SIZE REDUCTION
SIZE REDUCTIONSIZE REDUCTIONApplied to all the ways in which
particles of solids are cut or broken into small
piecesImportanceReducing the particle size increases the reactivity
of the solidsIt permits separation of unwanted ingredients by
mechanical methodsIt reduces the bulk of fibrous materials for
easier handling and for waste disposalCOMMONLY USED METHODS IN SIZE
REDUCTION MACHINECompression
Impact
Attrition or rubbing
Cutting COMMINUTIONA generic term for size reduction; crushers
and grinders are types of comminuting equipment.ENERGY AND POWER
REQUIREMENT IN COMMINUTIONThe cost of power is a major expense in
crushing and grinding, so the factors that control the cost are
important. Crushing efficiency, nc The ratio of the surface energy
created by crushing to the energy absorbed by the solid. es is the
surface energy per unit area, and Awb and Awa are the areas per
unit mass of product and feed. Wn is the energy absorbed by a unit
mass of the material
Power required by the machineWork energy input
Power
Average particle size
Power
Empirical relationship: RITTINGERS AND KICKS LAWRittinger in
1867 states that the work required in crushing is proportional to
the new surface created.RITTENGERS LAW:
In 1885 Kicks proposed another law, which states that the work
required for crushing a given mass of material is constant for the
same reduction ratio, that is, the ratio of the initial particle
size to the final particle size.
BOND CRUSHING LAW AND WORK INDEXIn 1952 Bond postulated that the
work required for crushing and grinding to form particle of size Dp
from very large feed is proportional to the square root of the
surface-to-volume ratio of the product.
Work index (KW-hr/ton)Defined as the gross energy requirement in
kilowatt hours per ton (2000 lbs) of feed needed to reduce a very
large feed to such size 80% of the product passes a 100-m
screen.
MaterialSpecific GravityWork index, WiBAUXITE2.208.78CEMENT
CLINKER3.1513.45CEMENT RAW
MATL2.6710.51CLAY2.516.30COAL1.413.00COKE1.3115.13GRANITE
2.6615.13GRAVEL 2.6616.06GYPSUM
ROCK2.696.73HEMATITE3.5312.84LIMESTONE2.6612.74PHOSPHATE
ROCK2.749.92QUARTZ2.6513.57SHALE2.6315.87SLATE2.5714.30TRAP
ROCK2.8719.32PROBLEM 1What is the power required to crush 100 ton/h
of limestone if 80% of the feed passes a 2-in screen and 80% of the
product a 1/8-in screen?Problem 2Trap rock is crushed in a gyratory
crusher. The feed is nearly uniform 2-in spheres. The differential
screen analysis of the product is given in column 1 of table 1. The
power required to crush this material is 400 kW. Of this 10 kW is
needed to operate empty mill. By reducing the clearance between the
crushing head and the cone, the differential screen analysis of the
product becomes that given in column 2 in table 1. From Rittingers
law and Kicks law, calculate the power required for the second
operation. The feed rate is 110 ton/h.Table 1MESHFIRST GRINDSECOND
GRIND4/63.16/810.33.38/1020.08.210/1418.611.214/2015.212.320/2812.013.028/359.519.535/486.513.548/654.88.565/1006.2100/1504.3The
screen analysis shown on problem 2 applies to a sample of crushed
quartz. The density of the particles is 2650 kg/m3 (0.00265 g/mm3)
and the shape factor is 2 and sphericity is 0.571. For the material
between 28-mesh to 150-mesh in particle size of the 2nd grind,
calculate (a) Aw in mm2/g and Dw (mass mean diameter)Volume surface
mean diameter, , defined by;
