“SIZE

REDUCTION”

By

Engr. SHAHID MIRZA

Dated: 7th December, 2012

Size Reduction

Definition :

“Size reduction is applied to all the ways in which solids are cut or broken into smaller pieces.”

or

“Disintegration of the solid substance by mechanical forces without altering their state.”

Fundamentals

Methods of Size Reduction

Impact• For coarse, medium or fine particles,

• Example: hammer

Compression• For coarse type materials,

• Example: nut cracker

Attrition• Very fine articles of soft non abrasive

materials

• Example: file

Cutting• To attain definite particle shape or size

• Example: knife cutters

Different ways to attain Size Reduction

Factors effecting Size Reduction

Manner in which load is applied

Magnitude of the load

Nature of the material

Nature of the force

Rate of application of a force

Stringent market specificationEasy transport and handling of solid particles Increases the reactivity of solids especially in catalytic

reactions It permits separation of unwanted ingredients by

mechanical separationsCreate appropriate particle sizes for subsequent processingCreate a free-flowing material. Improve material blending & prevent segregation by

making different sized products with similar particle size distributions.

Why to Reduce Size

Energy Consumed In Crushing

Elastic deformation of the particles before fracture occur;

Inelastic deformation which results in size reduction;

Elastic distortion of the equipment;Friction between particles and the machine;In noise, heat & vibration in the plants;Friction losses in the plant itself:

Characteristics of Ideal Crusher

Have a large capacity

Require a small power input per unit of product

Yield a product of the single size or the size distribution required

Energy Requirement

Three laws governing Energy requirements are as given below:

Kick’s law

Rittenger’s law

Bond’s lawThe basic differential equation which states that the energy “dE” require to affect a small change “dL” in the size of the unit mass of the material is simple power function of the size.

PdE CLdL

RITTINGER’S Law

Rittinger, assumed that the energy required for size reduction is directly proportional, to the change in surface area. This leads to a value of -2 for p in equation as area is proportional to length squared. If we put:

      C = KRfC and so

dE / dL = KR fC L-2

where KR is called Rittinger's constant, and integrate the resulting form of we obtain:

      E = KR fC (1/L2– 1/L1)

where, KR is the Rittenger’s Constant (m4/kg) fC is the Crushing strength of material (N/m2) L1 is the feed size (m) L2 is the product size (m)

KICK’S Law

                               

Kick assumed that the energy required to reduce a material in size was directly proportional to the size reduction ratio L1/L2 .This implies that p is equal to -1 in equation 1.

Hence on integrating C = KRfC

and putting the limits we get

E = KK fC ln (L1/L2) 

where, KK is the Kick’s law constant (m3/kg) fC is the crushing strength of the material (N/m2) L1 is the feed size (m) L2 is the product size (m)

BOND’S Law

Bond defines the quantity Ei the work index: The amount of energy required to reduce unit mass of the material from an infinitely large particle size down to such a size that 80% of the product passes a 100µm .Bond’s crushing equation would be

where,Ei is the work index (J/kg)q is the reduction ratio (L1/L2) (-)L1 is the feed size (m)L2 is the product size (m)

2

100 11iE E

L q

Work Index for different materials

Material Work IndexkWatts h/Ton

Material Work IndexkWatts h/Ton

Bauxite 8.78 Phosphorus Rock

2.74

Clinker 3.15 Quartz 2.65

Clay 2.51 Slate 2.57

Coal 1.40 Trap Rock 2.87

Gravel 2.66 Granite 1.31

Gypsum 2.69 Shale 2.63

Iron Ore 3.53 Coke 1.31

Lime stone 2.66

Crushing Efficiency

Crushing efficiency is defined as the ratio of the surface energy created by crushing to the energy absorbed by the material.

ή = Es (Awb – Awa)

Wn

where

ή is the crushing efficiency

Es is the energy per unit area Awb

Awb is the surface area per unit mass of product

Awa is the surface area per unit mass of feed

Wn is the power input to the crusher

Most of the energy is lost in Friction while the rest is available for crushing.

Comparing the laws

It is common practice to assume thatKick’s proposal is applicable for large particle size

(coarse crushing and crushing).Rittinger’s for very small particle size (ultrafine

grinding).Bond formula being suitable for intermediate

particle size–the most common range for many industrial grinding processes.

Comparing the laws

It is generally advisable to rely on the past experience of equipment manufacturers and on tests in order to predict energy requirements for the milling of a particular material.

Problem 1

A material is crushed in a Blake Jaw Crusher such that the average size of the particle is reduced from 50mm to 10mm with the consumption of energy at the rate of 13.0 kW / (kg/s). What will be the consumption of energy needed to; crushed the same material of average size 75mm to an average size of 25mm:

(a) Assuming Rittinger’s law applies ?(b) Assuming Kick’s law applies ?

Which of these results would be regarded as being more reliable and why ?

Food is grinded from 6 mm to 0.12 mm particle diameter using a mill with a 7.5 kW motor. What reduction in throughput rate would you expect if the material was reduced to 0.08mm instead of 0.12 mm?

Problem 2

Methods of Crushing

Choke Crushing: The machine is kept full of

the material The discharge of the product

is impeded to stay for longer period.

Free Crushing: It involves the feeding of the

material at a comparatively low rate so that the product

can escape, readily. The time of stay in the

machine is short.

Suitable for small amount When entire size reduction is

completed in one step

Large feed is there Energy consumption is

optimized Low degree of crushing is

required

WET & DRY CRUSHING

Power consumption.Capacity.Removal of the Product.Dust formation.Solid handling.

Open & Closed Circuit Grinding

Open Circuit Grinding When the plant is operated such that the feed is

passed into the equipment once only. No Attempt is made to return the oversize

particles to the machine for further reduction.

Open & Closed Circuit Grinding

Closed Circuit Grinding When the plant is operated such that the

oversize particles are refluxed into the equipment until the desired size is attained.

Low power consumption is there and thus is preferred in industry.

Product

CHOICE OF EQUIPMENT

Factor Effecting Choice of Machinefor Crushing

HardnessStructureCrushing StrengthStickinessSoapinessExplosive MaterialHarmful Material

Factors Influencing Choice of Size Reduction Equipment

  Feed Size Product Size

Coarse Crushers 60 – 1.5 inch 2 – 0.75 inch

Intermediate Crushers 2 – 0.75 inch 0.75 inch – 200 mesh

Fine Crushers / Grinders

0.75 inch – 200 mesh

About 275 mesh

Ultra Fine Crushers 275 mesh Upto 325 mesh

Type of Equipments

Coarse Crushers

Intermediate Crushers

Blake Jaw Crusher Dodge Jaw Crusher Gyratory Crusher

Crushing Rolls Disc Crushers Edge Runner Mill Hammer Mill Single Roll Crusher

Continuing...

Fine Crushers

Ultra Fine Crushers

Roll mill Net Pendulum Mill Griffin Mill Ring Roll Mill Ball Mill

High Speed Hammer Mill Agitated Mill Fluid Energy Mill

Jaw Crushers Working Principle

They are coarse size reduction machines.They basically works under the influence of

Compression & Rubbing Force.One jaw is fixed called the anvil and the other is

moving jaw.Two types

Blake Jaw crusher Dodge Crusher

Mechanical Construction of Blake Jaw Crusher

Two jaws (anvil and the moving one)Crushing plates are made up of manganese steel.Max. space is at the top so max. pressure for large

particle is exerted at the top.One to the toggle plates is made weaker so as to

protect the equipment.Heavy flywheel is used as the load is intermittent.Power requirement depends upon the size &

capacity thus varying from 7 to 70 kW (feed rate of 10kg/s)

Diagram of Blake Jaw crusher

Difference Between Blake Jaw Crusher &Dodge Crusher

Blake Jaw Crusher Moving jaw is pivoted at the

top. Uniform product is not

obtained Max movement at the

bottom. More widely used. Little tendency to clog. Takes in small feed due to

small opening at the top.

Dodge Crusher Moving jaw is pivoted at the

bottom. More uniform product. Min movement at the

bottom. Less widely used Tendency to clog Takes in large feed due to

larger opening at the top.

Dodge Jaw Crusher

Jaw Crusher

Advantages Little head room required. Easy replacement of worn parts. Easy adjustment of set opening.

Disadvantages Expensive, heavy foundations necessary due to

intermittent crushing action. Emergency stopping impossible due to fly wheels. Re-start with choked crushing chamber impossible. Flat objects may pass uncrushed. A special feeder for constant feed rate is needed to

prevent choking.

BALL MILL

Mechanical Construction

Simplest of the size reducing machinesRotating hollow cylinderAxis could be horizontal or at a small angle to the

horizontalOutlet is covered with a coarse screen to prevent

ball escapeInner surface is lined with manganese steel

(abrasion-resistant), stoneware or rubber.Coefficient of frictionLift bars

Continuing...

Feed intake is of 50mm sizeEfficiency increment with hold up timeBalls occupy 30% - 50% of the volumeOptimum diameter proportional to the square root of

the feed sizeLarge / small ballsPebblesCompound mill

Figure

Compound mill

Terminology of Zone

Motion with in a ball mill

Factors Influencing the Size of the Product

Rate of the feedProperties of the feedWeight of the ballsDiameter of the ballsSlope of the millSpeed of the rotation of the millLevel of the material in the mill

Usage of the ball mill

Wet or dryCost of insulationInert atmosphereGrinding mediumAll degrees of hardnessBatch or continuousOpen or closed circuit grinding

Critical Speed of the ball mill

A rotational speed at which a ball fails to loose contact with the wall of the mill is known to be the critical speed.

It is denoted by

where,

nc = critical speed of the Ball mill

g = gravitational acceleration

R = inner radius of the ball mill

r = radius of the balls

1

2 ( )c

gn

R r

Figure

r

O

A

R - r

R

c

mgg

cosc

mgg

2( )

c

m R r wg

r

Derivation

Consider a single ball in operation reached at a point “A” on the periphery of the mill.

Let radius of the mill = R radius of the ball = r

The distance from the centre of the mill “O” and the centre of the ball (R – r) while α is the angle between the vertical and the radius AO.At “A” two forces are acting on the ball

(1) Force of gravity(2) Centrifugal force

(1) Force of gravity

As we know that F = mg for horizontal plane but here it is angled (α). So reviving it into rectangular components, we get

• mg cos α• mg sin α

As F = mg is not dimensionally consistent so we introduce gc . Hence we get

• mg cos α / gc

• mg sin α / gc

The component that keeps the ball in circular motion is the centripetal component of the force of gravity i.e.

-------- (i)cos

c

mg

g

(2) Centrifugal force

Centrifugal force = mv2 / r1

where v = r1 ω when (ω being = 2n)

Now centrifugal force becomes

where r1 = ( R – r )

introducing the conversion factor gc

------------- (ii)

2 21 1

1

( )mv m r

r r

2

2

( )

( )c

m R r

m R rg

Operating speed should be 60% to 80% of the Critical speed.

1

2 ( )c

gn

R r

Differentiate between Ball mill & Tube mill

Ball Mills Length to Diameter ratio

• Close to 1

Usage• Batch & Continous

Holding time• Less

Compartments• Usually 1

• Compound mill

Product size• Usually fine

Tube Mills

• Usually 4,3 – 1

• Usually batch

• High

• Usually 2 or more

• Compartment mill

• Fine or ultra fine

Differentiate between Ball mill & Rod mill

Ball Mills Length to Diameter ratio

• Close to 1 Usage

• Batch & Continous Holding time

• Less Compartments

• Usually 1• Compound mill

Product size• Usually fine

Product Quality • Not uniform

Rod Mills

• Usually 3,2 – 1

• Usually batch

• High

• Only one

• Ultra fine

• Uniform