CRUSHING LAWS

Content Crushing laws Rittinger law Kick’s Bond’s

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.

Basic Definitions Comminution : The whole operation of reducing the raw ore to the size required for mechanical separation or metallurgical processing . Crushing (dry) : Size reduction occurs preferentially on large fragments. Grinding (wet) : Size reduction is less selective –all pieces ground to fine particles Grinding

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 of the size. C = Constant related to the material, dE = differential energy required, dL = Change in particle dimension, P = exponent.

Von Rittinger’s law (1867): It states that the energy consumed in the size reduction is proportional to the area of new surface generated. putting p = −2, then integration gives: Writing C = KRfc fc is the crushing strength of the material. L2 & L1 are the final and initial particle sizes. KR is the Rittinger’s constant

Applications of Rittinger’s law Applicable to brittle materials undergoing fine milling. This theory ignore deformation before fracture.

Kick’s law (1885): It states that the work required is proportional to the reduction in volume of the particles concerned. putting p = −1, then integration gives: Writing C = KKfc, then Kick’s law, is obtained as: KK = kick’s constant

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. For compression of large particles kick’s theory is useful.

Bond’s Law(1952): This third law states that the net energy required in comminution is proportional to the length of the new cracks formed. Energy required is based on geometry of a crack expansion as it opens up. 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’s and Kick’s laws, by putting p = −3/2 in the general equation: Writing C = 5Ei then: Bond terms Ei the work index, L is measured in microns , 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.

Applications of Bond’s law This theory is useful for rough mill sizing. The work index is useful for comparing efficiency of milling operation

Limitations Of Comminution Laws The size and shape which can be determined by these methods is not very perfect. - It is determined on the average method. - The methods discussed above can’t measure the accurate area of the particles. So result may not be accurate . It is very difficult to determine accurate area of the finer particles by these methods. Even if the above conditions are determined, the surface areas of the cracks present in big particles would remain unaccounted.

Conclusions All the above equations are dimensionless. Rittinger’s law deals with measurements of surface areas . Kick’s law deals with volumes of product’s particles . Bond’s theory deals with lengths of cracks formed. Kick applies to coarse sizes (> 10 mm). Bond applies down to 100 µm. Rittinger applies to sizes < 100 µm .

Summary Rittinger’s law:- (p=-2.0) Energy α new surface area formed. Bond’s law:- (p=-1.5) Energy used in crack propagation α Crack length produced. Kick’s law:- (p=-1.0) Energy α Ratio of change in size.

References www.wikipedia.com www.google.com

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