Minerals Engineering 16 (2003) 983–991This article is also available online at:

www.elsevier.com/locate/mineng

Applying discrete element modelling to verticaland horizontal shaft impact crushers

N. Djordjevic, F.N. Shi *, R.D. Morrison

Julius Kruttschnitt Mineral Research Centre, The University of Queensland, Isles Road, Indooroopilly, Brisbane 4068, Australia

Received 25 June 2003; received in revised form 17 August 2003

Abstract

The PFC3D (particle flow code) that models the movement and interaction of particles by the DEM techniques was employed to

simulate the particle movement and to calculate the velocity and energy distribution of collision in two types of impact crusher: the

Canica vertical shaft crusher and the BJD horizontal shaft swing hammer mill. The distribution of collision energies was then

converted into a product size distribution for a particular ore type using JKMRC impact breakage test data. Experimental data of

the Canica VSI crusher treating quarry and the BJD hammer mill treating coal were used to verify the DEM simulation results.

Upon the DEM procedures being validated, a detailed simulation study was conducted to investigate the effects of the machine

design and operational conditions on velocity and energy distributions of collision inside the milling chamber and on the particle

breakage behaviour.

� 2003 Elsevier Ltd. All rights reserved.

Keywords: Crushing; Comminution; Modelling; Simulation

1. Introduction

Impact-induced rock fragmentation is relevant for

many fields of science and technology. The length scale

involved in this process span from domain of astro-

physics to domain of geophysics and finally to the scale

of fragments and agglomerates in the chemical and

pharmaceutical industries. Impact crushers have been

applied in mineral, food, coal and cement industries fora long time. The literature shows that substantial effort

has been expended in understanding the impact crusher

performance in relation to machine configuration and

operational conditions through experimental work and

mathematical modelling (Callcott, 1960; Austin et al.,

1979; Gotsis et al., 1985; Shi, 2002; Shi et al., 2003).

However, due to lack of detailed knowledge on velocity

and energy distributions of collision inside a millingchamber, the mechanisms are still not clear.

The discrete element method (DEM) was employed in

the present work to study the kinematics of the particle

motion within the impact crushers. The DEM was first

proposed by Cundall and Strack (1979) to model the

*Corresponding author. Tel.: +61-7-3365-5888; fax: +61-7-3365-

5999.

E-mail address: f.shi@uq.edu.au (F.N. Shi).

0892-6875/$ - see front matter � 2003 Elsevier Ltd. All rights reserved.

doi:10.1016/j.mineng.2003.08.007

behavior of soil particles subject to dynamic loadingconditions. Since its inception this technique has been

adapted to model a variety of physical systems. Mishra

(1991) and Mishra and Rajamani (1992, 1994) pioneered

the application of DEM to grinding mills and demon-

strated that despite the DEM simulations were two-

dimensional (2D), the technique was able to predict the

power draw of mills with reasonable accuracy over a

wide range of mill diameters. Over 10 years since then,the DEM technique has been widely applied to ball mills

(e.g. Cleary, 1998, 2001; van Nierop et al., 2001), SAG

mills (e.g. Rajamani et al., 2000; Morrison et al., 2001),

centrifugal mill (Inoue and Okaya, 1996; Cleary and

Hoyer, 2000). Meanwhile the DEM code has been ex-

tended from 2D to 3D, and the contact parameters in-

volved in theDEMmodel havebeen studiedandcorrected

to improve the simulation accuracy (e.g. Zhang andWhiten, 1996, 1998; Mishra and Murty, 2001).

The DEM has also been applied to studies of impact-

induced particle breakage. Potapov and Campbell

(1994) found that ratio of the impact velocity to prop-

agation velocity of the longitudinal (sound) waves in the

material (Vo=C) was a useful parameter that described

the rate at which the kinetic energy of the collision was

transferred to the strain energy of the particle. When thevalue of Vo=C was high, the produced fragments tended

984 N. Djordjevic et al. / Minerals Engineering 16 (2003) 983–991

to have an elongated shape. This was in agreement with

experimental results. Thornton et al. (1996) reported

about 2D DEM of agglomerates impacting the rigid

walls. Depending on the impact velocity and adhesive

strength between particles, three regimes were observed:

shattering, semi-brittle fracture and elastic rebound.

Mishra and Thornton (2001) have studied the impactbreakage of particle agglomerates. They found a dis-

tinct fracture pattern for dense agglomerates above

a threshold impact velocity. The produced fragment

size distributions showed a clear bi-modal distribu-

tion. However, application of the DEM to the impact

crushers was rare in the literature.

Over years the Julius Kruttschnitt Mineral Research

Centre (JKMRC) has successfully modelled two types ofimpact crushers: the vertical shaft impact crusher (Na-

pier-Munn et al., 1996) and the horizontal shaft swing

hammer mill (Shi, 2002; Shi et al., 2003). In the present

work the PFC3D (particle flow code) that models the

movement and interaction of particles by DEM tech-

niques was employed to model the two types of impact

crusher. Modelling of fragmentation has also been at-

tempted using a strain rate concept. The data collectedfrom a Canica crusher treating quartzite and a BJD

swing hammer mill treating coal were used to verify the

DEM simulation results of specific energy and fragment

size distribution.

Upon the DEM procedures being validated, a detailed

simulation study was conducted to investigate the effects

of the machine design and operational conditions on

velocity and energy distributions of collision inside themilling chamber and on the particle breakage behaviour.

Fig. 1. PFC3D model of vertical shaft Canica crusher (view from

below).

2. The PFC3D models of impact crushers

Impact crusher modelling has been performed using

the PFC3D discrete element code. This code models the

behaviour of particles, which may be enclosed within afinite volume by the 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 law of motion to a

particle, a force–displacement law to each contact and

constant updating of the wall position (Cundall and

Strack, 1979). Details of the DEM calculation of contact

force, shear stiffness and slip model are referred to otherpublication (Djordjevic, 2003).

Two types of impact crushers were modelled using

the PFC3D code. The Canica Model 90 is an industrial-

scale vertical shaft impact crusher with 5 impellers of

0.48 m in their tip rotating radius. The crusher is fed by

a belt feeder. Rocks drop into the centre of the rotor,

and are hit or accelerated by the impellers to impact on

the surrounding anvils. The distance from the rotorcentre to the surface of the anvil is 0.65 m. The Canica

crusher was employed to treat quartzite. The rotational

speeds of the crusher varied from 650 to 950 rpm in the

experiment at an average throughput of 102 tph.

The BJD swing hammer mill is a pilot-scale hori-

zontal shaft impact crusher. The hammer tip diameter is

0.38 m, mill width 0.20 m, with a nominal capacity of 3

tph when driven by a 5.6 kW motor. The rotor, rotatingat a fixed speed of 3000 rpm, carries four rows of rect-

angular hammers with a width 0.03 m, two rows of three

hammers and two rows of two hammers. The BJD

hammer mill was employed to treat coal.

The Canica vertical shaft impact crusher is repre-

sented by a cylindrical chamber and five rotating im-

pellers in the DEM simulations (Fig. 1). Feed comes

from 1 m above in the form of free falling particles. Thecode is designed to perform modelling in 3D. Similarly,

the model for the BJD horizontal shaft hammer mill is

given in Fig. 2. For simplicity in the DEM calculation

code, the double-shaft swing hammers were simplified as

single-shaft rigid hammers.

For the Canica vertical impact crusher, test data at

950 rpm was used. The feed ()75 mm +2.36 mm) was

converted to the distribution of number of particles ineach size fraction. A total of 341 particles were simu-

lated. The fine end of the feed ()2.36 mm) was truncated

as there were more than 8000 particles in this size frac-

tion, which takes a very long computing time. The

truncated )2.36 mm material (4% by weight of the total

feed) was added into the DEM simulation product for

comparison with the measured data. For the BJD hori-

zontal shaft crusher, on the other hand, the data from thetest of single lithotype coal (the dull coal) of narrowly

Fig. 2. PFC3D model of horizontal shaft BJD hammer mill.

0.0

20.0

40.0

60.0

80.0

100.0

0.1 1 10 100

Size (mm)

Cu

m. %

pas

sin

g

BJD product BJD feed

Canica productCanica feed

Fig. 3. Comparison of size distributions simulated by DEM (in lines)

with measured (in symbols) for the Canica vertical shaft impact

crusher and the BJD horizontal shaft hammer mill.

N. Djordjevic et al. / Minerals Engineering 16 (2003) 983–991 985

sized feed (8–16 mm) was used. 340 particles of same size

(11.3 mm) were simulated using the PFC3D code.

The DEM modelling calculates the total cumulative

energy applied to each particle, including various forms

of energy due to collisions between impellers and par-

ticles, particles and anvils, and particles to particles. Thetotal specific energy for the Canica test at 950 rpm, de-

termined through PFC3D modelling, is 0.43 kWh/t,

compared with 0.32 kWh/t kinetic energy determined

from the impeller tip velocity. For the BJD horizontal

hammer mill, the total specific energy determined by

DEM is 0.23 kWh/t. This is very close to the model

parameter Ecs ¼ 0:21 kWh/t fitted to the BJD hammer

mill experimental data (Shi et al., 2003).The fragmented product size distributions were then

determined from the specific energy using a relationship

established from the single particle impact breakage test

(Napier-Munn et al., 1996). A crusher model imple-

mented in the JKSimMet software was employed to es-

timate the product size distribution from the total energy

determined by the DEM. The crusher K-parameters

were kept constant as determined from the previousmodel fitting. The predicted size distributions were

compared with the experimental data, given in Fig. 3.

For the Canica vertical shaft impact crusher, the

DEM prediction of product size is in good agreement

with the experimental data at a size range coarser than

10 mm, but over-predicts for fine product. This may be

due to the fact that more than 8000 particles smaller

than 2.36 mm were removed from the DEM simulation.Although this fraction of materials only account for 4%

by weight in the feed, the cushion effect of these particles

on the collision energy may be significant. Thus the total

cumulative specific energy should be smaller than the

one presented in this work. Similarly, the DEM pre-

diction for the BJD horizontal shaft crusher is good at

coarser size fractions (>2 mm), but over-predicts fines.

This may be attributed to the over-simplified one-shaftconfiguration of hammers used in the DEM, while the

BJD mill operates with double-shaft swing hammers.

Nevertheless, the DEM predictions seem to follow

the general trends of the experimental data very well.

This verifies that the DEM simulations can provide

reasonable insight of the impact crusher performance. A

number of simulations regarding the effects of machine

design and operational conditions on the impact crusherwere then conducted.

3. Descriptions of particle kinematics by DEM simula-

tions

The impact crushers usually operate at very high ro-

tational speed (1000 rpm for the vertical shaft crusherand 3000 rpm for the horizontal shaft hammer mill in

this study). Dynamic motion of particles inside the

crushing chamber and the interaction between the

crushing element and the particles exerts a dominant

influence on product size distribution. However, such

knowledge is rare in the literature. Although high-speed

cine camera study on the motion of coal particles inside

the BJD hammer mill was attempted by researchers (e.g.Callcott, 1960), it was difficult to determine the impact

energy quantitatively. DEM simulations provide a

suitable tool to establish the particle kinematics and the

energy distribution patterns.

3.1. Specific energy in relation to particle size

Investigation was conducted of the effect of particlesize on the intensity of the introduced energy and the

nature of the energy split for various rotational speeds

0

0.1

0.2

0.3

0.4

0.5

0 20 40 60 80

Particle diameter (mm)

Sp

ecif

ic k

inet

ic e

ner

gy

(kW

h/t

)

650 rpm 850 rpm 950 rpm

0

0.1

0.2

0.3

0.4

0.5

0 20 40 60 80

Particle diameter (mm)

Sp

ecif

ic s

trai

n e

ner

gy

(kW

h/t

)

650 rpm 850 rpm 950 rpm

(a) (b)

Fig. 4. Specific energy as a function of particle size and speed of the crusher. (a) kinetic energy, (b) strain energy.

0

0.02

0.04

0.06

0.08

0.1

0.12

0 100 200 300 400 500

Distance from the centre of the crusher (mm)

Sp

ecif

ic e

ner

gy

(kW

h/t

)

Kinetic

Strain

Fig. 5. Specific strain and kinetic energy introduced as a function of

distance of the impact point from the centre of the impeller.

986 N. Djordjevic et al. / Minerals Engineering 16 (2003) 983–991

of the impellers in the vertical shaft crusher. The particle

size studied was in the range of 10–70 mm. Single

spherical particles were dropped from a height of 1 m, at

a position that corresponds to half of the impeller

length. The results show that kinetic energy is a domi-

nant form of energy and the amount of specific kinetic

energy (kWh/t) is a function of the particle size and the

rotational speed of impellers (Fig. 4a and b).When the impact crusher operates at a low rotational

speed (650 rpm), the specific kinetic and strain energy

are almost independent of the particle size. The ratio of

strain (deformation) energy to kinetic energy is practi-

cally constant (approximately 0.45). However, as the

rotational speed increases, both specific kinetic energy

and specific strain energy increase significantly below

certain particle sizes, but decrease for larger particlesizes. The ratio of strain energy to kinetic energy is

basically constant for small particles, but it increases for

large particles as the impeller speed increases.

3.2. Specific energy in relation to feed position

The effect of particles feeding position to the vertical

shaft impact crusher was investigated numerically forthe case of 40 mm-diameter particles in the crusher with

impellers rotating at a speed of 650 rpm. The energy

introduced to the particles is a function of the position

along the impeller where contact with the particle oc-

curs. Radial velocity of the specific point along the im-

peller is determined by the angular velocity of the

impeller and the distance from the rotation centre. In

order to minimise the rolling effect of the particles, thefriction coefficient between particles and crusher sur-

faces were increased to a high value. This may be re-

flected to the effect of irregular particle shape of natural

rock material, which often has a relatively high effective

coefficient of friction. Results show that both specific

kinetic and strain energy increase as the impact point

becomes closer to the tip of the impeller (Fig. 5).

3.3. Particle kinematics

DEM is a suitable tool for investigation of the par-

ticle motion after initial impact, particularly in gaining

insight into the particle motion when interception of theparticle by the impeller occurs away from the impeller

tip. Simulations were performed in the vertical shaft

impact crusher using a cube composed from a number

of rigid balls bonded together to represent a rock sam-

ple. The strength of the sample was kept constant, while

the impeller varied.

Fig. 6 shows that at low rotational speeds the rock

just bounces on the surface of the impeller, while athigher speeds some breakage occurs due to the initial

impact.

Fig. 7 shows the breakage process for the samples

built from 5 and 2.5 mm-radius balls respectively. As-

suming that bond strength between individual balls re-

mains the same, a decrease in the ball size (grain size in

real life) would produce a particle of higher strength.

Fig. 7 demonstrates that the initial impact results in

Fig. 6. Collision of particles with impeller at various rotational speeds. (a) Sample remains intact after collision with impeller rotating at 100 rpm, (b)

sample remains intact after collision with impeller rotating at 500 rpm, (c) breakage occurs after collision with impeller rotating at 700 rpm.

Fig. 7. Breakage process of particles built from different grains at an impeller speed of 900 rpm. (a) Sample immediately after impeller impact (grain

radius¼ 5 mm); (b) sample immediately after impeller impact (grain radius¼ 2.5 mm); (c) sample immediately after impact to anvil (grain radius¼ 5

mm); (d) sample immediately after impact to anvil (grain radius¼ 2.5 mm).

N. Djordjevic et al. / Minerals Engineering 16 (2003) 983–991 987

breakage of particles close to the surface of the impeller.

The tensile strain causes the sample to split. The heavily

damaged sample slides along the surface of the impeller

towards its tip. Comparing Fig. 7a with b, the particlewith smaller grain size appear to be less damaged after

colliding with the impeller. This supports the assump-

tion that particles with smaller grain size have a higher

strength.

It is interesting to observe that both large and smallfragments tend to migrate along the surface of the

988 N. Djordjevic et al. / Minerals Engineering 16 (2003) 983–991

impeller towards its tip. When they reach the tip, the

fragments take-off with a maximum possible velocity

towards the surrounding anvils of the crusher. The

dominant phase of fragmentation occurs when the par-

ticles hit the anvils.

3.4. Energy distribution

In order to further investigate the effect of the inter-

cept position on the energy introduced into particles, a

25 mm cube made from 125 balls was placed in the

vertical shaft impact crusher at a distance of 5 and 45 cm

Fig. 8. Resultant velocities for the samples intercepted by the impeller at diff

the centre), (b) close to the tip of the impeller (45 cm away from the centre)

Fig. 9. Accumulated specific energy for the samples intercepted by the impelle

from the centre), (b) close to the tip of the impeller (45 cm away from the c

from the centre of the crusher respectively. Rotational

rate of the impeller was kept constant (1000 rpm). Re-

sultant (vector sum) velocity and total accumulative

specific energy of the cube are given in Figs. 8 and 9.

When particles are dropped close to the centre, the

impact velocity is not sufficient to cause fragmentation.

Particles are then translated and bounced along thelength of the impeller until they reach its tip. They are

accelerated at the tip speed towards the crusher anvils.

In such cases the initial fragmentation due to impact is

missed, but the secondary fragmentation due to impact

on the surrounding anvils remains.

erent positions. (a) Close to the centre of the crusher (5 cm away from

.

r at different positions. (a) Close to the centre of the crusher (5 cm away

entre).

N. Djordjevic et al. / Minerals Engineering 16 (2003) 983–991 989

On the other hand, where the particle is intercepted

near the tip of impeller, the initial impact is sufficient

to fragment the sample. After the impact, the individ-

ual grains are directed towards the crusher anvils

where further fragmentation occurs. However, the ini-

tial fragmentation due to the impact of impeller is

dominant. Although the peak resultant velocity of theball intercepted near the impeller tip is slightly smaller

than that intercepted near the impeller centre (87.4 vs.

89.8 m/s), the total accumulative specific energy intro-

duced into the sample is about 23% higher (0.87 vs. 0.71

kWh/t).

Fig. 9 also shows that the amount of energy intro-

duced into the particles rapidly increases when the

sample hits the crusher anvils and becomes heavilyfragmented. Particularly there is a large increase in shear

energy. This occurs due to the large increase in the

surface area of fragments that are sliding in contact with

the crusher anvils. The shear forces are a significant

factor in producing fines.

0

200

400

600

800

1000

1200

1400

1600

1800

0 500 1000 1500 2000 2500 3000 3500

Rotational velocity (rpm)

Ind

uce

d s

tres

s (M

Pa)

d = 0.5 m

d = 0.1 m

Fig. 10. Effect of the rotational speed and distance of the impact point

from the centre of rotation on the intensity of induced stress in the

rock.

4. Analytical modelling of rock fragmentation in impactcrushers

An impact crusher fragments the rock by the dynamic

strain energy introduced into the feed by the impactor.

The process of dynamic fragmentation, by its nature,

exploits the existence of flaws and micro-discontinuities.

Hence, product fragments tend to be of good quality

and shape. Specific fragmentation energy introducedinto the rock is a function of the impacting velocity. The

initial impact velocity is a function of the rotational

velocity of the crusher as well as the position along the

impeller, where falling feed becomes intercepted by the

rotating impellers.

For high velocity crushers, the initial collision is fre-

quently a significant cause of fragmentation. Any sub-

sequent crushing only complements the crushing actionof the impeller. The intensity of dynamic stress induced

by the impeller and by impact into the fixed surface can

be calculated using a simple equation:

S ¼ qVpVpp ð1Þ

where S is the dynamic stress (Pa), q is the rock density

(kg/m3), Vp is the propagation velocity of the longitu-

dinal stress wave in the material (m/s), Vpp is the peak

particle velocity (m/s).

The peak particle velocity at the contact point of the

rock and impeller, for the simplest case, is equal:

Vpp ¼ Vi ð2Þ

where Vi is impact velocity (m/s).

Impact velocity of the impeller is determined by the

angular (rotational) velocity of the impeller as well as

the distance from the centre of rotation where impact

occurs, described by the formula:

Vi ¼ Xd ð3Þ

where X is the angular velocity of the impeller (rad/s), dis the distance from the centre along the impeller where

collision occurs (m).

Using this simple model, it can be shown that inten-

sity of initial impact stress is determined by the rota-

tional speed and distance from the centre of rotationwhere collision occurs (Fig. 10).

Effect of the initial impact can be calculated based on

the theory of dynamic fragmentation developed by

Grady (1985). Based on energy considerations at high

strain rates, Grady developed a relationship for the

mean fragment size based on the induced strain rate and

rock properties such as fracture toughness, density and

the propagation velocity of elastic waves, using theequation:

D ¼ 4:472� Klcq� Vp � Sr

� �2=3

ð4Þ

where D is mean fragment size produced by the impact

(m), Klc is fracture toughness (mode 1) of the rock

(Pam0:5), q is rock density (kg/m3), Vp is propagation

velocity of the longitudinal elastic waves in the rock (m/

s), Sr is the induced strain rate (1/s).

Grady’s model has been successfully applied in the

modelling of rock fragmentation induced by explosives.The strain rate in the sample is defined as the difference

in rock particle velocity at the point of impact and at the

opposite, free end of the rock sample. The strain rate

can be calculated from the rotational velocity of the

impeller and the radial distance between the centre of

rotation and impact point:

0

5

10

15

20

25

0 500 1000 1500 2000 2500 3000 3500

Rotational speed (rpm)

Mea

n fr

agm

ent s

ize

(mm

)

d = 0.3 m

d = 0.5 m

Fig. 11. The influence of the rotational speed on the impact-induced

mean fragment size at two different impact positions (initial rock size

L ¼ 0:1 m).

990 N. Djordjevic et al. / Minerals Engineering 16 (2003) 983–991

Sr ¼Vpp1 � Vpp2

Lð5Þ

where Vpp1 and Vpp2 are particle peak velocities at the

impact point and at the free end of the particle respec-tively, and L is linear dimension of the rock sample (m).

Considering that particle peak velocity Vpp1 at the

interface of the impeller and rock is equal to the impeller

impact velocity Vi , and that Vpp2 at the free end of the

rock sample is of opposite sign of Vpp1 (due to reflection

from the free surface), and ignoring strain attenuation in

the rock sample and the effect of transit time, the strain

rate can be represented as

Sr ¼2� ViL

ð6Þ

Combining Eqs. (3), (4) and (6) gives the mean product

size due to impact:

D ¼ 4:472� Klc � L0:133� q� Vp � pWd

� �2=3

ð7Þ

where W is rotational speed in rpm.

Application of this equation for the case of a rock

with density q ¼ 2650 kg/m3, Vp ¼ 4000 m/s, fracture

toughness Klc ¼ 1 MPam0:5, size L ¼ 0:1 m and radial

distance of the impact point from the centre of rotation

of d ¼ 0:5 and 0.3 m respectively, produces the follow-ing diagram (Fig. 11).

Investigation was further carried out on the size dis-

tribution of the fragmentation using a PFC3D model of

rock sample with cubical shape comprising 343 balls

(6 mm diameter). The size of the cube was 42 mm. Balls

bond strength was kept constant. The speed of the

crusher varied in the range 800–1000 rpm. It was ob-

served that the intensity of fragmentation was a functionof the rotational speed of the impeller. For low rota-

tional speeds, fragmentation initially did not occur until

it impacts on the crusher anvil. Forces induced into the

crusher anvil were always higher than that induced from

the impacting impeller. As speed of the impeller in-

creases, initial impact becomes a significant cause of

0

20

40

60

80

100

0 10 20 30 40

Fragment diameter (mm)

Cu

m. w

t% p

assi

ng

1000 rpm900 rpm800 rpm

(a) (b

Fig. 12. Fragment size distributions created by different breakage mechanis

crusher anvils.

fragmentation. These effects are demonstrated in Fig.

12.

5. Conclusions

The DEM technique provides estimates that consider

single particles and some particle interactions in the

impact crushers. The distribution of collision energies

can be converted into a product size distribution for a

particular ore type using impact breakage test data. The

PFC3D code has been applied to two types of impactcrusher: the industrial-scale vertical shaft impact crusher

and the pilot-scale horizontal shaft swing hammer mill.

Upon the DEM procedures being validated, a de-

tailed simulation study has been conducted to investi-

gate the effects of the machine design and operational

conditions on velocity and energy distributions of col-

lision inside the milling chamber. Analytical modelling

of rock fragmentation has also been attempted using astrain rate concept.

0

20

40

60

80

100

0 10 20 30 40

Fragment diameter (mm)

Cu

m. w

t% p

assi

ng

1000 rpm900 rpm800 rpm

)

ms. (a) Impacted by the impellers, (b) impacted by the impellers and

N. Djordjevic et al. / Minerals Engineering 16 (2003) 983–991 991

The results show that DEM can be used to model the

particle flow behaviour, energy utilisation and product

size in the impact crushers, and thus assist in machine

and process design.

Acknowledgements

The authors wish to acknowledge the assistance of

Dr. Toni Kojovic in providing the breakage data that

were used for the Canica crusher modelling. The data of

the BJD hammer mill were from ACARP Project

C8057, for which the financial support from ACARP

and BHP-Billiton Port Kembla steelworks is greatly

appreciated. Useful discussions with Dr. Peter Cundallof ITASCA are acknowledged. The work was funded by

the JKMRC.

References

Austin, L.G., Jindal, V.K., Gotsis, C., 1979. A model for continuous

grinding in a laboratory hammermill. Powder Technol. 22, 199–204.

Callcott, T.G., 1960. A study of size reduction mechanism of swing

hammer mills. J. Inst. Fuel 33, 529–539.

Cleary, P.W., 1998. Predicting charge motion, power draw, segrega-

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

charge composition. Int. J. Miner. Process. 63, 79–114.

Cleary, P.W., Hoyer, D., 2000. Centrifugal mill charge motion and

power draw: comparison of DEM predictions with experiment. Int.

J. Miner. Process 59, 131–148.

Cundall, P.A., Strack, O.D.L., 1979. A discrete model for granular

materials. G�eeotechnique 1, 47–65.

Djordjevic, N., 2003. Discrete element modelling of the influence of

lifters on power draw of tumbling mills. Miner. Eng. 16, 331–336.

Gotsis, C., Austin, L.G., Luckie, P.T., Shoji, K., 1985. Modelling of a

grinding circuit with a swing-hammer mill and a twin-cone

classifier. Powder Technol. 42, 209–216.

Grady, D.E., 1985. Fragmentation under impulsive stress loading. In:

Fourney, W.L. et al. (Eds.), Fragmentation by Blasting. Society for

Experimental Mechanics, Connecticut, USA, pp. 63–72.

Inoue, T., Okaya, K., 1996. Grinding mechanism of centrifugal mills––

a simulation study based on the discrete element method. Int. J.

Miner. Process. 44–45, 425–435.

Mishra, B.K., 1991. Study of media mechanics in tumbling mills by the

discrete element method. PhD Thesis, The University of Utah.

Mishra, B.K., Murty, C.V.R., 2001. On the determination of contact

parameters for realistic DEM simulations of ball mills. Powder

Technol. 115, 290–297.

Mishra, B.K., Rajamani, R.K., 1992. The discrete element method for

simulation of ball mills. Appl. Math. Modell. 16, 598–604.

Mishra, B.K., Rajamani, R.K., 1994. Simulation of charge motion in

ball mills: Part 1. Experimental verifications. Int. J. Miner. Process.

40, 171–186.

Mishra, B.K., Thornton, C., 2001. Impact breakage of particle

agglomerates. Int. J. Miner. Process. 61, 225–239.

Morrison, R.D., Cleary, P.W., Valery, W., 2001. Comparing power

and performance trends from DEM and JK modelling. SAG 2001,

Department of Mining and Minerals Process Engineering, Univer-

sity of British Columbia, Vancouver, pp. 284–300.

Napier-Munn, T.J., Morrell, S., Morrison, R.D., Kojovic, T., 1996.

Mineral comminution circuits: their operation and optimisation.

ISBN 0 646 28861 x. Julius Kruttschnitt Mineral Research Centre,

Brisbane.

Potapov, V.A., Campbell, C.S., 1994. Computer simulation of impact-

induced particle breakage. Powder Technol. 81, 207–216.

Rajamani, R.K., Mishra, B.K., Venugopal, R., Datta, A., 2000.

Discrete element analysis of tumbling mills. Powder Technol. 109,

105–112.

Shi, F.N., 2002. Development of a power-draw model for estimation of

the dynamic recirculating load of swing hammer mills with internal

classifiers. Trans. Inst. Min. Metall. (Sect. C: Mineral Precess. Extr.

Mettall.), 111/Proc. Australas. Inst. Min. Metall., September–

December, p. 307.

Shi, F.N., Kojovic, T., Esterle, J.S., David, D., 2003. An energy-based

model for swing hammer mills. Int. J. Miner. Process 71, 147–166.

Thornton, C., Yin, K.K., Adams, M.J., 1996. Numerical simulation of

the impact fracture and fragmentation of agglomerates. J. Phys. D:

Appl. Phys. 29, 424–435.

van 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.

Zhang, D., Whiten, W.J., 1996. The calculation of contact forces

between particles using spring and damping models. Powder

Technol. 88, 59–64.

Zhang, D., Whiten, W.J., 1998. An efficient calculation method for

particle motion in discrete simulations. Powder Technol. 98, 223–

230.