Particle Size Reduction

comminution

Introduction

• 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 second phase.

– 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

requirements.– 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’sand 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 =∞.

Exercise

Energy utilization

• 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 follows:– In producing elastic deformation of the particles before fracture

occurs.– In producing inelastic deformation which results in size

reduction.– In causing elastic distortion of the equipment.– In friction between particles, and between particles and the

machine.– 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 crusher:– 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 single machine.

• 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

mills.• 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

greater.– It may be necessary to dry the product.

Nature of the material to be crushed

• Hardness: 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.

• Structure: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.

• 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:Such materials must be ground wet or in the presence of an inert atmosphere.

• Materials yielding dusts that are harmful to the health:Such material must be ground under conditions where the dust is not allowed to escape.

TYPES OF CRUSHING EQUIPMENT

Jaw Crushers

• 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 manganese steel

• 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.

Dodge jaw crusher

Bal

l mill

Co

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ion

• 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

Wo

rkin

g• 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 other end.

• 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 various sizes.

• 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 shell.

Fact

ors

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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 lining.

• 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.

Cri

tica

l sp

eed

of

bal

l mill Ball mill operates at 50 to 75 percent

of critical speed.

Ball mill operating at correct speed

Exercise

Ad

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s• 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

other mils.• 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

Few problems• 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 mm/tons)?

• 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.