ball milling_final final

8/3/2019 Ball Milling_final Final

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Introduction:In its simplest form, the ball mill consists of a rotating hollow cylinder,

partially filled with balls, with its axis either horizontal or at a small angle to thehorizontal. The material to be ground may be fed in through a hollow trunnion at

one end and the product leaves through a similar trunnion at the other end.

The inner surface of the cylinder is usually

lined with an abrasion-resistant material such

as manganese steel, stoneware 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 orstoneware 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.


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The ball mill is used for the grinding of a wide range of materials, including

coal, pigments, and feldspar for pottery. The efficiency of grinding increases with

the hold-up in the mill, until the voids between the balls is filled. Further increase

in the quantity then lowers the efficiency.

In a ball mill size reduction is by impaction and the forces acting inside a ball mill

are:

centrifugal force (lifts along the sides of the wall) and gravity force (causes the ball to drop on the feed)

Advantages of the ball mill

The mill may be used wet or dry although wet grinding facilitates theremoval of the product.

The costs of installation and power are low. 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.

AIM

To determine the particle size distribution and specific surface area of thegiven material.

To plot graphs of : specific surface area vs. time of grinding and rate ofgrinding vs. specific surface area

APPARATUS

Batch Ball Mill, Set of Sieves, Sieve Shaker, Stop Watch, Weighing BalanceEXPERIMENTAL PROCEDURE

Experiment procedure:

1. The ball mill should be filled with steel balls (20mm) up to 50% of its volume.

2. The sample (calcite) of known weight (200 gm) is put into the mill. Sieveanalysis is performed on the sample using a standard set of sieves.


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3. Place the sample in ball mill, run the mill, whose speed is adjusted to 75% of the

critical speed which is calculated from the formula given below:

Where,

Nc- Critical speed (sec

-1)

R - Radius of ball mill (m),

r - Radius of the ball (m) and

g - Gravitational constant (m/sec2

).

4. Stop the mill, empty the contents on to a paper, remove the balls make sure the

sample doesnt stick to the balls.

5. The sample is taken and sieve analysis is performed using set of sieves ranging

from 2000, 1000, 500, 125, 90 m. The sieving time is about 10 minutes. 6. Place

the entire sample back to the ball mill and continue the runs for three different time

intervals (2, 2, and 5 minutes).Perform sieve analysis for each of these time

intervals.

7. Calculate the specific surface area of the sample obtained for each interval oftime using sieve analysis data.

8. Graph is made for the Specific surface vs. Time and the curve is fitted to a

quadratic expression using regression analysis. From the above expression we get

the rate expression. Rate of grinding vs. Time is plotted and the results are

discussed.


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TYPICAL BALL MILL

OBSERVATIONS

Initial amount of Calcite taken 200 gm

Density of calcite taken (p) 1.9 gm/ccSphericity of the sample (p) 0.78

Diameter of the ball mill vessel (2R) 150 mm

Diameter of the ball (2r) 20 mm

rpm of the ball mill (Nop) 88.02 rpm

CALCULATION OF OPERATIONAL SPEED:

Nop

= 0.75 * Nc

Where Nc is the critical speed of the ball mill which can be calculated from

mentioned equation for Critical speed.


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Nop

= 0.75*(1/(2*3.14)*(981/(7.5-1))^0.5)

= 1.467 rev/sec

= 1.467 * 60 rpm

= 88.02 rpm

Specific surface area:

Initially, the specific surface area and size fractions are calculated:

Sieve

size

(m)

Weight

retained

(gm)

Weight

Fraction

(Xi)

Average

Diameter (Di)

(m)

(Xi/Di)(/

m)

Specific

surface area

(m2/kg)

2000 164.08 0.81648089

2

2000 0.00040824 1.652802269

1000 34.19 0.17013336 1500 0.00011342

2

0.459201281

500 2.1 0.01044984

1

750 1.39331E-

05

0.056409634

125 0.53 0.00263734

1

312.5 8.43949E-

06

0.034168121

90 0.01 0.00004976 107.5 4.62884E-

07

0.001874031

< 90

0.05 0.00024880

6

45 5.52902E-

06

0.022384775

Total 200.96 1 0.00055002

7

2.226840111

The total surface area before the start of the experiment (Grinding time =0 min) =

2.226 m2

/kg


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After 2 minutes, the specific surface area and size fractions are calculated:

Sieve

size

(m)

Weight

retained

(gm)

Weight

Fraction

(Xi)

Average

Diameter (Di)

(m)

(Xi/Di)(/

m)

Specific

surface area

(m2/kg)

2000 48.85 0.24450673

2

2000 0.00012225

3

0.494954978

1000 39.12 0.19580559

6

1500 0.00013053

7

0.528492357

500 29.84 0.14935682

5

750 0.00019914

2

0.806248054

125 46.74 0.23394564

3

312.5 0.00074862

6

3.030887456

90 9.63 0.04820061

1

107.5 0.00044837

8

1.815302253

< 90

25.61 0.12818459

4

45 0.00284854

7

11.53262548

Total 199.79 1 0.00449748

3

18.20851058

The Total Specific Surface Area after grinding time=2 minutes is 18.20851058

m2/kg

After another 2 minute run, the specific surface area and size fractions

are calculated:

Sieve

size (m)

Weight

retained

(gm)

Weight

Fraction

(Xi)

Average

Diameter (Di)

(m)

(Xi/Di)(/

m)

Specific surface

area (m2/kg)

2000 20.77 0.1053565

99

2000 5.26783

E-05

0.213273364

1000 15.36 0.0779141

73

1500 5.19428

E-05

0.210295546

500 17.3 0.0877548

95

750 0.00011

7007

0.473712624

125 68.47 0.3473166 312.5 0.00111 4.499667518


7/12

28 1413

90 19.51 0.0989652

02

107.5 0.00092

0607

3.727167613

< 90

55.73 0.2826925

03

45 0.00628

2056

25.43353037

Total 197.14 1 0.00853

5703

34.55764704


m2

/kg

After another 5 minute run, the specific surface area and size fractions are

calculated:

Sieve

size (m)

Weight

retained

(gm)

Weight

Fraction

(Xi)

Average

Diameter (Di)

(m)

(Xi/Di)(/

m)

Specific surface

area (m2/kg)

2000 4.63 0.0235863

47

2000 1.17932

E-05

0.047745843

1000 1.74 0.0088639

84

1500 5.90932

E-06

0.023924483

500 1.59 0.0080998

47

750 1.07998

E-05

0.043724055

125 35.75 0.1821192

05

312.5 0.00058

2781

2.359449007

90 26.81 0.1365766

68

107.5 0.00127

0481

5.143667903

< 90125.78 0.6407539

4845 0.01423

897757.64792076

Total 196.3 1 0.01612

0741

65.26643205


m2

/kg


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Sources of Error:-

There might be error in measuring the speed of rotation of the ball mill. Thedisplayed value may be above or below the operating speed.

We make an assumption that the average diameter of the particles trapped inthe first sieve compartment is 2.mm, but the average diameter of particles in

first sieve compartment is more than 2mm.

There is a loss in the total amount of sample as we keep transferring samplefrom and to ball mill for different intervals of time.

As particles gets finer and finer, during sieve analysis particles get struck inthe pores, due to which proper screening is not possible.

Average Particle Diameter (Di) is assumed exact, due to which there is aninherent error.


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Graphs:

1. Specific Surface Area vs. Time of Grinding:

The above graph shows the variation of specific surface area versus time.

The corresponding curve obtained is fit to power series whose equation is

y = 12.034x0.746

(for x > 0 i.e., time>0)

The rate at which specific area varies with time (slope) gives grinding rate.

Grinding rate = dy/dx = 8.977x-0.254

y = 12.034x0.746

0

10

20

30

40

50

60

70

0 2 4 6 8 10

Specificsurfacearea(m2/kg)

Time (min)


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2. Batch Grinding Rate vs. time

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8 9 10

grindingrate(m^2/kg/min)

time (min)

3


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ERROR ANALYSIS

The error in the surface area can be calculated as follows, in terms of

weights retained in each sieve:

( ) (

)

S = S1 +S2+S3

( )

S = Specific surface area (m2/kg)

is the mass fraction of the material retained in the i th sieve is the mass of the material retained on the i th sieveWis the total mass of Calcite, which has been sieved

The error in the weighing machine is 0.01 gm. So, = = 0.01 gm. Initially S = 2.226840111 m2/kg 0.00761 m2/kg ;

S = (2.226840111

0.00761) m2/kg

After 2 min S = 18.20851058 m2/kg 0.008455 m2/kg ;S = (18.208510580.008455) m2/kg

After 4 min S = 34.55764704 m2/kg 0.009398 m2/kg ;S = (34.557647040.009398) m2/kg

After 9 min S = 65.26643205 m2/kg 0.011002 m2/kg ;


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S = (65.266432050.011002) m2/kg

Conclusions:

The obtained data demonstrates that: The specific surface area increases with increase in the hold-up time .The

smaller the particles are the larger the specific surface area is.

The increase of specific surface area with-hold up time is governed by thepower law.

The grinding rate falls with time of grinding, i.e. the smaller the particles getthe more difficult it becomes to grind them further.

The grinding rate also falls with increase in specific area, i.e. the coarserparticles are easier to grind than the finer particles.

ball milling_final final

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