Investigation of interparticle breakage as applied to cone crushing.pdf

Pergamon

Minerals Engineering, Vol. 10, No. 2, pp. 199-214, 1997 1997 Published by Elsevier Science Ltd Printed in Great Britain. All rights reserved

PII:0892--6875(96)00146-X 0892-6875/97 $17.00+0.00

INVEST IGAT ION OF INTERPARTICLE BREAKAGE AS APPL IED TO CONE CRUSHING

C.M. EVERTSSON and R.A. BEARMAN?

Machine and Vehicle Design, Chalmers University of Technology, 412 96 Gothenburg, Sweden I" Centre for Mining Technology and Equipment, Isles Road,

Indooroopilly, Queensland 4068, Australia (Received 29 September 1996; accepted 15 November 1996)

ABSTRACT

The brealazge of material in cone type gyratory crushers is traditionally regarded as relying upm single particle breakage. In the last ten years the emphasis has shifted with manufacturers trying to generate higher degrees of interparticle breakage. Increasing the degree of interparticle crushing is claimed to improve crushing efficiency and product shape.

The current study uses form conditioned crushing tests (geometry controlled compression) to investigate how multiple particles respond to crushing loads. By variation of test parameters the breakage characteristics of a rock material can be determined and compared to traditional single particle crushing.

The selection function, S (probability of crushing a single particle), seems to be related to the ratio between stroke and bed height, s/b, with a second order polynomial in s/b. An analysis of a given crusher chamber gives selection values in the range O. 05 < S < O. 4. Given the geometry of this chamber it is clear that much of the breakage will be interparticle. However, the selection values indicate that the efficiency of crushing is poor.

Using the approach outlined a mechanistic crusher model has been developed. The model seeks to describe the crushing process in relation to the machine operating parameters, chamber geometry and the material characteristics of the feed. In this way predictions of material flow and product size gradation are obtained that can be used to improve the understanding and design of crushers. 1997 Published by Elsevier Science Ltd Keywords Comminution; crushing; modelling; simulation; particle size

INTRODUCTION

Production of ballast material is a process which is challenging to analyse due to the complex structure of dependencies between the different process parameters. Of particular interest is the breakage mode. Two modes have been identified: interparticle breakage and single particle breakage. Interparticle breakage occurs when a particle has contact points shared with other surrounding particles.

Presented at Minerals F.ngineerin& '96, Brisbane, Australia, August 26-28, 1996

199

200 C.M. Evertsson and R. A. Bearman

After catastrophic breakage cracking generates two or more daughter fragments and fines due to attrition at the contact points. All particles are not broken in this breakage mode. Interpartiele breakage is believed to be an important breakage mode in cases where a significant amount of the feed is smaller than the closed side setting. Examples of this type of crushing were investigated among others by Eloranta [1].

Breakage between liners (single particle breakage) is a breakage mode which occurs when the distance between the chamber walls are equal to or smaller than the particle size before it is broken. For breakage between liners all particles are broken during a stroke.

Briggs and Bearman [2] used a Modified Hopkinson Pressure Bar for studies of single particle breakage. With this equipment they were able to measure strength and damage of single rock fragments with good accuracy.

The objective of this work is twofold. One aim is to get a better understanding of the interparticle breakage process of relevance in a cone crusher. Of special interest is the understanding of how selection and breakage behaviour depend of the machine parameters. The other aim is to develop a mechanistic model which can be used for analysis and prediction of the performance of cone crushers at the design phase.

CRUSHING PROCESS

A crushing process in a crushing machine is characterized by three process elements, Evertsson [3]:

Selection S = the probability of a particle to be broken. Breakage B = the actual size reduction resulting in smaller particles. Classification C = size separation process occurring between subsequent reduction cycles.

Whiten [4] has at first sight a similar, but indeed a different approach when modelling crushers for simulation of crushing plants. The main difference is that the crusher is simplified to a single crushing zone and that model parameters are fitted to full-scale data. After full-scale tests Whiten's approach provides a good tool for optimization of a given design. Although a very useful simulation tool the Whiten model cannot be considered as a design tool.

A reduction cycle for a cone crusher can be modelled as shown in Figure 1. Here it is assumed that no internal classification occurs which is reasonable for a choke-fed crusher. During the stroke of the cone some particles are selected for breakage depending on how and to what level they are stressed. When a particle breaks the sizes of the daughter fragments are controlled by the specific breakage appearance of the material. The particles that have not reached a critical stress level will be left unbroken. However, they can contribute to the generation of fines due to attrition at the contact points.

I

.~ S ~ B .~

,i I I feed , I product

( I -S)f

-~. S-Selection I- Machin e B =Breakage Material

parameters characteristics

Fig. 1 Model of a single reduction cycle. Feed and product is represented by f and p.

The machine parameters of a cone crusher are eccentric rotational speed of the cone, chamber geometry, closed side setting, stroke, power consumption and hydraulic pressure. The rock material to be crushed is characterized by some strength parameter, elastic modulus, attrition behaviour and breakage behaviour.

Investigation of interparticle breakage 201

PARAMETER CHARACTERIZAT ION

An attempt to describe the dependencies between machine parameters, inherent material properties, feed and product properties is shown in Table 1. Independent machine parameters are rotational eccentric speed, closed side setting and stroke. The inherent material properties are independent. All other parameters are in one way or another dependent of at least one other parameter.

TABLE 1 Relationships between machine parameters, material characteristics, feed and product properties. Dependencies in any direction between two parameters are marked X.

I=independent parameter, D=dependent parameter.

Machine parameters Eccentric speed, n

Close side setting

Stroke

Chamber geometry

Hydraulic pressure

Power

Capacity

Material properties, inh. Material strength

Attrition resistance

Feed Size distribution

Particle shape

Material strength

Prc~tuct Size distribution

Particle shape

: Material strength

i! I

I

l

D XX-

DXXXX-

DXXXXX

DXXXX

I

I

D

D

D

DXXXXX

DXXXXX

D 'X X X X X

~ ~ g~'~ ~ ~ -

- ~

X -

x! XXX-

XX

XX

X XXXXX-

X X XXX

X X X

Another way to illustrate the dependencies between the independent parameters and the crushing result is to formulate a so called interdependency matrix. The interdependency matrix relates the input to the output parameters as showa in Eq. (1).

202 C.M. Evertsson and R. A. Boatman

Power / XXXXXXXX Product size | = XXXXXXXX

Product shape / Product strength]

Speed CSS

Stroke Material strength

Attrition resistance Feed size

Feed shape Feed strength

(1)

An X in the interdependency matrix symbolizes a dependency between two parameters. If the interdependency matrix had been diagonal the crushing process would have been an easy problem to solve. In that case a input parameter would only affect a single output parameter. The process would have been easy to tune if for example speed would have been the only parameter affecting capacity.

A process with a triangular interdependency matrix would have been possible to tune by adjusting the input process parameters in correct order. In the case of crushing with existing crusher equipment such as jaw and cone crushers the interdependency matrix will be different from triangular. This fact implies the complexity of the crushing process. As an example we notice from Eq. (1) that the product size distribution is affected by all the independent parameters.

The reduction process for the single reduction cycle described in Figure 1 leads to the mathematical expression which describes the size distribution of the product:

p = BSf + (I-S)f = [BS + (I-S)]f (2)

Where p is the product size distribution, is the feed size distribution. B and S are matrix operators corresponding to breakage and selection. I is a unity matrix. This equation only describes how the size distribution changes for a single size reduction cycle.

DESCRIPTION OF GEOMETRY

From the machine parameters rotational speed, closed side setting, nominal stroke and chamber geometry two other independent parameters can be derived. These parameters are effective bed height, ben, and effective stroke, ser f. The effective bed height and stroke give a better description of the ernshing conditions and makes it possible to compare different types of machine layouts.

In an operating cone crusher the nominal stroke is not utilized to compress and thereby crush the material in the crusher chamber. There is a so called critical speed of a crusher defined as the speed when the material, at some point, will fall freely in the crushing chamber. Due to the effort ,o achieve high capacity the rotational speed of the cone is normally over critical and therefore the effective stroke is always less than the nominal stroke. This fact is important to consider when comparing laboratory results and parameters with chamber geometry.

saf = s(n, Shorn) < Snom (3)

The bed height at a given point is a function of eccentric speed, nominal stroke, closed side setting, distance from pivot point and chamber geometry.

bcf f = b(n, S,o m, ess, rpivo t, chamber geometry) (4)

Usually the material is subjected to more than one reduction cycle as it passes through a crusher. In a typical gyratory or cone crusher the effective bed height and stroke varies with the dismac~ from the pivot


point. The bed heilOt decreases while the stroke increases in this direction. For a given material the breakage and selection function depends on the parameters effective bed height and stroke:

B = B(Sen, b eff) (5)

S -- S(sen, b o~) (6)

Because breakage and selection varies between the reduction cycles the reduction process for a cone crusher can be written:

P = H [BiSi+(1-Si )l f (7) i=l

DETERMINATION OF SELECTION AND BREAKAGE

Breakage and selection functions can be determined by two main methods. One way is to fit the breakage and selection function to full-scale data. The other method is to perform separate laboratory tests under controlled conditions. It is not possible to isolate the results from one single reduction cycle in an operating cone crusher which is a reason why full-scale tests are not suitable for this purpose.

In order to determine the selection and breakage function after one single reduction cycle a simple laboratory test was designed. The principle of the test is shown in Figure 2.

Serf b eff

T Fig.2 The principle of the test equipment with characteristic parameters.

The test equipment is designed to simulate the conditions to which a volume of material is subjected in a real crushing chamber. The laboratory test corresponds to the part of the machine cycle when the liners moves towards each other. The material is then locked between the chamber walls and can only deform elastically and/or break into smaller particles.

The strain rate for the compressed material in a cone crusher is determined by the rotational speed n, nominal stroke Snom and the distance r from the pivot point. The maximum time derivative of the distance between the linen for a given total stroke is:

b = ~ns (8)

At normal operating conditions the maximum velocity of the cone relatively to the concave is below 0.5 m/s. It is assumed that the breakage appearance and selection function are independent of the strain rate


at this level.

The crushing result (i e size distribution and shape) is stated to be dependent of the parameters bed height b, stroke s and initial size of the crushed particles x o. By keeping the degree of compression s/b constant and varying the bed height the degree of interpartiele breakage can be varied.

Expected results from the tests are elementary base functions describing the size distributions after breakage. These base functions are believed to be quite different depending on the mode of breakage. The mode of breakage was discussed by Evertsson [2]. A breakage operator which combines different breakage functions (modes) can be written as:

Bm~, = ~ BiMi (9) i=l

The matrix B i is triangular with elements given from a breakage function which describes a particular breakage mode. When a breakage mode is activated the corresponding breakage (base) function is expected to be constant. The mode matrix, Mi, is of diagonel type with non-zero elements at positions corresponding to the size ranges that are broken in a particular breakage mode.

The probability of a particle being broken, selection, is obtained directly from the compression tests. The selection function is believed to be dependent of the s/b-ratio and particle size. lfa narrow size distribution of particles is defined by +Xl-X o, then the value of S is obtained as the weight fraction passing a given sieve size, see Figure 3.

The breakage function, B, is obtained by normalising the size distribution curve below size x I with the value of S.

100% l ** Weight , ,,s 1 S- S fraction[ B(:),~

st result Size 0

X 1 X 0

Fig.3 Value of S is equal to the total weight fraction passing size x~. B.function is obtained by dividing the size distribution below xl with the value of S.

ENERGY ASPECTS

By integration of the crushing force P over the stroke s it is possible to obtain the applied energy E A. The applied energy corresponds to the shaded area in Figure 4.

Investigation of interpartile breakage 205

P

~lb f

S Fig.4 Typical example of P,s-relationship from a crushing test. The area under the graph corresponds to the applied energy.

The energy can be compared to the degree of reduction which is obtained by sieve analysis. The way in which the degree of reduction should be defined is not clear.

The applied energy corresponds to the energy consumed in breakage of the particles and energy losses. The loss of energy which occurs immediately after a rupture is due to acoustic emission and thermal loss. Attrition of particles occurs during the compression which also consumes energy.

Eapplie d = Eel~ c + Efriction = Ebreakag e + Etoss (10)

Enos, = E o~ + Ethe, ~ + E~o" (11)

The efficiency of breakage can be quantified through the concept of energy utilization which is defined as new surface produced per unit of applied energy:

Energy utilization = As

Eapplied (12)

Here As is the increase in specific surface per unit mass and Eapplie d is the average applied energy per unit mass.

The energy utilization is higher for single particle breakage than for multiple breakage. Multiple particle breakage has a lower energy utilization because of frictional losses and local crushing at contact points (attrition).

Buss et al. [5] found that for fully confined particle bed tests the energy utilization was constant i.e. not depending of the applied energy. The tested material was quartz and the energy range was 10-110 J/g. In the case of partially confined beds the energy utilization decreases relatively to fully confined beds when the applied energy increases.

Larger particles are weaker than smaller ones and therefore produce a greater surface area for a given expenditure of energy. This fact was proven by Rose [6] who performed drop weight tests using a bed of cement clinker.

SELECTION

Selection, S, is by definition the probability of a single particle being broken when a population of particles is subjected to a compressive load. There are two criteria which must be fulfilled if a particle should be selected for breakage:


.

2. The particle must be located in such a way that a sufficient number of contact points are achieved. The stress level must reach a critical value (Briggs and Bearman [7]).

If selection is to be described with a mathematical function it looks suitable to adopt the following conditions:

1 11 lm I : ]1

:0 ds limit

In practice there will be a minimal s/b-value below which the selection is equal to zero. This is natural since there must be some compression before the particles have enough contact points so the stress level in some of the particles can reach the critical value. Even if no particles are broken below (s/b)min generation of fines will probably occur due to attrition.

S

1

0

I )l I I I

"~ s /b ( s / b )min ( s / b )lirait

Fig.5 Selection function that fulfils the set of conditions.

A maximal theoretical compression (s/b)limit can be calculated from initial packing density and the inherent density of the rock. At (s/b)limi t the selection is assumed to be equal to unity.

limit Pinh

A diabase with a typical initial packing density of 1300 kg/m3 and an inherent material density of 2900 kg/m 3 will then have a (s/b)limit--0.55.

EXI~'ERIMENTAL RESULTS

The equipment used for the compression tests consists of a crushing chamber according to Figure 2. It consists of a steel cylinder with a diameter of 100ram and two circular steel platens. The chamber contains 20-70 panicles of size + 16-19mm depending of the required bed be~ht . The chamber is loaded in a hydraulic press. Total crushing force P and stroke s is recorded on a XY-recorder,


A number of replicate tests were performed under identical conditions for every test point. The spread of results, was low especially for size fractions below 4ram.

Three different types of rock material were tested, The rock types were fine-grained diabase, fine- to medium-grained gaeissic granite and medium grained gneissic diorite. All the tested materials were taken from the tertiary stage in operating quarries. The materials were sieved to a size fraction +16-19mm. The aim of using such a short fraction is to be able to perform back calculations to achieve the selection and breakage function. Test were performed both with a constant reduction ratio s/b, in which the bed height b was varied, and constant bed height with varying stroke s.

Results From Tes~ with Constant Reduction Ratio

Three different bed heights 20, 55 and 80ram were used in the tests with constant reduction ratio. The results are shown in Figure 6.

A substantial difference between 20mm and 55ram bed height was found. A bed height of 20mm corresponds to a mono-layer of particles. In this case the breakage mode is purely breakage between liners. With 55ram and 80ram bed height the breakage mode is interparticle. There is a small difference between the two tests which supports the theory of breakage modes given in Eq. (9).

For the purpose of this work a 55mm bed height is assumed to give a pure interparticle breakage. This bed height is used in tests with constant bed height and variable s/b-ratio.

0.9

0.8

0.'7

~. 0.6

"'3 0..5

~ 0.4 0.3

0.2

0.!

0 t..-- . .-- . . .h.ICE 0.031 :..062

+ = 80ram o = 55ram x = 20ram

Normalized Cumulated Particle Weight Distribution

. . . . . . . . . . . , . . . . . . . : . . . . . . . , . . . . . . . , , . ,

Z

"" i . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. - . i . . . .

0.125 0.25 0.5 1 Particle Size, [mm]

16 32

Fig.6 Normalized breakage functions for granite from tests with different bed height.

Results from Tests with Constant Bed Height

Compression test:~ with constant bed height were performed in order to study the effect of different s/b-


ratios. The s/b-ratios were 0.10, 0.17, 0.25 and 0.38. In all these tests the material was diabase. Granite and diorite were tested for comparison at s/b=0.25.

The achieved values for selection are shown in Figure 7. A second order polynomial is fitted to the test data together with the theoretical (s/b)limit -value.

In Figure 8 normalized size distributions resulting from four different s/b-ratios are shown. It is obvious that the overall reduction increases when the s/b-ratio increase. A function, given in Eq. (14), with s/b as parameter and four constants was fitted to the test data.

. . . . . . t, +%(s/b) + ((~3 + 0~4 (s /b ) )Xs B (x s, s/b) = (1 - (x 3 ct 4 Ls/o))) xs (14)

Here x s is a particle size relative to the initial particle size x o. x s is defined in Eq. (15). Here Xmi n is a small particle size (=0.008ram).

X s

f = log 2 ] X-Xmin

t X o -Xmi n (15)

After fitting Eq. (14) to the data for diabase in Figure 8 the following numbers for the constants are achieved:

a 1=21.7759 ot2=-43.4615 t~3=-0.0029 ot4=0.4191

1

0.9

0.8

0.7

0.6

"~ 0.5

0.4

0.3

0.2

0.1

Selection vs s/b for interparticle breakage )(

x i ] S = -4 .1387(s3 +45386s-0245631 b .

0.1 0.2 0.3 0.4 0.5 0.6 s/b

Fig.7 Selection as a function of s/b. A second order polynomial can be fitted to the data.

Investigation of intetlaatticle breakage 209

Normalized Cumulated Particle Weight Distribution, data2130m

~1 + Gt2(s/b) B = ( 1 - (Ct-, + o~4(s /b ) ) )x s + (oc 3 + tx4(s /b ) )x s [] .....

o.~ .i . . . . . . . i . . . . . . . i . . . . . . . i . . . . . . . i . . . . . . . i . . . . . . . i . . . . . . . ! . . . . . i. . . . . . . .

~ o.~,I .! ....... i ....... i ...... ! ....... i ....... ~ i i i i i ! ...... ! ....... i . . . . :: .......

e~

/ -~ 0 .~; . . . . . . . . . . . . . . . . ~ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ~0.4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ~ .......

0.3 : . . . . . . . : . . . . . . . : . . . . . . : . . . . . . . :" s /b ! . . . . . . . / . . . . . . . . . . .

i ! i E o.=. i ....... i ....... i ............. i~o :2~ ....... i .......

0 0.031 .'..062 0.125 0.25 0.5 1 2 4 8 16 32

Part ic le Size, [ram]

F ig .8 S ize d i s t r ibut ions a f ter compress ion tests o f d iabase . Four d i f fe rent s /b were tested.

Comparative tests were performed in order to obtain the difference in crushing behaviour between the three rock types. The resu l ts are shown in F igure 9. Normalized Cumulated Particle Weight Distribution

i w ! # . .

C9

] o = Granite i :: :: :: :: ] o.s x = Diabase . . . . . ! . . . . . . . ! . . . . . . . ! . . . . . . . ! . . . . . . . i " l ' / 0.7 h

~.~J .O . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . " . . . . . . . ~ ' '~ . . . . . . . . . .

.~o .5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ! . . . . . . . . . . . .

~ C).40.2! 0.3

0.l --

0 0.031 :..D62 0.125 0.25 0.5 1 2 4 8 16 32

Part ic le Size, [mm]

F ig .9 Size d i s t r ibut ions for the three d i f fe rent rock mater ia l s tested at s /b=0.25 .


The diabase achieved the smallest size-reduction for a given s/b-ratio. The relative amount of fines was highest for diorite.

Conclusions from Compression Crushing Tests

The difference between crushing a mono-layer of particles compared to interparticle breakage is substantial in the case of geometry controlled crushing. For bed heights over 55ram the crushing is purely interparticle for the initial size fraction +16-19mm.

The selection function can be described with a second order polynomial in s/b.

The maximal crushing force increases exponentially with s/b. The applied energy increases with increasing maximal crushing force. Selection-values over 0.8 for interparticle breakage do not seem possible to achieve in practice as the loads in the crushing chamber will become excessive.

The relationship between selection and the maximal crushing force is linear in the region of technical interest (0 < S

Pivot point

Investigation of interparticle breakage

b(r) 211

Mantle profile

r ( r l , b l )

Concave profile

i n ~ ~ (r2' b2) O, O) ~" Closed position

Open positio . ~ Fig, 10 Geometry of a simple cone crusher chamber. Cross-section profiles

of cone and mantle are described with straight lines.

We assume the following numbers for the geometry

(rl,b])=(400,100) (r2,b2) =(850,38) [ram]

cPcone = 3 5 * CPstroke = 1.2"

and from those we achieve the numbers for the s/b-ratio which is shown in Figure 12. Other numbers of interest which can. be derived from the geometry are stroke, open and dosed side setting:

max

Sno m = r 2 tan (P,~,ke = 17.8 nun

oss r2 +0.5 max = Som = 46 .9mm css = r2--0.5snomn~ = 29 . lmm

Now, the breakage process for the assumed crusher can be described with Eq. (7), the interpretation of which is shown in Figure 11. The operators S i and B i are affected by the machine parameter (s/b)eff and material characteristics. The (s/b)eff -ratio is taken from Figure 12.

f

feed

I . . . , , - - - - - - o - - - - - | o - - - - - o . . . . . . . . . . . q t . - o - - - o - - - . . . . . . .

o P , 0 o

: ["~o--" I ~ Vl r '7" ] ~ : p2 Pn- I r '7" ] ~ : Pn

. . . /:: l ( I -S l ) f I :! I... ( I 'S2)pl li I ( I-Sn)Pn-I

...... li iIi, S2 , . . . . . . . . . . . ~,bJeff, 1 cnaractemtics ~,bJeff 2 character~tics ~,bJeff N characteristics

Fig. 11 Model of a cone crusher with N subsequent crushing events. Overall crushing result can be described with Eq. (7).

212 C.M. Evertsson and R. A. Bcarman

0.5 ~-

0.4~

0.3~-

0.2~

0.1

15thl!:

I !

. . . . . . . . . . . . . . . . . . . . i ............

i 00 100 200 300 400 500 600 700 800 900 1000

Distance from pivot point, r [mm]

Fig. 12 Nominal s/b ratio for the geometry in Figure 10 as a function of the distance from the pivot point. The arrows mark where a volume of material is crushed for the case with N=5.

Assumption 2 and 3 will together give the nominal s/b-ratio at each crushing event, but the s/b-value will always be to large. Due to dynamic effects we have concluded earlier that the effective stroke always is less (or equal) with the nominal stroke. At this stage the best assumption is that ser f is a fraction of s, e.g.:

.6 ,

If the inlet of the crusher chamber is much larger than the largest particle and if the nip angle is small enough the mode of breakage will be interparticle. If this is the case the material characteristics data in Figure 7 and 8 give the numerical values of the elements in the operators S i and B i for a given (s/b)eff - value, see Table 2.

TABLE 2 Values of S and (s/b)~ in different strokes.

(s/b)

1st stroke i 0.042

2nd stroke

0.064

3rd stroke

0.097

4th stroke

0.151

5th stroke

0.254

Selection S 0 0.028 0.156 0.344 0.641

The crushing result after each event is calculated by using Eq. 7. An arbitrary feed size distribution is given in Figure 13. The results are presented in Figure 14.


0.9

0.8

3.7

2 o6

.~ 0.5

o.4

0.3

0.2

0.1

0 0.031

Feed size distribution

i . . . . . . . ! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

.~ . . . . . . . ~ . . . . . . . ~ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . , . . . . . . . . . . . . . .

i . . . . . . . " . . . . . . . . . . . . . . . " . . . . . . . ' . . . . . . . . . . . . . . . " . . . . . . . " . . . . .

.i . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

~.,362 0.125 t

0.25 0.5 1 2 Particle Size, [ram]

4 16 32

Fig. 13 Feed size distribution chosen for simulation.

At the first stroke the (s/b)eff -value is below 0.06 and therefore the selection function is zero. No size reduction takes p]tace and the product size distribution is identical to the feed size distribution.

Product size distribution in each zone n=5 1

09 i 0.8

0.7 .- -Z-

"-' 0.ol . . . .

.~o.5

~ 0.4 0.3

0.2

0.1

0 (I.031 2..D62 0.125 0.25 0.5 2 4 8 16 32

Particle Size, [mm]

Fig.14 Simulated product size distributions in each crushing zone.

214 c.M. Evertsson and R. A. Bearman

At the second stroke S is approximately 0.03 and a slight size reduction is achieved.

During the third, fourth and fifth stroke the main part of the total size reduction takes place. The (s/b)eff - value is high as is the selection function S and the breakage function B.

In this study the material flow through the crusher is assumed to have constant velocity through the crusher chamber. This is probably the gravest assumption of the ones made in this work. At the same time this assumption implies a need for further research. By modelling how a single rock or a material volume passes through the crusher chamber it will be possible to obtain better information of the locations where the crushing occurs and the total number of reduction cycles which a material volume is subjected to.

The flow model will provide an important contribution to the mechanistic understanding of how a cone crusher operates.

CONCLUSIONS

Given the stated assumptions the following conclusions can be drawn:

The total size reduction seems to be more dependent on the selection function than on the breakage function. This fact implies that effective size reduction is governed by high (s/b)e ff -values.

The mechanistic modelling method which has been developed governs the detailed understanding of how and where in the cavity a volyme of rock material is exposed to size reduction. By using the method as a analytical tool it is possible to improve the performance of cone crushers.

The upper half of the assumed crusher is highly ineffective. This part acts more as a feeder than a crusher. ACKNOWLEDGEMENTS

Prof. G6ran Gerbert, Machine and Vehicle Design, is gratefully acknowledged for his supervision and for valuable discussions.

The author is grateful and wants to thank the following companies and organizations for their financial support: Development Fund of the Swedish Construction Industri (SBUF), Gatu & Vag AB, National Swedish Sand and Crushed Stone Association (GMF), NCC Baggermanns AB, Nordberg-Lokomo AB, R~sj6 Kross AB, Sabema Material AB, Skanska AB, Svedala Industri AB, Swedish Rock Engineering Research (SveBeFo), Swedish National Road Administration (V~igverket).

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REFERENCES

Eloranta, J., Influence of Crushing Process Variables on the Product Quality of Crushed Rock, PhD Thesis, Tampere University of Technology, (1995). Briggs, C.A. & Bearman, R.A., An Investigation of Rock Breakage and Damage, Minerals Engineering, 5(5), 489-497 (May 1996). Evertsson, C.M., Prediction of Size Distributions from Compressing Crusher Machines, Proceedings EXPLO '95 Conference, Brisbane, 173-180, (4-7 Sept. 1995). Whiten, W.J., Models and Controls Techniques for Crushing Plants, Control 84, Mini. Metall. Process, AIME Annual Meeting, Los Angeles, USA, 217-225, (Feb. 1984). Buss, B., Hanische, J. &Sehubert, H., Uber das Zerkleinergungsverhalten seitlich begrenzter und nichi-begrenzter Kornschichten bei Druckanspruchung, Neue Bergbautechnik, 12(5), 277-283 (1982). Rose, H.E., Drop Weight Tests as the Basis for Calculations of the Performance of Ball Mills, Proc. lOth Int. Miner. Process. Congr., London, Publ. IMM (London), 143-147 (April 1973). Briggs, C.A. & Bearman, R.A., The Assessment of Rock Breakage and Damage, Proceedings EXPLO '95 Conference, Brisbane, 16%172, (4-7 Sept. 1995).

Investigation of interparticle breakage as applied to cone crushing.pdf

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