4
Levin B Value
Levin (1989), proposed a method to generate a signature plot
suitable for fine grinding using the apparatus of the Bond ball
mill. The Levin B value is generally used in three contexts,
• specific energy prediction for fine grinding,
• performing quality-control benchmarking of labora-
tory results, and
• a modified Functional Performance assessment of a
ball milling circuit Doll et al, (2020).
The Levin B value is computed using the parameters of
a Bond ball mill work index test, per Equation (10):
B P Fp%passingh
G
100
4900
.23
.18
100
0
0 #=-^
(10)
where, Fd%passing is the percentage of the feed to the test
that already passes the closing screen size (P100).
RESULTS AND DISCUSSION
Feed Size Correction Example
The correction for feed size should be applicable to the
case of a “Sd-bwi” result from a SAGDesign test program.
The Sd_bwi is determined by placing the SAGDesign mill
contents into a Bond ball mill grindability apparatus, and
then running the ball mill test using the standard Bond
procedure. Only the feed size distribution is different to a
standard Bond ball mill work index test.
A series of 10 samples for an Andean copper project
were treated to both the SAGDesign test (including Sd_
bwi) and the standard Bond ball mill work index test with
180 µm closing screens. The SAGDesign results (with the
non- standard ball mill feed) are given in Table 1.
The regular Bond ball mill work index test, with feed
prepared by stage-crushing, was also determined for all
samples. This “proper” Bond test (Wi_Bond) is compared
with the corrected Wi values from the Sd_bwi samples
(Wi_corr), as shown in Table 2. Assuming a normal varia-
tion of ±8% on the repeatability of the Bond ball mill work
index test, then all samples have less deviation between
the corrected Wi and the actual Bond Wi versus what we
would expect from a simple repeated test.
The conclusion is the difference observed between a
regular Bond ball mill work index and a Sd_bwi is not due
to the feed to Sd_bwi being ground in a SAG mill, it is due
to the finer size of feed material introduced into the ball
mill grindability apparatus.
Product Size Correction Example
Calibration sample chosen for this example had three ball
mill grindability tests performed at different closing screen
sizes. Three Bond ball mill work index tests performed for a
Canadian gold mine are presented in Table 3.
The signature plot in Figure 3 is obtained by fitting a
power-model to the E versus P80 data from Table 3. The
Hukki exponent (–α) for Bond equations is –0.56, and the
Hukki exponent (–α) for Morrell equations is –0.69.
These exponents can now be used to correct a
larger data set of samples “similar to” the calibration
samples by computing each sample’s K values using
Table 1. SAGDesign Sd_bwi results (with non-standard
feed)
Sample F
80 ,µm P
80 ,µm g/rev Sd_bwi
A 1373 145 2.625 12.8
B 1381 138 2.665 11.9
C 1370 138 2.748 11.7
D 1369 139 3.083 10.5
E 1829 139 2.309 13.0
F 1734 137 2.579 12.1
G 1798 138 2.265 13.2
H 1618 137 2.519 12.1
I 1639 136 2.445 12.8
J 1602 137 2.442 12.3
Table 2. Bond ball mill work index results (with standard feed) and corrected Wi from Sd_bwi
F80, µm P80, µm g/rev
Wi_Bond
(Wi units)
Wi_corr
(Wi units)
Diff
(Wi units)
Diff
(%)
A 2288 145 2.58 11.0 10.5 –0.5 –4.9%
B 1927 144 2.82 10.4 10.1 –0.4 –3.7%
C 1926 143 2.96 10.0 9.9 –0.2 –1.8%
D 1601 145 3.44 9.3 9.0 –0.3 –3.2%
E 1845 144 2.54 11.5 11.4 –0.1 –1.1%
F 1887 143 2.83 10.5 10.3 –0.1 –1.0%
G 1840 143 2.45 11.8 11.5 –0.3 –2.3%
H 1877 143 2.96 10.1 10.5 0.5 4.6%
I 1928 144 2.66 10.9 10.8 –0.2 –2.1%
J 1948 143 2.73 10.7 10.8 0.1 1.1%
Levin B Value
Levin (1989), proposed a method to generate a signature plot
suitable for fine grinding using the apparatus of the Bond ball
mill. The Levin B value is generally used in three contexts,
• specific energy prediction for fine grinding,
• performing quality-control benchmarking of labora-
tory results, and
• a modified Functional Performance assessment of a
ball milling circuit Doll et al, (2020).
The Levin B value is computed using the parameters of
a Bond ball mill work index test, per Equation (10):
B P Fp%passingh
G
100
4900
.23
.18
100
0
0 #=-^
(10)
where, Fd%passing is the percentage of the feed to the test
that already passes the closing screen size (P100).
RESULTS AND DISCUSSION
Feed Size Correction Example
The correction for feed size should be applicable to the
case of a “Sd-bwi” result from a SAGDesign test program.
The Sd_bwi is determined by placing the SAGDesign mill
contents into a Bond ball mill grindability apparatus, and
then running the ball mill test using the standard Bond
procedure. Only the feed size distribution is different to a
standard Bond ball mill work index test.
A series of 10 samples for an Andean copper project
were treated to both the SAGDesign test (including Sd_
bwi) and the standard Bond ball mill work index test with
180 µm closing screens. The SAGDesign results (with the
non- standard ball mill feed) are given in Table 1.
The regular Bond ball mill work index test, with feed
prepared by stage-crushing, was also determined for all
samples. This “proper” Bond test (Wi_Bond) is compared
with the corrected Wi values from the Sd_bwi samples
(Wi_corr), as shown in Table 2. Assuming a normal varia-
tion of ±8% on the repeatability of the Bond ball mill work
index test, then all samples have less deviation between
the corrected Wi and the actual Bond Wi versus what we
would expect from a simple repeated test.
The conclusion is the difference observed between a
regular Bond ball mill work index and a Sd_bwi is not due
to the feed to Sd_bwi being ground in a SAG mill, it is due
to the finer size of feed material introduced into the ball
mill grindability apparatus.
Product Size Correction Example
Calibration sample chosen for this example had three ball
mill grindability tests performed at different closing screen
sizes. Three Bond ball mill work index tests performed for a
Canadian gold mine are presented in Table 3.
The signature plot in Figure 3 is obtained by fitting a
power-model to the E versus P80 data from Table 3. The
Hukki exponent (–α) for Bond equations is –0.56, and the
Hukki exponent (–α) for Morrell equations is –0.69.
These exponents can now be used to correct a
larger data set of samples “similar to” the calibration
samples by computing each sample’s K values using
Table 1. SAGDesign Sd_bwi results (with non-standard
feed)
Sample F
80 ,µm P
80 ,µm g/rev Sd_bwi
A 1373 145 2.625 12.8
B 1381 138 2.665 11.9
C 1370 138 2.748 11.7
D 1369 139 3.083 10.5
E 1829 139 2.309 13.0
F 1734 137 2.579 12.1
G 1798 138 2.265 13.2
H 1618 137 2.519 12.1
I 1639 136 2.445 12.8
J 1602 137 2.442 12.3
Table 2. Bond ball mill work index results (with standard feed) and corrected Wi from Sd_bwi
F80, µm P80, µm g/rev
Wi_Bond
(Wi units)
Wi_corr
(Wi units)
Diff
(Wi units)
Diff
(%)
A 2288 145 2.58 11.0 10.5 –0.5 –4.9%
B 1927 144 2.82 10.4 10.1 –0.4 –3.7%
C 1926 143 2.96 10.0 9.9 –0.2 –1.8%
D 1601 145 3.44 9.3 9.0 –0.3 –3.2%
E 1845 144 2.54 11.5 11.4 –0.1 –1.1%
F 1887 143 2.83 10.5 10.3 –0.1 –1.0%
G 1840 143 2.45 11.8 11.5 –0.3 –2.3%
H 1877 143 2.96 10.1 10.5 0.5 4.6%
I 1928 144 2.66 10.9 10.8 –0.2 –2.1%
J 1948 143 2.73 10.7 10.8 0.1 1.1%