Testwork: Bond ball mill work index - Revision history

Alex Doll: /* Corrections and adjustments */

2026-05-25T20:49:30Z

Corrections and adjustments

← Older revision		Revision as of 20:49, 25 May 2026
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	The grams per revolution can be computed by rearranging Bond's laboratory equation:		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}		<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>


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	'''Correct for 'non standard' feed size'''		'''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]]		If the ball mill test feed material was too small for the stage crushing to make a normal F<sub>80</sub>, 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 ===		=== Computing Mib from incomplete Ball Mill Work Index data ===

Alex Doll: /* Derived values composed from WiBM results */

2026-05-25T20:48:35Z

Derived values composed from WiBM results

← Older revision		Revision as of 20:48, 25 May 2026
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	** Units are kWh/t based on Morrell's empirical calibration.		** Units are kWh/t based on Morrell's empirical calibration.
	** This value is used in the [[:Category:SMC Model\|Morrell Mi models]].		** 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		** <math> Mib = \frac{18.18}{P_{100}^{0.295} \times (gpr) \left [ P_{80}^{f(P_{80})} - F_{80}^{f(F_{80})} \right ]}</math> kWh/t
	** where: f(''x'') = -0.293 - ''x''/10⁶		** 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'''.		* ''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.		** 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].		** 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		** <math> B = \frac{4900 \times (gpr)^{0.18}}{P_{100}^{0.23} (100 - Fd%passing)} </math> mWh/rev

	=== Modelling ===		=== Modelling ===

Alex Doll: /* Test Outputs */

2026-05-25T20:46:23Z

Test Outputs

← Older revision		Revision as of 20:46, 25 May 2026
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	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:		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}}})}		<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 Wi<sub>BM</sub> results===		===Derived values composed from Wi<sub>BM</sub> results===

Alex Doll at 08:45, 4 March 2026

2026-03-04T08:45:12Z

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

2024-07-03T13:31:52Z

Testwork: Bond Ball Mill Work Index

← Older revision		Revision as of 13:31, 3 July 2024
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	[[Category:Amelunxen SGI Model]]		[[Category:Amelunxen SGI Model]]
	==Testwork: Bond Ball Mill Work Index==		==Testwork: Bond Ball Mill Work Index==
	{{Test\|name=Bond Ball Mill Work Index\|Abrev=Wi<sub>BM</sub>\|Alt=BWI\|F80=~~2500~~ µm\|P80=75-300 µm\|Models=Bond models, SGI, Morrell Mi}}		{{Test\|name=Bond Ball Mill Work Index\|Abrev=Wi<sub>BM</sub>\|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 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''.

Alex Doll: /* Corrections and adjustments */

2024-02-22T18:02:40Z

Corrections and adjustments

← Older revision		Revision as of 18:02, 22 February 2024
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	=== Corrections and adjustments ===		=== Corrections and adjustments ===

	'''Estimate of ~~P80~~ when ~~P100~~ is known'''		'''Estimate of P<sub>80</sub> when P<sub>100</sub> is known'''

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

Alex Doll: /* Derived values composed from WiBM results */

2024-02-22T18:01:10Z

Derived values composed from WiBM results

← Older revision		Revision as of 18:01, 22 February 2024
Line 42:		Line 42:
	** where: f(''x'') = -0.293 - ''x''/10⁶		** 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'''.		* ''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.		** 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].		** 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		** <math>B = \frac{4900 × (gpr)^{0.18}}{P_{100}^{0.23} (100 - Fd%passing)}</math> mWh/rev

Alex Doll: /* Computing Mib from incomplete data */

2024-02-19T17:34:37Z

Computing Mib from incomplete data

← Older revision		Revision as of 17:34, 19 February 2024
Line 85:		Line 85:
	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]]		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 data ===		=== 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.		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.

Alex Doll: /* Derived values composed from WiBM results */

2023-10-12T16:05:04Z

Derived values composed from WiBM results

← Older revision		Revision as of 16:05, 12 October 2023
Line 40:		Line 40:
	** This value is used in the [[:Category:SMC Model\|Morrell Mi models]].		** 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		** <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		** 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'''.		* ''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.		** 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.

Alex Doll: /* Derived values composed from WiBM results */

2023-10-12T16:03:05Z

Derived values composed from WiBM results

← Older revision		Revision as of 16:03, 12 October 2023
Line 40:		Line 40:
	** This value is used in the [[:Category:SMC Model\|Morrell Mi models]].		** 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		** <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'''.		* ''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.		** 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.

← Older revision		Revision as of 08:45, 4 March 2026
Line 33:		Line 33:
	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:		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>~~		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 Wi<sub>BM</sub> results===		===Derived values composed from Wi<sub>BM</sub> results===
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	** Units are kWh/t based on Morrell's empirical calibration.		** Units are kWh/t based on Morrell's empirical calibration.
	** This value is used in the [[:Category:SMC Model\|Morrell Mi models]].		** 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		** \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		** 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'''.		* ''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.		** 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].		** 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		** B = \frac{4900 × (gpr)^{0.18}}{P_{100}^{0.23} (100 - Fd%passing)} mWh/rev

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

	[[File:P80_P100-powermodel.png]]		[[File:P80_P100-powermodel.png]]
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	The grams per revolution can be computed by rearranging Bond's laboratory equation:		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>~~		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}