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Mechanistic modelling of mineral sizers

R. Heng a, K. Cheng a, D. Tuppurainen b, R.A. Bearman b,*, S. Oswald c

a Department of Mechanical Engineering, University of Western Australia, 35 Stirling Highway, Crawley, WA 6009, Australiab Rio Tinto Technical Services, G.P.O. Box A42, Perth, WA 6837, Australia

c Hamersley Iron, P.O. Box 21, Dampier, WA 6713, Australia

Received 4 March 2003; accepted 13 May 2003

Abstract

Comminution in mineral processing must be tailored to the final product requirements. In many cases the requirement for

comminution is to generate the maximum amount of size reduction in the minimum number of equipment stages. There are howevercertain applications where maximum size reduction, or fines generation, are not desirable.

In such cases, and where the material characteristics allow, the application of twin rolls, toothed mineral sizers is often ad-

vantageous. This paper examines the function of an MMD 625 mineral sizer in terms of its mechanical design parameters and its

interaction with the feed material. Using the understanding developed during the study a mechanistic predictive model of the sizer is

generated that allows analysis of product size distribution, wear and throughput.

2003 Elsevier Ltd. All rights reserved.

Keywords: Comminution; Crushing; Modelling

1. Introduction

Key sectors of the minerals industry require commi-

nution machinery that can crush material to a given size

without over-crushing. These include:

• Coal––due to relatively fragile nature of the material

and the undesirability of fines.

• Iron ore––in cases where fines are of a lower value, or

where ultrafines should be minimized.

In such applications, equipment that is capable of

inputting high energy levels should be avoided. It should

also be noted that in the examples given above the

commodities are those regarded as bulk materials. Asbulk materials command a relatively low price, any

process equipment used in their treatment should be

capable of high throughputs particularly in relation to

the capital cost.

One device capable of high throughputs coupled with

restrained comminution is the mineral sizer. As the

name implies sizers combine a classification (sizing) and

crushing (top size control) function due to their design.

The main feature of mineral sizers is that the crushingtakes place between toothed crushing rolls and/or sta-

tionery surfaces. Other advantages claimed include:

• Ability to deal with high clay content, or sticky feed.

• Design is self-screening, thus removing the require-

ment to pre-screen.

The focus of this paper is the MMD 625 mineral

sizer, where the 625 designation refers to the distance in

millimetres between the centres of the two crushing rolls.

MMD are the original and largest manufacturer of

mineral sizers with their range covering various duties

from a primary sizer (MMD 1500) down to the MMD500. Due to the varying machine duties the design and

configuration of the MMD machines differs.

The machines designed for primary duty are the

largest throughput coarse comminution devices avail-

able. Typically the MMD 1500 machine is capable of

taking a feed size of 2 m down to a produce size of )350

mm at a rate of 10,000 tph. The MMD 625 is regarded

as a secondary machine and can be delivered in a variety

of length with either inward or outward rotation of the

crushing rolls. The main performance control features of

the MMD 625 are:

* Corresponding author. Tel.: +61-8-9327-2920; fax: +61-8-9327-

2999.

E-mail address: [email protected] (R.A. Bearman).

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

doi:10.1016/S0892-6875(03)00178-X

Minerals Engineering 16 (2003) 807–813This article is also available online at:

www.elsevier.com/locate/mineng

http://mail%20to:%[email protected]/



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• Length of crushing rolls––throughput;

• Inward/outward rotation––size reduction top size

control and throughput;

• Rolls speed––throughput;

• Rolls separation––top size control, size reduction and

throughput;

• Rolls/stationery surface separation––size reduction

and throughput;

• Tooth configuration––manageable feed top size and

size reduction.

The MMD 625 sizers modelled in this paper are in-

stalled at the Hamersley Iron Yandicoogina operation in

Western Australia. The operation produces a )10 mm

pisolitic iron ore at a rate of 18 million tones per annum

from a three stage crushing and screening circuit. Two

MMD 625 machines act as secondary crushers receiving

an all in feed from a primary jaw crusher. Product from

the sizers is screened using three high ‘‘G’’ force banana

screens, with the undersize reporting to final productand the oversize being crushed using three tertiary

MP1000 cone crushers set at 14 mm closed side setting

in closed circuit with the screens.

The MMD 625 sizer is shown in Fig. 1 and has the

following configuration:

• Outward rotation––crushing between toothed rolls

and stationary fingers;

• Rolls speed: 60 rpm;

• Rolls teeth––stationery teeth gap: 70 mm.

Tooth design comprises five teeth on a segment with48 segments on each roll (96 segments per machine), the

tooth design is shown in Fig. 2.

The machine configuration at the Yandicoogina op-

eration was determined by MMD to meet the process

specification of 1400 tph (per machine) and a product

top size of 80 mm.

2. MMD sizer model

The MMD 625 sizes and crushes material in a variety

of ways due to the geometry of the teeth and the inter-

action with the feed material. The model consists of

eight modules (see Fig. 3), where each module corre-

sponds to a distinct stage within the machine. By having

this design, the modules can be edited or replaced

without affecting the functionality of the whole pro-

gram.

The aim of the modelling is to determine:

• product size distribution,• throughput,

• power consumption,

• rate and pattern of tooth wear.

The rate and pattern of tooth wear being of particular

importance as this in turn impacts the other process

parameters that are being calculated (Fig. 3).

The key information passed between each module is

the percentage weight of feed of a specific particle size at

a particular tooth position. This information can be

represented in a 2D matrix as shown in Fig. 4.

Fig. 1. Plan view of MMD 625 Sizer at Hamersley Iron Yandicoogina.

Fig. 2. Tooth configuration for MMD 625.

FeedDistribution

ParticleMovement

OuterScreening

SpecificEnergyBreakage

Tooth and F ingerWear Profile

Product SizeDistribution

RedistributionFeedDistribution

ParticleMovement

OuterScreening

SpecificEnergyBreakage

Tooth and F ingerWear Profile

Product SizeDistribution

Redistribution

Fig. 3. Flow chart for the fundamental model.

Fig. 4. Matrix of percentage weight, particle size, tooth position.

808 R. Heng et al. / Minerals Engineering 16 (2003) 807–813

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For the previous example, particles in the )5000 mm

to +4204 mm size fraction, at the 3rd tooth position

represent 0.05% by weight of the original feed. 5000 mm

has been assigned the value of the maximum feed size

for this model. This is deemed to be in excess of the run-

of-mine feed that a primary crushing device could be

expected to handle. By default the top row of % weights

will always contain zero, as no feed can be in excess of

5000 mm in size.

The size fractions differ by a factor of 1 ffiffi24

p . Compared

to the standard sieve sizes that differ by 1 ffiffi2

p to allow a

greater resolution to be obtained for the particle sizes. In

the matrix, the number of teeth, n, is a parameter that

can be entered into the model by the user.

2.1. Feed distribution module

Given the design of the MMD sizer the feed distri-

bution along the length of the machine and the position

of the falling curtain of feed with respect to the rolls is

particularly important as this controls the maximum

throughput of the machine and the wear pattern of the

teeth.

The feed system into the MMD sizers at Yandicoo-

gina consists of a conveyor belt that empties into a

trouser leg chute that splits the feed to the two parallel

sizers. Due to constraints with the feed system the dis-

tribution along the length of the sizers is biased towards

the centre section of the rolls and the curtain of feed

tends to fall to the outside of the rolls. As these factors

have a major impact on the process performance of the

sizers a method of modelling this feed distribution isrequired. The feed distribution modules aim is to sim-

ulate the way feed enters the sizer. To cater for the va-

riety of feed distributions, the model employs three types

of feed profiles: uniform, triangular or parabolic. The

‘‘a’’ and ‘‘b’’ parameters correspond to the tooth posi-

tion of the feed boundaries. This allows uneven feed to

be modelled, and will enable the user to determine the

effect of different feed arrangements (Fig. 5).

2.2. Particle movement module

Particle motion within the sizer is a critical aspect in

understanding how material is captured and broken.

The action of the machine is that material falls in a

curtain between the two outward rotating rolls and

material that is smaller than the rolls separation falls

through without breakage, but the larger material is

carried by the teeth to the outside where it is broken

between the teeth and the stationary ‘‘fingers’’.

The function of the particle movement module is

twofold:

• To determine the proportion of particles that will

pass through the centre of the sizer, without undergo-

ing breakage and concomitantly the amount report-

ing for breakage.

• Model the movement of particles from the centre of

the sizer to the outer edge.

Trapezoids were selected as having the optimal shape

for calculating the probability of passing easily. The

probability of a particle passing through the gap is de-

termined using the ratio of passable area to total area. In

Fig. 6 below the rock will pass through the light-col-

oured hole if its centroid falls within the darkenedtrapezoid.

Probability of passage

¼ Passable area

Total area

¼ ðAverage length Particle diameterÞ ð? Height Particle diameterÞTotal area

The probability of selection for passage described

above is analogous to the selection function used in

many other types of breakage modelling. In this case the

more mechanistic approach to the issue of selection was

taken due to the action of the MMD and the existence of

a selection function for each tooth. It should also benoted that the selection function will change dramati-

cally with wear and the non-uniform wear rate and

pattern.

Fig. 5. The uniform, triangular, parabolic feed profiles.

Height

Average Length

⊥

Fig. 6. Possible area that a particle may pass.

R. Heng et al. / Minerals Engineering 16 (2003) 807–813 809

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Fig. 7 shows the selection function for a single

toothed segment containing five offset teeth (as per Fig.

2). At an instant when a single tooth is at its minimum

setting (70 mm) the last of the five teeth on the segment

will be at 110 mm, this variation is illustrated in Fig. 7

against the particle size reporting for selection.

The variation in selection function along the length of

five toothed segments is shown in Fig. 8.

The particle movement section deals with the change

in position of the rocks as they move from the middle of

the sizer to the breakage side. Since it is assumed that

the sizer is under steady state conditions, any vertical

trajectories can be ignored.

From video footage it was determined that the

movement of the rocks is random. Thus it is appropriate

to use the random normal distribution function to cal-culate the probability of rock trajectories. The only

parameter that is required in such a case is the standard

deviation of normal distribution. From the video, it was

observed that no rock moved more than nine teeth po-

sitions in either direction. Therefore if we assume that 18

teeth positions is equivalent to 3d, the standard devi-

ation for the entire profile is d 3.

2.3. Outer screening module

Just as the gaps in the middle of the sizer will act to

screen undersized material, a similar effect occurs on the

outer edge of the sizer. In this instance the crucial factor

is the geometry of the fingers. Before and after each

breakage event, undersized particles may fall through

the gaps in the stationary fingers.

The action of the outer section where the teeth and

stationary fingers interact is critical in determining the

size reduction behaviour of the sizer. The stationary

fingers are located on ‘‘in-fill’’ boxes so that their posi-

tion relative to the teeth can be adjusted to account for

wear. On the MMD 625 there are five fingers per in-fill

box. The sizing function of this outer area is particularly

important as there is no method of adjusting the gap

between the rolls to account for wear.

As with the particle movement module the selection of

material for breakage is a key element and the calcula-

tion of the function is undertaken in the same manner.

2.4. Specific energy module

Any rock undergoing breakage will have a particular

amount of energy applied to it. This module determines

the amount of energy that will be applied to a rock,

according to the machine geometry. Once the specific

energy is determined, the sizes and proportions of

breakage products can be calculated.

Kicks theory (1885) states that the energy consumed

in size reduction is proportional to the reduction in

volume of the particles undergoing breakage. Hukki(1975) demonstrated that Kicks work is most applicable

for crushing applications where the particles are larger

than 1 cm in diameter. In order to obtain a value for the

constant of proportionality, drop weight tests by Briggs

(1997) have been analysed. By fitting a log curve to the

data, a value of 0.321 kW h/t has been determined.

Thus Kicks law can be used in the following form:

E ¼ 0:321 ln d

gap

where E is the specific energy (kW h/t), d is the initial

particle size (mm), gap is the gap size between the fingers

and the teeth (mm).It is important to note that the geometry of the ma-

chine and the rock strength parameters (captured within

the coefficient) are the sole determining factors for the

specific energy. It must be noted that another advantage

of using the Kick equation is that the coefficient also

takes into account the efficiency of energy transfer.

2.5. Breakage module

Single particle tests to determine the comminution

behaviour of rock can be separated into pendulum and

7090

110

1030

5070

90

0

0.5

1

Gap (mm) Particle Size (mm)

Probability of Selection

for Passage

Fig. 7. Particle passage selection function for single segment con-

taining five offset teeth.

7 0 9

0 1 1 0 8

0 1 0 0 7

0 9 0

1 1 0 8

0

1 0 0 7

0 9 0

1 1 0

1 0

3 0

5 0

7 0

9 0

0

0.5

1

Probability of Selection

for Passage

Gap (mm)Particle

Size

(mm)

Fig. 8. Variation in selection function over five segments.

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drop weight based tests. The twin pendulum test relies

on the particle being broken between an input pendulum

released from a known height and a rebound pendulum.

The drop weight test differs in that the particles are

placed on a hard surface and struck by a falling weight.

Both these approaches have been used extensively in the

field of comminution.

The JKMRC has specialized in the application of

these test methods since the work of Narayanan and

Whiten (1988) highlighted their use in the field of

comminution modelling. Recent developments at the

JKMRC have seen the twin pendulum being replaced by

the drop weight apparatus.

The drop weight apparatus is seen to have several

advantages including:

• extended input energy range compared to the twin

pendulum devices,

• shorter time span of operation compared to the pen-

dulum test,• extended particle size range,

• ability to conduct particle bed breakage studies.

The standard drop weight device is fitted with a 20 kg

mass, which can be extended to 50 kg. The effective

range of drop heights is 0.05–1.0 m, which represents a

wide energy range from 0.01 to 50 kW h/t (based on 10–

50 mm particles).

Following sample preparation the mean mass of each

set of particles to be broken is calculated. Based on the

required specific input energy for each test, the height

from which the drop weight is to be released is deter-mined using the relationship below:

hi ¼ m E is

0:0272 M d

where hi is the initial height of the drop weight above the

anvil (cm), m is the mean mass of each set of particles

(kg), M d is the mass of the drop weight (kg), E is is spe-

cific input energy (kW h/t).

Typically 10 mm is added to the calculated drop

height for each test. This ensures that the required final

specific comminution energy is obtained, since after

breaking a particle the drop weight is brought to rest at

a height above the anvil. The average offset can bemeasured for each sample of particles broken, in which

case the applied energy is

E is ¼ 0:0272 M d ðhi hf Þm

where hf is the average height at which the drop weight

comes to rest above the anvil.

The results from the drop weight tests provide an

energy/input size/product size relationship. This rela-

tionship is analyzed using a set of curves to describe the

size distribution produced from breakage events of in-

creasing size reduction or energy input.

The descriptor employed in this approach is the t

parameter. Each product size distribution curve is nor-

malized with respect to the input size to give percentage

passing figures for various fractions. Therefore t 10 is the

percentage passing 1/10th of the original feed size and t 2

is the percentage passing 1/2 of the original feed size.

The t 10 parameter is the most often quoted parame-ter. Typically in a crusher t 10 is 10–20%, whereas in a

tumbling mill values in the range 20–50% are expected.

To make use of this description of ore breakage the

marker points t 2, t 4, t 25, t 50 and t 75 are stored in a

matrix form against t 10. This same data can be repre-

sented graphically as shown in Fig. 9.

Fig. 9 is a powerful graph as each vertical line (or

value of t 10) represents an entire cumulative percent

passing mass size distribution.

The t 10 value is related to the specific comminution

energy by the equation

t 10 ¼ Að1 eb E csÞwhere t 10 is the percentage passing 1/10th of the initial

mean size, E cs is the specific comminution energy (kW h/

t), A, b are the ore impact breakage parameters.

The A parameter represents the theoretical limiting

value of t 10, whilst ‘‘b’’ is the slope of the t 10 versus E cs

graph.

Using this approach to comminution the key factors

are t 10, E cs, A and b. The relation of these parameters to

other measures of rock strength are examined later.

2.6. Tooth and finger wear

The teeth and fingers of the sizer will wear signifi-

cantly over time causing an increase in the gap size.

The mechanism of wear in the sizer was examined to

determine an appropriate simplification that could be

used in the model. Initial thoughts on the type of wear

that is experienced by the sizer teeth were weighted to-

wards the idea of gouging wear. To investigate this issue

a series of micrographs were taken of the surface.

The results of the examination contradicted the initial

thoughts, in that the percentage of gouging wear seen on

the surface was less than 5–10%, with a majority of the

0

20

40

60

80

100

0 10 20 30 40 50

t10 (%)

C u m u

l a t i v e P e r c e n t P a s s i n g

t75

t50

t25

t10

t4

t2

Fig. 9. Size distribution parameter t versus t 10.


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The model assumes normal feed conditions, uses

machine geometry values derived from the appropriate

engineering drawings.

The model shows good correlation with the measured

data, although it tends to overestimate the size reduction

in the lower end of the size distribution curve. The di-

vergence is minor and well within the measurement ac-

curacy of the sampling. Should the divergence be due to

deficiencies in the model it is suggested that the main

causes could be either the selection function used, or the

shape of the feed material particles.

4. Conclusion

Product size distribution and crushing component

wear are key parameters in determining the performance

of a crushing device. This paper has described the key

modules used in the modelling of the MMD 625 Mineral

Sizer. Using machine geometry, ore breakage charac-teristics and representations of selection and energy

input a model has been derived that successfully predicts

product size distribution and tooth wear. The next stage

of the work is to apply similar techniques to the primary

MMD mineral sizers at the Robe River Pannawonica

operation.

Acknowledgements

The authors would like to thank operations staff at

Hamersley Iron Yandicoogina (John Smoothy), MMD

(Alan Potts, Ali Benbia) and Transmin (Ross Nunn,

Evan Douglas).

References

Briggs, C.A., 1997. A Fundamental Model of a Cone Crusher, Ph.D.

Thesis, University of Queensland.

Hukki, R.T., 1975. The principles of comminution: an analytical

summary. Engineering Minerals Journal.

Kick, F., 1885. Das Gesetz der Proportionalen Widerstande und seine

Anwendung, Leipzig.Narayanan, S.S., Whiten, W.J., 1988. Determination of comminution

characteristics from single particle breakage tests and its applica-

tion to ball mill scale-up. In: Trans. IMM, vol. 97, Section C, pp.

C115–C124.


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