10
that the choice “is dictated by extraneous circumstances.”
He noted that wet grinding would typically provide a Work
Index of 12, compared to 16 for dry.
In 1956, the Portland Cement Association published
its then internal-confidential report to its membership
describing the Allis-Chalmers ball mill grindability test
and Bond’s Third Theory equation using the test to size
ball mills and to quantify the relative efficiency of plant
grinding installations “to check all the variables in any
grinding set-up.” It expounded on the accuracy with which
the method predicted full scale milling energy usage. “The
Allis-Chalmers ball mill test is recommended for adoption
as a standard grindability test for the cement industry.”
In the March, 1957, E&MJ, Bond responded to ques-
tions raised by J.F. Meyer concerning the interpretation of
his theories considering a very low speed (59% of critical),
low (20%) ball charge ball mill displaying 40% lower Work
Index than a parallel one at normal conditions. While suffi-
cient data were lacking for proper analysis, Bond suggested
that “in mill classification,” or preferential grinding of the
significantly heavier mineral, played an important role in
this instance.
In September, 1957, Bond presented “Tumbling Mills
and Structural Clay Products” to the American Ceramic
Society. He presented his Third Theory, and made general
observations regarding the use of rod and ball mills for the
preparation of structural clay products.
That December of 1957 Bond published
“Comminution Exposure Constant by the Third Theory”
in Mining Engineering. This was a largely theoretical work
which attempted to quantify how much larger particles are
preferentially exposed to work input. A variation of an ear-
lier unpublished method (see Figure 5) to fit particle size
distributions to an equation was presented. He also stated
that the best overall size reduction “efficiency” is obtained
on single sized particles. Using the Work Index equation,
he showed how more narrowly sized particles in closed-
circuit ball milling result in better grinding efficiency com-
pared to open circuit, and the resulting product sizing is
also narrower. While the matter is compounded by classifi-
cation effects (which are neglected), as well as the grinding
environment’s effectiveness on different particle sizes, this
paper does suggest that there is a grinding benefit with fines
removed from ball mill feed.
In the May, 1958, issue of Mining Engineering in
“Grinding Ball Size Selection” Bond updated his recom-
mended ball sizing equation from that which he gave in
1952 in “Mathematics of Crushing and Grinding,” add-
ing “theoretical considerations” related to his Work Index
theory. (It was later amended to that used today.) He also
provided an updated rod sizing equation and tables for
start-up equilibrium ball and rod charge media sizes and
gave average media wear rates expressed in consumption
“per 24-hour day for each 100 hp drawn grinding silicious
materials.”
Bond and B. B. Whitney (General Superintendent at
Inspiration Copper Company in Arizona) presented “The
Work Index in Blasting” to a Colorado School of Mines
rock mechanics symposium in April, 1959. From the esti-
mated power yield of dynamite and three blasts conducted
there with different loading they concluded that the Third
Theory can be applied to blasting. Analysis of blast data
from other properties indicated that crushing Work Index
is likely lower than that for blasting.
“Confirmation of the Third Theory” was submit-
ted to SME by Bond in November, 1958, presented in
San Francisco in February 1959, and published in AIME
Transactions in 1960. Bond used experiments in the 12"
× 12" laboratory ball mill and crack length assumed to be
related to surface area to demonstrate the Third Theory
premise that useful work done is directly proportional to
length of new cracks formed, and so the inverse of square
root of particle size. He introduced the correction factor to
be used for P80 less than 70 microns ((P80 +10.3)/1.145 x
P80) “to account for the increased work done in producing
sub-grind-limit particles.” He states when material has part
of its fines removed its resistance to size reduction based on
the 80% passing size is increased, and provides a needed
correction factor to apply to that value.
In the same paper he also presented a new “Third
Theory size distribution plot” to deal with unaccounted
Figure 5. Size distribution chart
(courtesy of Robert S. Jermyn, Allis-Chalmers)
that the choice “is dictated by extraneous circumstances.”
He noted that wet grinding would typically provide a Work
Index of 12, compared to 16 for dry.
In 1956, the Portland Cement Association published
its then internal-confidential report to its membership
describing the Allis-Chalmers ball mill grindability test
and Bond’s Third Theory equation using the test to size
ball mills and to quantify the relative efficiency of plant
grinding installations “to check all the variables in any
grinding set-up.” It expounded on the accuracy with which
the method predicted full scale milling energy usage. “The
Allis-Chalmers ball mill test is recommended for adoption
as a standard grindability test for the cement industry.”
In the March, 1957, E&MJ, Bond responded to ques-
tions raised by J.F. Meyer concerning the interpretation of
his theories considering a very low speed (59% of critical),
low (20%) ball charge ball mill displaying 40% lower Work
Index than a parallel one at normal conditions. While suffi-
cient data were lacking for proper analysis, Bond suggested
that “in mill classification,” or preferential grinding of the
significantly heavier mineral, played an important role in
this instance.
In September, 1957, Bond presented “Tumbling Mills
and Structural Clay Products” to the American Ceramic
Society. He presented his Third Theory, and made general
observations regarding the use of rod and ball mills for the
preparation of structural clay products.
That December of 1957 Bond published
“Comminution Exposure Constant by the Third Theory”
in Mining Engineering. This was a largely theoretical work
which attempted to quantify how much larger particles are
preferentially exposed to work input. A variation of an ear-
lier unpublished method (see Figure 5) to fit particle size
distributions to an equation was presented. He also stated
that the best overall size reduction “efficiency” is obtained
on single sized particles. Using the Work Index equation,
he showed how more narrowly sized particles in closed-
circuit ball milling result in better grinding efficiency com-
pared to open circuit, and the resulting product sizing is
also narrower. While the matter is compounded by classifi-
cation effects (which are neglected), as well as the grinding
environment’s effectiveness on different particle sizes, this
paper does suggest that there is a grinding benefit with fines
removed from ball mill feed.
In the May, 1958, issue of Mining Engineering in
“Grinding Ball Size Selection” Bond updated his recom-
mended ball sizing equation from that which he gave in
1952 in “Mathematics of Crushing and Grinding,” add-
ing “theoretical considerations” related to his Work Index
theory. (It was later amended to that used today.) He also
provided an updated rod sizing equation and tables for
start-up equilibrium ball and rod charge media sizes and
gave average media wear rates expressed in consumption
“per 24-hour day for each 100 hp drawn grinding silicious
materials.”
Bond and B. B. Whitney (General Superintendent at
Inspiration Copper Company in Arizona) presented “The
Work Index in Blasting” to a Colorado School of Mines
rock mechanics symposium in April, 1959. From the esti-
mated power yield of dynamite and three blasts conducted
there with different loading they concluded that the Third
Theory can be applied to blasting. Analysis of blast data
from other properties indicated that crushing Work Index
is likely lower than that for blasting.
“Confirmation of the Third Theory” was submit-
ted to SME by Bond in November, 1958, presented in
San Francisco in February 1959, and published in AIME
Transactions in 1960. Bond used experiments in the 12"
× 12" laboratory ball mill and crack length assumed to be
related to surface area to demonstrate the Third Theory
premise that useful work done is directly proportional to
length of new cracks formed, and so the inverse of square
root of particle size. He introduced the correction factor to
be used for P80 less than 70 microns ((P80 +10.3)/1.145 x
P80) “to account for the increased work done in producing
sub-grind-limit particles.” He states when material has part
of its fines removed its resistance to size reduction based on
the 80% passing size is increased, and provides a needed
correction factor to apply to that value.
In the same paper he also presented a new “Third
Theory size distribution plot” to deal with unaccounted
Figure 5. Size distribution chart
(courtesy of Robert S. Jermyn, Allis-Chalmers)