

Percent solids

← Older revision		Revision as of 20:10, 26 February 2016
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	=== Percent solids ===		=== Percent solids ===
	The model is run with a fixed 80% solids by weight <sup>[[Bibliography:_Mill_power_draw_models\|Doll, 2013]]</sup>. This is because the form of the equation proposed by Austin appears to have the %solids term in the wrong place (denominator of the expression rather than the numerator where other models put it).		The model is run with a fixed 80% solids by weight <sup>[[Bibliography:_Mill_power_draw_models\|Doll, 2013]]</sup>. This is because the form of the equation proposed by Austin appears to have the %solids term in the wrong place (denominator of the expression rather than the numerator where other models put it). The calibration presented at IMPC 2016 suggests the fixed %solids term is reasonably valid over the range of 60% to 80% solids.

Alex Doll: /* Percent solids */

2016-02-26T20:09:33Z

Percent solids

← Older revision		Revision as of 20:09, 26 February 2016
Line 27:		Line 27:

	=== Percent solids ===		=== Percent solids ===
	The model is run with a fixed 80% solids by wt<sup>[[Bibliography:_Mill_power_draw_models\|Doll, 2013]]</sup>. This is because the form of the equation proposed by Austin appears to have the %solids term in the wrong place (denominator of the expression rather than the numerator where other models put it).		The model is run with a fixed 80% solids by weight <sup>[[Bibliography:_Mill_power_draw_models\|Doll, 2013]]</sup>. This is because the form of the equation proposed by Austin appears to have the %solids term in the wrong place (denominator of the expression rather than the numerator where other models put it).

Alex Doll: /* Mill cone angles */

2016-02-26T20:09:00Z

Mill cone angles

← Older revision		Revision as of 20:09, 26 February 2016
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	To account for cone ends of mills, an allowance of 5% is used <sup>[[Bibliography:_Mill_power_draw_models\|Doll, 2013]]</sup> instead of the formula proposed by Austin.		To account for cone ends of mills, an allowance of 5% is used <sup>[[Bibliography:_Mill_power_draw_models\|Doll, 2013]]</sup> instead of the formula proposed by Austin.

			=== Percent solids ===
			The model is run with a fixed 80% solids by wt<sup>[[Bibliography:_Mill_power_draw_models\|Doll, 2013]]</sup>. This is because the form of the equation proposed by Austin appears to have the %solids term in the wrong place (denominator of the expression rather than the numerator where other models put it).

Alex Doll: /* Model Form */

2015-04-19T16:57:26Z

Model Form

← Older revision		Revision as of 16:57, 19 April 2015
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	* ''ρ<sub>X</sub>'' is the density of component ''X'', t/m<sup>3</sup>		* ''ρ<sub>X</sub>'' is the density of component ''X'', t/m<sup>3</sup>
	* ''φ<sub>C</sub>'' is the mill speed as a fraction of critical (eg. 0.75 for 75% of critical)		* ''φ<sub>C</sub>'' is the mill speed as a fraction of critical (eg. 0.75 for 75% of critical)

			=== Mill cone angles ===
			The model supports flat-ended mills (cone angle of 0°) or a cone angle of 15°. Any other value entered for the cone angle will be treated as 15°.

	To account for cone ends of mills, an allowance of 5% is used <sup>[[Bibliography:_Mill_power_draw_models\|Doll, 2013]]</sup> instead of the formula proposed by Austin.		To account for cone ends of mills, an allowance of 5% is used <sup>[[Bibliography:_Mill_power_draw_models\|Doll, 2013]]</sup> instead of the formula proposed by Austin.

Alex Doll at 04:58, 7 February 2014

2014-02-07T04:58:49Z

← Older revision		Revision as of 04:58, 7 February 2014
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	[[category:Models]]		[[category:Models]]
			[[category:Mill power draw models]]
	==History==		==History==
	The SAG mill model by proposed by [[Bibliography:_Mill_power_draw_models\|Leonard Austin (1990)]] was largely based on modifications of earlier tumbling mill models by Hogg & Fuerstenau and F. Bond. The model uses a kinetic-potential energy balance to describe the power draw of a mill charge. Many geometric components of the earlier models were fit to empirical relationships measured by Austin.		The SAG mill model by proposed by [[Bibliography:_Mill_power_draw_models\|Leonard Austin (1990)]] was largely based on modifications of earlier tumbling mill models by Hogg & Fuerstenau and F. Bond. The model uses a kinetic-potential energy balance to describe the power draw of a mill charge. Many geometric components of the earlier models were fit to empirical relationships measured by Austin.

Alex Doll: /* Model Form */

2014-02-07T04:52:44Z

Model Form

← Older revision		Revision as of 04:52, 7 February 2014
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	* ''L'' is the mill effective grinding length (also referred to as the 'belly length), m		* ''L'' is the mill effective grinding length (also referred to as the 'belly length), m
	* ''J<sub>total</sub>'' is the mill total volumetric filling as a fraction (eg. 0.30 for 30%)		* ''J<sub>total</sub>'' is the mill total volumetric filling as a fraction (eg. 0.30 for 30%)
	* ''ε<sub>B</sub>'' is the ~~rosity~~ of the rock and ball load (use 0.3)		* ''ε<sub>B</sub>'' is the porosity of the rock and ball load (use 0.3)
	* ''w<sub>C</sub>'' is the charge %solids, fraction by weight (use 0.80 <sup>[[Bibliography:_Mill_power_draw_models\|Doll, 2013]]</sup>)		* ''w<sub>C</sub>'' is the charge %solids, fraction by weight (use 0.80 <sup>[[Bibliography:_Mill_power_draw_models\|Doll, 2013]]</sup>)
	* ''J<sub>balls</sub>'' is the mill volumetric filling of balls as a fraction (eg. 0.10 for 10%)		* ''J<sub>balls</sub>'' is the mill volumetric filling of balls as a fraction (eg. 0.10 for 10%)

Alex Doll at 00:15, 5 December 2013

2013-12-05T00:15:38Z

← Older revision		Revision as of 00:15, 5 December 2013
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			[[category:Models]]
	==History==		==History==
	The SAG mill model by proposed by [[Bibliography:_Mill_power_draw_models\|Leonard Austin (1990)]] was largely based on modifications of earlier tumbling mill models by Hogg & Fuerstenau and F. Bond. The model uses a kinetic-potential energy balance to describe the power draw of a mill charge. Many geometric components of the earlier models were fit to empirical relationships measured by Austin.		The SAG mill model by proposed by [[Bibliography:_Mill_power_draw_models\|Leonard Austin (1990)]] was largely based on modifications of earlier tumbling mill models by Hogg & Fuerstenau and F. Bond. The model uses a kinetic-potential energy balance to describe the power draw of a mill charge. Many geometric components of the earlier models were fit to empirical relationships measured by Austin.