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The effect of using concave surfaces as grinding media
C4-86
Proceedings of the XXI International Mineral Processing Congress
THE EFFECT OF USING CONCAVE SURFACES AS GRINDING MEDIA F.L. von Kfiiger*, J.D. Donda ~ M.A.R. D r u m m o n d * , A.E.C. Peres ~
~
*Escola de Minas, UFOP, Ouro Preto, Brasil, ~ Mineragao, Mariana, Brasil, de Engenharia, U F M G , Belo Horizonte, Brasil
Abstract
This paper presents an analysis of the effect of utilizing crushing bodies of special shapes as grinding medium. The crushing bodies utilized in this study were modified spheres with a concave portion. Grinding efficiency is expected to increase with the increasing available surface area of the grinding medium. A grinding ball with concavity has a smaller volume than a sphere of the same radius. Therefore, the convex-concave ball has a smaller mass with the same surface area, providing a larger specific surface area and a greater charge density. In the case of contact between the convex and concave surfaces, the probability of a crushing action over larger particles is higher than for smaller particles, causing preferential grinding of larger particles. Experiments were carried out in laboratory and consisted of batches of the same feed, ground first with conventional grinding balls. Part of the grinding medium of conventional grinding balls was then replaced by special concave-convex balls, increasing the specific surface area of the grinding balls. The results of the grinding experiments showed an effective selectivity of the grind, and in some cases, an increase in the fineness of the ground product, for a percentage of the concave area in the charge up to about 10%. Increasing the percentage of the concave bodies, the relative motion of the charge units became more irregular, causing a negative impact on grinding efficiency.
Keywords: grinding, crushing bodies, concave surfaces, grinding efficiency, grinding selectivity Introduction
The grinding media most often employed in fine grinding are spheres and truncated cones (Cylpebs). Other shapes, like cylinders, cones, cubes and hexagons, were studied. This paper analyzes the effect of utilizing crushing bodies of special shapes as a grinding medium. The crushing bodies utilized in this study were modified spheres with a concave portion. This shape, the new concave bodies, when compared with the spheres, presents a larger specific surface area. The consequence o f this higher specific surface area could be an increase in the grinding efficiency. Another feature that should be put in consideration is the grinding selectivity that arises from the area of contact between concave and convex surfaces. The large particles protect the small ones, similar to the action o f the rods in the rod mills. The comparison between the concave bodies and the spherical bodies can be done in the same fashion as the comparison between spheres and Cylpebs. Grinding tests were carried out with balls and concave bodies, varying the percentage of concave area in the mill charge.
Comminution, Classification and Agglomeration
C4-87
Background on grinding media Wills (1997) says: "grinding within a tumbling mill is influenced by the size, quantity, the type of motion and space between the individual pieces of the medium in the mill." Grinding is a random process subject to the laws of probability. The degree of grinding of a particle depends on its probability of entering a zone between pieces of grinding media, and the probability of contact with the grinding media after entry. Grinding takes place by several mechanisms, including impact or compression, due to forces applied almost normally to the particle surface, chipping due to oblique forces, and abrasion due to forces acting parallel to the surfaces. These mechanisms deform the particles and change their shape, beyond certain limits determined by their degree of elasticity, to achieve breaking. MINTEK (1991) reports that non-spherical grinding media, such as cones or Cylpebs, have been manufactured and marketed on the basis of a number of claimed advantages over spheres. A substantial reduction in foundry costs is possible, as a result of the high yield of metal in finished castings. For an equal mass of grinding charge, such shapes provide a higher grinding surface area, hence, it is claimed, more efficient grinding is attained. While testing cones and Cylpebs against balls, it was found that all three types of grinding media performed well, if the feed rate of the ore was kept relatively low. It was further found that neither cones nor Cylpebs achieved the same fineness of grind as an equal charge of balls, even though the surface-area of the non-spherical media was larger, casting doubt on the previously held assumption in this regard. Relative movement of units in a grinding charge plays an important role in grinding, particularly when conditions are predominantly abrasive. Such relative motion is expected to be easier with spherical media than non-spherical media, and to play a dominant role in the fineness of the grind. According to Cloos (1983), the grinding media should have the largest possible surface area, to provide a suitable contact surface with the material being ground, and be the heaviest possible, in order to have the necessary energy for breaking the ore particles. These requirements must be balanced, since the heavier the individual grinding media, the smaller the specific surface developed. The advantage of Cylpebs over balls lies in the surface area, and linear and point contact, which happens to Cylpebs, versus point contact only, which happens to spheres. As a result, the product will have a narrower-size spectrum than that verified by analogous rod mill grinding. By studying the geometrical attributes of balls versus Cylpebs, other advantages become clear. If we examine the two shapes, both made of the same material and having an equal diameter, the Cylpebs will have 50% greater surface area, 50% more weight and 50% more volume. It follows that for a specific diameter, the specific surface of the areas is the same. Further advantages of media surface area result from density and packing comparisons of the two shapes. Donda (1998) compared balls and Cylpebs of the same weight. Cylpebs have 15% more surface area than balls.
C4-88
Proceedings of the XXI International Mineral Processing Congress
The Cylpebs have a lower cost, and it was assumed that they have a larger grinding efficiency, due to their larger surface area. Laboratory tests show that, in spite of the larger surface area of the Cylpebs, the BSA (Blaine surface area) of the product was 7.5% less for the Cylpebs of the same weight as 30 mm diameter balls, and 11% less for the Cylpebs of same weight as 25 mm balls. In spite of the 15% larger surface area of the Cylpebs, that difference did not result in a larger surface generation in the product. Sepulveda (1990) states that the critical, controlling variable for ball charge optimization is the specific area exposed to impact by the charge. There is an optimum specific charge area exposed, which maximizes the grindability of any particular ore under consideration.
Assumptions Grinding efficiency increases with an increase in the available surface area of grinding medium. A grinding ball with a concavity has a smaller volume than a sphere of same radius. Therefore, the convex-concave ball has a smaller mass with the same surface area, providing a larger specific surface area. A concave surface allows a larger contact area with convex surfaces than the contact area between two convex surfaces; therefore, a concavity may simultaneously exert stress on a larger number of particles than a convex surface. The particles that are caught between the convex portion of a grinding ball, and the concave portion of another, would be trapped under the crushing action of the grinding medium for a longer time than in the case of two convex surfaces, where the particle would be under crushing action for a shorter contact time. In the case of contact between convex and concave surfaces, the probability of crushing action over larger particles is greater than for smaller particles, causing preferential grinding of larger particles.
Q
e o
Figure 1" Action of the concave grinding bodies.
Design of experiments Experiments were carried out in a laboratory and consisted of batches of the same feed that was first ground with conventional grinding balls. Then, part of the grinding medium balls was replaced by concave-convex balls, increasing the specific surface area of the grinding charge. The ore used was an iron ore concentrate from a commercial plant. Two types of concave balls made of cast iron were used, as sketched in Figure 2. The main characteristics of these bodies are presented in Table I.
Comminution, ClassificationandAgglomeration Type I
C4-89
Type II
Figure 2: Concave grinding bodies. Table I: Concave crushing bodies. Crushing bodies Diameter (mm) Weight (g) Overall area (cm2) Concave area ( c m Type I 38.8 181 47.3 9.8 Type II 38.8 148 47.3 13.4 The radius of the concavities is the same as the sphere radius.
2)
The harmonic mean size (HMS) is defined as the harmonic mean of the size fractions, weighted according to their mass and expressed approximately as: n+l
HMS=
/ /
/
Zmi/xi /=1
where: mi is the mass fraction of the ith screen fraction; x~ is the arithmetic mean of the size limits of the ith screen fraction. The harmonic mean size is a single value that provides an indication of the relative fineness of the grind obtained from a mill operating under different conditions, or using different types of grinding media under the same milling conditions.
First round of experiments The following parameters were adopted for the first round of experiments: mill dimensions, 20• cm 2, 67 rpm (72.0% of critical speed), 38% filling, 17.5 kg ball charge, 2.975 kg ore charge, 697 ml water (81% solids), 20 min, 40 min and 60 min grinding time. In this round of experiments, only the Type I concave was used, and just one size of balls, with the same weight as the Type I concave, as seen in Table II. Table II: Charge composition for the first round of tests. Test Sphere 36.2 mm diameter Type I concave Total charge area (cm2) Concave area of the charge (%)
1A 100 0 3,787 0.0
Crushing bodies of the charge (% wt) 2A 3A 4A 5A 80 60 40 20 20 40 60 80 3 , 9 4 5 4 , 1 0 2 4 , 3 1 3 4,430 4.7 9.1 13.5 17.3
6A 0 100 4,587 20.8
Proceedings of the XXI International Mineral Processing Congress
C4-90
40 m i n
20 m i n
A"
60 rain
1600
1200
2000
~" 1950
1150 1550 ll00
1900
1050
1500 0
20 %
40
60
80
100
1850 0
Concaves
20
40
60
80
100
0
% Concaves
20
40
60
80
I00
% Concaves
Figure 3" Blaine surface area (BSA) for the first round of tests, as a function of the percentage of type I concave crushing bodies in the charge. The Blaine surface area (BSA) data for the ground products, as seen in Figure 3, have a clear tendency to be reduced with an increase in the concave bodies o f the charge. 100
-
90 ~80=,~,.
6 0 ~
t=~.,~ 7060 ~ 2 2 0 / "
---o--- Test 2A - - ~,- - Test 3A
=
N 50
min
40 .... 35
] 45
] 55
[ 75
Screen aperture
Otm)
I 105
I 150
Figure 4: Size distribution of the first round of tests. The curves for the other tests are not plotted. Table III: Harmonic mean size (HMS) for the ground product of the first round of tests. Test
Feed
HMS total HMS >37 ~tm
36.30 70.67
HMS total HMS >37 tam
36.30 70,67
HMS total HMS >37 ~tm
36.30 70.67
1A
2A 3A 20 min grinding 28.37 28.31 28.54 60.19 61.46 60.63 40 min grinding 24,94 24.93 25.29 55.67 54.94 56.81 60 min grinding 23.06 23.08 23.10 52.00 52.90 51.72
4A
5A
6A
29.01 61.68
28.83 60.45
28.66 60.61
25.17 55.59
25.26 55.71
25.23 56.51
23.32 52.75
23.28 52.56
23.38 52.71
In most cases, the larger the concave area in the charge, the coarser is the ground product.
Second round of experiments The second round o f experiments was carried out under the following operating condition: the same mill and body charge as the first round o f tests was used, with the exception that grinding time was only 40 min.
Comminution, Classification and Agglomeration
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Table IV: Charge composition for the second round of tests. Test
Crushing bodies of the charge (% weight) 2B 3B 4B 5B 80 60 40 20 20 40 60 80 3,945 4,102 4,313 4,430 4.7 9.1 13.5 17.3
1B 100 0 3,787 0.0
Sphere 36.2 mm diameter Type I concave Total charge area (cm2) Concave area of the charge (%)
6B 0 100 4,587 20.8
The previous round o f tests did not show a reduction o f the fineness in the product with the introduction o f the concave bodies. In order to highlight the selectivity effect, the second set o f tests was performed on the coarsest possible ore, in relation to the size o f the concave bodies. 2150 2100 2050 < 2000 1950 1900 0
+
,
i
1
20
40
60
80
1
100
% Concaves
Figure 5" Blaine surface area (BSA) for the second round of tests, as a function of the percentage of Type I concave crushing bodies in the charge. 100 -
,~ 90 = 80 ~" .,~ 70 ~=60 j " ~ . . .
5O 35
Test 1B --.o.-_- Test 2B -'~ Test4B
.",,,
I 45
I I 55 75 Screen aperture Otto)
I 105
! 150
Figure 6: Size distribution of the second round of tests. The other tests are not plotted. Table V: Harmonic mean size (HMS) for the ground product of the second round of tests. Test HMS total HMS >37 gm
Feed 77.63 103.89
1B 25.66 59.50
2B 25.46 57.98
3B 25.63 57.62
4B 26.43 58.64
5B 25.95 58.81
6B 25.91 58.56
With a coarser feed, the product is finer, in the range b e t w e e n 37 g m to 150 gm, for all percentages o f concave areas in the charge, confirming the selectivity effect.
Proceedings of the XXI International Mineral Processing Congress
C4-92
Third round of experiments The third round o f experiments was performed with the following operating parameters: mill dimensions, 20x20 cm 2, 68 rpm (72.4% o f critical speed), % filling, 12 kg ball charge, 1.9 kg ore charge, 630 ml water (75% solids), and 40 min. grinding time. In this round o f experiments, we first tested only balls. Three other tests were done with concave bodies substituting balls with the same weight. To improve the use o f the concave surfaces, different sizes o f balls were used. The ball distribution follows B o n d ' s charge equilibrium equation, Y = (X/B) 3"8 (2) where Y is the percentage o f the total equilibrium charge passing any size X, and B is the diameter o f the larger ball. Table VI: Charge composition for the third round of tests. Test
Crushing bodies in the charge (% weight) 2C 3C 4C 24.2 35.2 21.4 21.4 21.4 11.6 11.6 11.6 5.4 5.4 5.4 2.2 2.2 2.2 24.2 24.2 35,2 35.2 3341.4 3449.1 3817.2 3700.8 0.0 4.8 14.5 10.5 1C 24.2 35.2 21.4 11.6 5.4 2.2
Sphere 35.5 mm diameter Sphere 33 mm diameter Sphere 28 mm diameter Sphere 23 mm diameter Sphere 18 mm diameter Sphere 13 mm diameter Type I concave Type II concave Total charge area (cm2) Concave area in the charge (%) 100 -
..
90
.
11
-~;-~--- - . . . . . . .
,,,
.~-. . . . . .
I
Test 1C
~' 80 - A , ~ "
---o--- Test 2C
_=
- - ~,- - Test 3C
=
/,.-
70
,I
d 60
I
35
45
I
I
I
55 75 Screen aperture (gm)
lO5
150
Figure 7: Size distribution of the third set of tests. Test 4 is not plotted. Table VII: Harmonic mean size (HMS) for the ground product of the third round of tests. Test HMS total HMS >37 ~tm
Feed 29.77 77.46
1C 22.65 47.79
2C 22.57 47.14
3C 23.90 48.71
4C 22.69 47.19
Figure 7 shows that a finer product was obtained with a 5% concave area o f Type I bodies in the charge, for the size range between 35 ~tm and 150 ~tm. Test 3, with almost 15% o f concave area o f both types, produced a coarser product. Test 4, with
Comminution, Classification and Agglomeration
c4-93
about 10% of concave area of Type II bodies, did not produce any significant difference in the fineness of the product. The curve for test 4 lies in between the curves for tests 1 and 2 and is not plotted. There was a better use of the grinding surface: the 40 min grinding time in the third round of tests is almost the same as the 60 min grinding time in the first round of tests, with a similar feed. Conclusions
The initial assumption of increasing grinding efficiency with an increase in specific charge area was not proven. In all tests, there was a reduction of the product BSA (Blaine surface area) for increasing concave surface area and total surface area. For up to about 10% of the concave area of the charge, there was a trend toward a finer ground product. Apparently, the increase in the proportion of concave bodies with a less regular shape causes the charge to have less smooth movement, causing a negative impact on the grinding efficiency. The expected increase on Cylpebs grinding efficiency related to their larger specific surface area does not occur, perhaps for the same reason. On other hand, the selectivity of the grinding was proven to be effective, as highlighted in the second round of tests. When grinding coarse feeds, for instance, to feed a flotation plant, this selectivity effect may cause a positive impact on flotation recoveries, due to the reduction of fines lost in de-sliming. References
Cloos, U., 1983. Cylpebs: an alternative to balls as grinding media. World Mining, 10/83, 59. Donda, J.D., 1998. Estudo do Comportamento de um Itabirito do Quadrilfitero Ferrifero Quanto Superficie. MSc. Thesis, Universidade de Sao Paulo, Sao Paulo, Brasil. MINTEK, 1991. The selection of grinding balls for specific ores and the development of a suitable theory of ball wear. Application Report No. 10, MINTEK, Randburg, South Africa. Septilveda, J.E., 1990. Ball Mill Grinding: 40 Years After Bond, Proceedings. VI Simposium sobre Molienda, Armco Chile Procesamiento de Minerales S.A., Vifia del Mar, Chile, 13-32. Wills, BA, 1997. Mineral Processing Technology. Butterworth-Heineman, Oxford, England.
Proceedings of the XXI International Mineral Processing Congress
THE EFFECT OF USING CONCAVE SURFACES AS GRINDING MEDIA F.L. von Kfiiger*, J.D. Donda ~ M.A.R. D r u m m o n d * , A.E.C. Peres ~
~
*Escola de Minas, UFOP, Ouro Preto, Brasil, ~ Mineragao, Mariana, Brasil, de Engenharia, U F M G , Belo Horizonte, Brasil
Abstract
This paper presents an analysis of the effect of utilizing crushing bodies of special shapes as grinding medium. The crushing bodies utilized in this study were modified spheres with a concave portion. Grinding efficiency is expected to increase with the increasing available surface area of the grinding medium. A grinding ball with concavity has a smaller volume than a sphere of the same radius. Therefore, the convex-concave ball has a smaller mass with the same surface area, providing a larger specific surface area and a greater charge density. In the case of contact between the convex and concave surfaces, the probability of a crushing action over larger particles is higher than for smaller particles, causing preferential grinding of larger particles. Experiments were carried out in laboratory and consisted of batches of the same feed, ground first with conventional grinding balls. Part of the grinding medium of conventional grinding balls was then replaced by special concave-convex balls, increasing the specific surface area of the grinding balls. The results of the grinding experiments showed an effective selectivity of the grind, and in some cases, an increase in the fineness of the ground product, for a percentage of the concave area in the charge up to about 10%. Increasing the percentage of the concave bodies, the relative motion of the charge units became more irregular, causing a negative impact on grinding efficiency.
Keywords: grinding, crushing bodies, concave surfaces, grinding efficiency, grinding selectivity Introduction
The grinding media most often employed in fine grinding are spheres and truncated cones (Cylpebs). Other shapes, like cylinders, cones, cubes and hexagons, were studied. This paper analyzes the effect of utilizing crushing bodies of special shapes as a grinding medium. The crushing bodies utilized in this study were modified spheres with a concave portion. This shape, the new concave bodies, when compared with the spheres, presents a larger specific surface area. The consequence o f this higher specific surface area could be an increase in the grinding efficiency. Another feature that should be put in consideration is the grinding selectivity that arises from the area of contact between concave and convex surfaces. The large particles protect the small ones, similar to the action o f the rods in the rod mills. The comparison between the concave bodies and the spherical bodies can be done in the same fashion as the comparison between spheres and Cylpebs. Grinding tests were carried out with balls and concave bodies, varying the percentage of concave area in the mill charge.
Comminution, Classification and Agglomeration
C4-87
Background on grinding media Wills (1997) says: "grinding within a tumbling mill is influenced by the size, quantity, the type of motion and space between the individual pieces of the medium in the mill." Grinding is a random process subject to the laws of probability. The degree of grinding of a particle depends on its probability of entering a zone between pieces of grinding media, and the probability of contact with the grinding media after entry. Grinding takes place by several mechanisms, including impact or compression, due to forces applied almost normally to the particle surface, chipping due to oblique forces, and abrasion due to forces acting parallel to the surfaces. These mechanisms deform the particles and change their shape, beyond certain limits determined by their degree of elasticity, to achieve breaking. MINTEK (1991) reports that non-spherical grinding media, such as cones or Cylpebs, have been manufactured and marketed on the basis of a number of claimed advantages over spheres. A substantial reduction in foundry costs is possible, as a result of the high yield of metal in finished castings. For an equal mass of grinding charge, such shapes provide a higher grinding surface area, hence, it is claimed, more efficient grinding is attained. While testing cones and Cylpebs against balls, it was found that all three types of grinding media performed well, if the feed rate of the ore was kept relatively low. It was further found that neither cones nor Cylpebs achieved the same fineness of grind as an equal charge of balls, even though the surface-area of the non-spherical media was larger, casting doubt on the previously held assumption in this regard. Relative movement of units in a grinding charge plays an important role in grinding, particularly when conditions are predominantly abrasive. Such relative motion is expected to be easier with spherical media than non-spherical media, and to play a dominant role in the fineness of the grind. According to Cloos (1983), the grinding media should have the largest possible surface area, to provide a suitable contact surface with the material being ground, and be the heaviest possible, in order to have the necessary energy for breaking the ore particles. These requirements must be balanced, since the heavier the individual grinding media, the smaller the specific surface developed. The advantage of Cylpebs over balls lies in the surface area, and linear and point contact, which happens to Cylpebs, versus point contact only, which happens to spheres. As a result, the product will have a narrower-size spectrum than that verified by analogous rod mill grinding. By studying the geometrical attributes of balls versus Cylpebs, other advantages become clear. If we examine the two shapes, both made of the same material and having an equal diameter, the Cylpebs will have 50% greater surface area, 50% more weight and 50% more volume. It follows that for a specific diameter, the specific surface of the areas is the same. Further advantages of media surface area result from density and packing comparisons of the two shapes. Donda (1998) compared balls and Cylpebs of the same weight. Cylpebs have 15% more surface area than balls.
C4-88
Proceedings of the XXI International Mineral Processing Congress
The Cylpebs have a lower cost, and it was assumed that they have a larger grinding efficiency, due to their larger surface area. Laboratory tests show that, in spite of the larger surface area of the Cylpebs, the BSA (Blaine surface area) of the product was 7.5% less for the Cylpebs of the same weight as 30 mm diameter balls, and 11% less for the Cylpebs of same weight as 25 mm balls. In spite of the 15% larger surface area of the Cylpebs, that difference did not result in a larger surface generation in the product. Sepulveda (1990) states that the critical, controlling variable for ball charge optimization is the specific area exposed to impact by the charge. There is an optimum specific charge area exposed, which maximizes the grindability of any particular ore under consideration.
Assumptions Grinding efficiency increases with an increase in the available surface area of grinding medium. A grinding ball with a concavity has a smaller volume than a sphere of same radius. Therefore, the convex-concave ball has a smaller mass with the same surface area, providing a larger specific surface area. A concave surface allows a larger contact area with convex surfaces than the contact area between two convex surfaces; therefore, a concavity may simultaneously exert stress on a larger number of particles than a convex surface. The particles that are caught between the convex portion of a grinding ball, and the concave portion of another, would be trapped under the crushing action of the grinding medium for a longer time than in the case of two convex surfaces, where the particle would be under crushing action for a shorter contact time. In the case of contact between convex and concave surfaces, the probability of crushing action over larger particles is greater than for smaller particles, causing preferential grinding of larger particles.
Q
e o
Figure 1" Action of the concave grinding bodies.
Design of experiments Experiments were carried out in a laboratory and consisted of batches of the same feed that was first ground with conventional grinding balls. Then, part of the grinding medium balls was replaced by concave-convex balls, increasing the specific surface area of the grinding charge. The ore used was an iron ore concentrate from a commercial plant. Two types of concave balls made of cast iron were used, as sketched in Figure 2. The main characteristics of these bodies are presented in Table I.
Comminution, ClassificationandAgglomeration Type I
C4-89
Type II
Figure 2: Concave grinding bodies. Table I: Concave crushing bodies. Crushing bodies Diameter (mm) Weight (g) Overall area (cm2) Concave area ( c m Type I 38.8 181 47.3 9.8 Type II 38.8 148 47.3 13.4 The radius of the concavities is the same as the sphere radius.
2)
The harmonic mean size (HMS) is defined as the harmonic mean of the size fractions, weighted according to their mass and expressed approximately as: n+l
HMS=
/ /
/
Zmi/xi /=1
where: mi is the mass fraction of the ith screen fraction; x~ is the arithmetic mean of the size limits of the ith screen fraction. The harmonic mean size is a single value that provides an indication of the relative fineness of the grind obtained from a mill operating under different conditions, or using different types of grinding media under the same milling conditions.
First round of experiments The following parameters were adopted for the first round of experiments: mill dimensions, 20• cm 2, 67 rpm (72.0% of critical speed), 38% filling, 17.5 kg ball charge, 2.975 kg ore charge, 697 ml water (81% solids), 20 min, 40 min and 60 min grinding time. In this round of experiments, only the Type I concave was used, and just one size of balls, with the same weight as the Type I concave, as seen in Table II. Table II: Charge composition for the first round of tests. Test Sphere 36.2 mm diameter Type I concave Total charge area (cm2) Concave area of the charge (%)
1A 100 0 3,787 0.0
Crushing bodies of the charge (% wt) 2A 3A 4A 5A 80 60 40 20 20 40 60 80 3 , 9 4 5 4 , 1 0 2 4 , 3 1 3 4,430 4.7 9.1 13.5 17.3
6A 0 100 4,587 20.8
Proceedings of the XXI International Mineral Processing Congress
C4-90
40 m i n
20 m i n
A"
60 rain
1600
1200
2000
~" 1950
1150 1550 ll00
1900
1050
1500 0
20 %
40
60
80
100
1850 0
Concaves
20
40
60
80
100
0
% Concaves
20
40
60
80
I00
% Concaves
Figure 3" Blaine surface area (BSA) for the first round of tests, as a function of the percentage of type I concave crushing bodies in the charge. The Blaine surface area (BSA) data for the ground products, as seen in Figure 3, have a clear tendency to be reduced with an increase in the concave bodies o f the charge. 100
-
90 ~80=,~,.
6 0 ~
t=~.,~ 7060 ~ 2 2 0 / "
---o--- Test 2A - - ~,- - Test 3A
=
N 50
min
40 .... 35
] 45
] 55
[ 75
Screen aperture
Otm)
I 105
I 150
Figure 4: Size distribution of the first round of tests. The curves for the other tests are not plotted. Table III: Harmonic mean size (HMS) for the ground product of the first round of tests. Test
Feed
HMS total HMS >37 ~tm
36.30 70.67
HMS total HMS >37 tam
36.30 70,67
HMS total HMS >37 ~tm
36.30 70.67
1A
2A 3A 20 min grinding 28.37 28.31 28.54 60.19 61.46 60.63 40 min grinding 24,94 24.93 25.29 55.67 54.94 56.81 60 min grinding 23.06 23.08 23.10 52.00 52.90 51.72
4A
5A
6A
29.01 61.68
28.83 60.45
28.66 60.61
25.17 55.59
25.26 55.71
25.23 56.51
23.32 52.75
23.28 52.56
23.38 52.71
In most cases, the larger the concave area in the charge, the coarser is the ground product.
Second round of experiments The second round o f experiments was carried out under the following operating condition: the same mill and body charge as the first round o f tests was used, with the exception that grinding time was only 40 min.
Comminution, Classification and Agglomeration
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Table IV: Charge composition for the second round of tests. Test
Crushing bodies of the charge (% weight) 2B 3B 4B 5B 80 60 40 20 20 40 60 80 3,945 4,102 4,313 4,430 4.7 9.1 13.5 17.3
1B 100 0 3,787 0.0
Sphere 36.2 mm diameter Type I concave Total charge area (cm2) Concave area of the charge (%)
6B 0 100 4,587 20.8
The previous round o f tests did not show a reduction o f the fineness in the product with the introduction o f the concave bodies. In order to highlight the selectivity effect, the second set o f tests was performed on the coarsest possible ore, in relation to the size o f the concave bodies. 2150 2100 2050 < 2000 1950 1900 0
+
,
i
1
20
40
60
80
1
100
% Concaves
Figure 5" Blaine surface area (BSA) for the second round of tests, as a function of the percentage of Type I concave crushing bodies in the charge. 100 -
,~ 90 = 80 ~" .,~ 70 ~=60 j " ~ . . .
5O 35
Test 1B --.o.-_- Test 2B -'~ Test4B
.",,,
I 45
I I 55 75 Screen aperture Otto)
I 105
! 150
Figure 6: Size distribution of the second round of tests. The other tests are not plotted. Table V: Harmonic mean size (HMS) for the ground product of the second round of tests. Test HMS total HMS >37 gm
Feed 77.63 103.89
1B 25.66 59.50
2B 25.46 57.98
3B 25.63 57.62
4B 26.43 58.64
5B 25.95 58.81
6B 25.91 58.56
With a coarser feed, the product is finer, in the range b e t w e e n 37 g m to 150 gm, for all percentages o f concave areas in the charge, confirming the selectivity effect.
Proceedings of the XXI International Mineral Processing Congress
C4-92
Third round of experiments The third round o f experiments was performed with the following operating parameters: mill dimensions, 20x20 cm 2, 68 rpm (72.4% o f critical speed), % filling, 12 kg ball charge, 1.9 kg ore charge, 630 ml water (75% solids), and 40 min. grinding time. In this round o f experiments, we first tested only balls. Three other tests were done with concave bodies substituting balls with the same weight. To improve the use o f the concave surfaces, different sizes o f balls were used. The ball distribution follows B o n d ' s charge equilibrium equation, Y = (X/B) 3"8 (2) where Y is the percentage o f the total equilibrium charge passing any size X, and B is the diameter o f the larger ball. Table VI: Charge composition for the third round of tests. Test
Crushing bodies in the charge (% weight) 2C 3C 4C 24.2 35.2 21.4 21.4 21.4 11.6 11.6 11.6 5.4 5.4 5.4 2.2 2.2 2.2 24.2 24.2 35,2 35.2 3341.4 3449.1 3817.2 3700.8 0.0 4.8 14.5 10.5 1C 24.2 35.2 21.4 11.6 5.4 2.2
Sphere 35.5 mm diameter Sphere 33 mm diameter Sphere 28 mm diameter Sphere 23 mm diameter Sphere 18 mm diameter Sphere 13 mm diameter Type I concave Type II concave Total charge area (cm2) Concave area in the charge (%) 100 -
..
90
.
11
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I
Test 1C
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- - ~,- - Test 3C
=
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d 60
I
35
45
I
I
I
55 75 Screen aperture (gm)
lO5
150
Figure 7: Size distribution of the third set of tests. Test 4 is not plotted. Table VII: Harmonic mean size (HMS) for the ground product of the third round of tests. Test HMS total HMS >37 ~tm
Feed 29.77 77.46
1C 22.65 47.79
2C 22.57 47.14
3C 23.90 48.71
4C 22.69 47.19
Figure 7 shows that a finer product was obtained with a 5% concave area o f Type I bodies in the charge, for the size range between 35 ~tm and 150 ~tm. Test 3, with almost 15% o f concave area o f both types, produced a coarser product. Test 4, with
Comminution, Classification and Agglomeration
c4-93
about 10% of concave area of Type II bodies, did not produce any significant difference in the fineness of the product. The curve for test 4 lies in between the curves for tests 1 and 2 and is not plotted. There was a better use of the grinding surface: the 40 min grinding time in the third round of tests is almost the same as the 60 min grinding time in the first round of tests, with a similar feed. Conclusions
The initial assumption of increasing grinding efficiency with an increase in specific charge area was not proven. In all tests, there was a reduction of the product BSA (Blaine surface area) for increasing concave surface area and total surface area. For up to about 10% of the concave area of the charge, there was a trend toward a finer ground product. Apparently, the increase in the proportion of concave bodies with a less regular shape causes the charge to have less smooth movement, causing a negative impact on the grinding efficiency. The expected increase on Cylpebs grinding efficiency related to their larger specific surface area does not occur, perhaps for the same reason. On other hand, the selectivity of the grinding was proven to be effective, as highlighted in the second round of tests. When grinding coarse feeds, for instance, to feed a flotation plant, this selectivity effect may cause a positive impact on flotation recoveries, due to the reduction of fines lost in de-sliming. References
Cloos, U., 1983. Cylpebs: an alternative to balls as grinding media. World Mining, 10/83, 59. Donda, J.D., 1998. Estudo do Comportamento de um Itabirito do Quadrilfitero Ferrifero Quanto Superficie. MSc. Thesis, Universidade de Sao Paulo, Sao Paulo, Brasil. MINTEK, 1991. The selection of grinding balls for specific ores and the development of a suitable theory of ball wear. Application Report No. 10, MINTEK, Randburg, South Africa. Septilveda, J.E., 1990. Ball Mill Grinding: 40 Years After Bond, Proceedings. VI Simposium sobre Molienda, Armco Chile Procesamiento de Minerales S.A., Vifia del Mar, Chile, 13-32. Wills, BA, 1997. Mineral Processing Technology. Butterworth-Heineman, Oxford, England.