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The impact of end-wall effect on the charge trajectory in tumbling model mills
International Journal of Mineral Processing 144 (2015) 75–80
Contents lists available at ScienceDirect
International Journal of Mineral Processing journal homepage: www.elsevier.com/locate/ijminpro
The impact of end-wall effect on the charge trajectory in tumbling model mills M. Maleki-Moghaddam, A.R. Ghasemi, M. Yahyaei, S. Banisi ⁎ Shahid Bahonar University of Kerman, Mining Engineering Group, Engineering Faculty, Islamic Republic Blvd., Kerman, P.O. Box 761175-133, Iran
a r t i c l e
i n f o
Article history: Received 27 June 2014 Received in revised form 10 September 2015 Accepted 7 October 2015 Keywords: Comminution SAG mill Charge shape Impact point
a b s t r a c t Direct observation of the charge shape and its motion in industrial mills is not possible, it is then customary to use transparent end, small-scale mills (i.e., model mills) to determine the charge trajectory directly by visualization methods. Because of a short length of the model mills, the end-wall effects could introduce a significant bias on the observed charge trajectories and shape. In this research, the end-wall effect was investigated by gradually increasing the model mill length and analysing the charge trajectory and shape variation at given operating conditions (i.e., ball filling, mill speed, liner type). The special design of the model mill with the diameter of 100 cm made it possible to increase the mill length in steps of 3.6 cm up to 21.6 cm. Four types of liners, five steel ball fillings (10, 15, 20, 25, 30% v/v) and three mill speeds (55, 70, 85% of critical speed) were tested. The results indicated that when the mill length was below 10.8 cm the end-walls prevented the charge from free falling. This resulted in lower impact point angles and lower power draws compared with the case of no end-wall effect. When the same experiments were performed using an iron ore instead of balls with the same size range, the impact of end-wall effect was more pronounced. For a mill length of 3.6 cm, an increase of 30% in the speed (from 55 to 85%) with the iron ore charge, the torque decreased by 41% (from 3.7 to 2.2 kgf·m) when mill filling was 30%. At the same operating conditions, when steel balls were used the torque decreased only by 19% (from 9 to 7.2 kgf·m). Three-dimensional DEM simulations also resulted in similar conclusions. © 2015 Elsevier B.V. All rights reserved.
1. Introduction Grinding is the most energy intensive operation which constitutes the major portion of operating and capital costs of mineral processing plants. Hence, a vast number of research works have been carried out with the aim of performance improvement (Mishra and Rajamani, 1990; McElroy et al., 2009). Direct observation of charge shape and its motion in industrial mills is not possible, it is then customary to use transparent end, small-scale mills (i.e., model mills) to determine the charge trajectory directly by visualization methods. Morrell (1993) used a laboratory mill with one transparent end and photographed the load under various operating conditions. Then he proposed various empirical equations to relate the positions of toe and shoulder and inner load radius to mill speed and filling. Kallon et al. (2011) developed and tested a model linking the circulation rate of charge particles with physical mill parameters using experimental data derived from positron emission particle tracking (PEPT). Traditionally, the optimization and design of grinding circuits have been based on costly and time-consuming laboratory experimentation and pilot plant testing. One solution which could be beneficial is to use numerical tools, such as the discrete element method (DEM), which could be ⁎ Corresponding author. E-mail address: [email protected] (S. Banisi).
http://dx.doi.org/10.1016/j.minpro.2015.10.005 0301-7516/© 2015 Elsevier B.V. All rights reserved.
used to predict the behaviour of granular materials. DEM is a technique which requires minimal experimental effort, and its results can be easily scaled up from the laboratory to industrial size mills. Currently, this method is commonly used particularly in modelling AG and SAG mills due to the complexity of these machines (Mishra and Rajamani, 1990; Rajamani, 2006; Powell et al., 2008; McElroy et al., 2009). Nevertheless, experimental validation is the most important step in the process of testing codes. The most frequently applied validation methodologies are ball trajectory tracking and power draw monitoring in laboratory scale mills (van Nierop et al., 2001). This demonstrates that the endwall effects are very important contributors to the accuracy of the simulation and experimental results. A number of researchers have also addressed the influence of endwall boundaries on the flow of the granular materials in rotating drums. For example, Cleary (2009) studied the axial transport of the particles in a ball mill and showed that looking along the shoulder from the feed end towards the grate one can see that the shoulder is distinctly higher at the ends and lower in the middle. The frictional interaction with the rotating end-walls supports and lifts the nearby charge more leading to noticeably higher shoulder positions. Far from the end-wall effect the charge slumps more and has a lower shoulder and higher toe position. Experiments in fully closed drums also indicate that the end-walls may initiate the axial band formation of segregated particles (Liu et al., 2008). In other words, particles with specific size
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M. Maleki-Moghaddam et al. / International Journal of Mineral Processing 144 (2015) 75–80
Table 1 Main characteristics of four industrial liners used.
Sarcheshmeh (New liner) Sarcheshmeh (Worn liner) Gol-E-Gohar (old liner) Gol-E-Gohar (New liner)
Liner number
No. of lifters in rows
Liner width (mm)
Lifter height (mm)
Lifter face angle (°)
1
60
250
152
14
2
60
250
90
62
3
36
125
225
7
4
36
125
225
30
and density could be accumulated in certain locations along the mill axis. As to flow patterns, Santomaso et al. (2004) suggested that friction plays an important role at the end plates; the crucial role of the plates could be observed by about 10% increase of the surface slope because of the friction of the bed with the end-walls. Recently, it was demonstrated that this effect is localized to the end-walls when the axial length of the drum is greater than its diameter (Liu et al., 2008). They concluded that the end-wall effect becomes significant as the mill length decreases. Since the model mill length at which the end-wall effect could be assumed to be negligible has not been addressed extensively, in this research this issue was investigated experimentally. This task was fulfilled by gradually increasing the model mill length and analysing the charge trajectory and shape variation at a given operating condition (i.e., ball filling, mill speed, liner type). 2. Methodology 2.1. The model mill The model mill with the diameter of 100 cm and special design made it possible to increase the mill length in steps of 3.6 cm up to 21.6 cm. In other words, the mill length could be increased by 6-fold. The transparent end of the mills made accurate trajectory determination possible by taking film and photographs. A 2.5 kW motor with a variable speed drive was used which provided sufficient flexibility to test various operating conditions. The scale down ratios of 9 to 1 and 10 to 1 was used to construct the model mill using mill dimensions of two plants. In order to exactly duplicate the plant liner arrangements in the mill, four types of 3.6 cm-long polyurethane rings, which were scaled-down versions of the liners, were accurately machined to be used in the model mill. The choice of polyurethane over steel liners was because of
easier machining which was crucial in duplicating the plant liner arrangements. The tests performed in the model mill using steel and polyurethane liners did not show any change in the charge trajectory indicating that the effect of change in the friction coefficients of the liners on the charge trajectory could be neglected. The four liner types were: new and worn (after 5184 h of operation) liners of SAG mill at the Sarcheshmeh copper complex, and old and new liners of AG mills at the Gol-E-Gohar Iron ore company which were numbered from 1 to 4, respectively (Table 1). In this research, the end-wall effect was investigated by gradually increasing the model mill length from 3.6 cm up to 21.6 cm. Fig. 1 shows a scaled-down model of the liner No. 3 and 10.8 cm-long mill fitted by three liners each with the length of 3.6 cm (new liner of the Gol-E-Gohar Iron ore company AG mill). 2.2. Measurement details The main aim of the experimental stage was to determine how the shape of the mill charge changed as the mill length, lifter type, the volume of the charge and rotational speed were varied. Experiments were performed for each type of liner in the model mill. The mill charge consisted of 4 to 12 mm diameter steel and plastic (62.5% 10–12 mm, 32.5% 7–9 mm and 5% 4–6 mm). The plastic balls used to keep the weight of the mill in the range of the torque metre especially when the mill length was in its maximum (i.e., 21.6 cm). Experiments were also conducted using an iron ore only with the same size distribution of balls. A transparent plexiglass faceplate made photographing of the tumbling charge possible. The model mill was operated at 55, 70 and 85% of critical speed (Cr.S.) for five levels of mill filling (10, 15, 20, 25 and 30% by volume). The shoulder, toe and charge impact points were measured in degrees starting from the horizontal line passing the mill centre (i.e., 3 o'clock position) and moving counter clockwise. A typical snapshot of the charge shape and charge impact point is shown in Fig. 1b. The experimental mill was also equipped with a torque sensor. During the tests, the mill torque was measured and recorded with a high speed card recorder. The tumbling ball charge was photographed with a high-speed camera (240 fps). To increase the accuracy of the results, more than 20 photographs during a period of 2 min were used to measure the angular displacement of the toe, shoulder and charge impact point; the average values and standard deviations were then reported. An electronic protractor (MB-Ruler version 4.0) and an angular grid with 1° intervals were used to determine the positions. To re-examine the measurements' accuracy, all tests were repeated and photographed by another camera (90 fps). The difference between the results obtained by two cameras was found to be less than 2° indicating a reasonable accuracy. The charge impact point and shape
Fig. 1. (a) 3.6 cm-long scaled-down model of new liner of the Gol-E-Gohar Iron ore company AG mill; (b) 10.8 cm-long mill fitted by three liners each with the length of 3.6 cm.
M. Maleki-Moghaddam et al. / International Journal of Mineral Processing 144 (2015) 75–80
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Fig. 2. Variation of shoulder (a) and impact point (b) positions with liner type, speed and mill filling.
variation were analysed by increasing the model mill length from 3.6 cm to 21.6 cm.
3. Results and discussions 3.1. Charge shape and trajectory in the 2D model mill In order to determine the end-wall effect in the 2D model (i.e., short length) mill at different operating conditions, a 100 cm × 3.6 cm mill was used. As the mill rotates the charge is lifted up with the rising face of the mill until the shoulder is reached. At this point the bulk of the charge falls away towards the toe region. The toe angle is the highest point reached by the bulk of the charge in the toe region of the mill. The shoulder angle was chosen to be the point where the trajectories of the bulk particles near the lifters began to diverge from the mill shell. The variation of shoulder position with liner type, mill filling and speed is shown in Fig. 2a. The effect of liner type was not found significant given the measurement error. As expected, the increase in filling moved the shoulder position to higher angles. The same trend was observed for the mill speed because of the charge elongation (i.e., expansion of charge when speed is increased). For an increase of 30% in the speed (from 55 to 85% of critical speed), the shoulder angle increased by 21° (from 40 to 61°) when mill filling was 30%. The impact point position was assumed to be the point with the highest concentration of impacts on the liner by cataracting balls. The variation of impact point position with liner type, mill filling and speed is shown in Fig. 2b. As the amount of filling increased the impact points, on account of an increase in the force exerted from the charge,
Fig. 3. Variation of torque with the mill speed and liner types.
decreased. For liner No. 1, when the filling varied from 10 to 30% the impact points changed from 182 to 176°. Variation of toe location (measured in angles) with liner type, speed and mill filling was also determined. As expected, the position of toe changed as the mill filling increased. When the mill filling varied from 10 to 30%, the toe angle decreased from 248 to 217° (85% of critical speed; liner No. 1). The effect of liner type on the position of toe, at any given operational conditions, was not found significant considering the measurement error. 3.2. Torque variation in the 2D model mill The power drawn by the mill could be determined considering the ball contact forces acting on the liners and the load behaviour. The power is generally calculated by: Power ¼ 2πNτ
ð1Þ
where N is the mill rotation speed and τ is torque. In this study, torque which is directly proportional to the mill power draw was measured to study the effect of various parameters. Any change in the shape of charge and the amount of the charge in free flight will be reflected in the measured torque. It is important to note that the effect of an increase in the mill speed does not affect the torque by itself rather the change in the shape of the charge and the amount of charge in free flight cause the change in the torque. In other words, the change in the load behaviour (at a constant filling) due to the change in the mill speed and liner type is reflected in the torque measurements. The torque of the load at different operating conditions in the 3.6 cm long model mill was measured by a torque sensor. The variation of torque at three different charge shapes at constant filling of 30% was measured (Fig. 3). The three charge shapes were obtained by running the mill at 55%, 70%, and 85% of critical speed (Cr.S.), respectively, and using four types of liners. The results indicated that as the amount of charge in the free flight increased, the measured torque decreased. Since the mill length was short (i.e., 3.6 cm), due to some bridging between the end-walls and interlocking of the particles, the charge was lifted to a higher point. This resulted in a higher shoulder position and also the balls' impact points became closer to 9 o'clock and above positions. In this situation, these impacts helped the rotation of the mill (i.e., positive torque) and consequently the power draw decreased. In addition, the movement of toe towards lower angles (9 o'clock position) because of falling balls further decreased the measured torque (Fig. 3). It should be noted that there is a direct relationship between the amount of in-flight balls and the share of the balls' impact to locations close to the 9 o'clock and above positions which decrease the power draw. In other words, the higher the amount of in-flight balls the higher the power draw reduction because of impacts which assist the rotation of the mill.
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Fig. 4. Variation of toe location (measured in angles) with mill length and speed; (a) 15% filling; (b) 25% filling.
Fig. 5. Variation of shoulder location with liner length and speed; (a) 15% filling; (b) 25% filling.
In the case of the 36 mm long mill where balls with diameters from 5 to 12 mm are used there are likely to be only 4 layers of balls along the model mill length. The layer against the end window stacks effectively, resulting in an elevated trajectory which is not representative of the charge inside the industrial mills. Because in practice, the aspect ratios of industrial mills are larger. The tests were repeated but instead of steel balls an iron ore was used as the charge (size charge and amount of filling kept constant). The torque decreased by 41% (from 3.7 to 2.2 kgf·m) when the mill speed increased from 55 to 85%. Whereas, in the case of steel
balls this reduction was only 19% (from 9 to 7.2 kgf·m). These results indicated that when the ore was used the material shear strength produced by the interlocking of the non-circular shaped particles increased. This in turn decreased the impact point angles which led to lower torques. 3.3. Mill length and the end-wall effect In this research, the end-wall effect was investigated by gradually increasing the model mill length from 3.6 cm to 21.6 cm. In other words,
Fig. 6. Variation of impact point location with liner length and speed; (a) 15% filling; (b) 25% filling.
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79
and increased the balls in flight leading to the lower impact point angles and lower power draw. The experiments were also carried out using steel balls in 10.8 cm and 21.6 cm length mills. The comparison of charge shapes and impact points in these two mills showed that the end-wall effect was negligible in 10.8 cm-long and longer model mills. 3.4. Charge behaviour and torque variation
Fig. 7. Measured torque at different speeds and liners (liner No. 4; 25% filling).
the mill length could be increased in six intervals each with a length of 3.6 cm. Experiments were performed for liner No. 4 (Gol-E-Gohar new liner) using polyurethane balls and locations of the toe, shoulder and charge impact point were identified. Variation of toe location with mill length and speed is shown in Fig. 4. Note that only two mill fillings (10 and 25%) are given in Fig. 4. At the short mill length (i.e., 3.6 cm) the toe position is higher and compared to the 10.8 cm-length mill the toe moved to the 9 o'clock position by 9° (i.e., lower toe angle values). Above the 10.8 cm-length mill the variation in toe locations was not found significant which indicated no end-wall effect situation. By increasing the mill speed and mill filling due to the charge elongation the toe position moved towards the 9 o'clock position. The variation of shoulder position with the mill length and speed is shown in Fig. 5. When the mill length increased from 3.6 to 10.8 cm, the shoulder angle decreased from 73 to 62° (85% of critical speed; 25% filling). The shoulder position moved towards the 12 o'clock position when the mill length was short than 10.8 cm. The increase in the shoulder position angle as the mill speed and filling increased was also recorded which was higher than that of the toe. In Fig. 6 variation of impact point position with liner type, mill filling and speed is shown. When the mill length increased from 3.6 cm to 10.8 cm, the impact point locations moved from 208 to 235° (70% of critical speed; 25% filling). This meant that the charge impacted the liners at lower angles. It was concluded that on average the 3.6 cm length mill elevated the impact point of the charge up to 20°. For the mill longer than 10.8 cm the variation in impact point locations was not found significant. As expected, the increase in the mill speed and filling decreased the impact point positions but the change was more pronounced in the case of the mill speed. The study of the charge trajectory and shape variations in all tests indicated that when the mill length was below 10.8 cm there were lower than 12 layers of balls along the mill length. In this situation, the end-walls exerted additional force to the layers of charge
The torque of the load at different operating conditions was measured in the mill with a length of 21.6 cm (known as 3D mill) when liner No. 4 was used. To identify the maximum torque, different charge shapes were generated by varying the mill speed from 55% to 85% (Fig. 7). The snapshots of the mill charge captured by the high speed camera are also shown in Fig. 7. The trend of the torque change with the mill speed indicates a maximum. The gradual increase in the torque was due to lifting the charge to a higher point (moving from mill speed 55 to 76% Cr.S.). In this situation the centre of gravity moves upwards and towards the mill shell. In other words, the load is lifted up along the mill shell. At 76% of critical speed, a maximum torque is observed beyond which the centre of gravity of the whole load begins to move towards the centre of the mill, as it is seen at 85% of critical speed (Fig. 7). The reduction in the measured torque can also be related to lower impact point angles which assists the rotation of the mill. 3.5. Charge shape and trajectory in the 10.8 cm length model mill To investigate the charge shape and trajectory in the 10.8 cm length model mill a set of experiments were performed for liners No. 1 and No. 2 with steel balls. The variation of shoulder and impact point positions with liner type, mill filling and speed is shown in Fig. 8. When the mill speed was 85% the shoulder angle was 42.9° but for the 3.6 cm length mill it was found to be 61°. An increase of 18.1° in the shoulder position and 9° for the toe position was the contribution of the end-wall effect. Nevertheless, the trends of change of shoulder and impact point positions with mill filling for both mills were similar. In the case of the impact point position for the shorter mill at the same conditions (85% Cr.S.; liner No. 1; 30% filling) the angle was 10° lower than that of the longer mill. The difference in the shoulder and impact points of liners No. 1 and No. 2 originates from the significant change in the lifter height due to wear. 3.6. Comparison of the measured data and DEM simulated results Three-dimensional DEM simulations were performed at the same operating conditions in order to predict the charge shape and impact point. In this research, the academic version of the DEM solutions software, KMPCDEM, was used. Fig. 9 shows the typical images taken from the experiment, DEM simulations of 10.8-cm and 21.6-cm model mills
Fig. 8. Variation of shoulder (a) and impact point (b) positions (mill length: 10.8 cm; 85% of critical speed).
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Fig. 9. The typical images taken from the (a) experiment, (b) DEM simulations of 11.8-cm model mill and (c) DEM simulations of 21.6-cm model mill (liner No. 1, 5% filling, 60% of critical speed).
at the same operating conditions (liner No. 1, 5% filling, 60% of critical speed). There is a good agreement between the simulated and measured positions of shoulder, toe, and impact points. The DEM simulation results (Fig. 9a and b) also reconfirmed that above the 10.8 cm length mill the end-wall effect was negligible. 4. Conclusions - The end-wall effects were investigated in a model mill with the diameter of 100 cm by gradually increasing its length from 3.6 cm to 21.6 cm. - A significant end-wall effect was observed when the mill length was smaller than 10.8 cm and there were lower than 12 layers of balls along the mill length. The end-walls essentially exerted an additional force to the layers of charge and increased the amount of balls in free flight which resulted in the lower impact point angles and torque. - The end-wall effect which occurred in mills with the length of 3.6 cm resulted in an average of 13° increase in the shoulder position and 9° reduction in the toe angle compared to the case with no endwall effect. - When the mill length was short (i.e., 3.6 cm), due to bridging between the end-walls and interlocking of the particles, the torque decreased from 3.7 to 2.2 kgf·m for different charge shapes obtained by varying the mill speed from 55% to 85%. However, in the mill with a length of 21.6 cm the torque started from 5.9 kgf·m for the 55%, increased to peak (6.3 kgf·m) at around 75% and then dropped off (6 kgf·m) for 85% of critical speed. - The end-wall effect was more pronounced (i.e., a difference of 22% in torque reduction) when media used were iron ore particles instead of steel balls. This was attributed to higher interlocking of irregular particles in comparison to spherical balls.
- Three-dimensional DEM simulations using KMPCDEM reconfirmed the experimental conclusions indicating that the end-wall effect on the 10.8-cm length and longer model mills with a diameter of 100 cm is negligible.
Acknowledgements The authors would like to thank Gol-E-Gohar Iron ore company and the Sarcheshmeh copper complex for supporting of this research and permission to publish the article. Special appreciation is also extended to the operating, maintenance, metallurgy and R&D personnel for their continued help. References Cleary, P.W., 2009. Ball motion, axial segregation and power consumption in a full scale two chamber cement mill. Miner. Eng. 22 (9–10), 809–820. Kallon, D.V.V., Govender, I., Mainza, A.N., 2011. Circulation rate modelling of mill charge using position emission particle tracking. Miner. Eng. 24, 282–289. McElroy, L., Bao, J., Yang, R.Y., Yu, A.B., 2009. A soft-sensor approach to flow regime detection for milling processes. Powder Technol. 188, 234–241. Mishra, B.K., Rajamani, R.K., 1990. Numerical simulation of charge motion in ball mill. 7th European Symposium on Comminution, pp. 55–563. Morrell, S., 1993. The Prediction of Power Draw in Wet Tumbling Mills. University of Queensland, Australia (Doctorate Thesis). Nierop, M.A., Glover, G., Hinde, A.L., Moys, M.H., 2001. A discrete element method investigation of the charge motion and power draw of an experimental two-dimensional mill. Int. J. Miner. Process. 61, 77–92. Powell, M.S., Govender, I., McBride, A.T., 2008. Applying DEM output to the unified comminution model. Miner. Eng. 21, 744–750. Rajamani, R., 2006. Semi-autogenous mill optimization with DEM simulation software. Adv. Commun. SME Publ. 4, 209–214. Santomaso, A., Olivi, M., Canu, P., 2004. Mechanisms of mixing of granular materials in drum mixers under rolling regime. Chem. Eng. Sci. 59 (16), 3269–3280. Liu, X., Ge, W., Xiao, Y., Li, J., 2008. Granular flow in a rotating drum with gaps in the side wall. Powder Technol. 182, 241–249.
Contents lists available at ScienceDirect
International Journal of Mineral Processing journal homepage: www.elsevier.com/locate/ijminpro
The impact of end-wall effect on the charge trajectory in tumbling model mills M. Maleki-Moghaddam, A.R. Ghasemi, M. Yahyaei, S. Banisi ⁎ Shahid Bahonar University of Kerman, Mining Engineering Group, Engineering Faculty, Islamic Republic Blvd., Kerman, P.O. Box 761175-133, Iran
a r t i c l e
i n f o
Article history: Received 27 June 2014 Received in revised form 10 September 2015 Accepted 7 October 2015 Keywords: Comminution SAG mill Charge shape Impact point
a b s t r a c t Direct observation of the charge shape and its motion in industrial mills is not possible, it is then customary to use transparent end, small-scale mills (i.e., model mills) to determine the charge trajectory directly by visualization methods. Because of a short length of the model mills, the end-wall effects could introduce a significant bias on the observed charge trajectories and shape. In this research, the end-wall effect was investigated by gradually increasing the model mill length and analysing the charge trajectory and shape variation at given operating conditions (i.e., ball filling, mill speed, liner type). The special design of the model mill with the diameter of 100 cm made it possible to increase the mill length in steps of 3.6 cm up to 21.6 cm. Four types of liners, five steel ball fillings (10, 15, 20, 25, 30% v/v) and three mill speeds (55, 70, 85% of critical speed) were tested. The results indicated that when the mill length was below 10.8 cm the end-walls prevented the charge from free falling. This resulted in lower impact point angles and lower power draws compared with the case of no end-wall effect. When the same experiments were performed using an iron ore instead of balls with the same size range, the impact of end-wall effect was more pronounced. For a mill length of 3.6 cm, an increase of 30% in the speed (from 55 to 85%) with the iron ore charge, the torque decreased by 41% (from 3.7 to 2.2 kgf·m) when mill filling was 30%. At the same operating conditions, when steel balls were used the torque decreased only by 19% (from 9 to 7.2 kgf·m). Three-dimensional DEM simulations also resulted in similar conclusions. © 2015 Elsevier B.V. All rights reserved.
1. Introduction Grinding is the most energy intensive operation which constitutes the major portion of operating and capital costs of mineral processing plants. Hence, a vast number of research works have been carried out with the aim of performance improvement (Mishra and Rajamani, 1990; McElroy et al., 2009). Direct observation of charge shape and its motion in industrial mills is not possible, it is then customary to use transparent end, small-scale mills (i.e., model mills) to determine the charge trajectory directly by visualization methods. Morrell (1993) used a laboratory mill with one transparent end and photographed the load under various operating conditions. Then he proposed various empirical equations to relate the positions of toe and shoulder and inner load radius to mill speed and filling. Kallon et al. (2011) developed and tested a model linking the circulation rate of charge particles with physical mill parameters using experimental data derived from positron emission particle tracking (PEPT). Traditionally, the optimization and design of grinding circuits have been based on costly and time-consuming laboratory experimentation and pilot plant testing. One solution which could be beneficial is to use numerical tools, such as the discrete element method (DEM), which could be ⁎ Corresponding author. E-mail address: [email protected] (S. Banisi).
http://dx.doi.org/10.1016/j.minpro.2015.10.005 0301-7516/© 2015 Elsevier B.V. All rights reserved.
used to predict the behaviour of granular materials. DEM is a technique which requires minimal experimental effort, and its results can be easily scaled up from the laboratory to industrial size mills. Currently, this method is commonly used particularly in modelling AG and SAG mills due to the complexity of these machines (Mishra and Rajamani, 1990; Rajamani, 2006; Powell et al., 2008; McElroy et al., 2009). Nevertheless, experimental validation is the most important step in the process of testing codes. The most frequently applied validation methodologies are ball trajectory tracking and power draw monitoring in laboratory scale mills (van Nierop et al., 2001). This demonstrates that the endwall effects are very important contributors to the accuracy of the simulation and experimental results. A number of researchers have also addressed the influence of endwall boundaries on the flow of the granular materials in rotating drums. For example, Cleary (2009) studied the axial transport of the particles in a ball mill and showed that looking along the shoulder from the feed end towards the grate one can see that the shoulder is distinctly higher at the ends and lower in the middle. The frictional interaction with the rotating end-walls supports and lifts the nearby charge more leading to noticeably higher shoulder positions. Far from the end-wall effect the charge slumps more and has a lower shoulder and higher toe position. Experiments in fully closed drums also indicate that the end-walls may initiate the axial band formation of segregated particles (Liu et al., 2008). In other words, particles with specific size
76
M. Maleki-Moghaddam et al. / International Journal of Mineral Processing 144 (2015) 75–80
Table 1 Main characteristics of four industrial liners used.
Sarcheshmeh (New liner) Sarcheshmeh (Worn liner) Gol-E-Gohar (old liner) Gol-E-Gohar (New liner)
Liner number
No. of lifters in rows
Liner width (mm)
Lifter height (mm)
Lifter face angle (°)
1
60
250
152
14
2
60
250
90
62
3
36
125
225
7
4
36
125
225
30
and density could be accumulated in certain locations along the mill axis. As to flow patterns, Santomaso et al. (2004) suggested that friction plays an important role at the end plates; the crucial role of the plates could be observed by about 10% increase of the surface slope because of the friction of the bed with the end-walls. Recently, it was demonstrated that this effect is localized to the end-walls when the axial length of the drum is greater than its diameter (Liu et al., 2008). They concluded that the end-wall effect becomes significant as the mill length decreases. Since the model mill length at which the end-wall effect could be assumed to be negligible has not been addressed extensively, in this research this issue was investigated experimentally. This task was fulfilled by gradually increasing the model mill length and analysing the charge trajectory and shape variation at a given operating condition (i.e., ball filling, mill speed, liner type). 2. Methodology 2.1. The model mill The model mill with the diameter of 100 cm and special design made it possible to increase the mill length in steps of 3.6 cm up to 21.6 cm. In other words, the mill length could be increased by 6-fold. The transparent end of the mills made accurate trajectory determination possible by taking film and photographs. A 2.5 kW motor with a variable speed drive was used which provided sufficient flexibility to test various operating conditions. The scale down ratios of 9 to 1 and 10 to 1 was used to construct the model mill using mill dimensions of two plants. In order to exactly duplicate the plant liner arrangements in the mill, four types of 3.6 cm-long polyurethane rings, which were scaled-down versions of the liners, were accurately machined to be used in the model mill. The choice of polyurethane over steel liners was because of
easier machining which was crucial in duplicating the plant liner arrangements. The tests performed in the model mill using steel and polyurethane liners did not show any change in the charge trajectory indicating that the effect of change in the friction coefficients of the liners on the charge trajectory could be neglected. The four liner types were: new and worn (after 5184 h of operation) liners of SAG mill at the Sarcheshmeh copper complex, and old and new liners of AG mills at the Gol-E-Gohar Iron ore company which were numbered from 1 to 4, respectively (Table 1). In this research, the end-wall effect was investigated by gradually increasing the model mill length from 3.6 cm up to 21.6 cm. Fig. 1 shows a scaled-down model of the liner No. 3 and 10.8 cm-long mill fitted by three liners each with the length of 3.6 cm (new liner of the Gol-E-Gohar Iron ore company AG mill). 2.2. Measurement details The main aim of the experimental stage was to determine how the shape of the mill charge changed as the mill length, lifter type, the volume of the charge and rotational speed were varied. Experiments were performed for each type of liner in the model mill. The mill charge consisted of 4 to 12 mm diameter steel and plastic (62.5% 10–12 mm, 32.5% 7–9 mm and 5% 4–6 mm). The plastic balls used to keep the weight of the mill in the range of the torque metre especially when the mill length was in its maximum (i.e., 21.6 cm). Experiments were also conducted using an iron ore only with the same size distribution of balls. A transparent plexiglass faceplate made photographing of the tumbling charge possible. The model mill was operated at 55, 70 and 85% of critical speed (Cr.S.) for five levels of mill filling (10, 15, 20, 25 and 30% by volume). The shoulder, toe and charge impact points were measured in degrees starting from the horizontal line passing the mill centre (i.e., 3 o'clock position) and moving counter clockwise. A typical snapshot of the charge shape and charge impact point is shown in Fig. 1b. The experimental mill was also equipped with a torque sensor. During the tests, the mill torque was measured and recorded with a high speed card recorder. The tumbling ball charge was photographed with a high-speed camera (240 fps). To increase the accuracy of the results, more than 20 photographs during a period of 2 min were used to measure the angular displacement of the toe, shoulder and charge impact point; the average values and standard deviations were then reported. An electronic protractor (MB-Ruler version 4.0) and an angular grid with 1° intervals were used to determine the positions. To re-examine the measurements' accuracy, all tests were repeated and photographed by another camera (90 fps). The difference between the results obtained by two cameras was found to be less than 2° indicating a reasonable accuracy. The charge impact point and shape
Fig. 1. (a) 3.6 cm-long scaled-down model of new liner of the Gol-E-Gohar Iron ore company AG mill; (b) 10.8 cm-long mill fitted by three liners each with the length of 3.6 cm.
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Fig. 2. Variation of shoulder (a) and impact point (b) positions with liner type, speed and mill filling.
variation were analysed by increasing the model mill length from 3.6 cm to 21.6 cm.
3. Results and discussions 3.1. Charge shape and trajectory in the 2D model mill In order to determine the end-wall effect in the 2D model (i.e., short length) mill at different operating conditions, a 100 cm × 3.6 cm mill was used. As the mill rotates the charge is lifted up with the rising face of the mill until the shoulder is reached. At this point the bulk of the charge falls away towards the toe region. The toe angle is the highest point reached by the bulk of the charge in the toe region of the mill. The shoulder angle was chosen to be the point where the trajectories of the bulk particles near the lifters began to diverge from the mill shell. The variation of shoulder position with liner type, mill filling and speed is shown in Fig. 2a. The effect of liner type was not found significant given the measurement error. As expected, the increase in filling moved the shoulder position to higher angles. The same trend was observed for the mill speed because of the charge elongation (i.e., expansion of charge when speed is increased). For an increase of 30% in the speed (from 55 to 85% of critical speed), the shoulder angle increased by 21° (from 40 to 61°) when mill filling was 30%. The impact point position was assumed to be the point with the highest concentration of impacts on the liner by cataracting balls. The variation of impact point position with liner type, mill filling and speed is shown in Fig. 2b. As the amount of filling increased the impact points, on account of an increase in the force exerted from the charge,
Fig. 3. Variation of torque with the mill speed and liner types.
decreased. For liner No. 1, when the filling varied from 10 to 30% the impact points changed from 182 to 176°. Variation of toe location (measured in angles) with liner type, speed and mill filling was also determined. As expected, the position of toe changed as the mill filling increased. When the mill filling varied from 10 to 30%, the toe angle decreased from 248 to 217° (85% of critical speed; liner No. 1). The effect of liner type on the position of toe, at any given operational conditions, was not found significant considering the measurement error. 3.2. Torque variation in the 2D model mill The power drawn by the mill could be determined considering the ball contact forces acting on the liners and the load behaviour. The power is generally calculated by: Power ¼ 2πNτ
ð1Þ
where N is the mill rotation speed and τ is torque. In this study, torque which is directly proportional to the mill power draw was measured to study the effect of various parameters. Any change in the shape of charge and the amount of the charge in free flight will be reflected in the measured torque. It is important to note that the effect of an increase in the mill speed does not affect the torque by itself rather the change in the shape of the charge and the amount of charge in free flight cause the change in the torque. In other words, the change in the load behaviour (at a constant filling) due to the change in the mill speed and liner type is reflected in the torque measurements. The torque of the load at different operating conditions in the 3.6 cm long model mill was measured by a torque sensor. The variation of torque at three different charge shapes at constant filling of 30% was measured (Fig. 3). The three charge shapes were obtained by running the mill at 55%, 70%, and 85% of critical speed (Cr.S.), respectively, and using four types of liners. The results indicated that as the amount of charge in the free flight increased, the measured torque decreased. Since the mill length was short (i.e., 3.6 cm), due to some bridging between the end-walls and interlocking of the particles, the charge was lifted to a higher point. This resulted in a higher shoulder position and also the balls' impact points became closer to 9 o'clock and above positions. In this situation, these impacts helped the rotation of the mill (i.e., positive torque) and consequently the power draw decreased. In addition, the movement of toe towards lower angles (9 o'clock position) because of falling balls further decreased the measured torque (Fig. 3). It should be noted that there is a direct relationship between the amount of in-flight balls and the share of the balls' impact to locations close to the 9 o'clock and above positions which decrease the power draw. In other words, the higher the amount of in-flight balls the higher the power draw reduction because of impacts which assist the rotation of the mill.
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Fig. 4. Variation of toe location (measured in angles) with mill length and speed; (a) 15% filling; (b) 25% filling.
Fig. 5. Variation of shoulder location with liner length and speed; (a) 15% filling; (b) 25% filling.
In the case of the 36 mm long mill where balls with diameters from 5 to 12 mm are used there are likely to be only 4 layers of balls along the model mill length. The layer against the end window stacks effectively, resulting in an elevated trajectory which is not representative of the charge inside the industrial mills. Because in practice, the aspect ratios of industrial mills are larger. The tests were repeated but instead of steel balls an iron ore was used as the charge (size charge and amount of filling kept constant). The torque decreased by 41% (from 3.7 to 2.2 kgf·m) when the mill speed increased from 55 to 85%. Whereas, in the case of steel
balls this reduction was only 19% (from 9 to 7.2 kgf·m). These results indicated that when the ore was used the material shear strength produced by the interlocking of the non-circular shaped particles increased. This in turn decreased the impact point angles which led to lower torques. 3.3. Mill length and the end-wall effect In this research, the end-wall effect was investigated by gradually increasing the model mill length from 3.6 cm to 21.6 cm. In other words,
Fig. 6. Variation of impact point location with liner length and speed; (a) 15% filling; (b) 25% filling.
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and increased the balls in flight leading to the lower impact point angles and lower power draw. The experiments were also carried out using steel balls in 10.8 cm and 21.6 cm length mills. The comparison of charge shapes and impact points in these two mills showed that the end-wall effect was negligible in 10.8 cm-long and longer model mills. 3.4. Charge behaviour and torque variation
Fig. 7. Measured torque at different speeds and liners (liner No. 4; 25% filling).
the mill length could be increased in six intervals each with a length of 3.6 cm. Experiments were performed for liner No. 4 (Gol-E-Gohar new liner) using polyurethane balls and locations of the toe, shoulder and charge impact point were identified. Variation of toe location with mill length and speed is shown in Fig. 4. Note that only two mill fillings (10 and 25%) are given in Fig. 4. At the short mill length (i.e., 3.6 cm) the toe position is higher and compared to the 10.8 cm-length mill the toe moved to the 9 o'clock position by 9° (i.e., lower toe angle values). Above the 10.8 cm-length mill the variation in toe locations was not found significant which indicated no end-wall effect situation. By increasing the mill speed and mill filling due to the charge elongation the toe position moved towards the 9 o'clock position. The variation of shoulder position with the mill length and speed is shown in Fig. 5. When the mill length increased from 3.6 to 10.8 cm, the shoulder angle decreased from 73 to 62° (85% of critical speed; 25% filling). The shoulder position moved towards the 12 o'clock position when the mill length was short than 10.8 cm. The increase in the shoulder position angle as the mill speed and filling increased was also recorded which was higher than that of the toe. In Fig. 6 variation of impact point position with liner type, mill filling and speed is shown. When the mill length increased from 3.6 cm to 10.8 cm, the impact point locations moved from 208 to 235° (70% of critical speed; 25% filling). This meant that the charge impacted the liners at lower angles. It was concluded that on average the 3.6 cm length mill elevated the impact point of the charge up to 20°. For the mill longer than 10.8 cm the variation in impact point locations was not found significant. As expected, the increase in the mill speed and filling decreased the impact point positions but the change was more pronounced in the case of the mill speed. The study of the charge trajectory and shape variations in all tests indicated that when the mill length was below 10.8 cm there were lower than 12 layers of balls along the mill length. In this situation, the end-walls exerted additional force to the layers of charge
The torque of the load at different operating conditions was measured in the mill with a length of 21.6 cm (known as 3D mill) when liner No. 4 was used. To identify the maximum torque, different charge shapes were generated by varying the mill speed from 55% to 85% (Fig. 7). The snapshots of the mill charge captured by the high speed camera are also shown in Fig. 7. The trend of the torque change with the mill speed indicates a maximum. The gradual increase in the torque was due to lifting the charge to a higher point (moving from mill speed 55 to 76% Cr.S.). In this situation the centre of gravity moves upwards and towards the mill shell. In other words, the load is lifted up along the mill shell. At 76% of critical speed, a maximum torque is observed beyond which the centre of gravity of the whole load begins to move towards the centre of the mill, as it is seen at 85% of critical speed (Fig. 7). The reduction in the measured torque can also be related to lower impact point angles which assists the rotation of the mill. 3.5. Charge shape and trajectory in the 10.8 cm length model mill To investigate the charge shape and trajectory in the 10.8 cm length model mill a set of experiments were performed for liners No. 1 and No. 2 with steel balls. The variation of shoulder and impact point positions with liner type, mill filling and speed is shown in Fig. 8. When the mill speed was 85% the shoulder angle was 42.9° but for the 3.6 cm length mill it was found to be 61°. An increase of 18.1° in the shoulder position and 9° for the toe position was the contribution of the end-wall effect. Nevertheless, the trends of change of shoulder and impact point positions with mill filling for both mills were similar. In the case of the impact point position for the shorter mill at the same conditions (85% Cr.S.; liner No. 1; 30% filling) the angle was 10° lower than that of the longer mill. The difference in the shoulder and impact points of liners No. 1 and No. 2 originates from the significant change in the lifter height due to wear. 3.6. Comparison of the measured data and DEM simulated results Three-dimensional DEM simulations were performed at the same operating conditions in order to predict the charge shape and impact point. In this research, the academic version of the DEM solutions software, KMPCDEM, was used. Fig. 9 shows the typical images taken from the experiment, DEM simulations of 10.8-cm and 21.6-cm model mills
Fig. 8. Variation of shoulder (a) and impact point (b) positions (mill length: 10.8 cm; 85% of critical speed).
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Fig. 9. The typical images taken from the (a) experiment, (b) DEM simulations of 11.8-cm model mill and (c) DEM simulations of 21.6-cm model mill (liner No. 1, 5% filling, 60% of critical speed).
at the same operating conditions (liner No. 1, 5% filling, 60% of critical speed). There is a good agreement between the simulated and measured positions of shoulder, toe, and impact points. The DEM simulation results (Fig. 9a and b) also reconfirmed that above the 10.8 cm length mill the end-wall effect was negligible. 4. Conclusions - The end-wall effects were investigated in a model mill with the diameter of 100 cm by gradually increasing its length from 3.6 cm to 21.6 cm. - A significant end-wall effect was observed when the mill length was smaller than 10.8 cm and there were lower than 12 layers of balls along the mill length. The end-walls essentially exerted an additional force to the layers of charge and increased the amount of balls in free flight which resulted in the lower impact point angles and torque. - The end-wall effect which occurred in mills with the length of 3.6 cm resulted in an average of 13° increase in the shoulder position and 9° reduction in the toe angle compared to the case with no endwall effect. - When the mill length was short (i.e., 3.6 cm), due to bridging between the end-walls and interlocking of the particles, the torque decreased from 3.7 to 2.2 kgf·m for different charge shapes obtained by varying the mill speed from 55% to 85%. However, in the mill with a length of 21.6 cm the torque started from 5.9 kgf·m for the 55%, increased to peak (6.3 kgf·m) at around 75% and then dropped off (6 kgf·m) for 85% of critical speed. - The end-wall effect was more pronounced (i.e., a difference of 22% in torque reduction) when media used were iron ore particles instead of steel balls. This was attributed to higher interlocking of irregular particles in comparison to spherical balls.
- Three-dimensional DEM simulations using KMPCDEM reconfirmed the experimental conclusions indicating that the end-wall effect on the 10.8-cm length and longer model mills with a diameter of 100 cm is negligible.
Acknowledgements The authors would like to thank Gol-E-Gohar Iron ore company and the Sarcheshmeh copper complex for supporting of this research and permission to publish the article. Special appreciation is also extended to the operating, maintenance, metallurgy and R&D personnel for their continued help. References Cleary, P.W., 2009. Ball motion, axial segregation and power consumption in a full scale two chamber cement mill. Miner. Eng. 22 (9–10), 809–820. Kallon, D.V.V., Govender, I., Mainza, A.N., 2011. Circulation rate modelling of mill charge using position emission particle tracking. Miner. Eng. 24, 282–289. McElroy, L., Bao, J., Yang, R.Y., Yu, A.B., 2009. A soft-sensor approach to flow regime detection for milling processes. Powder Technol. 188, 234–241. Mishra, B.K., Rajamani, R.K., 1990. Numerical simulation of charge motion in ball mill. 7th European Symposium on Comminution, pp. 55–563. Morrell, S., 1993. The Prediction of Power Draw in Wet Tumbling Mills. University of Queensland, Australia (Doctorate Thesis). Nierop, M.A., Glover, G., Hinde, A.L., Moys, M.H., 2001. A discrete element method investigation of the charge motion and power draw of an experimental two-dimensional mill. Int. J. Miner. Process. 61, 77–92. Powell, M.S., Govender, I., McBride, A.T., 2008. Applying DEM output to the unified comminution model. Miner. Eng. 21, 744–750. Rajamani, R., 2006. Semi-autogenous mill optimization with DEM simulation software. Adv. Commun. SME Publ. 4, 209–214. Santomaso, A., Olivi, M., Canu, P., 2004. Mechanisms of mixing of granular materials in drum mixers under rolling regime. Chem. Eng. Sci. 59 (16), 3269–3280. Liu, X., Ge, W., Xiao, Y., Li, J., 2008. Granular flow in a rotating drum with gaps in the side wall. Powder Technol. 182, 241–249.