Safe Assign Mill

7/31/2019 Safe Assign Mill

1/19

Document1 1

Abstract

The objective of this experiment is to get an understanding of the behaviour of solid particulate

materials when they are grinded, basically comminution. Focus is given to mill speed, grinding time

grinding media to material ratio and how the particles reduce size through looking on the sieve sizes.

A 500 g sample was used of sand as the ore and has been grinded for a maximum of 16 minutes. It has

been found that the longer a particle is grinded the finer it becomes. Graphs have been plotted of

frequency and cumulative basis and it has been seen that they are same as the theoretical ones

although not as smooth. One can plot the frequency basis curve by considering the slope of the

cumulative basis curve or by simply plotting the mass fraction, x of the particles against size, d. The

second choice has been given preference in the experiment. The mean diameter curves almost all had

the same shape, the only difference was that the frequency basis mean diameters were larger as

compared to cumulative basis in terms of values.

Symbol Description Units in SI System

d diameter of particle m

x mass fraction -

n number of particles -

sum -

Subscripts

i ith value

A arithmetic

V volume

W weight


2/19

Document1 2

1. INTRODUCTION

Milling is a very important branch in the study of size reduction of particles; in order for particles to be

handled accordingly they must be reduced to the certain desired size. There many factors that affect the

size reduction of particles including toughness, agglomeration and size of the particles themselves.

Another characteristic of the materials which must be considered when grinding is the particle sizedistribution. Amongst many processes used for particle size distribution are the laser diffraction,

microscopy analysis and sieving so in the preceding experiment as method of sieving has been used.

The many size reduction equipments include crushers, mills. A choice of the mill is often taken for finer

particles such as sand and so one has to choose between a rod mill and a ball mill. In the rod mil the

material is grinded by steel or carbon rods to the desired size. The feed of the sand (ore) is very

important to note i.e. no too much ore may introduced in the mill if there are a few rods. Rods are

advantageous because they tend to separate many sticky particles not to stick to each other in the mill.

This is because of their weight they put the particles together themselves and separate them again.

Another most important factor to consider in the rod mill is its speed. At slow speed the rods roll overeach other and at high speed they get aligned to the walls of the mill so one has to choose a moderate

speed for the mill


3/19

Document1 3

2. THEORY

Size distribution is mostly represented in two ways; on the cumulative basis and on the frequency basis.

Figure 2.1 and 2.2 show the cumulative and the frequency basis respectively.

In the cumulative basis a certain amount of particles smaller than a given size is plotted against that

respective size. Say particles present on a certain sieve (600 um sieve) are less than 50 % then the

particles less than 50 % are plotted against sieve size. For an example given the following data,

Sieve Size (m)

Mass after 2 minutes of crushing

(g)

Mass %

1180 0 0

850 14 2.972399151

600 266.1 56.49681529

425 125 26.53927813

300 40.8 8.662420382

212 15.1 3.205944798

150 10 2.123142251

Pan 0

Total: 471 0

Figure 2.1 Curve depicting particle size distribution

for the cumulative basis

Figure 2.2 Curve depicting particle size

distribution on the frequency basis


4/19


5/19

Document1 5

dnkddxs

3 (2.1.2)

Thereafter an integral sign is introduced on both sided of the equation

(2.1.3)

Summing up in equation (2.1) the following equation which tells that the total mass fraction of any given

sample is 1

ndkx3 s 1x also in equation (2.1.3) 1

1

0

dx

The mean shortest distance from the curve to the vertical (y-)axis is described by the following equation

1

0

1

0

1

0 ddx

dx

ddx

DW

Knowing that 1x also in equation (2.1.3) 1

1

0 dx we can substitute these in the above equationand get

(2.2)

The above equation, Dw is then used as the mass mean diameterfor the preceding calculations in the

report.

Putting equation (2.1.2) in equation (2.2) achieves the mass mean diameter in terms of numbers

(2.3)

1

0

3

1

0

dnkddx s

iiW xd

dx

x

dxD

1

3

4

3

4

3

3

nd

nd

ndk

ndk

ndk

dndkD

s

s

s

s

W


6/19

Document1 6

(2.3)

For the volume mean diameter, if all the particles are of the same diameter Dv, then volume will also be

the same that is,

33 kndnkD V

nk

kndD V

3

3

nk

ndk3

(2.4)

Substitution of equation (2.1.1) achieves:

3

3

1

3

3

1

1

1

d

x

k

dd

x

kD

s

s

V

3

3

1

1

1

1

d

x

k

xk

s

s

3

3

d

x

x

3

3

n

ndDV


7/19

Document1 7

3

3

1

d

x

For the arithmetic mean diameterthe following relation is available,

ndnDA

n

ndDA

Substituting equation (2.1.1) obtains the following:

3

1

3

1

1

1

d

x

k

ddx

kD

s

s

A

3

1

2

1

1

1

d

x

k

d

x

k

s

s

3

2

d

x

d

x

DA

(2.4)

3. PROCEDURE

Equipment: Mill, Tumbler setup, 8 Steel Rods, Sand, Stopwatch, Scale, Sieves, Sieve Shaker

1. Sand of 500 g was measured out, sieved for 10 minutes with a full nest of sieves on the shaker,and taken as a reference sample

2. Eight steel rods were added to the mill together with sand and the tumbling mill setup speedwas already adjusted

3. The sand samples were then grinded for 2 minutes, 4minutes 8 minutes and 16 minutes on themill

4. Each of the sand samples was being sieved for 10 minutes with a full nest of sieves on the sieveshaker after grinding


8/19

Document1 8

4. RESULTS

Table 4.1: Lab results showing mass in grams on the sieves for different times

Table 4.2: Calculated retained and passing mass percentages for the different masses of different times

MassBefore

Crushing(g)

Mass(%)

Mass(%)

Massafter2

Mass(%)

Mass(%)

MassAfter4

inutes(g)

Mass(%)

Mass(%)

MassAfter8

inutes(g)

Mass(%)

Mass(%)

Massafter16

inutes(g)

Mass(%)

Mass(%)

3.3 0.7 99.3 0 0 100 0 0 100 0 0 100 0 0 100

100.4 20.9 79.1 35.2 7.3 92.7 14 3 97 14 3 97 1.6 0.4 99.7

310.4 83.4 16.3 322 74.1 25.9 266.1 59.5 40.5 269.7 60.4 39.6 130.9 29.6 70.4

79.7 99.4 0.6 87.8 92.3 7.7 125 86 14 121.7 86.3 13.7 159.4 65.1 34.9

2.8 99.9 0.02 22.8 97 3 40.8 94.7 5.3 39.4 64.7 5.3 85.2 84.2 15.8

0.1 100 0 9 98.9 1.1 15.1 97.9 2.1 15.3 97.9 2.1 35.3 92 8

0 100 0 5.3 100 0 10 100 0 9.7 100 0 35.7 100 0

0 100 0 9.6 100 0 18.2 100 0 17.5 100 0 46.4 100 0

Sieve Size

(m)

Mass Before

Crushing (g)

Mass after 2

minutes of

crushing (g)

Mass After 4

minutes (g)

Mass After 8

minutes (g)

Mass after 16

minutes (g)

1180 3.3 0 0 0 0

850 100.4 35.2 14 14 1.6

600 310.4 322 266.1 269.7 130.9

425 79.7 87.8 125 121.7 159.4

300 2.8 22.8 40.8 39.4 85.2

212 0.1 9 15.1 15.3 35.3

150 0 5.3 10 9.7 35.7

Pan 0 9.6 18.2 17.5 46.4

Total: 496.7 491.7 489.2 469.8 448.1


9/19

Document1 9

Figure 4.1 Frequency PSD plotted against sieve size for the size reduction of particles

Figure 4.2 Cumulative PSD against sieve/particle size

Table 4.3 Arithmetic mean diameter(DA), volume surface mean diameter(DV), mass mean diameter (DW)

variations in micrometers with time in minutes

Diameters (m) Time (min)DA Dv Dw

536.5 565 624.5 0

350.1 430.3 560.0 2

0

10

20

30

40

50

60

70

80

90

0 200 400 600 800 1000 1200 1400

DiffrentialPSDMa

ss%

Sieve size, d (m)

Differential PSD Mass % Vs Sieve Sieve

0 min (reference

sample)

2 min

4 min

8 min

16 min

0

20

40

60

80

100

120

0 500 1000 1500

Mass%ofSandParticles

Sieve size, d (m)

Cumulative PSD: Mass % Vs Sieve Size

0 min (before

crushing)

2 min

4 min

8 min

16 min


10/19

Document1 10

300.2 374.6 513.0 4

301.5 376.6 515.0 8

227 281.3 415.2 16

Figure 4.3: Graph showing arithmetic mean diameter volume surface mean diameter and mass mean diameter

plotted against time

Table 4.4: Depicts frequency (passing) and cumulative (retained) particle size diameters (DA , DV and DW )

with time during size reduction

0

100

200

300

400

500

600

700

0 5 10 15 20

Diameter(m)

Time (min)

Mean Diameters Against Time

DA

Dv

Dw

Frequency or Differential PSD Diameter(m)

Cumulative PSD Diameter(m)

Time(min)

DA Dv Dw DA Dv Dw

686.2 512.8 760.8 512.9 533.9 573.8 0

575.7 326.9 654.5 326.9 402.7 527.4 2

517.1 277.0 596.9 277.0 344.3 477.0 4

518.7 278.4 598.0 278.4 346.3 480.0 8

399.6 208.5 512.7 208.5 249.5 358.0 16


11/19

Document1 11

Figure 4.4 : Cumulative particle size diameters are depicted by this figure from 0 to 16 minutes

Figure 4.5: Frequency (passing) particle size distribution diameters are shown against time

5. RESULTS DISCUSSIONS

From table 4.1 it can be seen that the mass is mostly retained on the 600 m sieve, that is most of the

mass about 60% of the total mass is accumulated on this sieve. However after grinding for 16minutes it

can then be seen that a higher mass percentage is obtained on the preceding sieve, the 425 m sieve.

This is collateral to the theory because grinding time is a big factor in grinding of particles or any other

material. Looking at table 4.2, one can see that the percentage of the mass retained on the first sieve is

0

100

200

300

400

500

600

700

0 5 10 15 20

Diameter(m)

Time (min)

Cumulative PSD Diameters Vs Time

DA for cum.

Dv for cum.

Dw for cum.

0

100

200300

400

500

600

700

800

0 5 10 15 20

Dia

meter(m)

Time (min)

Frequency PSD Diameters Vs Time

DA

DvDw


12/19

Document1 12

relatively small, this due to the fact that the first sieve aperture is big so the particles just go through

without that much hindrance. The mass percent passing is just the opposite of the mass percent

accumulated that is to say almost 100 % of the particles go through due to the same reasoning of the

aperture and particle size.

Figure 4.1 shows the curves reach a single peak then they go down again the single peak reached thereshows the frequently occurring size. To add, the peak is quite sharp and is not as smooth as can be seen

in most theory cases, this can be due to that there is not enough data to compensate for a smooth

curve, there are few plotting points. Figure 4.2 is the cumulative basis curve which is just a cut of the

frequency curve, it can be viewed as the frequency basis curve cut in half, this is the curve where d50 the

cut size can be obtained.

Comparing the diameters in table and figure 4.3, a trend can be seen in all the diameters that they

decrease with time. The diameter with the largest values is the mass mean diameter, here a product of

sieve size and mass percent is accounted. The same can be seen in table and figure 4.4 as well as figure

4.5. Also the diameters of the frequency basis are larger than the diameters of the cumulative basis

which is because of the unequal mass percentages available for cumulative and frequency basis.

Another observation can be said of the equal values of arithmetic and volume mean diameters for

frequency and cumulative basis respectively.

6. CONCLUSION

As can be seen from the results the optimum grinding time applicable is 16 minutes which is if the

particles are grinded long enough they become finer and little or no need for returning them back to the

mill is necessary. So this means for a 100 mesh (150 m) the grinding time will be 16 minutes because of

high number in 16 minutes of crushing for 16 minutes, high number is equal to finer particles.

The results obtained from the experiment are relevant to the ones found in theory the decreasing of

particle sizes as one grinds, the shape of cumulative and frequency curves etc. Therefore this concludes

that the experiment has been successful with a few exceptions there and there. An example of the

exceptions can be that the mass of the ore (sand) does not remain the same throughout the experiment

due to the fact that same gets agglomerated on the sieves. Some portion of the ore turns into dust and

scatters around the lab never returning to the mill.

For future references the speed of the mill can also be included in the report maybe by way of

calculating it so in the discussion mention of the speed values can be made. Other two important factors

are the shape of the mean diameter graphs and choice of the ore. In the practical manual inclusion of

the shape of mean diameters graphs can be described so it can be easy to compare these with the ones

that a student obtains. About the choice of the ore, a more stable ore can be chosen and the meaning of

that is that an ore that does not turn into dust quick and clogs the sieves or gets attached to the mill. Or

more simply equipment that does not allow for this to happen can be used.


13/19

Document1 13

7. REFERENCES

7. 1. Coulson, J.M. & Richardson (1984): Particle Technology and Separation Processes Volume 2Fifth Edition , New York Pergamon Press USA

7. 2. http//:www.showmegold.org/news/mesh.htm ( 18 May 2012)


14/19

Document1 14

8. APPENDIX A

Sample Calculations

Table 4.2

To get the values for the mass % cumulated and retained on this, first the mass percent on each sieve

was obtained.

E.g. for the 1180 m sieve and looking at mass before crushing the mass % is

For the 850 m, taking mass after two minutes of crushing mass % =

Table 4.2.1: A table for sieve size and the mass % on each respective sieve for the different times, with

values rounded off to one decimal place, was then compiled

Sieve Size(m)fgruiu

iruruuiruir

Mass %Before

Crushing (g)

Mass % after 2minutes of crushing

(g)

Mass % After

4 minutes (g)

Mass % After

8 minutes (g)

Mass % after

16 minutes (g)

1180 0.7 0.0 0.0 0.0 0.0

850 20.2 7.2 2.9 3.0 0.4

600 62.5 65.5 54.4 57.4 29.2

425 16.0 17.9 25.6 25.9 35.6

300 0.6 4.6 8.3 8.4 19.0

212 0.02 1.8 3.1 3.3 7.9

1500.0 1.0 2.0 2.1 8.0Pan 0.0 2.0 3.7 0.0 0.0

Thereafter the Mass % Retained and Passing was calculated thus:

Mass retained E.g. for mass before crushing

Mass % retained on the 1180 m sieve = Mass % on the 1180 m sieve

= 0.7 %

Mass % retained on the 850 m sieve =Mass % on the 1180 m sieve + Mass % on the 850 m sieve

= 0.7+20.2=20.9 %

Mass % retained on the 600 m sieve = Mass % retained on the 850 m sieve + Mass % on the 600 m

sieve

= 62.5+20.9= 83.4 %

And so the same was done for Mass after 2 minutes of crushing, 4 minutes, 8 minutes and 16 minutes

Mass Passing E.g. for mass after 2 minutes of crushing

Mass % passing on the 1180 m sieve = 100 % - Mass % retained on the 1180 m sieve

= 100-0 = 100%


15/19

Document1 15

Mass % passing on the 850 m sieve = 100 % - Mass % retained on the 850 m sieve

= 100-7.3 = 92.7 %

And so the same was done for Mass before crushing, after 4 minutes of crushing, 8 minutes and 16

minutes

Table 4.2.2: Shows the mass % retained/accumulated and passing through the different times on each

sieve with sieve size in microns

Table 4.3

Arithmetic mean diameter (DA)

Equation (2.1) was used to get this diameter. Mass fractions, x, were obtained by dividing the mass

percentages in table 4.2.1 by 100 and d was taken as the sieve size.

e.g. for the sample before crushing (reference sample)

x = 0.7/100=0.007 and sieve size is 1180 m

Sv.

Size(um)

MassBefore

Crushing(g)

Mass(%)

Mass(%)

Massafter2

Mass(%)

Mass(%)

MassAfter4

inutes(g)

Mass(%)

Mass(%)

MassAfter8

inutes(g)

Mass(%)

Mass(%)

Massafter16

inutes(g)

Mass(%)

Mass(%)

11803.3 0.7

99.30

0 1000

0 1000

0 1000 0 100

850

100.4 20.9

79.1

35.2

7.3 92.7

14

3 97

14

3 97

1.6 0.4 99.7600

310.4 83.416.3

32274.1 25.9

266.159.5 40.5

269.760.4 39.6

130.9 29.6 70.4

42579.7 99.4

0.687.8

92.3 7.7125

86 14121.7

86.3 13.7159.4 65.1 34.9

3002.8 99.9

0.0222.8

97 340.8

94.7 5.339.4

64.7 5.385.2 84.2 15.8

2120.1 100

09

98.9 1.115.1

97.9 2.115.3

97.9 2.135.3 92 8

1500 100

05.3

100 010

100 09.7

100 035.7 100 0

Pan0 100

09.6

100 018.2

100 017.5

100 046.4 100 0

m

pan

panDA

5.536105.54652

102.97591

0

212

0

1180

00002.0

300

006.0

425

16.0

600

625.0

850

202.0

1180

007.0

0

150

0

212

00002.0

300

006.0

425

16.0

600

625.0

850

202.0

1180

007.0

9

6

33333333

22222222


16/19

Document1 16

*Note: in all the equations no (one decimal place) rounded off values have been used instead values

have been used that have 9 decimal places, look at x on table below.

Table A1: Sieve sizes raised to the powers of 3 and 2 and non-rounded off mass fractions

d2 d3 x (before crushing)

1392400 1643032000 0.006643849

722500 614125000 0.202134085

360000 216000000 0.624924502

180625 76765625 0.16045903

90000 7000000 0.005637206

44944 9528128 0.000201329

22500 3375000 0

The same was done for all the other values i.e. for 2 min, 4 min, 8 min and 16 min

Volume surface mean diameter (Dv)

Also here the values in table 4.2.2 were used as mass fraction by diving them by 100 and the equation

that has been made use of is equation (2.2). Sample after 2 minutes of crushing was taken as an

example.

m

pan

DV

3.430101.25517

1

02.0

150

01.0

212

018.0

300

046.0

425

179.0

600

655.0

850

072.0

1180

0

1

38-

3

23333333


17/19

Document1 17

Table A3: Sieve sizes raised to the power of 3 and non-rounded off mass fractions

The same was done for all the other values i.e. for sample before crushing, 4 min, 8 min and 16 min.

Mass mean diameter (Dw)

Table 4.2.2 was made use of the same way it was used for DA and Dv to calculate Dw, as well. Equation

(2.4) was used here. Sample after 4 minutes of crushing was taken as an example.

Table A3: Sieve sizes and non-rounded off mass fractions

d x

1180 0

850 0.029724

600 0.564968

425 0.265393

300 0.086624

212 0.032059

150 0.021231

Table 4.4

d3 x (2 min)

1643032000 0

614125000 0.0730139

216000000 0.667911276765625 0.1821199

27000000 0.0472931

9528128 0.0186683

3375000 0.0109936

m

DW

0.513

02.0150031.0212083.0300256.0425544.0600029.085001180


18/19

Document1 18

The same equations and the table 4.2.2 and the same values rounded off to 9 decimal places were used.

Retained and passing mass percentages were not used directly instead they were multiplied by the mass

(grams) on the sieves to get a new mass value so the mass fractions were obtained from these. Table A3:

Mass % Passing/100 x mass and mass fraction passing for different times

2 4 8 16

passing/100 x mass

3.3 0.0 0.0 0.0 0.0

79.4 32.6 13.6 13.6 1.6

51.6 83.4 107.9 106.8 92.2

0.5 6.8 17.5 16.7 55.6

0.0 0.7 2.2 2.1 13.5

0.0 0.1 0.3 0.3 2.8

0.0 0.0 0.0 0.0 0.0

0.0 0.0 0.0 0.0 0.0

Total Total Total Total Total

134.8 123.6 141.4 139.5 165.7

mass frac passing

0.0 0.0 0.0 0.0 0.0

0.6 0.3 0.1 0.1 0.0

0.4 0.7 0.8 0.8 0.6

0.0 0.1 0.1 0.1 0.3

0.0 0.0 0.0 0.0 0.1

0.0 0.0 0.0 0.0 0.0

0.0 0.0 0.0 0.0 0.0

0.0 0.0 0.0 0.0 0.0


19/19

Document1 19

Table A4: Mass % Retained/100 x mass and mass fraction retained for different times

0 2 4 8 16

retained/100 x mass

0.0 0.0 0.0 0.0 0.0

21.0 2.6 0.4 0.4 0.0

258.8 238.6 158.2 162.9 38.7

79.2 81.0 107.5 105.0 103.8

2.8 22.1 38.6 37.3 71.7

0.1 8.9 14.8 15.0 32.5

0.0 5.3 10.0 9.7 35.7

0.0 9.6 18.2 17.5 46.4

Total Total Total Total Total134.8 123.6 141.4 139.5 165.7

mass frac retained

0.0 0.0 0.0 0.0 0.0

0.1 0.0 0.0 0.0 0.0

0.7 0.7 0.5 0.5 0.1

0.2 0.2 0.3 0.3 0.4

0.0 0.1 0.1 0.1 0.3

0.0 0.0 0.0 0.0 0.1

0.0 0.0 0.0 0.0 0.1

Documents

Safe Assign Mill