Testwork: Bond ball mill work index - Revision history

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

Alex Doll: /* Corrections and adjustments */

2024-02-22T18:02:40Z

Corrections and adjustments

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

2024-02-22T18:01:10Z

Derived values composed from WiBM results

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

2024-02-19T17:34:37Z

Computing Mib from incomplete data

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

2023-10-12T16:05:04Z

Derived values composed from WiBM results

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

2023-10-12T16:03:05Z

Derived values composed from WiBM results

Alex Doll: /* Corrections and adjustments */

2023-08-30T15:31:20Z

Corrections and adjustments

Alex Doll: /* Test Outputs */

2023-08-30T15:28:22Z

Test Outputs

Alex Doll: /* Corrections and adjustments */

2023-08-30T15:25:28Z

Corrections and adjustments

@@ 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:
-<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===
@@ Line 39: / Line 39: @@
 ** 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
+** \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].
-** <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 ===
@@ Line 64: / Line 64: @@
 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]]
@@ Line 76: / Line 76: @@
 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}

@@ Line 4: / Line 4: @@
 [[Category:Amelunxen SGI Model]]
 ==Testwork: Bond Ball Mill Work Index==
-{{Test|name=Bond Ball Mill Work Index|Abrev=Wi<sub>BM</sub>|Alt=BWI|F80=2500 &micro;m|P80=75-300 &micro;m|Models=Bond models, SGI, Morrell Mi}}
+{{Test|name=Bond Ball Mill Work Index|Abrev=Wi<sub>BM</sub>|Alt=BWI|F80=2440 &micro;m|P80=75-300 &micro;m|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''.

@@ Line 59: / Line 59: @@
 === 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)

@@ Line 42: / Line 42: @@
 ** 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.
+** 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

@@ 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, &amp; 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.

← Older revision		Revision as of 15:31, 30 August 2023
Line 66:		Line 66:

	[[File:P80_P100-powermodel.png]]		[[File:P80_P100-powermodel.png]]
		+
		+	'''Estimate grams per revolution when only P100 is known'''
		+
		+	NI43-101 reports often provide P<sub>100</sub> and the work index. To estimate the other parameters, you can assume:
		+	* the P<sub>80</sub> is 0.92 × (P<sub>100</sub>, µm)<sup>0.96</sup>
		+	* assume the F<sub>80</sub> 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 P<sub>80</sub> basis, use the [[Ball mill work index adjustment]] method of Josefin & Doll.		To adjust a ball mill grindability test work index or Mib value to a different P<sub>80</sub> basis, use the [[Ball mill work index adjustment]] method of Josefin & Doll.

← Older revision		Revision as of 15:28, 30 August 2023
Line 34:		Line 34:

	<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>		<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>
−
−	NI43-101 reports often provide P<sub>100</sub> and the work index. To estimate the other parameters, you can assume:
−	* the P<sub>80</sub> is 0.92 × (P<sub>100</sub>, µm)<sup>0.96</sup> (see below for details)
−	* assume the F<sub>80</sub> is 2440 µm (see Nikolić & Doll paper in preparation)
−
−	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>

	===Derived values composed from Wi<sub>BM</sub> results===		===Derived values composed from Wi<sub>BM</sub> results===