CHAPTER

Size Reduction of Solids

N industries that process raw material in the From this, it might appear that the best method
I solid state or use solid material in the processing of causing rupture to take place in solid material
of fluids, reduction in the size of the solid par- would be the applieation of shearing loads. How-
ticles is frequently required. In the production of ever, the orientation of crystals in solid matter is
gypsum plaster, the raw gypsum rock is removed usually so irregular that the direct application of
from the quarry in large blocks, sometimes 5 ft in compressive loads is just as effective as shearing loads.
diameter. It must be reduced to particles fine АП equipment for size reduction of solids uses com-
enough to pass through a 100-mesh screen in order pression, or shear, or both, as disrupting forces.
to provide sufficient specific surface for hydration
to take place rapidly. This means a reduction in
OBJECTIVES
size from 60 in. to 0.005 in. Pigments in paints must
be very fine in order to give good coverage when 'The purpose of size reduction is not only to make
applied to a surface. "httle ones out of big ones" when the effectiveness
Reduction in size involves the production of can be measured by the degree of fineness of the
smaller mass units from larger mass units of the same product, but also to produce a product of the desired
material; it therefore follows that the operation must size or size range. The size requirements for various
cause fracture to take place in the larger units. This products may vary widely, and hence different ma-
fracturing or shattering of the larger mass units is chines and procedures are employed. A size range
accomplished by the application of pressure. АП entirely satisfactory for one purpose may be highly
true solid materials are crystalline in nature; that is, undesirable for another, even when the same sub-
the atoms in the individual crystals are arranged in stance is involved. Powdered coal is widely used for
definite repeating geometric patterns, and there are firing industrial furnaces, and lump coal is also fed
certain planes in the crystal along which shear takes into furnaces by mechanical stokers. But powdered
place more readily. The pressure applied must be coal could not be used in the stoker, and lump coal
sufficient to cause failure by shear along these could not be used in the equipment designed for
cleavage planes. If the shear along these planes re- firing pulverized or powdered coal.
sults in deformation but not rupture, the deformation In many cases, it is necessary to use a product with
is called plastic deformation. The segments of the rather narrow limits in size variation. It is usually
crystal slide along on each other like a pack of cards, impossible to accomplish this by size reduction only.
the only result being а change in dimensions of the Screening and classification by various means are
crystal. In order to bring about actual size reduc- required to secure the desired limitation in size
tion, it is necessary that the material be actually range. The two unit operations of size reduction and
fractured and that shear movement, once started, size separation are further closely associated in that
results in complete separation of the segments be- laboratory screen analyses are necessary to evaluate
tween which the shear failure occurred. the effectiveness of a given size reduction operation
25
26 SIZE REDUCTION OF SOLIDS

as well as to furnish data for estimating the power or which are divided according to the types of machines
energy required. best adapted to each stage. The three steps are:
Ores of metals consist of varying amounts of 1. Coarse size reduction: feeds from 2 to 96 in. or
valuable minerals associated with undesired gangue more.
minerals. The first step in processing ores for the 2. Intermediate size reduction: feeds from 1 to 3
recovery of metal values is the separation of the in.
values from the gangue, since the ore as taken from 3. Fine size reduction: feeds from 0.25 to 0.5 in.
the mine contains both types of minerals together in
solid masses. Unless the valuable mineral exists in
OPERATING VARIABLES
great enough concentration to permit the ore to be
reduced to the metal without previous treatment, in The moisture content of solids to be reduced in size
which case the gangue is usually separated in the is important. If it is below З or 4 per cent by weight,
molten state, it is necessary to break up the ore mass no particular difficulties are encountered; indeed, it
mechanically, thus freeing the valuable minerals appears that the presence of this amount of moisture
from the gangue. The minerals are then separated is of real benefit in size reduction if for no other
by gravity or flotation methods resulting in concen- reason than for dust control. When moisture content
tration of the valuable minerals. exceeds about 4 per cent, most materials become
The purposes of size reductions are therefore two- sticky or pasty with a tendency to clog the machine.
fold: (1) To produce solids with desired size ranges This is particularly true in the coarse and inter-
or specifie surfaces. (2) To break apart minerals or mediate stages.
crystals of chemical compounds which are inti- А large excess of water (50 per cent or more)
mately associated in the solid state. facilitates the operation by washing the feed into
and the product out of the zone of action and by
furnishing a means for transporting the solids about
STAGES OF REDUCTION
the plant as a suspension or slurry. Wet grinding is
For successful size reduction, it is necessary that mostly confined to the fine stage of reduction.
every lump or particle must be broken by contact The reduction ratio is the ratio of the average
with other partieles or by direct contact with the diameter of the feed to the average diameter of the
moving parts of the machine. As the breaking action product. Most machines in the coarser ranges of
proceeds, the number of particles increases, requiring crushing have a reduction ratio from about 3 to 7.
more contacts per unit mass. Thus the capacity of a Fine grinders may have a reduction ratio as high as
partieular machine of fixed dimensions, as in tons per 100.
day, is much less for small sizes than for the larger In free erushing, the crushed product with what-
sizes, since it is necessary for the smaller particles to ever fines have been formed is quickly removed after
remain in the machine for longer periods of time to a relatively short sojourn in the crushing zone. The
sustain the required number of contacts. No device product may flow out by gravity, be blown out with
has been developed capable of automatically adjust- compressed air, be washed out with water, or be
ing itself to the varying requirements of contact. In thrown out by centrifugal force. This method of
commercial operations, sufficient capacity in the operation prevents the formation of an excessive
intermediate and fine ranges of size reduction is amount of fines by limiting the number of contacts.
obtained either by operating several similar units in In choke feeding (the antithesis of free crushing),
parallel or, better, by employing machines which the crusher is equipped with a feed hopper and kept
furnish greater numbers of contacts per unit of filled (or choked) so that it does not freely discharge
time. the crushed product. This increases greatly the pro-
Machines providing the required large number of portion of fines produced and decreases the capacity.
contacts, particularly for smaller-size material, have In some instances choke feeding may result in econ-
been developed, primarily for the last stages of size omy of operation, eliminating one or more reducing
reduction. stages because of the large quantity of fines pro-
For commercial reduction in size of masses of duced.
solids 1 ft or more in diameter to 200-mesh size, Each stage in size reduction may, and frequently
usually at least three stages or steps are followed does, have a size-separating unit following it. If the
 COARSE SIZE REDUCTION 27
oversize material is returned to the crusher, the oper- ize this, one or two heavy flywheels are mounted on
ation is termed closed circuit. If no material is re- the main shaft of the crusher. The machine is
turned for recrushing, the operation is called open driven by flat belts or V-belts.
circuit. Closed-circuit operation is economical of
crushing power, which at best is high, permits smaller
units per given tonnage, and produces a material
with greater uniformity of size.
Although the size of the feed is an important
factor in the selection of a machine, other factors
must be considered, such as hardness or structure of
л
the material. From the standpoint of crushing, ÀÑ
minerals with a Mohs hardness of 4 or less are classed Ñ
NÑ
as soft; others are considered hard. Machines for the NNÑ
coarse preliminary crushing of soft materials do not N
1
need to be so sturdily constructed or so elaborate in ил
N

design as machines for breaking hard materials. In

the finer size ranges, similar machines are used for journal
both hard and soft materials. Toggle
Machines exerting a tearing action and called
disintegrators are employed for reducing the size of Fic. 18. Sectional drawing of Blake-type jaw crusher.
fibrous materials such as wood and asbestos. (Allis-Chalmers Mfg. Co.)

The Dodge crusher (Fig. 19) is subject to uneven

COARSE SIZE REDUCTION stresses inherent in its design and therefore is made
Machines for the coarser stages of size reduction only in small sizes. It differs from the Blake crusher
handle feed sizes from 3 to 4 in. and up. For hard in that the movable jaw is pivoted at the bottom
materials, either jaw, gyratory, or disk crushers are and the width of the discharge opening remains
used. For soft materials where the production of praetically constant, thereby yielding a more closely
fines is to be limited, as in crushing coal for sale, such sized product. No toggles are required, the jaw being
devices as hammer mills or toothed rolls are em- operated through the pitman by the eccentric. If
ployed. only one size-reducing machine is being employed,
the uniformity in size of product may be of advan-
Coarse Crushers for Hard Materials tage, but otherwise the machine is of limited use.
Jaw Crushers. Jaw crushers are represented by
Movable jaw
the Blake and Dodge types and operate by applying
a crushing pressure. A! Movable
& jaw frame
The Blake crusher (Fig. 18) consists essentially of a
cast-steel frame supporting one fixed and one mov- Озы,S
<i аа Е
Pitman
able jaw. The jaws are made of cast steel lined with
a tough abrasion resistant metal, such as manganese
steel. The movable jaw is pivoted at the top and
operated by the eccentric, pitman, and toggles. The Eccentric
pitman is given a nearly vertical motion by the ec-
centric, and, since one of the toggles is mounted in
rigid journals at one end of the crusher frame, the
reciprocating motion of the pitman causes the other Fia. 19. Sectional drawing of Dodge-type jaw crusher.
toggle to move the jaw back and forth. The jaw is (Allis-Chalmers Mfg. Co.)
held against the toggle by a tension link and spring.
Crushing is accomplished only when the movable The power is applied through a long lever, and if the
jaw moves toward the fixed jaw. This means an crusher becomes clogged enormous stresses are set
intermittent power requirement. In order to equal- up in the members which become excessive in ma-
28 SIZE REDUCTION OF SOLIDS

TABLE 6. CAPACITIES OF BLAKE JAW CRUSHERS

(Allis-Chalmers Mfg. Co.)
MEER
CITAR AW ан coo Ja oin. реВ БИШЕ А шы eT. REESE

: ; a Recom-
Size of Feed Туре Discharge Setting, in. mended ||Chonan

Opening, of Jaw Rpm Motor | Weight,

Length Plates * Horse- lb
оар oy || | oe з 4 5 6 7 8 9 To 12 power

A 2 TT 1672215207: 28T 235 15 10,000

15 X 10
B 16 23 28 35 47

24 X 15 A 22 28 35 48 60T 210 35 27,000

B 25 34 43 52 69 86

36 x 24 A 45 67 88 110T 210 75 70,000

B 80 102 127 170

42 x 40 A 90 103 130 155T | 190T р 190 125 140,000

B 140 164 197 230 263

48 X 36 A 120 155 187 225 190 150 145,000

B 187 224 262 300

48 X 42 A 120 |155 |187 | 225 190 150 160,000

B 187 224 262 300

60 x 48 A 150 210 240 265 300T 170 200 215,000

B 262 314 368 420 472

84 X 56 A 360 425 480T | 565T | 630T 90 200 422,000

B

84 x 60 A 360 425 480 565 630 90 250 430,000

B

84 X 66 A 420 480 510 570 630 90 250 460,000

B

* A — standard jaw plates (smooth). T T = tons per hour.

В = 'Nonchoking" jaw plates (corrugated). д

TABLE 7. CAPACITIES OF DODGE CRUSHERS 'There are many different designs of jaw crushers,
(Allis-Chalmers Mfg. Co.) some of which combine shear with compression. The
Universal jaw crusher (Fig. 20) combines the prin-
Size of а А : Recom-
ciples of the Dodge and Blake crushers. It gives two
Feed DOSES UI UE mended Crusher crushing strokes per revolution because the pivot
Openings, |. Rpm Motor Weight,
Length Horse- lb is above the bottom end of the jaw, causing the
X Gape, in. 1$ 34 1 11 power bottom of the jaw to move forward while the upper
end of the jaw recedes.
6х4 MT* lT| 1T 275 3 1,100 Gyratory Crushers. Gyratory crushers were
957 1 2 3T 235 6 3.250
1225598 1% 3 4 220 10 5,400 developed later to supply a machine with greater
15 X 11 2 4 6 200 15 13,500 capacity. Actually, the crushing action of gyratories
is similar to the action of jaw crushers in that the
* T — tons per hour.
moving crushing element approaches to and recedes
from a fixed crushing plate.
chines with gapes * above 11 in. The constant open-
Figure 21 shows a suspended-spindle type of gyra-
ing of the jaws at the discharge end gives the Dodge
tory, consisting of an outer frame carrying an in-
crusher an annoying tendency to clog which is absent
verted conical surface known as “сопсауеѕ” and an
in the Blake crusher.
inner gyrating crushing head. The conical crushing
* Gape is the greatest distance between the jaws or crush- head is supported on a spindle which hangs from a
ing surfaces. suitable bearing in the upper portion of the machine.
 COARSE SIZE REDUCTION 29

Eccentric _ сч
+
shaft zT
V

ANS
SS
EES

PAS АК

Concaves = NN
NW
2277777
Ve
25
2

Circular shaft
Eccentric shaft

AUR

Jaw pivots "Spring and link hold

at this point jàw agalnst pivot point

Fig. 20. Sectional drawing of Universal streamlined roller- Етс. 21. Sectional drawing of gyratory crusher of suspended-
bearing jaw crusher. (Universal Engineering Corp.) spindle type. (Allis-Chalmers Mfg. Co.)

TABLE 8. CAPACITIES OF GYRATORY CRUSHERS

(Allis-Chalmers Mfg. Co.)

Finest Setting * Coarsest Setting 1

Recom-
tend p Driving mended Crusher
ing, : Я : à И
SC sagt in. и Capacity Pis еа M Pulley, rpm a e " Weight, lb
CLERI DERE, tons/hr Ea Rer tons/hr р
ing, in. ing, in.

214 X 10 $4 1 700 3 700

8 х 34 1% 25 216 47 450 15-25 20,000
10 x 40 134 39 3% 93 400 25-40 30,000
18 х 45 2 63 3% 128 875 50—75 45,000
16 x 56 3 120 4 176 350 60—100 62,000
20 х 68 316 152 5 245 330 75-125 94,000
30 х 90 4 285 6% 450 325 125-175 169,000
86 х 126 5 365 6% 525 300 175-225 263,000
42 X 132 5% 475 6% 615 300 200-275 286 ,000
50 X 162 6 740 7M 845 250 225-300 575,000
54 X 162 614 875 8 1050 250 225—300 630,000
60 x 174 614 990 10 1440 250 225-300 725,000
60 X 182 6% 1420 10% 1900 250 300-500 1,000,000

* Finest permitted for this size gyratory.

+ Coarsest permitted for this size gyratory.
30 SIZE REDUCTION ОЕ SOLIDS

The lower end of the spindle is a circular shaft free Taggart 5 * formula:
to rotate in an eccentric sleeve. The eccentric sleeve T =0.6LS
is driven from a rotating main shaft through a set
of bevel gears and rotates within a fixed cylindrical where 7' = capacity (tons/hr).
housing. The crushing spindle is free to rotate. But, L = length of feed opening (in jaw crushers,
as soon as feeding of the machine starts, rotation normal to gape; in gyratories, the
ceases and gyration is the only motion, causing the perimeter of a circle whose diameter
head to approach and recede from the concave sur- is the arithmetic average of the diam-
faces, breaking the feed by a crushing pressure as it eters of the two cones) (in.).
passes down through the crusher. S = greatest width of discharge opening (in.).
In the fixed-spindle gyratory (Fig. 22), the eccen- Exercise. Compare the capacities as estimated by the
tric sleeve is inserted between the fixed vertical shaft Taggart formula with those given in Table 6.
and the movable vertical cone. By rotating this
The power requirements for jaw and gyratory crush-
ers are about the same, but the gyratory load is
somewhat more uniform since it is crushing contin-
uously whereas the jaw crusher works intermittently.
In choosing between a jaw crusher or a gyratory
crusher for a given installation’, capacity is the
criterion. If capacity requirements are small enough
so that one jaw crusher is adequate, the jaw crusher
Crushing Eccentric sleeve is the usual choice because of its lower original cost
surfaces Movable and upkeep. If capacity requirements are large
enough to keep a gyratory in continuous operation,
the gyratory is usually preferred. Taggart’ states
an empirical rule that “if the hourly tonnage to be
crushed divided by the square of the gape in inches
is less than 0.115, use a jaw crusher; otherwise, a
gyratory."

Coarse Crushers for Soft Materials

Bevel gear driving the eccentric sleeve Such materials as coal, gypsum, some types of
limestone, ice, fire clay and shales are less hard than
Fra. 22. Sectional drawing of Telsmith parallel pinch crusher. 4 on the Mohs scale and do not require the heavy and
(Smith Engineering Works.) expensive types of crushers needed for hard mate-
rials. Frequently, the size reduction desired for these
eccentric sleeve the axis of the cone is given a soft materials excludes the very fine ranges, and most
cylindrieal motion with a “parallel pinching" action of the crushers designed for such materials produce a
on the material being crushed. small amount of excessively fine material.
Gyratory crushers have large capacity because the The Bradford breaker for coal (Fig. 23) combines
action is continuous. The capacity is similar to that the two features of breaking and screening. The
of a jaw crusher having the same gape and a length periphery of the machine is a reinforced screen which
L equal to the perimeter of the gyratory. Since all allows the coal, when sufficiently reduced in size, to
the coarse crushers have greater capacities than the pass through. Breaking is accomplished by rotation
devices for the finer ranges of size reduction, a of the cylinder. The coal is lifted on interior shelves
gyratory of sufficient size to handle the required size and broken by falling and striking the coal below
of feed may have an excessive capacity. Jaw crush- as the cylinder is rotated. Harder material such as
ers, therefore, are frequently used for the first coarse slate and tramp iron are not broken and gradually
breaking operation, followed by gyratories. pass out from the open end of the breaker as indi-
Capacities of jaw and gyratory crushers with cated.
gapes of 4 in. to 2 ft may be approximated by the * The bibliography for this chapter appears on p. 45.
 COARSE SIZE REDUCTION 31

Coal feed

Reinforced screen

Open end interior

for discharge of shelves
uncrushed material
Discharge

Fig. 23. Phantom drawing of Bradford breaker. Run-of-mine coal enters through the chute at the far end, is lifted, falls,
and is broken by the impact, passing through perforations into the chute below; rock and refuse are plowed out as indicated
in the foreground. (Pennsylvania Crusher Co.)

Driven gear on
shaft of ~
toothed roll
Crushing plate

Spring holds
crushing plate
in position

Fra. 24. Sectional drawing showing operation of toothed roll crusher. (Link-Belt Co.)
32 SIZE REDUCTION OF SOLIDS

A toothed roll crusher for coal, gypsum, ice, or other speed within a sturdy housing. The hammers deliver
soft materials (Fig. 24) accomplishes breaking by heavy blows to the feed material while it is in sus-
pressure of the teeth against the larger lumps of the pension, driving it against a breaker plate until it is
fine enough to pass through the openings in the cage
bars at the bottom of the mill constituting the screen.
Some of these mills are built in extremely large sizes,
the individual hammers weighing as much as 250 1b.
Very sturdy housings are required for such hammer
mills. The same type is also adapted to fine pul-
verizing, the size of the product being controlled by
the sizes of the discharge screens. The hammer
mill is probably the most versatile type of crushing
Revolving device currently available. For wet material the
_ disk
cages or screens are replaced with corrugated grind-
ing plates.
A so-called squirrel-cage disintegrator (Fig. 26) is
useful in tearing apart fibrous material such as wood
blocks and asbestos. The device consists of two or
more concentric cages rotated in opposite directions.
The feed is introduced into the inner cage. Centrifu-
Fig. 25. Sectional drawing showing operation of a hammer gal force drives the material into the spaces between
mill. (Al”%s-Chalmers Mfg. Co.)
the rotating cages where it is torn apart, and thence
material, disintegrating it in much the same manner into the outer casing from which it is discharged to
as ice is broken up manually with an ice pick. a conveyor or storage bin.
Excessive production of fines is thus prevented.
Knobbed and smooth rolls (Fig. 30) are also widely INTERMEDIATE SIZE REDUCTION
used for coarse crushing of soft materials.
A hammer mill (Fig. 25) may be used for coal or Cone crushers, developed since the 1920’s, have
even fibrous material. Heavy blocks of steel are gained such wide acceptance that they may be re-
attached by pins to a disk or disks revolving at high garded as standard in the intermediate range. А

reed hopper

> è
Concentric cages
Pulley for driving
outer cage Pulley for driving
inner cage

Fic. 26. Cutaway view of squirrel-cage disintegrator. (С. О. Bartlett and Snow Co.)
 INTERMEDIATE SIZE REDUCTION 33

Feed distributing plate

Lever for rotating support for

a plate to 7
opening

Main shaft, \

Xx

Bearing plate т

Mapered eccentric journal

Fia. 27. Sectional drawing of cone crusher. (Nordberg Mfg. Co.)

standard cone crusher is shown in Figs. 27 and 28.

The drive is similar to that of the gyratory crusher.
The inner cone or “crushing head" is supported by
the tapered eccentric journal which is rotated by the
bevel gears driven by the main shaft. The entire
weight of the crushing head and spindle 1з supported
on а bearing plate supplied with oil under pressure. _ Stationary
crushing plate
The operation is quite similar to that of the gyratory
Inner cone or
crusher, but there are two important points of differ-
ence. The outer stationary crushing plate flares
outward to provide an increasing area of discharge
so that the machine can quickly clear itself of the
reduced product. This stationary crushing plate
is held in position by a nest of heavy helical tension
springs so that when tramp iron or other uncrushable
objects enter the crushing zone the plate is lifted,
preventing fracture of the plate and injury to the
machine. These cone crushers are available in two Ес. 28. Cutaway view showing action of cone crusher.
sizes, the standard (Fig. 27) for coarser feed, and a (Nordberg Mfg. Co.)
34 SIZE REDUCTION OF SOLIDS

so-called “short head" for finer feed. The feed to vented by a device in the bearing of one roll which
cone crushers must be dry and rather uniformly gives it a limited lateral motion simultaneously with
sized. Cone crushers give best results when operat- the rotation. The size reduction accomplished by
ing in closed circuit with screens. rolls is relatively small, the average diameter of the
'The Telsmith Gyrasphere, Fig. 29, is à variation product being about one-fourth that of the feed.
of the cone crusher. The crushing head is spherical Cone crushers are replacing rolls for intermediate
in contour, and the crushing plate is held in position size reduction of ores because their reduction ratio
by springs under compression instead of tension. is two or three times that of rolls and they require
The drive and oiling system is similar to that of the less maintenance.

Springs (compression)

Crushing plate

Crushing head

Shaft supporting `
crushing head

Rotating cylinder

Fic. 29. Sectional drawing of Telsmith Gyrasphere. (Smith Engineering Works.)

cone crusher. Тһе spherical head facilitates dis- The diameter and spacing of rolls may be varied
charge of the crushed product. over rather wide ranges, allowing considerable vari-
Crushing rolls consist of two heavy cylinders re- ations in size of feed and product. This flexibility is
volving toward each other, the feed being nipped and a favorable characteristic of crushing rolls, which,
pulled downward through the rolls by friction. As combined with the low initial cost, has encouraged
shown in Fig. 30, modern crushers drive both rolls the wide adoption of rolls for moderate size reduction
positively, breakage being prevented by mounting of all sizes. The proper diameter and spacing of the
the bearings of one of the rolls against nests of heavy rolls, the capacity in tons per hour, and the required
compression springs. Since there is a considerable horsepower for crushing rolls may be computed as
amount of wear on the rolls, the crushing surface follows.
consists of a tough steel sleeve which is shrunk on The coefficient of friction of the mineral against
to the main cylindrical casting, making possible the the steel surfaces of the rolls incorporated with a
replacement of worn crushing surfaces. The wearing relationship between the dimension of the material
of grooves in the surface of the rolls is largely pre- to be crushed and the diameter of the rolls determines
 INTERMEDIATE SIZE REDUCTION 35

Belt - driven pulleys

Crushing sleeve
Roll bearings
Heavy nuts used in
adjusting roll spacing

Compression springs

Heavy lock nuts to

adjust roil

Fig. 80. Crushing rolls. (Denver Equipment Co.)

whether or not a particle will be drawn into the rolls D, = maximum dimension of the product (mini-
and crushed. Figure 31 is a line diagram showing the mum distance between rolls).
outline of a spherical particle in position to be Fr = tangential force on the particle.
crushed between a pair of rolls. The vectors Рт and Fy = normal force on the particle.
Fy represent the forces acting on the particle at the Ев = resultant of Fr and Fy.
point of contact with the roll and may be represented
If Fg is at a negative angle (pointing downward)
by the resultant force Fg.
with the horizontal, as shown in Fig. 31, the particle
A, = angle of nip (the value for angle A in Fig. will be drawn between the rolls. If Fg is at a positive
31 corresponding to Fg being horizontal). angle with the horizontal, the particle will ride on the
— diameter of the rolls. rolls or be thrown up and out and will not be crushed.
D; — diameter of the feed particle. 'The angle A between the two tangents at the points
36 SIZE REDUCTION OF SOLIDS

of contact of the particle with the rolls indicates The limiting value for the angle A/2 at which the
whether or not the particle will be drawn between resulting force is horizontal is called the angle of bite.
the rolls. The theoretical capacity of rolls is the weight of a
The definition of the coefficient of friction is the ribbon of feed having a width equal to the width of
ratio of the force tangent to the surface to the force
normal to the surface. In Fig. 31, this is Fr/Fy.

Fia. 31. Forces exerted by crushing rolls for а spherical

particle in position to be crushed.

In the limiting case Ёк is horizontal and

Етс. 32. Forces exerted by crushing rolls on a slab at the
t (2) = zt approximate angle of bite.
No Ep
which is equal to the coefficient of friction. the rolls, a thickness equal to the distance between
If the particle is a sphere, the rolls, and а length equal to peripheral velocity
DD: of the rolls in linear units per interval of time. This
may be expressed in tons per hour:
Ly A ed
сЕ 60vL D,p
Жы. IDS а Е А6),
2000
САКБ
The value for the angle A corresponding to this where Т capacity (tons/hr).
limiting case is called the angle of nip, A». v peripheral velocity (fpm). For rolls up
For smooth steel rolls the value of the angle of to 72 in. in diameter, v is usually
nip A, is usually about 32 degrees for ordinary approximately equal to 300 + 84D,.
rocks. In industrial operations general practice is L |= width of rolls (ft).
to determine the theoretical minimum roll diameter D, = distance between rolls (ft).
D,, add 1 in. to allow for wear, and select the next р = density of material (lb/cu ft).
larger industrial roll.
The actual capacity is usually from 0.10 to 0.30 of
If the rolls are operating on a slab of steel (or a
the theoretical.
particle of similar shape) as indicated in Fig. 32,
With the increasing use of cone crushers for inter-
DONE mediate size reduction of ores, the application of
rolls in this field is being limited to the size range
cos — = — = = between cone crushers and fine grinders.
pn IE bc т a Gravity stamps. The oldest method for size reduc-
2 cos (A/2) tion of solids is undoubtedly a husky human being
swinging à heavy hammer. When man began to
devise mechanical methods for industrial operations,
 FINE SIZE REDUCTION 37
he naturally thought of a rock-crushing device in- and a surface rubbed against the stationary surface.
volving a weight to be lifted and dropped on the The upper and nether millstones used for grinding
material to be broken. For this reason the gravity flour from grain are typical. Such а machine causes
stamp is the oldest recorded method for size reduc- disintegration mainly by the application of shear
tion in the intermediate and fine size ranges. Gravity loads. Most recent devices in fine size reduction,
stamps are still used to а considerable extent because such as ball mills, depend more on impact than on
of the ease of construction in the field, especially for shearing forces. The division of the operations of
crushing gold ores when the gold is to be amal- size reduction into crushing and grinding is no longer
gamated with mercury, in spite of the fact that descriptive of the operations used in coarse size
capacity is low and the costs are relatively high. reduction, as distinct from fine size reduction.
Figure 33 is a modern type of stamp mill. The
stamps are vertical shafts raised by cams operating
under collars fastened to the upper part of the shafts.
Adjustable mz Feed chute
cone que MEE Hinged gate
Vertical shafts

/| Wm
Separator e ҮШ LI / „Еее hopper
body : Feed roll
E
Mill feeder
Feed-
Pressure s
spring
Grinding ring
Labyrinth Revolving bowl
d Grinding roll
Metal block Scrapers

Metal slab pr >—Thrust bearing

Worm Return oil port

ear
7 | Worm
Oil port
т Vertical shaft

Fic. 34. Cutaway and sectional diagram of bowl mill with

Fic. 33. Gravity stamp mill. (Allis-Chalmers Mfg. Со.) air classifier or separator. (Combustion Engineering Co.)

The lower end of each shaft is equipped with a In the transition from the old-style shear-grinding
heavy cylindrical metal block which strikes on a sta- devices to the widespread application of ball mills
tionary hard metal slab. Since a stamp mill has no and rod mills, several machines appeared in which
means of clearing itself of the crushed product, the the material is reduced in size between rollers, or
operation is usually carried out on suspensions of heavy balls, rolling against a crushing ring. In the
solids in water, which pass slowly through the crush- Chilean mill, the horizontal axes of the rolls are
ing zone. usually stationary, and the flat pan carrying the
'The reduction ratios in stamps may be as high as crushing ring revolves. The bowl mill (Fig. 34) may
150, making them one of the most flexible types of be regarded as its modern development.
machines for size reduction. The Raymond roller mill (Fig. 35) consists of
rollers suspended on balanced journals from a rapidly
rotating spider mounted on the upper end of the main
FINE SIZE REDUCTION shaft. The revolving rolls exert pressure on a sta-
Size reduction in the finer ranges has usually been tionary confining ring by centrifugal force. A plow
termed fine grinding. This is due to the fact that mounted on the apron or sleeve revolves with the
most of the older devices for reduction in this range shaft to throw the material into the crushing zone.
consisted of two main parts, a stationary surface This mill is usually provided with a sizing feature
38 SIZE REDUCTION OF SOLIDS

whereby the material cannot leave the machine The length of the eylinder is usually about equal to
until it is fine enough to pass through a screen of the diameter. Most ball mills are continuous in
given mesh or be lifted by a stream of air of constant operation, feed entering at one end and discharging

_—————єн
асаа SE

gu——————————Áá

= EE
[presi
eae Sea et
E

Whizzer | — ER.
throw- out (A Whizzer drive

В =
am
| Automatic 5
EA | f feeder
| == =a
Mill | = ў
throw- out ee
sa rp г T
ДӨЙ e
Main (
: Dt
SMI
SA Bre
Bit
DJUL
>
shaft] AS SQUE "d
== ax Ald 2 N BS : D
LE rM] WA A M а
A A КАК LES
se a ed
2 Шы
Р А | Journal
A KS Ne Ts Confining ring
Tow Crushing roll
E
ia A | NK ar. Plow AAAAAJ
S 7 ЕЗ АРИР

N N ox SSSSSSSSN San 53 in
у — gN U NR SS Iss
= emm Bl Ts SDA St EZA,
27274
LYLE

RRAN AR

Ета. 35. Cutaway and sectional diagram of Raymond roller mill with air classifier or separator. (Combustion Engineering Со.)

velocity. The so-called whizzer consists of vertical through the opposite end or through the periphery.
vanes rotating rapidly in a horizontal plane to knock They may be operated either wet or dry.
oversize particles out of the rising stream. In cylindrical ball mills the product may be dis-
Ball mills are horizontal rotating cylindrical or charged by overflow through a hollow trunnion (Fig.
conieal steel chambers, approximately half full of 36). The smaller particles are suspended and carried
steel or iron balls, or flint stones. The size reduction out by the circulating fluid, such as air or water.
is accomplished by the impact of these balls as they The Hardinge mill (Fig. 37) is typical of cylindro-
fall back after being lifted by the rotating chamber. conical ball mills. The larger balls and larger par-
 FINE SIZE REDUCTION

Hollow trunnion overflow

|

[ Feeder !

||
|
i
y

Fic. 36. Ball mill showing feeder and hollow trunnion. (Allis- Fia. 38, Interior view of empty ball mill showing grate and
Chalmers Mfg. Co.) rolled steel liners. (Allis-Chalmers Mfg. Co.)

ticles of feed are supposed to segregate to а certain vanes on the inner periphery of the cylinder, and dis-
extent in the cylindrical portion of the mill with the charged from the hollow trunnion by which the mill
greatest diameter. Whether ог not this supposition is supported. If the mill is supported by peripheral
is true, there is a definite relationship between size tires riding on rollers (Fig. 40), the material simply
of particles and size of balls required for effective flows out through the grate and through the open
size reduction. In any case the lifting effect on the end of the mill.
balls is greatest at the greatest diameter, and the Compound ball mills consist of two to four cylin-
larger balls will be most effective in size reduction at drical compartments separated by grates. Each
this point. successive compartment is of smaller diameter and
In “grate mills" the product passes out through the contains balls of smaller sizes for finer grinding.
openings in à vertical grate or diaphragm (Fig. 38).
In the trunnion mill, the product may be raised by
radial plates or scoops on the outside of the grate Holes for bolting -
(Fig. 39), pushed away from the grate by helical blocks to grate for -
controlling pulp level
Comparative
peripheral eo fpm 400 fpm 250 fpm
speeds

Discharge
Feed
| through
irunnion

Comparative 5-in. ball 3%-in. ball 23;

-in. ball
relation of crushing crushing crushing
size of balls | 2-in. material l-in. material 2%-in. material
to material = 15.6:1 = 43:1 =125:1 Fia. 39. Outside view of grate showing radial plates which
Cutaway diagram indicating idealized operation of raise the product and cause it to be discharged through the
Fra. 37.
(Hardinge Co.) hollow trunnion. (Allis-Chalmers Mfg. Co.)
conical ball mill.
40 SIZE REDUCTION OF SOLIDS

Fic. 40. Grate mill with open-end discharge. (The Mine and Smelter Supply Co.)

Such a mill is essentially a series of mills operating and therefore lie in the mill parallel to the axis. The
continuously. impact of the rods is received mainly by the larger
The liners of ball mills are replaceable and usually particles, causing preferential reduction on the
made from alloy steel. Other materials such as coarsest particles and giving a more closely sized
rubber, cast iron, ceramic, and rock products are product. Rod mills are more expensive to operate
sometimes used. The wear on liners is usually from than ball mills, but their use is indicated when a
0.1 to 0.5 Ib/ton of product. The balls introduced small proportion of fines is desired in the product.
into the mill vary from 1 to 6 in. in diameter, and Figure 41 shows the inside of a typical rod mill and
the wear is from 1 to З Ib/ton of product. It is indicates the wear and replacement of the rods by
customary to compensate for ball wear by introduc- their different diameters. When the rods become
ing one or more full-sized balls to the mill at least badly worn they must be removed before they bend
once a day. or break; if they become shorter than the diameter
Rod mills are similar to ball mills except that the of the mill they may become wedged in such a posi-
grinding media are steel rods rather than balls. The tion as to be held against the lining.
rods are always longer than the diameter of the mills Tube mill is a term used to identify a long cylin-
drical mill (usually about 22 ft long) utilizing pebbles
of flint and ceramic linings and usually operated
intermittently on a batch of material. Tube mills
have largely been replaced by ball mills except in
cases where iron in the product cannot be tolerated.

Operating Conditions
The rate of rotation of ball mills should be less
than the speed at which the charge is held against
the inside surface by centrifugal force, since no size
reduction would take place unless the balls fall upon
the material to be crushed. At low speeds where
the balls simply roll over each other and are not
carried up and dropped, only the smallest particles
are affected. The critical maximum speed may be
determined in the same manner as described for
Fic. 41. Interior view of rod mill showing rods in various trommel screens. With a correction made for the
states of wear from service. (Allis-Chalmers Mfg. Co.) diameter of the ball, the critical rate at sea level
 FINE SIZE REDUCTION 41
may be ascertained from the expression
|. 16.65
|». ND—d
where N — revolutions per minute.
D = diameter of the mill (ft).
d — diameter of the balls (ft).
At low speeds where the contents are simply
Fines
Produced
without
tumbled or rolled over, the power required to drive Circulation
Through)
(Once
Produced
with
Circulation
to
Mass
Ratio
Fines
of
Mesh)
(150
the mill varies directly with the speed of rotation.
At higher speeds slippage occurs between the con- 0 a 2 9 4 5 6
tents and the lining, and power requirements increase Circulating Load, Tons Circulated per Ton of Fresh Feed

more slowly with speed of rotation. Fic. 43. Relation between circulating load and production
Increasing the load (balls and material) in a ball of fines in a ball mill being operated in closed circuit.
mill will increase the power requirements until the
maximum value is reached, after which the power at the other end, as shown in Fig. 42a. The rela-
requirement decreases with increasing load as the tively fixed or constant pulp level provided by such a
center of gravity of the load approaches the axis of mill means that the effectiveness of grinding can be
rotation. For wet grinding the maximum power is controlled only by the size and quantity of balls or
required when the weight fraction of solids in the the rate of feed. With the use of diaphragms the
feed is about 0.60 to 0.75. The load may be in- pulp level may be independently controlled at any
creased by increasing the weight of balls introduced desired level by making the diaphragm or grate solid
into the mill, by operating on material (wet pulp) of for the desired distance from the periphery (Fig.
higher density, or by operating at a higher pulp 42b).
level. The pulp level or quantity of material being Lower pulp levels result in greater freedom of
ground in the mill is a major factor in the operation movement of the balls with consequent improvement
of the mill. in effectiveness of grinding. In a simple overflow
In the simple overflow type of continuous ball type of mill the balls lose kinetic energy when falling
mill (no diaphragm), the feed enters at one end and into the dense pulp, and the contact forces between
the product flows out through the hollow trunnion balls under the surface of the pulp is decreased.
Mills with diaphragms or grates blocked to maintain
the proper pulp level are reported to deliver 25 per
cent more product of the correct size range with an
IT: level increased power requirement of only 20 per cent.
Low levels of pulp and decreased time in the mill
result also in a decrease of overgrinding.
Closed circuit operation (see diagram accompany-
ing example, p. 44) is usually necessary in ball mill
operation since these mills do not have a sizing action
on their product. A sizing device, such as a “classi-
fier," is placed in series with the ball mill, and the
oversize material from the sizing operation is re-
turned to the mill for further size reduction. In such
operations, the circulating load may be the major
part of the feed. The present trend is to use high
circulating loads. The approximate relationship be-
tween the production of fines and circulating load is
shown in Fig. 48.
Ето. 42. (a) Sectional diagram of overflow ball mill. (b) Sec-
The capacity of ball mills depends very largely on
tional diagram of ball mill equipped with diaphragm or grate
allowing lower pulp levels. (Allis-Chalmers Mfg. Co.) the reduction ratio as well as on the hardness of the
42' SIZE REDUCTION OF SOLIDS

material, and it cannot be accurately calculated. Mines? A drop weight crusher (Fig. 44) was used
A reasonably conservative estimate of the capacity for accurate determination of the energy expended
of a cylindroconical (Hardinge type) ball mill in tons in crushing, and a rate of solution method for accu-
per 24 hr is rate determination of the surface of the particles.
The results of their measurements on quartz (510),
Maximum diameter X Length (ft)
Ci
where C; varies from 6 to З for most normal opera-
tions.
The normal capacity of cylindrical ball mills in
tons per 24 hr may be estimated as
Volume of mill (cu ft) Crushing
1Gram
of Surface
Produced
in
Square
Centimeters
@ 05 ТОШТО 208256 30% 3585400845 350)
where C usually varies from about 1 to 2. Kilogram
- Centimeters per Gram of Quartz

Fra. 45. Relation of energy input to surface produced in

crushing quartz with a drop weight crusher.?
ENERGY REQUIREMENTS
Although most of the power required for driving plotted in Fig. 45, show a constant energy require-
crushers and grinders is used in overcoming mechan- ment of 1 kg-cm for each 17.56 sq cm of new surface
ical friction, the actual energy used in size reduction produced for this quartz, or, as usually expressed,
is an important consideration and theoretically is 17.56 sq cm of new surface produced by the applica-
proportional to the new surface produced, as there tion of 1 kg-em of mechanical energy.
is no change in the material except size and the Rittinger’s number designates the new surface pro-
duced per unit of mechanical energy absorbed by the
Suspension material being crushed. The values vary for different
cord
materials, depending on the elastic constants and
Ball their relation to the ultimate strength and on the
manner or rate of application of the crushing force.
А few values of Rittinger's number as determined
by a drop weight crusher are given in Table 9.
Soft aluminum wire or
lead shot to prevent < chamber TABLE 9. DROP WEIGHT RITTINGER’S NUMBER
ball rebound FOR A FEW COMMON MINERALS?

Rittinger's Number

screw Mineral sq in./ft-lb sq cm/ft-Ib sq em/kg-cm

Quartz (SiO2) 37.7 243 17.56
Pyrite (FeS2) 48.7 314 22.57
Ес. 44. Diagram of a drop weight crusher.”
Sphalerite (ZnS) 121.0 780 56.2
creation of new surface. This principle was first Calcite (СаСОз) 163.3 1053 75.9
recognized by Rittinger. Rittinger’s law was first Galena (PbS) 201.5 1800 98.8

confirmed beyond doubt * by the U. S. Bureau of

'Тһе energy absorbed in crushing mixtures of these
*The principle known as Kick’s law, that “the energy
required to produce analogous changes of configuration of minerals can be calculated by addition if the propor-
geometrically similar bodies varies as the volumes or masses tion of each mineral is known in the various screen
of these bodies,” was at one time erroneously applied in the fractions before and after crushing. The most rapid
theory of crushing. It led to the false conclusion that the means of estimating the new surface produced is by
energy required in crushing was proportional to the decrease
in volume or mass of the particles. This principle is now
the use of screen analyses as discussed in Chapter 3.
recognized as applicable only to plastic deformation of par- Other methods, such as the rate of solution, are more
ticles within the elastic limit and not to crushing. precise but more difficult to execute.
 ENERGY REQUIREMENTS 43
The mechanical energy supplied to the crusher is lating the crushing effectiveness for any such opera-
always greater than that indicated by Rittinger's tion. In the ball mill with 178 lb of balls, the crush-
number, as friction losses and inertia effects in the ing effectiveness is 94/243 = 0.387. In this manner
equipment require more energy than the actual pro- the performance of various machines, and variations
duetion of new surface. Also, fracture is accom- in the same machine, can be compared.
plished, not by static loading, but by exceeding the The overall energy effectiveness (or efficiency) of a
minimum rate of loading or deformation. Even crusher is always much less than the crushing effec-
brittle substances adjust themselves to slowly applied tiveness, as the latter does not include the mechan-
loads, and fracture does not occur the instant the ical losses such as friction and inertia. The capacity
load is applied but only when the rate of loading of ball mills cannot be accurately calculated because
exceeds a certain minimum. of the effects of variables such as the relative grind-
The total energy supplied to the crusher, there- ability of the material and the range in size reduction.
fore, depends upon the rate of load application, which An approximate idea of the capacity and power
differs with the type of machine and conditions of requirements of ball mills, both cylindrical and
operation. Table 10 gives values for the new surface conical, may be gained by reference to Table 11.
produced per unit of energy supplied to the material
being crushed in a laboratory ball mill operated at TABLE 11. CAPACITY AND POWER REQUIRE-
the same speed but with varying weights of similar MENTS OF BALL MILLS
balls in the machine while grinding equal weights of
Approximate Average
quartz. Size, ft, Capacity, tons/24 hr
diam- Approximate Approxi- 7 — Motor
eter X Ball Load, mate 25 іп. іо V$in.to lin. to Horse-
TABLE 10. EXPERIMENTAL VALUES OF NEW length lb Rpm 48 mesh 65 mesh 100 mesh power

SURFACE PRODUCED PER UNIT OF ENERGY 3X2 1,000 35 12 9 5 6-8

FOR QUARTZ 3x4 2,000 35 24 18 10 12-15

4x4 3,300 30 42 30 20 20-25
Calculated by subtracting the energy required to drive the 5x4 5,000 29 80 55 30 30-40
mill containing balls but no material from the total energy 5x6 7,500 29 120 85 50 40-50
required to drive the operating mill for the same length of 6X3 6,000 25 125 85 50 50-60
time. 6х5 10,000 25 210 150 90 75—100
6х6 12,000 25 250 175 100 90-120
Total Weight
6 x 12 24, 000 25 500 340 200 150-200
of Balls in
XO 21,600 23 500 350 200 110-160
Ball Mill, Ib sq in./ft-lb sq cm/ft-Ib sq cm/kg-em
8х6 28,000 22 620 450 260 150-225
36 5.6 36 2.6 10x9 74,000 17 1500 1100 650 550-600
71 10.1 65 4.6
142 12:7 82 5.9 Cylindroconical M ills
178 14.6 94 6.8
2 x 25 600 40 4 3 2 2
249 121 78 5.6
3 x 24 1,100 35 12 10 9 5-8
Drop weight
35422 2,000 35 17 15 13 10
method 37.6 243 17.56
5x3 9,500 28 100 80 60 40-50
6x3 15,000 24 180 120 90 60-75

The new surface produced per unit of energy sup- 7X4 27,000 23 300 220 150 125

plied to the material being crushed in a ball mill is

8х4 38,000 21 480 350 270 175-200
12 X 6 110,000 16 1800 1400 1000 700-800
much less than for the drop weight crusher. This
may be explained by the high percentage of ineffec-
Illustrative Example. A ball mill operating in closed
tive blows and other losses in the ball mill. The circuit with a 100-mesh screen gives the screen analyses
important practical point is the variation in effec- below. The ratio of the oversize to the undersize (product)
tiveness of size reduction with the total weight of stream is 1.0705 when 200 tons of galena are handled per day.
The ball mill requires 15.0 hp when running empty (with
balls charged, showing a maximum value at about
the balls but without galena) and 20.0 hp when delivering
175 Ib of balls in this particular mill. 200 tons per day of galena. Find:
Values of the Rittinger number as determined in 1. The effectiveness of crushing based on drop weight
the drop weight crusher represent maximum effec- crushing as 1.00.
tiveness in size reduction and may be used in calcu- 2. The overall energy efficiency.
44 SIZE REDUCTION OF SOLIDS
3. The classifying screen effectiveness. Effectiveness of classifying screen

Oversize Undersize
_ tp(tr — tg) [ _ (l -zpr — “=|
Mill from from X gp(xp — ХЕ) (L — zp)zrp — ZR)
Feed, f ereen, Screen, Mass in Mill Size
Mesh weight 95 weight 95 weight % Product per Distribu-
— 4+ 6 10 0 0 Calculated Size Distribution 100 lb of tion,
ТТ ao Oversize, Mass
= (ue © 1.2 0 0 Mass Mass Oversize 4- % in
= 8 10 250 0 0 % in % in (Undersize/ Mill
— 10 + 14 3.5 0 0 Mesh Oversize Undersize 1.0705), lb Product
— 14 + 20 (all 0 0 — 28 + 33 13.67 0 13.67 7.07
— 20 + 28 15.4 0 0 — 35 + 48 32.09 0 32.09 16.60
— 48 + 65 27.12 0 27.12 14.02
— 28 + 35 18.5 13.67 0 — 65 +100 20.70 2.32 22.86 11.82
— 35 + 48 17.2 32.09 0 —100 +150 4.35 14.12. 17.52 9.07
— 48 + 65 526 27:12 0 —150 +200 2.07 13.54 14.72 7.62
— 65 +100 10.4 20.70 2182 — 200 0 70.02 65.35 33.80

—100 +150 6.5 4.35 14.12

100.00 100.00 193.33 100.00
—150 +200 ills 2.07 13.54
— 200 0 0 70.02 Mass % in mill product
Mass % undersize
100.00 100.00 100.00 Mass % oversize + 1.0705

193.33
Solution. The distribution of material smaller than 200 mesh in mill
100
- mesh classifying screen product from an extrapolation on a plot of
Mill feed log (mass retained, per cent) versus log (Dayg)
Mill product
is given below.

Average Mass Mass

Diameter % in % in
Ore) Mill Under- mn
Analysis. The Rittinger number measures the minimum microns Produet size n Davg
energy required to form new surface. If the new surface 63 6.98 14.46 1.65 0.378
created per unit time is calculated, then the minimum energy 45 5.90- 12.22 1.60 0.434
required for the formation can be calculated. 31.8 5.00 10.34 1.53 0.497
In order to evaluate the new surface of the product, the 22.5 4.24 oc f 1.50 0.585
minus 200-mesh fractions may be evaluated by the straight- 15.9 3.58 7.41 1.45 0.676
line plot, such as Fig. 15. This method is valid only for the 11.2 3.03 6.28 1.42 0.795
product of a mechanical crushing device and not for the 7.92 2.68 5.58 1.40 0.985
classifiel product. Therefore the size distribution of the 5.59 2.19 4.54 15970 ДОЛЛ.
mill product must be computed and extrapolated for the 3.84 0.20 0.41 1.35 0.144
mass fractions retained below 200 mesh. 'The sum of these
fractions must equal the minus 200-mesh fraction. 33.80 70.02 el
The fractions of mill product below 200 mesh are then con- avg
verted to fractions of the undersize stream. The surfaces Surface area for this fraction of the undersize stream
of the fractions are calculated either from the actual specific
5.611 X10 <6
surfaces in Fig. 16 or from the relationship (p. 22): mus Me. 45,250 sq cm/70.02 grams
7.43
6 mma
Total surface = — Mass Specific Actual
p > (О.у):
Screen % in Surface, Surface,
n is evaluated from the data of Fig. 17. Mesh Undersize sq cm/gram sq cm
— 65 +100 2.82 85.8 199.1
Theoretical effectiveness of ball mill
—100 +150 14.12 115.4 1,629.4
Minimum power required to create new surface —150 +200 18.54 155.1 2,100.0
— 200 70.02 45, 250.0
Power increase due to charge

Overall energy effectiveness of ball mill 100.00 49,180 sq cm surface

area/100
Minimum energy required to create new surface grams of
Total energy used undersize
 PROBLEMS 45
FEED SURFACE CALCULATIONS PROBLEMS
Actual
Mass Specific Surface, 1. A short-head cone crusher is available for crushing 2 tons
Screen % in Surface, sq cm/100 of pyrites per hour. On similar materials, the overall energy
Mesh Feed sqem/gram grams efficiency has been found to be 3.15 per cent. The raw feed
— 4+ 6 1.0 7.6 7.6 is to be crushed by a jaw crusher, whose product constitutes
— 6+ 8 1392 9.9 11.9 the feed to the cone crusher. The cone crusher operates in
= КЕР) 253) 12.5 28.8 closed circuit with a 14-mesh screen. The cone crusher
— 10-4 3.5 16.4 57.4 product and recycle stream analyses are given below. On
— 14 + 20 uot 21 149.8 the basis of calculations and of any assumptions which you
— 20 + 28 15.4 26.9 414.5 may find necessary, select a Dodge-type crusher that will
= P42) Sp 1615) 18.5 85.7 660.5 do the job.
= 35 + 48 NP? 47.2 811.8 The surface ratio (n) may be considered to be 6.5 above
— 48 + 65 1586 63.0 982.8 3 mesh. The full-load energy requirement for the short-head
— 65 +100 10.4 85.8 892.3 cone crusher is 5 hp. The recycle ratio (recycle stream/prod-
—100 +150 6.5 115.4 750.1 uct stream) is 1.
—150 +200 ШӘ 155.1 201.6
Product Recycle Stream
Mesh Mass % Mesh Mass %
4,968.8 sq cm total
surface /100 —14 + 20 29.8 = 8) qp 3.8
grams of feed —20 + 28 30.2 = 4b wed 10.0
New surface created = (49,180 — 4968) —28 + 35 25.0 = 6-8 19.6
—35 + 48 9.6 = 9 eil 26.0
44,212 sq cm/100 grams of feed —48 + 65 3.8 ==) чый: 86.6
—65 4-100 1.6 —14 +20 4.6
(44,212) (9072) (200)
Theoretical effectiveness = - 100.0 100.0
(6.452) (1.98) (10%) (24) (201.5) (5)

1.265 hp
= ———_ = 0.253
5 hp 2. А ball mill, operated in a closed circuit with a classifier,
is used to grind calcite after it has had preliminary crushing
1.265
Overall energy effectiveness = Со = 0.0688 in jaw crushers. Screen analyses of the various streams are
given below.
The ball mill feed (25 tons/hr) is estimated to have a
SCREEN EFFECTIVENESS CALCULATIONS specific surface of 202 sq cm/gram. When the ball mill is
operated with a recycle of 75 tons/hr, 75 kw are required to
zp = 1 — 0.0232 = 0.9768
drive the ball mill. Determine the efficiency of the ball mill.
тк = 0.0907 + 0.0762 + 0.3380 = 0.5049
Вай Recycle, Product,
тв = 0.0642
Mill Classifier Classifier
Feed, Sands, Overflow,
Screen effectiveness
mass % mass % mass %
_ (0.9768)(0.4407) [ (0.0232) (0.4407) Tyler Screen Mesh retained retained retained
= = semen = 0.914
(0.5049) (0.9126) (0.4951)(0.9126) 0.525 in. — 0.371 in. 4.7
0.371 in. — 3 mesh 20.1 6.3
— 3mesh + 4 mesh 17.9 7.0
BIBLIOGRAPHY — 4 + 6 12.1 8.2
— 6 + 8 8.6 9.3
1. Gaupin, A. M., Principles of Mineral Dressing, McGraw- — 8 + 10 5.5 3.0
Hill Book Co. (1939). — 10 + 14 4.7 154.
2. Gross, Joun, “Crushing and Grinding," U. S. Bur. Mines — 14 + 20 О 16.9
Bull. 402 (1938). Contains complete bibliography. — 20 + 28 90 20.7
3. Ricuarps, R. H., and С. E. Locks, Textbook of Ore Dress- — 28 + 35 2.9 Batt ARD
ing, 3rd ed., McGraw-Hill Book Co. (1939). — 35 + 48 159 2.8 Ж ӘТ.
4. von RrrriNGER, P. R., Lehrbuch der Aufbereitungskunde, — 48 + 65 2.0 1.4 19.8
Berlin (1867). — 65 +100 ШТ 12 1997
5. TacGART, A. F., Handbook of Mineral Dressing, John — 100 +150 IET 0.8 ПУТ
Wiley and Sons (1945). —150 +200 IS 0.6 9.8
6. Davis, E. W., “Ball Mill Crushing in Closed Circuit with —200 8.5 3.0 28.6
Screens,” Bull. Univ. Minn., 28, No. 42 (1925), Bull. 10,
School of Mines Exp. Sta. Totals 100.0 100.0 100.0
46 SIZE REDUCTION OF SOLIDS
3. A cement plant is grinding 10 tons/hr of а hard rock 5. Quartz from the mine is sent over a grizzly with 8-in.
(specific gravity, 3.8) in a high-speed disk grinder operating spacing and then to a Blake standard jaw crusher with
in a closed circuit with a 65-mesh screen. Regular checks a 40-in. by 42-in. feed opening and a 6-in. discharge setting.
upon the possibility of oversize particles passing through the The crusher operates at 190 rpm and handles 130 tons/hr of
screen show that all material in the undersize stream from feed. Screen analyses of the feed and product are given
the screen will pass through a 35-mesh screen. below.
Drop weight laboratory tests upon the material being (a) What are the theoretical. power requirements?
crushed indicate that the absorption of 1 ft-lb of energy will (b) What size motor is reeommended? Why?
result in creation of 110 sq cm of new surface and that the (In the size range indicated the average surface ratio may
specific surface ratios are identical with those of sphalerite. be assumed to be 8.0)
(a) If the energy efficiency of the grinder is 18 per cent
Feed Product
and the known streams have the analyses given below, what
Mass Mass
is the horsepower required by the grinder?
Screen Frac- Screen Frac-
(b) What is the effectiveness of the screen?
» Aperture, in. tion Aperture, in. tion
Raw Discharge Oversize —84 +28.6 0.181 —6 +4.23 0.123
Feed to from from —28.6 +24.0 0.343 —4.23 +2.99 0.248
Grinder, Grinder, Screen, —24.0 +20.3 0.220 222509 all 0.167
mass mass mass —20.8 +17.0 0.165 —2.11 +1.49 0.105
Mesh fraction fraction fraction —17.0 +14.3 0.054 SA sei 0s) 0.068
= 3 + 4 0.05 —14.3 +12.0 0.037 —1.05 -+0.81 0.051
— 4+ 6 0.10 —0.81 +0.57 0.046
= (Da m 0.20 —0.57 °+0.403 0.039
— 8+ 10 0.30 —0.403 +0.285 0.033
— 10 + 14 0.20 0.04 0.05 —0.285 70.201 0.028
— 14 + 20 0.10 0.08 0.10 —0.201 +0.142 0.025
— 20 + 28 0.05 0.16 0.20 —0.142 +0.100 0.023
= 28 + 35 0.24 0.30 —0.100 -+0.0707 0.018
— 35 + 48 0.17 0.2025 —0.0707 +0.0500 0.016
— 48 + 65 0.10 0.0975 —0.0500 +0.0353 0.010
— 65 +100 0.08 0.05 6. In an attempt to evaluate the efficiency of a 24-in. by
—100 +150 0.06
15-in. Blake Jaw crusher, a set of coarse analytical screens
—150 +200 0.04
was constructed from welded steel rods. The standard
—200 +270 0.02
Tyler 4/2 relationship between screen apertures was main-
—270 +400 0.01 tained in this series of large screens.
Calcite was fed to the crusher at the rate of 60 tons/hr.
4, A feed of 150 tons/day of pyrites must be comminuted The discharge setting of the jaws was 5 in. The crusher was
from the material size given below as feed (the product from a driven by a 35-hp motor. Screen analyses of the feed and
controlling screen) to the size range given below as product the product are given in the table below.
(the feed to a reduction process). A ball mill is to be used. (a) Calculate efficiency of the crusher, assuming the motor
It will be loaded with balls to operate at a crushing effective- was operating at an average of 16 its rating.
ness of about 32 per cent. (b) How many tons per hour of galena could be fed to the
(a) What size cylindrical mill should be selected? crusher and reduced over the same size range with the same
(b) What size motor will be needed to drive it? power?
(c) What is the overall energy efficiency? (c) What is the capacity according to Taggart’s formula?
Feed, mass Product, mass Feed, Product, Specific Surface
Mesh fraction fraction mass mass Ratio n for
— 8+ 4 0.036 Aperture of fraction fraction Average Diam-
— 4+ 6 0.192 Screen, on on eter of Mate-
— 6+ 8 0.365 in. screen Screen rial on Sereen
— 8+ 10 0.284 0.010 22.6 0.0 0.0
— 10 + 14 0.123 0.072 16.75 0.15 0.0 10.0
— 14 + 20 0.228 11.85 0.35 0.0 9.7
— 20 + 28 0.295 8.40 0525 0.0 9.5
= 28 + 35 0.170 5.93 OMS 0.0 9.0
— 85 + 48 0.098 4.20 0.10 0.05 8.6
— 48 +4 65 0.072 2.97 0.0 0.20 8.0
— 65 +100 0.046 2.10 0.0 0.45 m2
—100 +150 0.009 1.48 0.0 0.25 6.6
—150 +200 0.002 1.05 0.0 0.05 0:2
 PROBLEMS | 47
7. А grinder is to be used to reduce а siliceous оге of the will result in the creation of 110 sq cm of new surface. These
feed size shown below. Laboratory tests on similar equip- tests also indicate that the surface area ratios for the material
ment indicate that the product size given below will be satis- are identical with those of sphalerite.
factory, and that the grinder is approximately 8 per cent If the energy efficiency of the grinder is 18 per cent and the
efficient in converting input energy into size reduction as known streams have the analyses given below, what is the
evidenced by an increase in surface. horsepower required by the grinder? What is the effective-
It is estimated that a crusher to handle 10 short tons/hr ness of the screen?
will cost about $4000. If the crusher operates on a 24-hr
Raw Discharge Oversize
basis for 300 days/yr, it is estimated that maintenance costs, Feed to from from
overhead, and ordinary replacement costs will be about 50 per Grinder, Grinder, Screen,
cent of power costs. Electric power costs 2 cents/kwhr. mass mass mass
If this machine depreciates on a straight-line basis and its Mesh fraction fraction fraction
life is estimated at 10 yr, what is the processing cost per ton
— 8+ 4 0.10
of ore?
= S ae (0 0.20
Feed, mass Product, mass — 6+ 8 0.40
Tyler Mesh fraction fraction — 8+ 10 0.20
= @ 39 S 0.148 — 10 + 14 0.10 0.02 0.03
= 8 + 10 0.211 — 14 + 20 0.04 0.06
— 10 + 14 0.230 — 20 + 28 0.06 0.09
— 14 + 20 0.186 0.098 — 28 + 35 0.25 0.85
= 20 F 28 0.120 0.284 — 85 + 48 0.30 0.30
— 28 + 35 0.076 0.277 = 48 F 65 0.20 0.08
— 35 + 48 0.034 0.149 22650-1100 0.06 0.05
— 48 + 65 0.101 —100 +150 0.04 0.04
— 65 4-100 0.068 —150 +200 0.03
—100 +150 0.044
—150 +200 0.029 10. Quartz goes through two successive grinders on the
same shaft which draws a total of 20 hp. The feed averages
8. A roll crusher is to be used to crush medium hard quartz 2 in. in diameter and has a surface ratio n of 10. The grinders
(specific gravity, 2.65). The product from the crusher is to running empty require 2 hp. Their capacity is 3 tons/hr.
be fed to a number of rod mills (6 ft by 12 ft) at the rate of The analyses of their products are given below.
8 tons/hr to each mill. The power consumption of each rod (a) Calculate the horsepower used in each grinder.
mill is 160 hp, with an overall energy effectiveness or efficiency (b) Calculate the efficiency of the grinders if Rittinger’s
of 2.0 per cent. number (new surface produced per unit of energy) is 37.6
The rod mills operate in closed circuit with a 48-mesh sq in./ft-lb.
screen. The ratio of recycle to product is 1:1. Primary Grinder
If the surface ratio n for quartz is 10 for all sizes above
3 mesh, determine the setting (distance between the rolls) Mesh 0
in the roll crusher. = aber B 20
= Si ap Md 30
—14 + 28 30
Classifier Product Recycle Stream
—28 + 48 15
Mass Mass
—48 +100 5
Mesh Fraction Mesh Fraction
— 35 + 48 0.05 —20 +28 0.05 Final Grinder
— 48 + 65 0.80 —28 +35 0.10
— 65 +100 0.10 —35 +48 0.80 Mesh %
—100 +150 0.05 —48 +65 0.05 — 28 + 48 10
— 48 +100 20
—100 +200 30
9. Five tons of a hard rock (specific gravity, 3.8) are fed
—200 mesh + 0.001 in. 30
every hour to a cone crusher in closed circuit with a 48-mesh
upon the possibility of eversize — 0.001 in. + 0.0003 in. 10
screen. Regular checks
particles passing through the screen show that all material
in the undersize stream from the screen will pass through a 11. A Hardinge mill is grinding cement clinker (specific
28-mesh screen. l gravity, 2.2) in an open circuit at the rate of 20 tons/hr.
Drop weight laboratory tests upon the material being All grinder product must pass 48 mesh, and none is to be
crushed indicate that the absorption of 1 ft-lb of energy wasted. A total of 375 hp is required by the mill, with 5 hp