2
According to GMG (2021), the feed preparation for
the ball mill grindability test should be as follows: Stage
crush the ball mill test feed sample and screen through a
3.36 mm (6 Tyler mesh) screen. Avoid over-crushing by screen-
ing, then crushing the oversize successively until it all passes
the 3.36 mm screen. The choice of the 3.36 mm top size is
described by Man (2002).
Some samples arrive at the laboratory too fine to per-
form the stage crushing, and these samples are unsuitable
for determining a work index using Equation (1).
Bond (1962) notes: Laboratory grindability tests and
commercial grinding results have shown that with many mate-
rials the work index does not remain constant for different
product sizes as P becomes smaller, the Wi values may decrease,
remain constant, or increase. For this reason, the work index
has customarily been determined at a product size close to that
desired.
The “Bond” ball mill grinding apparatus is widely avail-
able at laboratories around the world and practitioners have
come up with other metrics that can be generated using the
same apparatus. Two of the more common examples are
the ‘Levin test’ (Levin, 1989) used to investigate fine grind-
ing of ores, and the ‘Mib’ value used in the context of Mi
specific energy consumption calculations (GMG, (2021b).
METHODOLOGY
In the event that a ball mill grindability test can not be per-
formed using the standard feed preparation method or in
the event that the product size from the test is significantly
different to the desired product size in the industrial plant,
then correction methods should be used to try to salvage a
work index that is adjusted for the expected difference due
to improper feed or product size.
Correction for Incorrect Feed Size (Work Index)
Nikolić, Doll &Trumić (2022) published an algorithm
for correcting for an incorrect feed size feeding a ball mill
grindability test. The method involves a simplified “princi-
pal component” analysis, Figure 1, where the test reduction
ratio forms the X axis (empirically calibrated to be F800.2/P
0.6) and the ore grindability terms form the Y axis (empiri-
cally calibrated to be G–0.82/Wi). A database of over three
hundred ball mill work index tests are plotted against these
principal components with “valid” test feeds (arbitrarily
set to where F80 2 mm) forming a regression equation.
Laboratory tests that intentionally used finer feeds (as fine
as 600 µm) are shown as data series that roughly match the
“valid” regression curve.
In the event that a ball mill work index test can not use
a properly prepared feed (for example, the test feed came
from a laboratory HPGR or SAG mill instead of stage
crushing), then the regression equation can be used to pre-
dict a corrected work index using Equation (2).
lne
Wicorr
P
G
0.033 2440 0.0904
.6
.2
80
0
0
–0.82
$
=
+o
(2)
The test feed size is replaced with 2440 µm, a typical
feed size observed for samples prepared by stage-crushing.
Note that simply substituting 2440 µm into Equation (1)
is not valid as the G term changes with the reduction ratio.
Correction for Incorrect Feed Size (Morrell Mib)
The Morrell (2008) Mib models are similar to the Bond
model, but calibrated to a different size exponent. The
same procedure described for work index can be applied.
The same database of testwork is interrogated and principal
component equations are iterated until the data set resolves
to a single model, as per Figure 2.
The equations for the principal components are differ-
ent to those for work index, resulting in a different correc-
tion Equation (3).
..02 lne
Mib
P
G
0 03 2440 0
.6
.5
.8 corr
0
80
0
0 =
+
-0.6
o
(3)
Correction for Incorrect Product Size (Work Index)
Josefin &Doll (2018) published an algorithm to correct ball
mill work index results to a different P80 size basis to what
was observed in the laboratory test. The method requires a
reference sample that has at least three ball mill work index
determinations at three different closing sizes. The refer-
ence sample provides a “Hukki exponent,” -α, after Hukki
(1962) for the ore that is going to be somewhat different to
the Bond exponent of -½. The reference sample work index
is measured at three different closing sizes, which is turned
into a “signature plot” by converting each test work index
in the equivalent industrial mill specific energy consump-
tion using the Bond third theory Equation (4).
E Witest F P 10 .
test test test
0 5 ##=---0.5 _i (4)
The three E are plotted against their P80, and a power-
model regression is fit that generates a signature plot. The
According to GMG (2021), the feed preparation for
the ball mill grindability test should be as follows: Stage
crush the ball mill test feed sample and screen through a
3.36 mm (6 Tyler mesh) screen. Avoid over-crushing by screen-
ing, then crushing the oversize successively until it all passes
the 3.36 mm screen. The choice of the 3.36 mm top size is
described by Man (2002).
Some samples arrive at the laboratory too fine to per-
form the stage crushing, and these samples are unsuitable
for determining a work index using Equation (1).
Bond (1962) notes: Laboratory grindability tests and
commercial grinding results have shown that with many mate-
rials the work index does not remain constant for different
product sizes as P becomes smaller, the Wi values may decrease,
remain constant, or increase. For this reason, the work index
has customarily been determined at a product size close to that
desired.
The “Bond” ball mill grinding apparatus is widely avail-
able at laboratories around the world and practitioners have
come up with other metrics that can be generated using the
same apparatus. Two of the more common examples are
the ‘Levin test’ (Levin, 1989) used to investigate fine grind-
ing of ores, and the ‘Mib’ value used in the context of Mi
specific energy consumption calculations (GMG, (2021b).
METHODOLOGY
In the event that a ball mill grindability test can not be per-
formed using the standard feed preparation method or in
the event that the product size from the test is significantly
different to the desired product size in the industrial plant,
then correction methods should be used to try to salvage a
work index that is adjusted for the expected difference due
to improper feed or product size.
Correction for Incorrect Feed Size (Work Index)
Nikolić, Doll &Trumić (2022) published an algorithm
for correcting for an incorrect feed size feeding a ball mill
grindability test. The method involves a simplified “princi-
pal component” analysis, Figure 1, where the test reduction
ratio forms the X axis (empirically calibrated to be F800.2/P
0.6) and the ore grindability terms form the Y axis (empiri-
cally calibrated to be G–0.82/Wi). A database of over three
hundred ball mill work index tests are plotted against these
principal components with “valid” test feeds (arbitrarily
set to where F80 2 mm) forming a regression equation.
Laboratory tests that intentionally used finer feeds (as fine
as 600 µm) are shown as data series that roughly match the
“valid” regression curve.
In the event that a ball mill work index test can not use
a properly prepared feed (for example, the test feed came
from a laboratory HPGR or SAG mill instead of stage
crushing), then the regression equation can be used to pre-
dict a corrected work index using Equation (2).
lne
Wicorr
P
G
0.033 2440 0.0904
.6
.2
80
0
0
–0.82
$
=
+o
(2)
The test feed size is replaced with 2440 µm, a typical
feed size observed for samples prepared by stage-crushing.
Note that simply substituting 2440 µm into Equation (1)
is not valid as the G term changes with the reduction ratio.
Correction for Incorrect Feed Size (Morrell Mib)
The Morrell (2008) Mib models are similar to the Bond
model, but calibrated to a different size exponent. The
same procedure described for work index can be applied.
The same database of testwork is interrogated and principal
component equations are iterated until the data set resolves
to a single model, as per Figure 2.
The equations for the principal components are differ-
ent to those for work index, resulting in a different correc-
tion Equation (3).
..02 lne
Mib
P
G
0 03 2440 0
.6
.5
.8 corr
0
80
0
0 =
+
-0.6
o
(3)
Correction for Incorrect Product Size (Work Index)
Josefin &Doll (2018) published an algorithm to correct ball
mill work index results to a different P80 size basis to what
was observed in the laboratory test. The method requires a
reference sample that has at least three ball mill work index
determinations at three different closing sizes. The refer-
ence sample provides a “Hukki exponent,” -α, after Hukki
(1962) for the ore that is going to be somewhat different to
the Bond exponent of -½. The reference sample work index
is measured at three different closing sizes, which is turned
into a “signature plot” by converting each test work index
in the equivalent industrial mill specific energy consump-
tion using the Bond third theory Equation (4).
E Witest F P 10 .
test test test
0 5 ##=---0.5 _i (4)
The three E are plotted against their P80, and a power-
model regression is fit that generates a signature plot. The