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Minerals Engineering 17 (2004) 1135–1142

Determination of lifter design, speed and filling effects in AG millsby 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 10MW. 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 Process-

ing 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 oppor-

tunity for improving grinding efficiency by choosing the appropriate combination of these variables. However, it is difficult to exper-

imentally 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–

25cm) and mill speed (50–90% of critical) on the power draw and frequency distribution of specific energy (J/kg) of normal impacts

in a 5m 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 ex-ceeds 10MW. Therefore, optimisation of the power uti-

lisation 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-

0892-6875/$ - see front matter � 2004 Elsevier Ltd. All rights reserved.

doi:10.1016/j.mineng.2004.06.033

* Corresponding author. Present address: JKMRC, Isles Road,

Indooroopilly 4096, Australia. Tel.: +61 7 3365 5888; fax: +61 7 3365

5999.

E-mail address: n.djordjevic@uq.edu.au (N. Djordjevic).

ciency by choosing the appropriate combination of mill

speed, filling and lifter design. However, it is difficult to

experimentally determine the interactions of these varia-bles in a full scale mill.

The discrete element method (DEM) has been proved

to be a useful tool in milling simulation and optimisa-

tion. A number of papers have been published in the lit-

erature 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 andmill speed effects. Cleary (1998, 2001) used DEM to

investigate charge behaviour and power consumption

1136 N. Djordjevic et al. / Minerals Engineering 17 (2004) 1135–1142

in relation to operating conditions, liner geometry and

charge composition in a 5m 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–

25cm) and mill speed (50–90% of critical) on the powerdraw and frequency distribution of specific energy (J/kg)

of normal impacts in a 5m diameter autogenous grind-

ing (AG) mill, with a mill charge volume varying be-

tween 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).

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

friction nil.

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 in-cludes application of the Newton�s 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 over-

lap. The magnitude of the overlap is related to the con-

tact force. There overlaps are small relative to the size ofthe particles.

During contact, the behaviour of a material is simu-

lated 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 Kn � Un � ni

where Fn is the normal contact force vector; Kn is normal

stiffness at the contact; Un is the relative contact dis-

placement in the normal direction and ni is unit normal

vector.

The incremental shear force is calculated using the

formula:

DF s ¼ �Ks � DU s

where Ks is the shear stiffness at contact and DUs is theincremental 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 enti-ties. Each contact is checked for slip conditions, by cal-

culating the maximum allowable shear contact force:

F sðmaxÞ ¼ l � jF nj

where l is the friction coefficient.

The energy state of the entire set of particles can be

examined by recording various forms of energy. Fric-

tional work is defined as the total cumulative energy dis-

sipated 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 contactsassuming a linear contact-stiffness model.

The PFC3D model of the mill is composed of a num-

ber 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 millcharge. 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 cylin-

drical 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, transla-

tional displacements of the charge along the length ofthe mill are minimal. The net-power draw of 1m thick

slice of 5m 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 20–150mm 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 10cm in all cases. Height

Fig. 2. Charge shapes for the mill with lifters of various heights, all with a coefficient of friction 0.3: (a) no-lifter, (b) 5cm lifters, (c) 10cm lifters,

(d) 15cm lifters, (e) 20cm lifters, and (f) 25cm lifters.

Table 1

Particle size distribution of the modelled mill charge

Particle diameter (mm) Number of particles

�150 + 90 96

�90 + 75 164

�75 + 53 290

�53 + 37.5 684

�37.5 + 28 1336

�28 + 20 2378

Total 4948

N. Djordjevic et al. / Minerals Engineering 17 (2004) 1135–1142 1137

of the lifters varied between 5 and 25cm. For each liftergeometry, 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 neces-

sary to determine the power draw without any lifting ac-

tion 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 willbe 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 powerdraws 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 · 105N/m and density

2650kg/m3.

The power draw of the mill comprises the power con-

sumed in rotating the empty mill (no-load power), to

abrade the charge without lifting the particles, and to liftthe charge which may eventually result in impact break-

age. 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 essentialrole of lifters is highlighted by the fact that without them

there would be essentially no net-power draw (assuming

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

1138 N. Djordjevic et al. / Minerals Engineering 17 (2004) 1135–1142

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 char-acterised with same coefficient of friction, net power

draw has a value of 49kW per unit of length of the mod-

elled mill. The entire power is consumed through abra-

sion of the charge and leads to gradual size reduction.

Net-power consumed by the mill without lifters is re-

ferred 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 5cm high lifters increases net power

draw to 77kW per unit length of the modelled mill.

Hence, an additional 28kW power is consumed for pro-

ducing 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 isconsumed 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 be-

tween particles and mill liners.

4. Effect of mill filling on power utilization

The fraction of net-power draw that will be con-

sumed by shearing and abrasion is determined by the

charge volume. In the case of mill with 500 particles

(7vol%), no-lifter power is about 52% of the net powerdraw with lifters. In the case of mill with 1500 particles

(20vol%) no-lifter power represents 70.5% of total net

power of the mill equipped with 5cm 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 en-

ergy 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 im-

pact energy is experimentally determined with a dropweight test (Napier-Munn et al., 1996), and that of size

reduction with the low intensity abrasion energy is

measured through tumbling test. A key feature of the

JKMRC AG/SAG model is that ratio of impact to abra-

sion 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 regard-less of the mill filling and lifter design. While this

assumption is adequate for industrial mills which oper-

ate at load close to maximum load, this modelling ap-

proach 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 differ-

ent mill filling levels. In the extreme case of single parti-cle, 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 oc-

curs within the main body of the charge, eventually fol-

lowed by the lifting of the particle, free fall and high

intensity impact. While particle is within the charge itbecomes subjected to numerous low-intensity force

applications which should result in a gradual size reduc-

tion 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 ex-

plains 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

0

10

20

30

40

50

60

70

80

2 4 6 10 14 18 22

net p

ower

dra

w(k

W)

number of lifters

Fig. 5. Effect of number of lifters on the net power draw (lifter height

20cm, width 10cm).

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).

0

20

40

60

80

5cm 10cm 15cm 20cm 25cmnet p

ower

dra

w (k

W)

net p

ower

dra

w (k

W)

0

20

40

60

80

5cm 10cm 15cm 20cm 25cmlifter height (cm)

lifter height (a) (

(c) (

Fig. 6. The effects of lifter height on net power draw for various mill speeds (5

70% critical speed, and (d) 60% critical speed.

N. Djordjevic et al. / Minerals Engineering 17 (2004) 1135–1142 1139

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 pre-

sented in Fig. 6. The sensitivity of the power draw to

the lifter height is much higher than what might be ex-

pected due to change of effective diameter of the mill.

The mill with low lifters tends to draw higher powerthan 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 velo-

city increases. This is due to the fact that propensity for

net p

ower

dra

w (k

W)

net p

ower

dra

w (k

W)

0

20

40

60

80

5cm 10cm 15cm 20cm 25cm

0

20

40

60

80

5cm 10cm 15cm 20cm 25cmlifter height (cm)

lifter height (cm)b)

d)

m mill with 30 lifters). (a) 90% critical speed, (b) 80% critical speed, (c)

0.5 1.0 1.5 2.0 2.5 3.0

0.

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

2.2

2.4

2.6

2.8

3.0

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

2.2

2.4

2.6

2.8

3.0

time (sec) x10^1 0.5 1.0 1.5 2.0 2.5 3.0

time (sec) x10^1

force (N) x10^3resultant force (N) x10^3

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

020406080

100120

80 100 150 200 240 300

particle diameter (mm)

net-p

ower

dra

w (k

W)

020406080

100120

80 100 150 200 240 300

particle diameter (mm)

net-p

ower

dra

w (k

W)

(a) (b)

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

1140 N. Djordjevic et al. / Minerals Engineering 17 (2004) 1135–1142

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, ignor-

ing height of the lifters. As the probability of centrifuge

is minimal for a slower velocity, the effect of lifter heighton 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 typ-

ical particles within the mill. In the case of low lifters

(e.g. 5cm), the average forces that are acting on a par-ticle are much smaller than that with higher lifters

(e.g. 15cm). 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 inten-

sity impacts. This is illustrated in Fig. 7, showing the

time history of the resultant force acting on a single

particle of 10cm diameter (within the charge) for the

mill equipped with 5 and 15cm high liftersrespectively.

In all discussions about the power draw of the mills it

is important to consider the nature of the charge size dis-

tribution. 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 (30cm). How-

ever, when the ratio of the lifter height to particle

diameter is kept constant (i.e. height = 80% of the dia-

meter), 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 ap-

plied 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 rota-

tion, 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, theactive force is a shear component of the predominantly

vertical force induced by the mass of superimposed par-

ticles and the centrifugal force.

Fig. 10. Impacts energy distribution.

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

lifters.

N. Djordjevic et al. / Minerals Engineering 17 (2004) 1135–1142 1141

Hence, stresses acting on the vertical side of the rec-

tangular shaped lifter will be mostly in a perpendicu-

lar–normal direction, while stresses acting on the top

of lifter will be predominantly shear stresses. Shear stres-

ses 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.

Fig. 11. Intensity of normal stresses for the cases of 25-cm-

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 inmagnitude 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 im-

pact energy frequency spectrum of the mill. The numberof very low energy impacts (0.1J) for a mill with only

two lifters is the highest, as shown in Fig. 10. However,

starting from relatively modest impact energy (2J), 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 stres-

ses 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 5cm 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 furtherheight 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 thenumber of lifter leads to an increase the proportion

of low intensity abrasion.

height lifters (left) and 5-cm-height lifters respectively.

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

• 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 abra-

sion breakage, but decreases high energy impactbreakage.

• 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

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tion, 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

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Djordjevic, N., 2003. Discrete element modelling of power draw of

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