Determination of lifter design, speed and filling effects in AG mills.pdf

Minerals Engineering 17 (2004) 1135–1142 This article is also available online at: www.elsevier.com/locate/mineng

Determination of lifter design, speed and filling effects in AG mills by 3D DEM N. Djordjevic *, F.N. Shi, R. Morrison Julius Kruttschnitt Mineral Research Centre, The University of Queensland, Brisbane 4068, Australia Received 28 April 2004; accepted 1 June 2004

Abstract The power required to operate large gyratory mills often exceeds 10 MW. Hence, optimisation of the power consumption will have a significant impact on the overall economic performance and environmental impact of the mineral processing plant. In most of the published models of tumbling mills (e.g. [Morrell, S., 1996. Power draw of wet tumbling mills and its relationship to charge dynamics, Part 2: An empirical approach to modelling of mill power draw. Trans. Inst. Mining Metall. (Section C: Mineral Processing Ext. Metall.) 105, C54–C62. Austin, L.G., 1990. A mill power equation for SAG mills. Miner. Metall. Process. 57–62]), the effect of lifter design and its interaction with mill speed and filling are not incorporated. Recent experience suggests that there is an opportunity for improving grinding efficiency by choosing the appropriate combination of these variables. However, it is difficult to experimentally determine the interactions of these variables in a full scale mill. Although some work has recently been published using DEM simulations, it was basically limited to 2D. The discrete element code, Particle Flow Code 3D (PFC3D), has been used in this work to model the effects of lifter height (5– 25 cm) and mill speed (50–90% of critical) on the power draw and frequency distribution of specific energy (J/kg) of normal impacts in a 5 m diameter autogenous (AG) mill. It was found that the distribution of the impact energy is affected by the number of lifters, lifter height, mill speed and mill filling. Interactions of lifter design, mill speed and mill filling are demonstrated through three dimensional distinct element methods (3D DEM) modelling. The intensity of the induced stresses (shear and normal) on lifters, and hence the lifter wear, is also simulated. 2004 Elsevier Ltd. All rights reserved. Keywords: Comminution; Grinding; Modelling; DEM

1. Introduction The power required to operate large mills often exceeds 10 MW. Therefore, optimisation of the power utilisation will have a significant impact on the overall economic performance and environmental impact of the mineral processing plant. Recent experience suggests that there is an opportunity for improving grinding effi* Corresponding author. Present address: JKMRC, Isles Road, Indooroopilly 4096, Australia. Tel.: +61 7 3365 5888; fax: +61 7 3365 5999. E-mail address: [email protected] (N. Djordjevic).

0892-6875/$ - see front matter 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.mineng.2004.06.033

ciency by choosing the appropriate combination of mill speed, filling and lifter design. However, it is difficult to experimentally determine the interactions of these variables in a full scale mill. The discrete element method (DEM) has been proved to be a useful tool in milling simulation and optimisation. A number of papers have been published in the literature by using DEM in modelling and simulation of comminution devices, majority of them being limited in 2D. Hlungwani et al. (2003) used a 2D laboratory ball mill to validate the DEM modelling of liner profile and mill speed effects. Cleary (1998, 2001) used DEM to investigate charge behaviour and power consumption

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N. Djordjevic et al. / Minerals Engineering 17 (2004) 1135–1142

in relation to operating conditions, liner geometry and charge composition in a 5 m ball mill, also limited to the 2D code. In the present work, Particle Flow Code 3D (PFC3D) has been used to model the effects of lifter height (5– 25 cm) and mill speed (50–90% of critical) on the power draw and frequency distribution of specific energy (J/kg) of normal impacts in a 5 m diameter autogenous grinding (AG) mill, with a mill charge volume varying between 7% and 20%. The trends established from the DEM study will be incorporated in developing a new tumbling mill model at the Julius Kruttschnitt Mineral Research Centre (JKMRC). 2. Discrete element modelling Particle Flow Code 3D (ITASCA Inc., 1999) models the behaviour of particles, which may be enclosed within a finite volume by non-deformable walls. The code keeps a record of individual particles and updates any contact with other particles or walls. Each calculation step includes application of the NewtonÕs laws of motion to all particles, a force–displacement law to each contact, and constant updating of the walls positions. PFC3D modelling is based on the assumption that the individual particles (balls) can be treated as rigid bodies. At contacts, rigid particles are allowed to overlap. The magnitude of the overlap is related to the contact force. There overlaps are small relative to the size of the particles. During contact, the behaviour of a material is simulated using a linear contact model. The contact force vector between two balls or ball and wall is composed of normal and shear components. The normal contact force vector is calculated using the formula: F n ¼ K n U n ni

The energy state of the entire set of particles can be examined by recording various forms of energy. Frictional work is defined as the total cumulative energy dissipated by frictional sliding at all contacts. Intensity of deformation can be assessed using strain energy, which is defined as the total strain energy stored at all contacts assuming a linear contact-stiffness model. The PFC3D model of the mill is composed of a number of walls which represent mill liner and lifters as well as balls which represents mill charge. The power of the mill is calculated for each instant of time by summing products of moments applied to the liner and lifters and rotational velocity of the mill. Power calculated with DEM refers to the net power associated with mill charge. Power required to rotate the empty mill (no-load power) cannot be modelled using PFC3D. The no-load power is determined by the efficiency of particular mill design, mill size and its rotational velocity. No-load power is about 5–10% of the gross power draw under typical working conditions (Morrell, 1996).

3. Effect of number of lifters on power utilization Previous work (Djordjevic, 2003) demonstrated that from the point of view of power draw modelling, a cylindrical tumbling mill could be represented with a vertical slice, where thickness of the slice was 20% of the mill length. In the absence of fluid flow in the mill, translational displacements of the charge along the length of the mill are minimal. The net-power draw of 1 m thick slice of 5 m diameter mill is modelled in this work. The charge of the modelled mill (Figs. 1 and 2), is composed of spherical particles in the range 20–150 mm diameter (Table 1). Net power draw was modelled for the case of mill with 30 identical rectangular shaped lifters. The lifter thickness was fixed at 10 cm in all cases. Height

where Fn is the normal contact force vector; Kn is normal stiffness at the contact; Un is the relative contact displacement in the normal direction and ni is unit normal vector. The incremental shear force is calculated using the formula: DF s ¼ K s DU s where Ks is the shear stiffness at contact and DUs is the incremental shear displacement at contact. PFC3D also includes a slip model. The slip model is defined by the friction coefficient at the contact, where the active relevant friction coefficient is taken to be the minimum friction coefficient of the two contacting entities. Each contact is checked for slip conditions, by calculating the maximum allowable shear contact force: F sðmaxÞ ¼ l jF n j where l is the friction coefficient.

Fig. 1. Charge shape for the mill without lifters, with coefficient of friction nil.


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Fig. 2. Charge shapes for the mill with lifters of various heights, all with a coefficient of friction 0.3: (a) no-lifter, (b) 5 cm lifters, (c) 10 cm lifters, (d) 15 cm lifters, (e) 20 cm lifters, and (f) 25 cm lifters. Table 1 Particle size distribution of the modelled mill charge Particle diameter (mm)

Number of particles

150 + 90 90 + 75 75 + 53 53 + 37.5 37.5 + 28 28 + 20

96 164 290 684 1336 2378

Total

4948

of the lifters varied between 5 and 25 cm. For each lifter geometry, the rotational velocity of the mill was varied in the range 50–90% of critical speed. In order to determine the effect of lifters and mill speed on the effective power draw of the mill it is necessary to determine the power draw without any lifting action first. This can be achieved by calculation of the no-lifters power with a coefficient of friction being set to nil. It is possible that in such a case, power draw will be minimal or nil, due to the symmetric shape of the charge around the vertical axis of the mill, Fig. 1.

The second phase includes introduction of the mill friction. The third phase includes introduction of lifters of constant width and number, but of different height. For each lifter height power draws at different mill speeds were determined. By comparing modelled power draws with those of the no-lifter mill, the effect of each new variable of mill design and operating conditions can be determined. In the simulations normal and shear stiffness of the particles were set 1 · 105 N/m and density 2650 kg/m3. The power draw of the mill comprises the power consumed in rotating the empty mill (no-load power), to abrade the charge without lifting the particles, and to lift the charge which may eventually result in impact breakage. Note that this is not the same as the no-load power in a real mill which requires energy to overcome friction in bearing and losses within mill motor. In the case of mill without lifters and in which the coefficient of friction is set to zero, the power draw of the real mill is only a form of no-load power. There is no power being transferred to the charge. The essential role of lifters is highlighted by the fact that without them there would be essentially no net-power draw (assuming

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nil friction), and consequently no comminution. In such case only this ‘‘no-load’’ power will be drawn and it will be completely wasted. As a result, the throughput of the machine will be nil. In the case of a mill which has some finite effective coefficient of friction (0.3) and charge which is also characterised with same coefficient of friction, net power draw has a value of 49 kW per unit of length of the modelled mill. The entire power is consumed through abrasion of the charge and leads to gradual size reduction. Net-power consumed by the mill without lifters is referred as no-lifter power. When the same mill is equipped with lifters, the mill will draw additional power for impact breakage and more intensive abrasion. The introduction of 5 cm high lifters increases net power draw to 77 kW per unit length of the modelled mill. Hence, an additional 28 kW power is consumed for producing high energy impacts. This indicates that abrasive action in the form of low energy impacts and shearing between particles and balls within the charge is the prevailing mechanism of power consumption within the mill. The increased power is consumed in introduction of impacts due to free falling particles as well as faster movement of the particles on top of charge and within the charge. Lifters are able to more efficiently transfer motion from the mill shell into the motion of the charge. However dominant part of the introduced net energy into the charge (63%) is consumed through low energy shearing between particles, or between particles and mill liners.

4. Effect of mill filling on power utilization The fraction of net-power draw that will be consumed by shearing and abrasion is determined by the charge volume. In the case of mill with 500 particles (7 vol%), no-lifter power is about 52% of the net power draw with lifters. In the case of mill with 1500 particles (20 vol%) no-lifter power represents 70.5% of total net power of the mill equipped with 5 cm high lifters (Fig. 3). Hence as the charge volume increases, the greater fraction of the net power draw will be consumed in the form of charge abrasion and low energy impacts, while the fraction of the net power that leads to high energy impacts will gradually decrease. Fig. 3 also shows that as the lifter height increases, a greater fraction of the power will be used without high intensity impacts. An increase in lifter height results in a reduced net power draw, which leads to an increased ratio of no-lifter net power to net power. In a current JKMRC SAG mill modelling approach, the relationship of size reduction and high intensity impact energy is experimentally determined with a drop weight test (Napier-Munn et al., 1996), and that of size reduction with the low intensity abrasion energy is

Fig. 3. Effect of mill filling on net power utilization.

measured through tumbling test. A key feature of the JKMRC AG/SAG model is that ratio of impact to abrasion breakage varies with size distribution in the mill load. Abrasion breakage dominates for coarse particles and impact breakage is the main mechanism for fine particles. However, the same relationship is used regardless of the mill filling and lifter design. While this assumption is adequate for industrial mills which operate at load close to maximum load, this modelling approach is not appropriate in terms of the trends demonstrated in Fig. 3 for mills with wide range of mill loads. Particle motion within the mill is different with different mill filling levels. In the extreme case of single particle, motion is essentially highly reproducible, and characterised by a period when particle is in touch with liner, the period of free fall and period of bouncing at the base of mill, Fig. 4. In the case of a particle within the mill charge, the dominant part of particle motion occurs within the main body of the charge, eventually followed by the lifting of the particle, free fall and high intensity impact. While particle is within the charge it becomes subjected to numerous low-intensity force applications which should result in a gradual size reduction due to abrasion.

5. Influence of lifter number, height and mill speed on net power draw The effect of the number of lifters on net power draw is clearly illustrated in Fig. 5. Power draw increases from a non-zero value to a stable value. After certain number of lifters a further increase in the number of lifters will not increase net power draw of the mill. This perhaps explains why the number of lifters is not included as a parameter in the empirical models of power draw. In practice all mills have more than the necessary number


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Fig. 4. Pattern of particle motion for the case of mill with singular particle (left) and for the case of mill with 1000 particles (right).

net power draw(kW)

70 60 50 40 30 20 10 0 2

4

6

10

14

18

22

number of lifters

net power draw (kW)

Fig. 5. Effect of number of lifters on the net power draw (lifter height 20 cm, width 10 cm).

80 60 40 20 0 5cm

15cm

20cm

25cm

lifter height

80 60 40 20 0 5cm

(c)

10cm 15cm 20cm lifter height (cm)

80 60 40 20 0

(b)

net power draw (kW)

net power draw (kW)

(a)

10cm

of lifters required for onset of steady state power draw. However, investigation in the angle of the loading edge of the lifter is not conducted in this study. Influence of lifter height on net power draw is presented in Fig. 6. The sensitivity of the power draw to the lifter height is much higher than what might be expected due to change of effective diameter of the mill. The mill with low lifters tends to draw higher power than the mill with higher lifters. Similar trends have been reported in literature (Cleary, 2001; Hlungwani et al., 2003). Higher lifters will result in more frequent impact events while consuming less power. Fig. 6 demonstrates that the influence of lifter height on net power draw increases as the mill rotational velocity increases. This is due to the fact that propensity for

net power draw (kW)

80

5cm


25cm

5cm


25cm

80 60 40 20

25cm

(d)

0

Fig. 6. The effects of lifter height on net power draw for various mill speeds (5 m mill with 30 lifters). (a) 90% critical speed, (b) 80% critical speed, (c) 70% critical speed, and (d) 60% critical speed.

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N. Djordjevic et al. / Minerals Engineering 17 (2004) 1135–1142 force (N) x10^3

resultant force (N) x10^3

3.0

3.0

2.8

2.8

2.6

2.6

2.4

2.4

2.2

2.2

2.0

2.0

1.8

1.8

1.6

1.6

1.4

1.4

1.2

1.2

1.0

1.0

0.8

0.8

0.6

0.6

0.4

0.4 0.2

0.2 0.

0.0

0.0 0.5

1.0

1.5

2.0

2.5

3.0

0.5

1.0

1.5

time (sec) x10^1

2.0

2.5

3.0

time (sec) x10^1

net-power draw (kW)

net-power draw (kW)

Fig. 7. Resultant force time history for the case of 5 cm high lifters (left) and 15 cm high lifters.

120

120

100 80

100 80 60 40 20 0 80

(a)

100

150

200

240

60 40 20 0 80

300

particle diameter (mm)

(b)

100

150

200

240

300

particle diameter (mm)

Fig. 8. Effect of the particle size on the net power draw of the mill. (a) Constant lifter height 30 cm and (b) lifter height = 80% particle diameter.

centrifuge will increase with the increases of lifter height and mill speed. Rotational velocity of the modelled mill is calculated based on the dimension of mill shell, ignoring height of the lifters. As the probability of centrifuge is minimal for a slower velocity, the effect of lifter height on power draw is insignificant. However, as the modern mills often operate at about 75% of critical speed or higher, the influence of the lifter height on power draw is significant. Influence of the lifter height can also be observed through the intensity of forces that are acting on typical particles within the mill. In the case of low lifters (e.g. 5 cm), the average forces that are acting on a particle are much smaller than that with higher lifters (e.g. 15 cm). In addition to that, in the case of higher lifters there is a much higher probability that particles will be lifted, resulting in their free fall and high intensity impacts. This is illustrated in Fig. 7, showing the time history of the resultant force acting on a single particle of 10 cm diameter (within the charge) for the mill equipped with 5 and 15 cm high lifters respectively. In all discussions about the power draw of the mills it is important to consider the nature of the charge size distribution. The impact of particle size on the net power draw is clearly highlighted in Fig. 8. The mill charge is composed of mono size particles. Fig. 8a shows that there is a large increase in power draw when particles be-

come much smaller than the lifter height (30 cm). However, when the ratio of the lifter height to particle diameter is kept constant (i.e. height = 80% of the diameter), the impact of particle diameter on the power draw becomes insignificant, as shown in Fig. 8b.

6. Intensity of stresses acting on lifters The lifter wear is directly proportional to the intensity of the induced stresses acting on the lifters. Stresses applied to the lifters were calculated from the moments acting on the lifter plates. From the moments and the known distance between lifters plate and centre of rotation, the average force was calculated. The average value of stress was then calculated from the average force and the area of the lifter. The stresses on the lifter were modelled for the case of vertical plate with the active side facing the charge, and for a plate corresponding to the flat top of the lifter. Considering that stresses are averaged over the entire surface of the lifter, the most significant factor is the mass of the particles. The force that opposes the motion of the vertical side of the lifter will predominantly act perpendicular to the plate. On the top of the lifter, the active force is a shear component of the predominantly vertical force induced by the mass of superimposed particles and the centrifugal force.


Fig. 9. Influence of number of lifters on the stress intensity applied on lifters.

Fig. 10. Impacts energy distribution.

Hence, stresses acting on the vertical side of the rectangular shaped lifter will be mostly in a perpendicular–normal direction, while stresses acting on the top of lifter will be predominantly shear stresses. Shear stresses will be responsible for the gradual wear of the lifters, resulting in a decrease of their height and reduction of milling efficiency. The modelled stresses show significant variation in stress intensity during each lifter revolution.

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The interaction of forces with the lifters results in variable induced stress, particularly the stresses that act on top of the lifters. As a result, a large number of balls will be superimposed which will result in higher forces and stresses acting on the lifters. The stresses acting perpendicular to the lifting side are higher in magnitude than the shear stresses acting along the top of the lifter. As the number of lifters increases, both normal and shear stresses decrease, Fig. 9. This finding is in agreement with in situ observations that severity of lifter wear decreases with increase in the number of lifters. Increasing the numbers of lifters will also alter the impact energy frequency spectrum of the mill. The number of very low energy impacts (0.1 J) for a mill with only two lifters is the highest, as shown in Fig. 10. However, starting from relatively modest impact energy (2 J), the number of impacts per second for the two lifters case drops at a much higher rate than for the mills with 14 and 22 lifters. The effect of the lifter height on the intensity of stresses that are acting on the lifters was also investigated. The results show that an increase of lifter height results in an increased intensity of stresses that are acting on the lifter. Fig. 11 shows the normal stresses induced to the lifters with 25 and 5 cm height respectively. The higher lifters will be exposed to the higher average stresses, due to the higher pile of the particles that are lifted. The higher stresses will cause higher initial wear rates. As the lifter height decreases due to wear, rate of further height reduction should slow down.

7. Conclusions In summary, the following conclusions may be drawn from the DEM simulations of the interactions of lifter design, mill speed and charge filling on energy utilisation in an AG mill: • Increasing a number of lifters leads to increase the proportion of high intensity impacts. A decrease the number of lifter leads to an increase the proportion of low intensity abrasion.

Fig. 11. Intensity of normal stresses for the cases of 25-cm-height lifters (left) and 5-cm-height lifters respectively.

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• An increase the number of lifters leads to an increase the net power draw, but only up to a stable value. • An increase mill filling leads to an increase the proportion of energy used for the low energy abrasion breakage, but decreases high energy impact breakage. • As the rotational speed increases, the mill draws more power with lower lifter height, but draws less power with higher lifters. • At constant lifter height, the mill draws more power when grinding smaller particles. At constant ratio of lifter height to particle size, the influence of particle size on mill power is not significant. • Less number of lifters and greater lifter height result in the greater stress intensity applied to the lifters, causing faster lifters/liners wears. After a certain number of lifters are reached, a further increase in the number of lifters will not result in a significant further reduction of stress intensity.

References Cleary, P.W., 1998. Predicting charge motion, power draw, segregation, wear and particle breakage in ball mills using discrete element methods. Miner. Eng. 11 (11), 1061–1080. Cleary, P.W., 2001. Charge behaviour and power consumption in ball mills: sensitivity to mill operating conditions, liner geometry and charge composition. Int. J. Miner. Process. 63, 79–114. Djordjevic, N., 2003. Discrete element modelling of power draw of tumbling mills. Trans. Inst. Mining Metall. (Section C: Miner. Process. Ext. Metall.) 112, C109–C114. Hlungwani, O., Rikhotso, J., Dong, H., Moys, M.H., 2003. Further validation of DEM modelling of milling: effects of liner profile and mill speed. Miner. Eng. 16, 993–998. Morrell, S., 1996. Power draw of wet tumbling mills and its relationship to charge dynamics, Part 2: An empirical approach to modelling of mill power draw. Trans. Inst. Mining Metall. (Section C: Miner. Process. Ext. Metall.) 105, C54–C62. Napier-Munn, T.J., Morrell, S., Morrison, R.D., Kojovic, T., 1996. Mineral comminution circuits. Their operation and optimisation. Julius Kruttschnitt Mineral Research Centre, Brisbane. PFC3D Particle Flow Code in 3 Dimensions, 1999. Itasca Consulting Group Inc., Minneapolis, Minnesota.

Determination of lifter design, speed and filling effects in AG mills.pdf

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