1
DoChE, GEC TCR
 Breaking large particles to smaller ones by the utilization of energy
 Compression, impact, attrition(rubbing), shear, cutting/tearing
Impact Attrition Shear Compression

DoChE, GEC TCR
2
ENERGY SPEND DURING SIZE REDUCTION:
o Elastic deformation before fracture occurs
o inelastic deformation of material leading to breakage
o Causing elastic distortion of the equipment
o Heat generation, noise and vibration
o Friction between material particles and between particle
and equipment surface
o Friction between equipment parts in movement

DoChE, GEC TCR
3
Crushing efficiency
Crushing efficiency is defined as the ratio of the
surface energy created by crushing to the energy
absorbed by the solid
where,
ηc = crushing efficiency
Wn = energy absorbed by the material, J/Kg
es = surface energy per unit area

DoChE, GEC TCR
4
Ab = area of the product, m2
Aa = area of feed, m2
Crushing efficiencies are low as surface energy
created is small ;
ranges from 0.06 to 1 %
Mechanical efficiency, ηm
Ratio of energy absorbed to the energy input
ηm = Wn /W
W= energy input, J/Kg
W = Wn /ηm = es(Ab-Aa)/ ηmηc

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5
OPERATIONS: Crushing vs. Grinding
Crushing
impact or compression only
Coarse product with high
irregularity from large lumps
Dry feed
Max. Reduction ratio –> 6-8
Heavy duty slow speed
machines
Low energy consumption
Grinding
compression and attrition
Crushed feed to Fine product
Dry or wet
As high as 100
Light duty, high speed
machines
High energy consumption
Equipments:
Jaw & gyratory crushers, crushing
rolls etc.
Equipments:
Hammer mill, attrition mill,
tumbling mill (ball, rod, tube)

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Ultra fine
grinders
• Fluid- energy
mill
• Agitated mill
Cutting
machines
• Knife cutter
• Dicer
• slitter
Feed size < 6mm
• Product : 1-
50µm
Product with
definite size and
shape
• 2-10 mm in length

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FACTORS INFLUENCING COMMINUTION
Nature of material
• Hardness
• Toughness (impact resistance)
• Crystallinity and Cleavage
• structure (fibrous, flake, granular)
Moisture content
• Dry grinding m.c.< 3%
• Wet grinding m.c.> 50%
• For 3% - 50% m.c. , grinding is difficult – material
tends to form sticky or pasty mass
•

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Crushing strength. The power required for crushing is almost directly
proportional to the crushing strength of the material.
Friability. The friability of the material is its tendency to fracture during
normal handling. In general, a crystalline material will break along well-
defined planes and the power required for crushing will increase as the
particle size is reduced.
Stickiness. A sticky material will tend to clog the grinding equipment and
it should therefore be ground in a plant that can be cleaned easily.
Soapiness. In general, this is a measure of the coefficient of friction of the
surface of the material. If the coefficient of friction is low, the crushing
may be more difficult.
Explosive materials must be ground wet or in the presence of an inert
atmosphere.
Materials yielding dusts that are harmful to the health must be ground
under conditions where the dust is not allowed to escape.

DoChE, GEC TCR
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Dry grinding Vs Wet grinding
Grinding may be carried out either wet or dry, although wet grinding is
generally applicable only with low speed mills.
The advantages of wet grinding are:
(a) The power consumption is reduced by about 20–30 per cent.
(b) The capacity of the plant is increased.
(c) The removal of the product is facilitated and the amount of
fines is reduced.
(d) Dust formation is eliminated.
(e) The solids are more easily handled.
Against this,
the wear on the grinding medium ~ 20 per cent greater, and
It may be necessary to dry the product.

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OPEN CIRCUIT AND CLOSED CIRCUIT GRINDING
Open circuit: material passed only once through the crusher
 FREE CRUSHING – Product removed continuously
as soon as it is formed.
• Large capacity. Very less fines
 CHOKE FEEDING - crusher equipped with feed
hopper and kept filled – does not freely discharge the
product
Feed Intermediate Product Product
crusher grinder

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Closed circuit grinding: Over size from product
separated & returned to crusher

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12
ENERGY AND POWER REQUIREMENTS

DoChE, GEC TCR
13
n
D
c
dD
dE 


ENERGY AND POWER REQUIREMENTS
E - Energy required per unit mass
D – Particle size
c, n – parameters
For n=1;
sb
sa
K
D
D
K
m
P
E ln
.


Kick’s law
‘Work required in crushing is constant for a given reduction
ratio irrespective of original size’
- Applicable to coarse crushing
--- (1)
--- (2)

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‘Work required in crushing α new surface created’
-applicable to fine grinding
-particle diameter is volume-surface dia.
For n=2 ;









sa
sb
R
D
D
K
m
P
E
1
1
. Rittinger’s law
--- (3)

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










sa
sb
B
D
D
K
m
P
E
1
1
.
For n=1.5
--- (5)
--- (4)
If Dsa >>> large size,
sb
B
D
K
m
P
E 
 .
BOND’S LAW
States that work required to form particle of size Dsb is proportional to
the square root of the surface to volume ratio of the product, sp/vp
sb
s
p
p
D
v
s

6


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









q
D
E
E
sb
i
1
1
100
Ei – work index  amount of energy required to reduce unit
mass of material from an infinite size to a size of 100 µm.
Size of material = size of mesh through which 80% of particles pass
through
To use eqn (4) work index is required, defined by;
i
i
B E
E
K 3162
.
0
10
100 3


 

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DoChE, GEC TCR
18
Solution:
a) Rittinger’s law
This is given by:
Thus: 13 = KR(1/10 - 1/50)
and: KR = 13 x 504/4 = 162.5 kW/(kg.mm)









sa
sb
R
D
D
K
m
P
E
1
1
.

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a) Kick’s law
This is given by:
Thus: 13 = KK ln(50/10)
and: KK = 13 /1.609 = 8.08 kW/(kg.mm)
sb
sa
K
D
D
K
m
P
E ln
.



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What is the power required to crush 100 TPH of limestone if 80% of the
feed passes a 2-in. screen and 80% of the product a 1/8 – in. screen?
Work index for limestone = 12.74 kWhr/ton
Solution:
Dpa= 2 x 25.4 =50.8 mm Dpb = 1/8 x 25.4 = 3.175 mm
Power, P = 100 ton/hr x 0.3162 x 12.74 kWhr (1/√3.175 – 1/√50.8)
= 169.6 kW

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Jaw crushers
 Works on impact
 Two jaws
1. Fixed
2. movable/swing
 Angle between jaws : 20o – 30o
 Impact speed : 250 – 400 times/minute
 feed size : upto 1.8 m Product size: 250 mm
 capacity = 1200 ton/hr
 Applications : Mining, metallurgical industries, Road,
railways etc.
 2 types : Blake & Dodge
Equipments:

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DoChE, GEC TCR
23
Single toggled Blake jaw crusher

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Toggles

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Tie rod

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Blake jaw crusher
Movable jaw is pivoted at the
top
Max. movement at bottom
No tendency to choke/clog
Suitable for high production
rate
Large reduction ratio not
possible
Low maintenance
Large sized equipment
Does not give uniform
product
Dodge Jaw crusher
Movable jaw is pivoted at the
bottom
Max. movement at top
tendency to choke/clog
Low production rate
Large reduction ratio
possible
High maintenance
Comparatively small size
Gives uniform product

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• Jaw crusher with
circular jaw.
• continuous
• less power required
• less maintenance
GYRATORY CRUSHER

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Crushing Rolls
Reduction by Compression
Heavy cylindrical rolls rotating at low speeds in opposite
directions
Speed: 50 – 300 rpm
Feed size: 12 – 75 mm Product size: 12 – 1 mm
Reduction ratio < 5

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29
Angle of nip, α

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30
T cosα
N sinα
T
N
For a particle to be crushed by roll, vertical component of radial force (N) by roll
should be less than vertical component of tangential frictional force (T)
ie., N sinα ≤ T cosα
Or, T/N ≥ tan α
>> µ ≥ tan α since, T/N = µ , coefft. of friction
For a typical roll α ≈ 16o

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Limiting size of particle that can be nipped
Depends on coefficient of friction
Esimated using
Dp, max = 0.04 r1 + b
r1 = roll radius
b= half the width of the gap between rolls
Max. size of product ≈ 2b
Theoritical capacity, Qth (kg/h)
= 60πD1D3 L N ρ
D1 = diameter of roll = 2r1
D3 = Distance between rolls = 2b
L = length of roll face,m
N =speed in rpm
ρ = Density of particles

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TUMBLING MILLS
Ball Mill, conical ball mill (uses
balls of diff. dia.) , tube mill
(long shell), rod mill (uses
short rods instead of balls),
Pebble mill
R = Radius of shell
r = Radius of ball
mu2/(R-r)
mg
mg cosθ
θ

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Critical speed (speed at which centrifuging occurs): Nc
mu2/ (R-r) = mg cosθ --- (1)
u = [(R-r)g cosθ ]½
Also, u = (R-r)ω = (R-r) 2πN
(R-r) 2πN=[(R-r)g cosθ ]½
2
/
1
2
/
1
)
(
cos
2
1
)
(
2
]
cos
)
[(













r
R
g
r
R
g
r
R
N




1/2
c
r)
(R
g
2π
1
N 









At critical speed, θ = 0, cosθ = 1, N= Nc
Operating speed
65-80% of Nc

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Ultrafine grinders
FLUID ENERGY MILL
Dry:
High speed hammer mill,
Fluid-energy / Jet mill
Wet:
Agitated mill
Colloid mill

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Hammer mill with classifier
Mikro-Atomizer
Colloid mill