SIZE REDUCTION
8th Edition
7th Edition
Section 21 Pages 21-8 to 21-11 Pages 21-45 to 21-73
Section 20 Pages 20-5 to 20-7 Pages 20-10 to 20-56
8th Edition
7th Edition
Section 21 Pages 21-8 to 21-11 Pages 21-45 to 21-73
Section 20 Pages 20-5 to 20-7 Pages 20-10 to 20-56
The hardness of the material as measured by the Mohs scale of (1) to (10) is a criterion of its resistance to crushing and has significant effect on the wear and tear of the size reduction device. Arranged in increasing scale of hardness based on the Mohs scale: Soft Materials: (1) talc, (2) gypsum, (3) calcite Intermediate Hardness: (4) fluorite, (5) apatite, (6) feldspar Hard Materials: (7) quartz, (8) topaz, (9) corundum, (10) diamond
1. Particle Size and Shape Volume of any particle (any shape), Surface area of any particle, Sp where: Dp
Vp
6b
Dp
aDp 2
arbitrarily chosen characteristic dimension of any particle a & b = geometric constants (dependent on the shape of the particle) Vp aDp 3 Dp where: shape factor 2 b Sp 6bDp 6 a (independent of size) 1 Sphericity,
s
For spheres and cubes
1.0 and s = 1.0
2. Specific Surface and Number of Particles in a Mixture For uniform particles of mass m: m volume p where: m mass of particles density of particles p For a single particle:
Vp
aDp
Number of Particles: N
Total Surface Area
3
m p p 3
aD p
m p A NS p aD p3
bD 6
2
p
A
6 m
p Dp
Specific Surface of a Mixture, Aw, ft2/lb mixture 1. Based on Differential Screen Analysis 6 1
n Aw ....... p Dp1 Dp2 Dpn 2
2. Based on Cumulative Screen Analysis
Aw
6
p
1
0
d Dp
Number of Particles in Mixture,
Nw
1. Based on Differential Screen Analysis
Nw
1
a p
N
n
n 1 Dp
3
2. Based on Cumulative Screen Analysis
Nw
1
a p
1
0
d Dp
3
3. Average Particle Size a. Volume-surface mean diameter
D v s
6
Aw p
b. Arithmetic Mean Diameter Nw
D N
Dp dN
0
Nw
c. Mass-means diameter 1
D w 0 Dpd
4. Particle Size Distribution in Comminuted Products For particles too fine to sieve accurately :
d
dD p
BD pk
This equation is used to extrapolate screen analysis data Integrating and simplifying, log n k 1 log Dp1n log B' equation of a straight line a. evaluate the value of (k+1) m (slope) b. evaluate the value of B’ y intercept
1. Rittinger’s Law – which states “that the work required in crushing is proportional to the new surface created.” P
Awb
Awa
T N where: P = theoretical power T = flow rate of the feed Awb = specific surface area of product Awa = specific surface area of feed N = Rittinger’s Number – new surface produced per unit of mechanical energy absorbed by the material being crushed.
2. Bond’s Crushing Law which states that “the work required to form particles of size Dp from very large feed is proportional to the square root of the surface to volume ratio of the product”.
P T
k
Sp Vp
k
6
Dp
where: K = constant which depends on type of machine & material
P T P T
1.46 Ei
1 X 2
0.3162 Ei
X 1
1 X 2
P in Hp; T in tons/min Ei in kW - h/ton; X1 & X2 in ft
1
X 1
1
P in kW; T in tons/hr Ei in kW - h/ton; X1 & X2 in mm
3. Kicks Law states that “energy required for crushing is proportional to the leg of the initial and final diameters”.
P T where:
Dp a Dpb
k log
Dpa Dpb
= size reduction ratio
In order to achieve successful size reduction, every lump or particle must be broken down by contact with other particles or with the moving parts of the machine. However, as the average particle size decreases, the number of particles increases therefore requiring more contacts for unit mass. Hence a solid has to undergo stages of size reduction.
Size range of feed is 1.5 in. to 9.6 in. in diameter or larger. 1. Jaw Crusher – consists of a swinging jaw which moves back and forth, working against a stationary surface called the anvil jaw, with which it forms a V-shape chamber. It is wide at the top and narrow at the bottom, where the crushing takes place. Jaws are lined with tough abrasion resistant material such as manganese. – employs a compressive force
a. Dodge Type Jaw Crusher - swinging jaw pivoted at the bottom - made of smaller size - less wide use because of its tendency to choke b. Blake Type Jaw Crusher - swinging jaw is pivoted at the top - toggle plates in the driving mechanism is relatively weak so that if any large stress is set up , it will just break - crushing faces are either manganese steel or chilled cast iron. - more commonly used than the Dodge type
- employs a crushing head in the frame of truncated core, mounted on a shaft - employs a compressive force - the crushing action takes place around the whole of the core - power consumption is lower - it has a large capacity per unit area of grinding surface - suitable only where large quantities of material are to be handled because of its high cost
with openings of 4 in. to 2 ft. can be determined by the Taggart Formula: T = 0.6 LS where: T = capacity (tons/hr) L = length of feed opening (in) for: jaw crushers (L) = normal to gape gyratory (L) = perimeter of the circle S = greatest width of discharge opening
About the same, but the gyratory load is somewhat more uniform since its crushing is continuous whereas jaw crusher works intermittently. Taggart’s Rule states 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.
For soft materials like coal, gypsum, some types of limestone, ice, fire clay and shales. 1. Bradford breaker for coal - combines the two features of breaking and screening - the coal enters through the chute at the far end, is lifted, falls and is broken by the impact as the cylinder is rotated perforations into the chute below; - rocks and refuse are plowed out 2. Toothed roll crusher - breaking by pressure of the teeth against the larger lumps of the material
3. Hammer Mill - the hammer deliver heavy blows to the feed material while it is in suspension, driving it against a breaker plate until it is fine enough to pass through the openings 4. Squirrel-cage disintegrator - for fibrous materials such as wood blocks and asbestos - two concentric cages rotate in opposite direction - the feed is introduced into the inner cage - centrifugal force drives the material into the spaces between the rotating cages where it is torn apart
This class covers machines that will take indefinitely coarse feeds or produce materials that will pass through 200 mesh screen 1. Crushing Rolls - Two rolls, one in adjustable bearings, rotate in opposite directions. The clearance between them can be adjusted according to the size of feed and the required size of product. The machine is protected by spring loading against damage from very hard material. Materials to be crushed is fed from above and is discharged from beneath the rolls.
2.Cone Crushers - Consists of a conical crushing head similar to that of the gyratory crusher. Operation is also similar to the latter. However what is different about the cone crusher is that the outer stationary crushing plate flares outward to provide 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 plate and injury to the machine.
3. Edge Runners - The only commonly used crusher of this general type is the one in which the pan rotates and the horizontal axis of the grinding wheels is stationary. - This machine is widely used in the clay industry, but little anywhere else and is usually known as dry pan or wet pan according to whether the clay is crushed with or without the addition of water. - This is not suited for hard rock crushing
Size reduction in the finer ranges is usually termed fine grinding. This is due to the fact that most of the older devices used for reduction in this range consisted of two parts, a stationary surface and a surface rubbed against the stationary surface. Such machines causes size reduction mainly by the application of shear loads. However more recent devices in fine size reduction, such as ball mills, depend more on impact than on shearing forces.
1. Pebble Mill
- Is a steel cylinder lying on its side and rotated about its long axis and containing an appropriate grinding medium. The material is introduced through a manhole in the center of the shell length after which the opening is closed hermetically by a cover plate. The discharge is through the same opening after replacing the cover plate with a grate with wide slots to hold back the balls.
2. Rod Mill - Rod mills are similar to pebble mills and ball mills except that the grinding media are steel rods rather than balls. The rods are always longer than the diameter of the mills and therefore lie in the mill parallel to the axis. As the mill turns, the rods drop on to lower ones, reducing the charge partly by impact and partly by grinding.
3. Ball Mills - consists of a horizontal cylinder whose diameter is roughly equal to its length, lined with heavy liner plates. The feed end consists of a helical feed scoop which lifts feed into the spiral feed liner from which it enters the mill. The load of the balls, the speed of revolution, the size of the balls and the rate of feed are all factors that are controlled so that the discharge leaving the discharge screen and the discharge funnel is of the desired size. The discharge screen is a coarse-mesh screen, not to screen out particles that have not been ground to the correct size but to keep back the any of the balls that may have entered the discharge end of the mill. The mill is rotated by the gear. The mill in operation will contain balls of various sizes. They are not put in various sizes but, since the balls are being continually worn away by attrition, new balls must be supplied from time to time.
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 will 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 rate at sea level may be ascertained from the expression:
N
76.65
D
where:
d
N = revolution per minute D = diameter of the mill (ft) d = average diameter of the balls (ft) At low speeds where the contents are simply tumbled or rolled over, the power required to drive the mill varies directly with the speed of rotation.
Depends on the reduction ratio as well as on the hardness of the material, and it cannot accurately be calculated The normal capacity of cylindrical ball mills in tons per 24 hours may be estimated as Capacity – volume of mill (cu. ft)/20°C where C varies from 1 to 2
