8
as yet undisclosed “correct theory,” and “a more satisfactory
concept of the theory of crushing and grinding” that would
include these factors. In fact, in his autobiography Bond
states that he had discovered his “Third Theory” some years
previously, and was busy checking and validating it before
public release. The published discussion strongly disputed
this paper’s findings, but it was nevertheless the harbinger
of what was to soon follow.
In 1950 Bond also published in Engineering and Mining
Journal the previously mentioned update of his 1937 paper
on classifier separation calculations, as well as “Selecting
Rods of the Proper Size for the Rod Mill.” From his data
base on industry operations, Bond presented an equation
relating the rod diameter being used to the feed F80 size,
the Allis-Chalmers rod mill ore grindability at 14 mesh,
mill speed and diameter, and ore specific gravity.
In the July, 1951, Pit and Quarry magazine Bond co-
authored the article “Principles of Crushing” with Frank E.
Briber, Jr., of the Allis-Chalmers crushing equipment divi-
sion, which they had presented at the National Crushed
Stone Association convention. They covered crushing
equipment types through rod milling, particle size distri-
butions represented by the eighty percent passing size, the
energy prediction equation of Wang, and stage-crushing
flowsheets.
Bond first publicly presented “The Third Theory of
Comminution” at the SME convention held in Mexico
City in October of 1951. He presented it again at the New
York meeting in February, 1952, and it was published in
Mining Engineering in May of 1952. However, the first
article written on it was “New Theory Explains Grinding”
in the April, 1952, issue of Chemical Engineering. It was
first to publish a brief, concise summary. “The new theory
states that the total work useful in breakage is inversely pro-
portional to the square root of the diameter of the product
particles and directly proportional to the length of the crack
tips formed.” And also “Wi is the work index or total kWh
per ton required to reduce from infinite size to eighty per-
cent passing 100 microns.” It cautioned that specific prob-
lems may call for correction factors in its application, but
wonderfully concludes that “now chemical engineers can
shoot for more efficient operations through closer predic-
tions and more accurate comparisons of all crushing and
grinding operations.” The article was not attributed to
Bond, and the brevity and clarity was such that it is attrib-
utable to a professional writer, but it clearly underwent his
review and approval.
The full publication of “The Third Theory of
Comminution” in Mining Engineering went into much more
detail, including large numbers of laboratory experimental
data and plant operating data. Empirical equations to con-
vert ball and rod mill test grindabilities and impact crushing
test values to work input values were given. He explained
these “represented the average of a number of installations,”
but were directly relatable to “a wet grinding overflow ball
mill, 7 ½ foot in diameter inside the shell operating in closed
circuit with a classifier. The rod mill equation applies to a
wet grinding overflow rod mill 6 foot in diameter inside the
shell, operating in open circuit.” Correlation of the “Third
Theory” (as Bond termed it, following the theories of Kick
and Rittinger) was first carried out with 559 laboratory ball
mill, rod mill and crushing impact tests on 144 materials
upon which multiple tests were performed. The consistency
of work index values at different screen closing sizes for the
ball mill and rod mill tests, as well as the impact crushing
tests, where available, all done on the same sample, he con-
sidered validation of the theory that energy consumption
was related to the square root of particle sizing. No statisti-
cal proof or measure of variability is given, and variability
far exceeded the stated experimental error estimate of five
percent. “Difference in the breakage characteristics” at dif-
ferent product sizes is mentioned. A second table compared
thirty-three plant “operating” work indices from data pub-
lished by Taggart (1945) to laboratory (crushing, rod and
ball mill) tests.
Once again, no statistical analysis is given, but the trend
is clear. No explanation is given of how laboratory test sam-
ples were obtained that would necessarily correspond with
the given plant data, i.e., their associated sampling error.
Later mentioned are “correction factors” for a number of
Figure 3. Bond’s plant vs. laboratory Work Index values,
1952
as yet undisclosed “correct theory,” and “a more satisfactory
concept of the theory of crushing and grinding” that would
include these factors. In fact, in his autobiography Bond
states that he had discovered his “Third Theory” some years
previously, and was busy checking and validating it before
public release. The published discussion strongly disputed
this paper’s findings, but it was nevertheless the harbinger
of what was to soon follow.
In 1950 Bond also published in Engineering and Mining
Journal the previously mentioned update of his 1937 paper
on classifier separation calculations, as well as “Selecting
Rods of the Proper Size for the Rod Mill.” From his data
base on industry operations, Bond presented an equation
relating the rod diameter being used to the feed F80 size,
the Allis-Chalmers rod mill ore grindability at 14 mesh,
mill speed and diameter, and ore specific gravity.
In the July, 1951, Pit and Quarry magazine Bond co-
authored the article “Principles of Crushing” with Frank E.
Briber, Jr., of the Allis-Chalmers crushing equipment divi-
sion, which they had presented at the National Crushed
Stone Association convention. They covered crushing
equipment types through rod milling, particle size distri-
butions represented by the eighty percent passing size, the
energy prediction equation of Wang, and stage-crushing
flowsheets.
Bond first publicly presented “The Third Theory of
Comminution” at the SME convention held in Mexico
City in October of 1951. He presented it again at the New
York meeting in February, 1952, and it was published in
Mining Engineering in May of 1952. However, the first
article written on it was “New Theory Explains Grinding”
in the April, 1952, issue of Chemical Engineering. It was
first to publish a brief, concise summary. “The new theory
states that the total work useful in breakage is inversely pro-
portional to the square root of the diameter of the product
particles and directly proportional to the length of the crack
tips formed.” And also “Wi is the work index or total kWh
per ton required to reduce from infinite size to eighty per-
cent passing 100 microns.” It cautioned that specific prob-
lems may call for correction factors in its application, but
wonderfully concludes that “now chemical engineers can
shoot for more efficient operations through closer predic-
tions and more accurate comparisons of all crushing and
grinding operations.” The article was not attributed to
Bond, and the brevity and clarity was such that it is attrib-
utable to a professional writer, but it clearly underwent his
review and approval.
The full publication of “The Third Theory of
Comminution” in Mining Engineering went into much more
detail, including large numbers of laboratory experimental
data and plant operating data. Empirical equations to con-
vert ball and rod mill test grindabilities and impact crushing
test values to work input values were given. He explained
these “represented the average of a number of installations,”
but were directly relatable to “a wet grinding overflow ball
mill, 7 ½ foot in diameter inside the shell operating in closed
circuit with a classifier. The rod mill equation applies to a
wet grinding overflow rod mill 6 foot in diameter inside the
shell, operating in open circuit.” Correlation of the “Third
Theory” (as Bond termed it, following the theories of Kick
and Rittinger) was first carried out with 559 laboratory ball
mill, rod mill and crushing impact tests on 144 materials
upon which multiple tests were performed. The consistency
of work index values at different screen closing sizes for the
ball mill and rod mill tests, as well as the impact crushing
tests, where available, all done on the same sample, he con-
sidered validation of the theory that energy consumption
was related to the square root of particle sizing. No statisti-
cal proof or measure of variability is given, and variability
far exceeded the stated experimental error estimate of five
percent. “Difference in the breakage characteristics” at dif-
ferent product sizes is mentioned. A second table compared
thirty-three plant “operating” work indices from data pub-
lished by Taggart (1945) to laboratory (crushing, rod and
ball mill) tests.
Once again, no statistical analysis is given, but the trend
is clear. No explanation is given of how laboratory test sam-
ples were obtained that would necessarily correspond with
the given plant data, i.e., their associated sampling error.
Later mentioned are “correction factors” for a number of
Figure 3. Bond’s plant vs. laboratory Work Index values,
1952