Size Reduction

Makhdoom Ibad Ullah Hashmi

Reference Book: Coulson & Richardson’s 5th Edition

Size reduction is a process of reducing large solid unit masses into small unit masses, coarse particles or fine particles. Size reduction process is also termed as Comminution or Diminution or Pulverizations.  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.

Reference: Coulson & Richardson’s 5th Edition

1. Impact —particle concussion by a single rigid force (hammer). 2. Compression—particle disintegration by two rigid forces (nutcracker). 3. Shear —produced when the particle is compressed between the edges of two hard surfaces moving tangentially. 4. Attrition —arising from particles scraping against one another or against a rigid surface (a file).

The energy requirement for particle size reduction is a function of input and output of particle size, hardness, strength and other properties of solids.

Various theories for energy requirement are:1. 2. 3.

Rittinger’s theory Kick’s theory Bond’s theory.

Coulson & Richardson’s 5th Edition Pg. No. 100

 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/L2 which 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: 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 =∞.

Coulson & Richardson’s 5th Edition Pg. No. 101

 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.

Coulson & Richardson’s 5th Edition Pg. No. 102

 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. Coulson & Richardson’s 5th Edition Pg. No. 103

 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 • Subjecting it to the action of a stream of fluid.

 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 Coulson & Richardson’s 5th Edition Pg. No. 106

 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:

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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 welldefined 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.

• 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

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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.

Heavy rolls rotating at slow speeds two heavy smooth faced metal rolls turning on parallel horizontal axis compression b/w rolls and then drop out

turn to each other with same speed 50 – 300 rpm narrow faces as compared to diameter feed 12 – 75 mm product 12 – 1 mm R.R < 5

The term grinder refers to a variety of size reduction machines for intermediate duty. Product from a crusher is often fed to a grinder for further reduction. Common commercial grinder machines are hammer mills, attrition mills, tumbling mills etc.

 A hammer mill is a machine whose purpose is to shred or crush

aggregate material into smaller pieces.  The material can be put into the machine from the inlet and then under the influence of the guiding plate into the pulverizing cabin. Later on, the materials will be ground with the hammer plates striking and sieve plates friction at fast speed, at last, with the help of centrifugal force and air current, the pulverized materials will be discharged from the foundation through sieve holes.  The basic principle is straightforward. A hammer mill is essentially a steel drum containing a vertical or horizontal rotating shaft or drum on which hammers are mounted. The hammers are free to swing on the ends of the cross, or fixed to the central rotor. The rotor is spun at a high speed inside the drum while material is fed into a feed hopper. The material is impacted by the hammer bars and is thereby shredded and expelled through screens in the drum of a selected size.

 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 abrasionresistant 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 

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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.

Ball mill operates at 50 to 75 percent of critical speed.

Ball mill operating at correct speed

Coulson & Richardson’s 5th Edition Pg. No. 129

 The mill may be used wet or dry although wet grinding

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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

Problem No. 1 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?

Problem No. 2 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)?

Problem No. 3 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)?

Problem No. 4 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).

Problem No. 5 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.