• In the materials processing industry, size
reduction or comminution is usually carried out
in order to:
– Increase the surface area because, in most reactions
involving solid particles, the rate of reactions is
directly proportional to the area of contact with a
– Break a material into very small particles in order to
separate the valuable amongst the two constituents.
– Achieve intimate mixing.
Mechanism of size reduction
Impact —particle concussion by a single rigid force (hammer).
Compression—particle disintegration by two rigid forces (nutcracker).
Shear —produced when the particle is compressed between the edges of
two hard surfaces moving tangentially.
Attrition —arising from particles scraping against one another or against a
rigid surface (a file).
Energy for size reduction
• The energy dE required to effect a small change dL in the size of
unit mass of material is a simple power function of the size.
• Rittinger’s law:
– putting p = −2, then integration gives:
– Writing C = KRfc, where fc is the crushing strength of the material, then
Rittinger’s law, first postulated in 1867, is obtained as:
– Since the surface of unit mass of material is proportional to 1/L, the
interpretation of this law is that the energy required for size reduction
is directly proportional to the increase in surface.
• Kick’s law:
– putting p = −1, then integration gives:
– Writing C = KKfc, then Kick’s law, is obtained as:
– This supposes that the energy required is directly related to the
reduction ratio L1/L2which means that the energy required to crush a
given amount of material from a 50 mm to a 25 mm size is the same as
that required to reduce the size from 12 mm to 6 mm.
• Bond’s Law:
– Neither of these two laws permits an accurate calculation of the energy
– Rittinger’s law is applicable mainly to that part of the process where
new surface is being created and holds most accurately for fine grinding
where the increase in surface per unit mass of material is large.
– Kick’s law, more closely relates to the energy required to effect elastic
deformation before fracture occurs, and is more accurate than
Rittinger’s law for coarse crushing where the amount of surface
produced is considerably less.
• Bond has suggested a law intermediate between Rittinger’s
and Kick’s laws, by putting p = −3/2 in the general equation:
• Writing C = 5Ei then:
• Bond terms Ei the work index, and expresses it as the amount
of energy required to reduce unit mass of material from an
infinite particle size to a size L2 of 100 μm, that is q =∞.
• One of the first important investigations into the
distribution of the energy fed into a crusher was carried out
by OWENS who concluded that energy was utilized as
– In producing elastic deformation of the particles before fracture
– In producing inelastic deformation which results in size
– In causing elastic distortion of the equipment.
– In friction between particles, and between particles and the
– In noise, heat and vibration in the plant, and
– In friction losses in the plant itself.
• Owens estimated that only about 10 per cent of the total
power is usefully employed.
Method of operating crusher
• There are two distinct methods of feeding material to a
– Free crushing; involves feeding the material at a
comparatively low rate so that the product can readily
escape. Its residence time in the machine is therefore
short and the production of appreciable quantities of
undersize material is avoided.
– Choke feeding; In this case, the machine is kept full of
material and discharge of the product is impeded so that
the material remains in the crusher for a longer period.
This results in a higher degree of crushing, although the
capacity of the machine is reduced and energy
consumption is high.
Mode of operation
• Open circuit grinding:
If the plant is operated, as in choke feeding, so that the
material is passed only once through the equipment,
the process is known as open circuit grinding.
• Closed circuit grinding:
If the product contains material which is insufficiently
crushed, it may be necessary to separate the product
and return the oversize material for a second crushing
This system which is generally to be preferred, is
known as closed circuit grinding
Separation may be done by:
•allowing the material to fall on to a screen
•or subjecting it to the action of a stream of fluid.
Classification of crushers
• it is not generally economical to effect a large reduction ratio in a
• The equipment used is usually divided into classes as given below,
according to the size of the feed and the product.
• A greater size reduction ratio can be obtained in fine crushers than
in coarse crushers
Types of grinding
• Grinding may be carried out either wet or dry.
• wet grinding is generally applicable only with low speed
• The advantages of wet grinding are:
– The power consumption is reduced by about 20–30 per cent.
– The capacity of the plant is increased.
– The removal of the product is facilitated and the amount of
fines is reduced.
– Dust formation is eliminated.
– The solids are more easily handled.
• Disadvantages are:
– The wear on the grinding medium is generally about 20 per cent
– It may be necessary to dry the product.
Nature of the material to be crushed
The hardness of the material affects the power consumption and the wear
on the machine. With hard and abrasive materials it is necessary to use a
low-speed machine and to protect the bearings from the abrasive dusts
that are produced.
Normal granular materials such as coal, ores and rocks can be effectively
crushed employing the normal forces of compression, impact, and so on.
With fibrous materials a tearing action is required.
• Moisture content:
It is found that materials do not flow well if they contain between about 5
and 50 per cent of moisture. Under these conditions the material tends to
cake together in the form of balls. In general, grinding can be carried out
satisfactorily outside these limits.
• Crushing strength:
The power required for crushing is almost directly proportional to the
crushing strength of the material.
• Crushing strength:
The power required for crushing is almost directly proportional to the
crushing strength of the material.
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.
A sticky material will tend to clog the grinding equipment and it should
therefore be ground in a plant that can be cleaned easily.
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
Such materials must be ground wet or in the presence of an inert
• Materials yielding dusts that are harmful to the health:
Such material must be ground under conditions where the dust is not
allowed to escape.
• Feed is admitted between two jaws set to form V open at the top.
• One jaw is fixed and is nearly vertical and does not move.
• While the other jaw is moveable and reciprocates in a horizontal
plane making an angle 20 – 30 degree with the fixed jaw.
• The jaws faces are flat or they may contain grooves. Jaw widths
varying from about 150 mm to 1.0 m with crushing faces formed of
• Large lumps caught between the upper part of the jaws are broken,
dropped into the narrow space below and are further crushed.
• After sufficient reduction they dropped off the machine.
• The jaws open and close 250 – 400 times per minutes depending
upon the speed.
• The most common type of jaw crusher is Blake jaw crusher / Stage
jaw crusher in which the moveable jaw is pivoted at the top so that
the maximum movement is at the bottom of the V due to which
there is a little tendency for this crusher to choke. Therefore it is
widely used in industries for crushing of hard rock for example in
cement and ceramic industries.
• In Dodge jaw crusher the moving jaw is pivoted at the bottom
because of which minimum movement is at the bottom as a
consequence more uniform product is obtained. It is not widely
used because of its tendency to chock.
• The ball mill consists of a rotating hollow cylinder, partially filled
with balls, with its axis either horizontal or at a small angle to the
horizontal. In large ball mill the shell might be 3 m in diameter and
4.25 m in length.
• The outlet is normally covered with a coarse screen to prevent the
escape of the balls.
• The inner surface of the cylinder is usually lined with an abrasion-resistant
material such as manganese steel, stonewear or rubber.
Less wear takes place in rubber-lined mills and the coefficient of
friction between the balls and the cylinder is greater than with steel
or stoneware linings. The balls are therefore carried further in
contact with the cylinder and thus drop on to the feed from a greater
height. In some cases, lifter bars are fitted to the inside of the
cylinder. Another type of ball mill is used to an increasing extent,
where the mill is vibrated instead of being rotated, and the rate of
passage of material is controlled by the slope of the mill.
• Grinding medium are the metalic balls are usually made of iron,
manganes or steel and occupy between 30 and 50 per cent of the
volume of the mill. The diameter of ball used will vary between 12
mm and 125 mm
• The ball mill is used for the grinding of a wide range of materials
and it copes with feed up to about 50 mm in size.
• The material to be ground may be fed in through a 60 degree cone
at one end and the product leaves through a 30 degree cone at the
• The efficiency of grinding increases with the hold-up in the mill,
until the voids between the balls are filled. Further increase in the
quantity then lowers the efficiency.
• Large balls deal effectively with the feed and the small ones are
responsible for giving a fine product.
• During grinding, the balls wear and are constantly replaced by new
ones so that the mill contains balls of various ages, and hence of
• As the shell rotates the large balls moves towards the point of
maximum diameter and small balls migrated towards the discharge.
• As the mill rotate the balls are picked up by the wall and carried
upward depending upon the speed where they loose contact and
falls to the bottom.
• In ball mill most of the reduction is done by impact as the balls are
dropped from the top of mill and remaining is done by compression
and attrition as the ball slides over each other and over the wall of
Factors influencing the size of the product
The rate of feed: With high rates of feed, less size reduction is effected since the material is
in the mill for a shorter time.
The properties of the feed material: The larger the feed the larger is the product under
given operating conditions. A smaller size reduction is obtained with a hard material.
Weight of balls: A heavy charge of balls produces a fine product. The weight of the charge
can be increased, either by increasing the number of balls, or by using a material of higher
density. Since optimum grinding conditions are usually obtained when the bulk volume of
the balls is equal to 50 per cent of the volume of the mill.
The diameter of the balls: Small balls facilitate the production of fine material although
they do not deal so effectively with the larger particles in the feed. For most economical
operation, the smallest possible balls should be used.
The slope of the mill: An increase in the slope of the mill increases the capacity of the
plant because the retention time is reduced, although a coarser product is obtained.
Discharge freedom: Increasing the freedom of discharge of the product has the same
effect as increasing the slope. In some mills, the product is discharged through openings in
• The speed of rotation of mill: At low speeds of rotation, the balls simply roll over one
another and little crushing obtained. At slightly higher speeds the balls are projected
short distances across the mill, and at still higher speeds they are thrown greater distances
and considerable wear of the lining of the mill takes place. At very high speeds, the balls
are carried right round in contact with the sides of the mill and little relative movement or
grinding takes place again. The minimum speed at which the balls are carried round in this
manner is called the critical speed at which no grinding take place.
Critical speed of ball mill
Ball mill operates at 50 to 75 percent
of critical speed.
Ball mill operating at correct speed
• The mill may be used wet or dry although wet grinding
facilitates the removal of the product.
• The costs of installation and power are low as compared to
• The ball mill may be used with an inert atmosphere and
therefore can be used for the grinding of explosive materials.
• The grinding medium is cheap.
• The mill is suitable for materials of all degrees of hardness.
• It may be used for batch or continuous operation.
• It may be used for open or closed circuit grinding. With open
circuit grinding, a wide range of particle sizes is obtained in
the product. With closed circuit grinding, the use of an
external separator can be obviated by continuous removal of
the product by means of a current of air or through a screen
• A certain crusher accepts a feed of rock having diameter of
0.75 in and discharge a product of diameter 0.2 in. the
power required to crush 12 tons per hr is 9.3 hp. What
should be the power required if the capacity is reduced to
10 ton per hr and as a consequence of which the diameter
of product become 0.15 in?
• What is the power required to crush 100 tons/hr of lime
stone if 80% of the feed passes through a 2 in screen and
80% of the product through 1/8 in screen (Ei = 12.74 kW hr
• It is required to crush 250 tons/hr of an ore which may be
classified as a soft material . The range of feed size is such
that 80% passes through an opening of 16 in. The product
size is to be such that 80% passes through an opening of 3
in. Estimate the power consumption per ton of feed (Ei =
13.1 kW hr mm/ton)?
• What will be the product size of the material having
reduction ratio of 10? If the energy required to crush 2 tons
of material is 100 kW hr. Assume Ei = 10 kW hr mm /ton).
• A crusher is reducing lime stone of crushing 70
MN/m2 from 6mm diameter average size to
0.1 mm average size. Energy required is 9
kW/(tons/hr). The same machine is used to
crush dolomite at the same rate from 6mm
diameter of average size to the product which
consist of 20% with an average diameter of
0.25 mm, 60% with an average diameter of
0.125 mm and the balance with an average
diameter of 0.085 mm. Estimate the power
required to drive a crusher. The crushing
strength of dolomite is 100 MN/m2.