- Email: [email protected]
Analysis of abrasion mechanism of grinding media in a planetary mill with DEM simulation
Advanced Powder Technology 21 (2010) 212–216
Contents lists available at ScienceDirect
Advanced Powder Technology journal homepage: www.elsevier.com/locate/apt
Translated Paper
Analysis of abrasion mechanism of grinding media in a planetary mill with DEM simulation Akira Sato, Junya Kano *, Fumio Saito Institute of Multidisciplinary Research for Advanced Materials, Tohoku University, Sendai, Japan
a r t i c l e
i n f o
Article history: Received 20 January 2010 Accepted 20 January 2010
Keywords: Abrasion powder Abrasion rate constant Impact energy Discrete element method Planetary ball mill
a b s t r a c t In order to investigate the abrasion phenomena in a planetary ball mill, we conducted the grinding operation without a powder and sought a correlation between the ball abrasion and the ball impact energy estimated by a Discrete Element Method (DEM) simulation. Experimental results showed that the mass of abraded balls increased in proportion to the grinding time in the early stage of grinding up to 75 min. The abrasion rate increases quadratically with the mill rotation speed. It decreases with an increase in ball diameter up to 12.7 mm and then slightly increases when the diameter is 15.8 mm. It also increases with an increase in the ball-filling ratio of the mill up to 50%. Similar tendencies are found in the impact energy calculated from the balls motion simulated by DEM. Therefore, it is said that the abrasion rate has a strong correlation to the impact energy of balls under any milling conditions. Ó 2010 The Society of Powder Technology Japan. Published by Elsevier B.V. and The Society of Powder Technology Japan. All rights reserved.
1. Introduction In grinding operations, wear powders from the milling devices are inevitably generated and mixed into the products. Those powders often influence the quality of the products and are addressed as ‘the contamination’. Hence it is preferable to remove the wear powder from the products. Generally, there are two methods to remove the wear powders: the physical and the chemical separations. However, both methods are likely to consume the cost and time. On the other hand, there have been several propositions of modification of devices or processes to avoid the occurrence of the wear powder as much as possible [1,2]. The purpose of the grinding is to get fine powders from the bulk, therefore it is trend to be focused on the property of the powder products and paid less attention for the quantitative investigation of the wear powder. While, in the tribological study, the investigation of the wear phenomenon has been well progressed [3,4]. It has been known that the solid–solid contact should cause the wear phenomena by the mutual friction even if the one is much softer than another one. However, wear phenomena in the grinding have hardly been reported so far. Thus, in this research work, to understand the wear phenomena in the grinding, the planetary ball mill has been focused as a model grinding device, and the movement of the media (balls) in this device has been simulated by the Discrete Element Method (DEM). From the simulation, the impact energy has been calculated and * Corresponding author. E-mail address: [email protected] (J. Kano).
compared to the wear rate constant obtained from the experiments to know if there is a relation between them. As a result, the new knowledge that there is the correlation between the wear rate constant and impact energy is reported in this paper. 2. Experiment The mill used in this work was a planetary ball mill (Frisch, Pulverisette-7). The mill pot is made of stainless steel, and its inner diameter and height are 40 and 38 mm, respectively. The material of the ball is also made of stainless steel. For the sake of the simplicity, the mill has been operated without sample powders. It would make the relation between the movement of the balls and the quantity of the wear powers clear. The mass of the wear powder occurred during the operation, Mc has been obtained by subtracting the mass of the mill devices (pot and balls) after operation from the mass of them before operation, hence the mass of the wear powder is described by this equation:
Mc ¼ Mb Ma
ð1Þ
where Ma is the mass of the pot and balls after operation, and Mb is that of them before operation. 3. Simulation Discrete Element Method (DEM) is one of the most popular techniques for simulating and analyzing the solid particle behavior. The contact between particles is expressed by the simulation
0921-8831/$ - see front matter Ó 2010 The Society of Powder Technology Japan. Published by Elsevier B.V. and The Society of Powder Technology Japan. All rights reserved. doi:10.1016/j.apt.2010.01.005
213
A. Sato et al. / Advanced Powder Technology 21 (2010) 212–216
Nomenclature Mb Mc n N
ball diameter (mm) impact energy (J/s) ball-filling ratio (%) abrasion rate constant (g/min) mass of balls (kg) mass of mill device after operation (g)
dB Ei J Kc M Ma
vr
model shown in Fig. 1. The interaction forces at the contact such as elastic forces and frictional forces are calculated by this model, and then the interaction forces are substituted into the Newton’s second law to get the motion of the particles. The parameters shown in Fig. 1 were derived by the material properties presented in Table 1. The validity of these parameters has been already studied [5–7]. It has been reported that the grinding phenomena are related to the impact energy of the balls calculated from the simulation [8– 10], then the wear rate could have also a relationship with this impact energy. To confirm the relation between them, the impact energy of the balls in a planetary ball mill has been calculated by the simulation of balls motion, which is shown as the snapshot in Fig. 2, and then it has been compared to the wear rate. The impact energy of balls, Ei given to the pot and balls are expressed in Eq. (2), where m is the mass of the balls, vr denotes the relative velocity on the collision between two balls, n is the number of the collision during the simulation and ts shows the time
Ei ¼
n 1 X mv 2r;j 2
ð2Þ
ts
j¼1
4. Results and discussion 4.1. Effect of the rotational speeds Fig. 3 shows the mass of the wear powder from the mill device as a function of the operation time at each rotational speed. Here, dB is the diameter of the balls, and J is the ball-filling ratio. The result indicates that the mass of the wear powder increases with an increase in the rotational speeds, N. At N = 100 and 200 rpm, the masses of wear powder, Mc are much lower than the others. It could be estimated that at the lower rotational speed, the balls would not have the enough energy to induce the wear phenomena strongly. At N = 300–600 rpm, Mc seems to be linearly proportional to the operation time. At N = 700 rpm, though Mc is also proportional to the operating time up to 75 min, it starts to increase rap-
un φ
u ηn
Kt Slider
Kn
μ ηt
(a) Compressive force
(b) Shear force
Fig. 1. DEM simulation model.
mass of mill device before operation (g) mass of wear powder (g) frequency of collisions (–) rotational speed (rpm) relative velocity (m/s)
idly after that. Although the exact reason of this tendency is unclear, it might be explained by the following two reasons: One is that the wear powders might behave like an abrasive compound and help to lead the further occurrence of the wear powder. The other could be that the mill device gets the frictional heat by long time operating with high rotational speeds, and then this heat might lead the material properties of the device to more brittle stage. It has been reported that Mc is proportional to the operating time in the wear tests using a vibrating mill and beads mills [11]. Accordingly, in this research work, Mc is assumed to increase linearly. Then, those slops of the lines were defined as the ‘wear rate constant’, Kc. Fig. 4 shows the relationship between Kc and N. Kc increases with an increase in N. It can be said that Kc is highly dependent on N.
4.2. Effect of the ball diameters Fig. 5 presents the mass of the wear powder, Mc as a function of the operation time at each ball diameters. At the early stage of the milling, Mc increases linearly to the operation time. Furthermore, the smaller balls seem more likely to be worn. In addition, the reason why this figure has no data after 75 min at dB 7.9 mm is the balls fractured at that time. Fig. 6 shows the relation between the wear rate constant, Kc derived from Fig. 5 and dB. The result indicates that Kc decreases with an increase in dB. It could be noted that the number of collision during the process decreases with an increase in dB, and also total surface area of the balls is small at the bigger dB. However, it is unclear why Kc reaches the minimum at dB = 12.7 mm, and then it increases at dB = 15.8 mm. To understand the reason of that, it is required to have more investigation.
4.3. Effect of ball-filling ratio Fig. 7 shows the mass of the wear powder, Mc as a function of the operation ratio at each ball-filling ratio, J. It was assumed that Mc would have been increased at the lager J. However, the result shows that Mc increases the most rapidly at the J = 50%. The relationship between Kc obtained from Fig. 7 and J is shown in Fig. 8. Kc reaches the maximum value at J = 50%, and then it starts to decrease. This could be considered because there were the larger number of the media balls inside of the pot at the larger J, which increases the number of collision during the operation. On the other hand, the reason for the decrease of Mc over J = 60 would be that there are excess number of the balls located in the pot, and they interrupt their movement each other, then the collisions
Table 1 Material properties and physical constants for DEM. Young’s modulus (Pa)
Poisson’s ratio (–)
Density (kg/ m3)
Friction coefficient (–)
2.1 109
0.3
7800
0.17
214
A. Sato et al. / Advanced Powder Technology 21 (2010) 212–216
Fig. 2. Schematic diagram of a planetary mill and balls position in the pots obtained from the simulation.
N [rpm]
Mass of wear powder, Mc [g]
Mass of wear powder, Mc [g]
0.5
100 200 300 400 500 600 700
0.4 0.3 0.2 0.1 0.0 0
20
40 60 80 100 Grinding time, t[min]
0.5 0.4 0.3 0.2 0.1 0.0
0
20
0.0025 0.0020 0.0015 0.0010 0.0005
40 60 80 100 Grinding time, t[min]
120
Fig. 5. The mass of wear powder from the mill device as a function of grinding periods of time, depending on ball diameter (N = 700 rpm, J = 60%).
Wear rate constant,Kc [g/min]
Wear rate constant, Kc [g/min]
0.6
120
Fig. 3. The mass of the wear powder from the mill device during milling as a function of operation time, depending on rotational speed (dB = 15.8 mm, J = 60%).
0.0000
dB [mm] 15.8 12.7 10.2 7.9 6.3
0.7
0.005 0.004 0.003 0.002 0.001 0.000
6
8
10
12
14
16
Ball diameter, dB [mm]
0
100 200 300 400 500 600 700 800 Rotational speed, N [rpm]
Fig. 6. Relation between wear rate constant and ball diameter (N = 700 rpm, J = 60%).
Fig. 4. Wear rate constant as a function of rotational speed of the mill (dB = 15.8 mm, J = 60%).
that are hard enough to cause the wear hardly happened as frequent as the others operational condition.
5. Relation between the wear rate constant and impact energy Fig. 9 shows that relationship between the calculated impact energy of the media balls, Ei and the rotational speed, N. The result indicates that Ei increases with an increase in N.
The relationship between Ei and the ball diameter, dB is shown in Fig. 10. It seems to have a different tendency from the relationship between Kc and dB, Ei seems to be stable at dB = 6.3–10.2 mm. Fig. 11 presents the relationship between Ei and ball-filling ratio, J. Ei increases with an increase in J up to J = 60%. However, it starts to decreases at J = 70%. This could be the same reason as the experiment. This is because there are too many balls loaded in the pot to have the strong collision to cause the wear. The wear experiment has revealed the relationship among the wear rate constant, the rotational speed, the ball diameters and
215
A. Sato et al. / Advanced Powder Technology 21 (2010) 212–216
0.6 0.5 0.4 0.3
Impact energy, Ei [J/s]
Mass of wear powder, Mc [g]
50
J [%] 30 40 50 60 70
0.7
0.2 0.1 0.0
0
20
40 60 80 100 Grinding time, t[min]
120
0.005 0.004 0.003 0.002 0.001 0.000
30
40 50 60 Ball-filling ratio, J [%]
70
Impact energy,Ei [J/s]
10 30
40 50 60 Ball-filling ratio, J [%]
70
Fig. 11. Relation between impact energy of balls and ball-filling ratio (N = 700 rpm, dB = 10.2 mm).
0.006 Rotational speed Ball-filling ratio Ball diameter
0.005 0.004 0.003 0.002 0.001 0.000
0
5
10
15
20
25
30
35
Fig. 12. Relation between wear rate constant determined experimentally and impact energy of balls calculated from the balls motion simulated by DEM.
the ball-filling ratio. The relation in impact energy and the rotational speed, the ball diameters and the ball-filling ratio have also been made clear by the simulation. It can be seen the correlation between the wear rate constant and impact energy (Fig. 12). The data are distributed on the same straight line or its neighborhood, even though there is a little bit variation. Hence, it could be said that there is a liner correlation between Kc and Ei, which may allows to predict the mass of the wear powder by the simulation.
30 25 20 15 10 5 0
100 200 300 400 500 600 700 800 Rotational speed, N [rpm]
Fig. 9. Impact energy of balls as a function of rotational speed of the mill (dB = 15.8 mm, J = 60%).
50 Impact energy, Ei [J/s]
20
Impact energy, Ei [J/s]
Fig. 8. Relation between wear rate constant and ball-filling ratio (N = 700 rpm, dB = 10.2 mm).
0
30
0
Wear rate constant, Kc [g/min]
Wear rate constant, Kc [g/min]
Fig. 7. The mass of wear powder from the mill device as a function of operation time, depending on ball-filling ratio (N = 700 rpm, dB = 10.2 mm).
40
45
6. Conclusion In this research work, the planetary ball mill has been focused and investigated the mass of the wear powder in the experiment condition without the powder samples. In the mean time, the impact energy of the balls has been calculated by the Discrete Element Method (DEM). Then the relationship between the wear rate constant and impact energy has been identified. From these approaches, it can be concluded as shown below.
40 35 30 25 20 15
6
8 10 12 14 Ball diameter, dB[mm]
16
Fig. 10. Impact energy of balls as a function of ball diameter (N = 700 rpm, J = 60%).
1) The mass of wear powder increases almost linearly with an increase in the operation time at the early stage, and then it starts to increase more rapidly. 2) The wear rate constant is dependent on the rotational speed, the diameter of the balls and ball-filling ratio. 3) There seems to be correlation between the impact energy calculated by DEM simulation and the wear rate constant. As a result, the prediction of the wear rate constant might be able to be done by the DEM simulation.
216
A. Sato et al. / Advanced Powder Technology 21 (2010) 212–216
References [1] M. Öhman, A. Nordin, H. Hedman, R. Jirjis, Reasons for slagging during stemwood pellet combustion and some measures for prevention, Biomass and Bioenergy 27 (2004) 597–605. [2] N.J. Evans, J.J. Davis, J.P. Byrne, D. French, Contamination-free preparation of geological samples for ultra-trace gold and platinum-group element analysis, Journal of Geochemical Exploration 80 (2003) 19–24. [3] N. Ohmae, J.M. Martin, S. Mori, Micro and Nanotribology, ASME (2005) 26– 34. [4] M.A. Nicholls, D.R. Norton, G.M. Bancroft, M. Kasrai, T. Do, B.H. Frazer, G.D. DeStasio, Tribology Letters 17 (2003) 205–216. [5] P.A. Cundall, O.D.L. Strack, A Discrete numerical model for granular assemblies Geotechnique, Geotechnique 29 (1979) 47–65.
[6] J. Kano, N. Chujo, F. Saito, A method for simulating three-dimensional motion of balls under the presence of powder sample in a tumbling ball mill, Advanced Powder Technology 8 (1997) 39–51. [7] J. Kano, F. Saito, Simulation of media motion in different type of mills, Funtai to Kogyo 30 (1998) 48–55. [8] J. Kano, H. Mio, F. Saito, Simulation of operational powder of a co-axial double rotating cylinders mill by the particle element method, Journal of Chemical Engineering Japan 32 (1999) 445–448. [9] J. Kano, H. Mio, F. Saito, M. Miyazaki, Correlation of grinding rate of gibbsite with impact energy in tumbling mill with mono-size balls, Minerals Engineering 14 (2001) 1213–1223. [10] H. Mori, H. Mio, J. Kano, F. Saito, Ball mill simulation in wet grinding using a tumbling mill and its correlation to grinding rate, Powder Technology 143–144 (2004) 230–239. [11] Sentan Funsai Gizyutu to Oyo, NGT (2005) 418.
Contents lists available at ScienceDirect
Advanced Powder Technology journal homepage: www.elsevier.com/locate/apt
Translated Paper
Analysis of abrasion mechanism of grinding media in a planetary mill with DEM simulation Akira Sato, Junya Kano *, Fumio Saito Institute of Multidisciplinary Research for Advanced Materials, Tohoku University, Sendai, Japan
a r t i c l e
i n f o
Article history: Received 20 January 2010 Accepted 20 January 2010
Keywords: Abrasion powder Abrasion rate constant Impact energy Discrete element method Planetary ball mill
a b s t r a c t In order to investigate the abrasion phenomena in a planetary ball mill, we conducted the grinding operation without a powder and sought a correlation between the ball abrasion and the ball impact energy estimated by a Discrete Element Method (DEM) simulation. Experimental results showed that the mass of abraded balls increased in proportion to the grinding time in the early stage of grinding up to 75 min. The abrasion rate increases quadratically with the mill rotation speed. It decreases with an increase in ball diameter up to 12.7 mm and then slightly increases when the diameter is 15.8 mm. It also increases with an increase in the ball-filling ratio of the mill up to 50%. Similar tendencies are found in the impact energy calculated from the balls motion simulated by DEM. Therefore, it is said that the abrasion rate has a strong correlation to the impact energy of balls under any milling conditions. Ó 2010 The Society of Powder Technology Japan. Published by Elsevier B.V. and The Society of Powder Technology Japan. All rights reserved.
1. Introduction In grinding operations, wear powders from the milling devices are inevitably generated and mixed into the products. Those powders often influence the quality of the products and are addressed as ‘the contamination’. Hence it is preferable to remove the wear powder from the products. Generally, there are two methods to remove the wear powders: the physical and the chemical separations. However, both methods are likely to consume the cost and time. On the other hand, there have been several propositions of modification of devices or processes to avoid the occurrence of the wear powder as much as possible [1,2]. The purpose of the grinding is to get fine powders from the bulk, therefore it is trend to be focused on the property of the powder products and paid less attention for the quantitative investigation of the wear powder. While, in the tribological study, the investigation of the wear phenomenon has been well progressed [3,4]. It has been known that the solid–solid contact should cause the wear phenomena by the mutual friction even if the one is much softer than another one. However, wear phenomena in the grinding have hardly been reported so far. Thus, in this research work, to understand the wear phenomena in the grinding, the planetary ball mill has been focused as a model grinding device, and the movement of the media (balls) in this device has been simulated by the Discrete Element Method (DEM). From the simulation, the impact energy has been calculated and * Corresponding author. E-mail address: [email protected] (J. Kano).
compared to the wear rate constant obtained from the experiments to know if there is a relation between them. As a result, the new knowledge that there is the correlation between the wear rate constant and impact energy is reported in this paper. 2. Experiment The mill used in this work was a planetary ball mill (Frisch, Pulverisette-7). The mill pot is made of stainless steel, and its inner diameter and height are 40 and 38 mm, respectively. The material of the ball is also made of stainless steel. For the sake of the simplicity, the mill has been operated without sample powders. It would make the relation between the movement of the balls and the quantity of the wear powers clear. The mass of the wear powder occurred during the operation, Mc has been obtained by subtracting the mass of the mill devices (pot and balls) after operation from the mass of them before operation, hence the mass of the wear powder is described by this equation:
Mc ¼ Mb Ma
ð1Þ
where Ma is the mass of the pot and balls after operation, and Mb is that of them before operation. 3. Simulation Discrete Element Method (DEM) is one of the most popular techniques for simulating and analyzing the solid particle behavior. The contact between particles is expressed by the simulation
0921-8831/$ - see front matter Ó 2010 The Society of Powder Technology Japan. Published by Elsevier B.V. and The Society of Powder Technology Japan. All rights reserved. doi:10.1016/j.apt.2010.01.005
213
A. Sato et al. / Advanced Powder Technology 21 (2010) 212–216
Nomenclature Mb Mc n N
ball diameter (mm) impact energy (J/s) ball-filling ratio (%) abrasion rate constant (g/min) mass of balls (kg) mass of mill device after operation (g)
dB Ei J Kc M Ma
vr
model shown in Fig. 1. The interaction forces at the contact such as elastic forces and frictional forces are calculated by this model, and then the interaction forces are substituted into the Newton’s second law to get the motion of the particles. The parameters shown in Fig. 1 were derived by the material properties presented in Table 1. The validity of these parameters has been already studied [5–7]. It has been reported that the grinding phenomena are related to the impact energy of the balls calculated from the simulation [8– 10], then the wear rate could have also a relationship with this impact energy. To confirm the relation between them, the impact energy of the balls in a planetary ball mill has been calculated by the simulation of balls motion, which is shown as the snapshot in Fig. 2, and then it has been compared to the wear rate. The impact energy of balls, Ei given to the pot and balls are expressed in Eq. (2), where m is the mass of the balls, vr denotes the relative velocity on the collision between two balls, n is the number of the collision during the simulation and ts shows the time
Ei ¼
n 1 X mv 2r;j 2
ð2Þ
ts
j¼1
4. Results and discussion 4.1. Effect of the rotational speeds Fig. 3 shows the mass of the wear powder from the mill device as a function of the operation time at each rotational speed. Here, dB is the diameter of the balls, and J is the ball-filling ratio. The result indicates that the mass of the wear powder increases with an increase in the rotational speeds, N. At N = 100 and 200 rpm, the masses of wear powder, Mc are much lower than the others. It could be estimated that at the lower rotational speed, the balls would not have the enough energy to induce the wear phenomena strongly. At N = 300–600 rpm, Mc seems to be linearly proportional to the operation time. At N = 700 rpm, though Mc is also proportional to the operating time up to 75 min, it starts to increase rap-
un φ
u ηn
Kt Slider
Kn
μ ηt
(a) Compressive force
(b) Shear force
Fig. 1. DEM simulation model.
mass of mill device before operation (g) mass of wear powder (g) frequency of collisions (–) rotational speed (rpm) relative velocity (m/s)
idly after that. Although the exact reason of this tendency is unclear, it might be explained by the following two reasons: One is that the wear powders might behave like an abrasive compound and help to lead the further occurrence of the wear powder. The other could be that the mill device gets the frictional heat by long time operating with high rotational speeds, and then this heat might lead the material properties of the device to more brittle stage. It has been reported that Mc is proportional to the operating time in the wear tests using a vibrating mill and beads mills [11]. Accordingly, in this research work, Mc is assumed to increase linearly. Then, those slops of the lines were defined as the ‘wear rate constant’, Kc. Fig. 4 shows the relationship between Kc and N. Kc increases with an increase in N. It can be said that Kc is highly dependent on N.
4.2. Effect of the ball diameters Fig. 5 presents the mass of the wear powder, Mc as a function of the operation time at each ball diameters. At the early stage of the milling, Mc increases linearly to the operation time. Furthermore, the smaller balls seem more likely to be worn. In addition, the reason why this figure has no data after 75 min at dB 7.9 mm is the balls fractured at that time. Fig. 6 shows the relation between the wear rate constant, Kc derived from Fig. 5 and dB. The result indicates that Kc decreases with an increase in dB. It could be noted that the number of collision during the process decreases with an increase in dB, and also total surface area of the balls is small at the bigger dB. However, it is unclear why Kc reaches the minimum at dB = 12.7 mm, and then it increases at dB = 15.8 mm. To understand the reason of that, it is required to have more investigation.
4.3. Effect of ball-filling ratio Fig. 7 shows the mass of the wear powder, Mc as a function of the operation ratio at each ball-filling ratio, J. It was assumed that Mc would have been increased at the lager J. However, the result shows that Mc increases the most rapidly at the J = 50%. The relationship between Kc obtained from Fig. 7 and J is shown in Fig. 8. Kc reaches the maximum value at J = 50%, and then it starts to decrease. This could be considered because there were the larger number of the media balls inside of the pot at the larger J, which increases the number of collision during the operation. On the other hand, the reason for the decrease of Mc over J = 60 would be that there are excess number of the balls located in the pot, and they interrupt their movement each other, then the collisions
Table 1 Material properties and physical constants for DEM. Young’s modulus (Pa)
Poisson’s ratio (–)
Density (kg/ m3)
Friction coefficient (–)
2.1 109
0.3
7800
0.17
214
A. Sato et al. / Advanced Powder Technology 21 (2010) 212–216
Fig. 2. Schematic diagram of a planetary mill and balls position in the pots obtained from the simulation.
N [rpm]
Mass of wear powder, Mc [g]
Mass of wear powder, Mc [g]
0.5
100 200 300 400 500 600 700
0.4 0.3 0.2 0.1 0.0 0
20
40 60 80 100 Grinding time, t[min]
0.5 0.4 0.3 0.2 0.1 0.0
0
20
0.0025 0.0020 0.0015 0.0010 0.0005
40 60 80 100 Grinding time, t[min]
120
Fig. 5. The mass of wear powder from the mill device as a function of grinding periods of time, depending on ball diameter (N = 700 rpm, J = 60%).
Wear rate constant,Kc [g/min]
Wear rate constant, Kc [g/min]
0.6
120
Fig. 3. The mass of the wear powder from the mill device during milling as a function of operation time, depending on rotational speed (dB = 15.8 mm, J = 60%).
0.0000
dB [mm] 15.8 12.7 10.2 7.9 6.3
0.7
0.005 0.004 0.003 0.002 0.001 0.000
6
8
10
12
14
16
Ball diameter, dB [mm]
0
100 200 300 400 500 600 700 800 Rotational speed, N [rpm]
Fig. 6. Relation between wear rate constant and ball diameter (N = 700 rpm, J = 60%).
Fig. 4. Wear rate constant as a function of rotational speed of the mill (dB = 15.8 mm, J = 60%).
that are hard enough to cause the wear hardly happened as frequent as the others operational condition.
5. Relation between the wear rate constant and impact energy Fig. 9 shows that relationship between the calculated impact energy of the media balls, Ei and the rotational speed, N. The result indicates that Ei increases with an increase in N.
The relationship between Ei and the ball diameter, dB is shown in Fig. 10. It seems to have a different tendency from the relationship between Kc and dB, Ei seems to be stable at dB = 6.3–10.2 mm. Fig. 11 presents the relationship between Ei and ball-filling ratio, J. Ei increases with an increase in J up to J = 60%. However, it starts to decreases at J = 70%. This could be the same reason as the experiment. This is because there are too many balls loaded in the pot to have the strong collision to cause the wear. The wear experiment has revealed the relationship among the wear rate constant, the rotational speed, the ball diameters and
215
A. Sato et al. / Advanced Powder Technology 21 (2010) 212–216
0.6 0.5 0.4 0.3
Impact energy, Ei [J/s]
Mass of wear powder, Mc [g]
50
J [%] 30 40 50 60 70
0.7
0.2 0.1 0.0
0
20
40 60 80 100 Grinding time, t[min]
120
0.005 0.004 0.003 0.002 0.001 0.000
30
40 50 60 Ball-filling ratio, J [%]
70
Impact energy,Ei [J/s]
10 30
40 50 60 Ball-filling ratio, J [%]
70
Fig. 11. Relation between impact energy of balls and ball-filling ratio (N = 700 rpm, dB = 10.2 mm).
0.006 Rotational speed Ball-filling ratio Ball diameter
0.005 0.004 0.003 0.002 0.001 0.000
0
5
10
15
20
25
30
35
Fig. 12. Relation between wear rate constant determined experimentally and impact energy of balls calculated from the balls motion simulated by DEM.
the ball-filling ratio. The relation in impact energy and the rotational speed, the ball diameters and the ball-filling ratio have also been made clear by the simulation. It can be seen the correlation between the wear rate constant and impact energy (Fig. 12). The data are distributed on the same straight line or its neighborhood, even though there is a little bit variation. Hence, it could be said that there is a liner correlation between Kc and Ei, which may allows to predict the mass of the wear powder by the simulation.
30 25 20 15 10 5 0
100 200 300 400 500 600 700 800 Rotational speed, N [rpm]
Fig. 9. Impact energy of balls as a function of rotational speed of the mill (dB = 15.8 mm, J = 60%).
50 Impact energy, Ei [J/s]
20
Impact energy, Ei [J/s]
Fig. 8. Relation between wear rate constant and ball-filling ratio (N = 700 rpm, dB = 10.2 mm).
0
30
0
Wear rate constant, Kc [g/min]
Wear rate constant, Kc [g/min]
Fig. 7. The mass of wear powder from the mill device as a function of operation time, depending on ball-filling ratio (N = 700 rpm, dB = 10.2 mm).
40
45
6. Conclusion In this research work, the planetary ball mill has been focused and investigated the mass of the wear powder in the experiment condition without the powder samples. In the mean time, the impact energy of the balls has been calculated by the Discrete Element Method (DEM). Then the relationship between the wear rate constant and impact energy has been identified. From these approaches, it can be concluded as shown below.
40 35 30 25 20 15
6
8 10 12 14 Ball diameter, dB[mm]
16
Fig. 10. Impact energy of balls as a function of ball diameter (N = 700 rpm, J = 60%).
1) The mass of wear powder increases almost linearly with an increase in the operation time at the early stage, and then it starts to increase more rapidly. 2) The wear rate constant is dependent on the rotational speed, the diameter of the balls and ball-filling ratio. 3) There seems to be correlation between the impact energy calculated by DEM simulation and the wear rate constant. As a result, the prediction of the wear rate constant might be able to be done by the DEM simulation.
216
A. Sato et al. / Advanced Powder Technology 21 (2010) 212–216
References [1] M. Öhman, A. Nordin, H. Hedman, R. Jirjis, Reasons for slagging during stemwood pellet combustion and some measures for prevention, Biomass and Bioenergy 27 (2004) 597–605. [2] N.J. Evans, J.J. Davis, J.P. Byrne, D. French, Contamination-free preparation of geological samples for ultra-trace gold and platinum-group element analysis, Journal of Geochemical Exploration 80 (2003) 19–24. [3] N. Ohmae, J.M. Martin, S. Mori, Micro and Nanotribology, ASME (2005) 26– 34. [4] M.A. Nicholls, D.R. Norton, G.M. Bancroft, M. Kasrai, T. Do, B.H. Frazer, G.D. DeStasio, Tribology Letters 17 (2003) 205–216. [5] P.A. Cundall, O.D.L. Strack, A Discrete numerical model for granular assemblies Geotechnique, Geotechnique 29 (1979) 47–65.
[6] J. Kano, N. Chujo, F. Saito, A method for simulating three-dimensional motion of balls under the presence of powder sample in a tumbling ball mill, Advanced Powder Technology 8 (1997) 39–51. [7] J. Kano, F. Saito, Simulation of media motion in different type of mills, Funtai to Kogyo 30 (1998) 48–55. [8] J. Kano, H. Mio, F. Saito, Simulation of operational powder of a co-axial double rotating cylinders mill by the particle element method, Journal of Chemical Engineering Japan 32 (1999) 445–448. [9] J. Kano, H. Mio, F. Saito, M. Miyazaki, Correlation of grinding rate of gibbsite with impact energy in tumbling mill with mono-size balls, Minerals Engineering 14 (2001) 1213–1223. [10] H. Mori, H. Mio, J. Kano, F. Saito, Ball mill simulation in wet grinding using a tumbling mill and its correlation to grinding rate, Powder Technology 143–144 (2004) 230–239. [11] Sentan Funsai Gizyutu to Oyo, NGT (2005) 418.