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Technical Note

Analysis and optimization of cone crusher performance

Dong Gang *, Fan Xiumin, Huang Dongming

School of Mechanical Engineering, Shanghai Jiaotong University, Shanghai 200030, PR China

State Key Laboratory of Mechanical System and Vibration, Shanghai Jiaotong University, Shanghai 200030, PR China

a r t i c l e i n f o

Article history:

Received 9 February 2009

Accepted 29 March 2009Available online 28 April 2009

Keywords:

Crushing

Mineral processing

Modelling

Classification

Particle size

a b s t r a c t

Solving practical problems in cone crusher design, the quantity of rock material falling out of the crushing

chamber during one eccentric rotation of the cone was analyzed. A simple and practical model for pre-

dicting cone crusher output is proposed. Based on previous research a model able to directly calculate

the mass percentage of flakiness in the product has been obtained and a method of analysing the varia-

tion of the flakiness percentage in the process of crushing is proposed. Taking the output prediction

model as an objective function, and the size reduction model and flakiness prediction model as con-

straints, optimization of the cone crusher has been achieved. The validity of this optimization was veri-

fied via full-scale testing. This work will prove useful for developing further cone crusher improvement

strategies.

2009 Elsevier Ltd. All rights reserved.

1. Introduction

Cone crushers are widely used in the mining and aggregates

industry to crush blasted rock material. The key performanceparameters of a cone crusher include the output; particle size

and particle shape. In previous research on cone crusher perfor-

mance the output was calculated by integrating the mass-flow

field over a horizontal cross-section of the crushing chamber

(Evertsson, 2000). The complicated integral needs more time to

solve and results in lower computational efficiency; especially for

optimizing the process. To predict the product quality,Evertsson

(1997) modeled the process of crushing as a series of crushing

events and created the size reduction model. Magnus and Everts-

son (2006)studied the factors that may influence product flakiness

and presented an empirical model for predicting the product

shape. However, this model does not include any information of

size distribution; so it could not be used to calculate the mass per-

centage of flakiness in the product directly.

Our aim is to present a simple and practical model for calculat-

ing the output of a cone crusher and predicting the mass percent-

age of flakiness.

2. Analysis and modeling of cone crusher output

The operational part of the cone crusher is the crushing cham-

ber, which consists of a mantle and a concave liner. As shown in

Fig. 1, the axis of the mantle intersects the axis of the crushing

chamber at point O, which is the pivot point. The angle between

the two axes is c, which is the eccentric angle. During operation

of the crusher, the mantle moves around the axis of the crushingchamber. In the process of crushing, rock material enters the

crushing chamber and keeps falling until they reach the choke le-

vel. Then rock material is pushed against the concave liner by the

mantle and is then crushed. As the mantle moves away from the

concave liner, the rock material becomes loose and falls again.

After several cycles, the rock material comes to the shaded area,

as shown inFig. 1.

The output of cone crushers is the material that falls out of

the crushing chamber during the single eccentric rotation of

the mantle, which is just the material in the ring space

around the mantle (Lang, 1998). As shown in Fig. 1, the

shaded area is the cross-section of the ring space and DL is

the height of the ring space, which is also the falling distance

of the material.

Based on the analysis of material kinematics, the nominal fall-

ing timetncan be calculated. Previous research in this area has re-

vealed the existence of a time delaytd, during which the material

does not move relative to the concave liner (Evertsson, 2000).

The time delay depends on the moisture content of the material.

Under normal conditions, it is about 0.01 s. Taking the design of

PYB1750 cone crusher, a Chinese cone crusher made by Shanghai

Jianshe Luqiao Machinery Co., Ltd., as an example, the nominal fall-

ing timetnis 0.09 s and the falling timetuis about 0.08 s. The cor-

responding falling distance DLis 41.2 mm.

With DL and the given chamber geometry, the area of the sha-

dow DSand the volume of ring space DVcan be calculated using

Eq.(1), whereDr is the mean diameter of the ring space.

0892-6875/$ - see front matter 2009 Elsevier Ltd. All rights reserved.doi:10.1016/j.mineng.2009.03.020

* Corresponding author. Address: School of Mechanical Engineering, Shanghai

Jiaotong University, Shanghai 200030, PR China. Tel.: +86 21 62933362; fax: +86 21

62932070.

E-mail address:dgang@sjtu.edu.cn(D. Gang).

Minerals Engineering 22 (2009) 10911093

Contents lists available at ScienceDirect

Minerals Engineering

j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / m i n e n g

mailto:dgang@sjtu.edu.cnhttp://www.sciencedirect.com/science/journal/08926875http://www.elsevier.com/locate/minenghttp://www.elsevier.com/locate/minenghttp://www.sciencedirect.com/science/journal/08926875mailto:dgang@sjtu.edu.cn

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DV DSDrp 1

Taking the base diameter of coneDcas the substitute forDr, the

output of the cone crusher,Q, can be derived, as shown in Eq. (2),

wheren (r min1) is rotational speed,g is the volumetric filling ra-

tio, andq is the bulk density of final product. The volumetric filling

ratio gdescribes how the crushing zone volume is filled. The meth-

od for calculating has been presented by Evertsson (2000).

Q 60DVngq 60DSDpngq 2

Actually the output is also affected by some other factors, suchas the size distribution of the feed and material hardness. These

should be taken into account. As shown in Eq.(3), coefficientKsde-

scribes the influence of the size distribution of the feed on crusher

output, and the value range is 11.4. The coefficientKh describes

the influence of material hardness on crusher output, and the value

range is 0.751. The method for calculating the coefficients was

presented byLang (1998).

Q 60DSDpngqKsKh 3

For a given material, it is obvious that the output depends on

the mechanical design of the crusher.

3. Analysis of product quality

In mineral engineering, particle size and shape are two key fac-

tors that reflect the quality of product (Bouquety et al., 2007).

In previous research the process for the material flowing

through the crushing chamber can be modeled as a series of suc-

cessive crushing events (Evertsson, 1997; Gauldie, 1953). As a re-

sult, the size distribution of the final product can be described by

Eq.(4), where F is the initial feed,P is the size distribution vector

of the final product,m is the total number of crushing zones,Si is

the selection function, and Bi is the breakage function. Both Siand Bi are determined by the compression ratio (s/b)i, which de-

scribes how much the rock material is compressed in the crushing

zonei.

PYmi1 B

iSi ISi" #

F 4

The previous research has revealed that the particle shape

mainly depends on the average particle size of the feed and the

closed side setting (CSS) of the crusher. Magnus and Evertsson

(2006)presented an empirical model that describes the influence

of the two factors on the flakiness index, which represents the

mass percentage of flakiness in the product. The flakiness index

should be measured by means of the European Standard SS-EN

933-3 (1997). The model is shown in Eq.(5), where

Fis the averageparticle size of the feed,PSIZEis the particle size andFIF;CSS;PSIZE

is the flakiness index of the product at a chosenPSIZE.

FIF;CSS;PSIZE 0:24

F

1:25F 20

CSS

2P2SIZE

1:25F 20

CSS

PSIZE 1:25F 5

The empirical model predicts the flakiness distribution of the

product. However, it can not be used to calculate the percentage

of flakiness in the product directly, because it does not include

any information about the size distribution of the product. In this

work Eq. (5)is associated with Eq. (4), so that the percentage of

flakiness can be achieved as shown by Eq. (6), where PSIZEj is the

average size of the particles in the size range j, FIjF; CSS;PSIZEj isthe percentage of flakiness in the size range j, Pj is a component

of the vectorPand represents the proportion of particles in the size

rangej compared to the total product, andk is the total number of

size classes. As a result, FITOTALis just the percentage of flakiness in

the total product.

FITOTALXkj1

PjFIjF;CSS;PSIZEj 6

For the crushing events from 1 toi, the crushing zones from 1 to

icould be regarded as a complete crushing chamber and CiMiis the

CSS of the crushing chamber. Accordingly, Eq. (6)can be used to

calculate the percentage of flakiness in the discharged material of

crushing zonei.Fig. 2shows the percentage of flakiness in the dis-

charged material of each crushing zone of the PYB1750 cone

crusher.

The graph shows that after the rock material enters the crush-

ing chamber, the flakiness index of the rock material gradually in-

creases, as the crushing events proceed. During this phase the large

rock particles get crushed into several smaller particles, so the

Fig. 2. Percentage of flakiness in the discharge materials from each crushing zone ofthe PYB1750 cone crusher.

Fig. 1. Analysis of the process whereby rock materials fall through the crushing

chamber.

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mass percentage of flakiness will certainly increase. Then the flak-

iness index reaches the maximum of the curve shown inFig. 2and

then decreases. After the small particles have been crushed several

times, the flakiness of the rock material decreases rapidly. So re-

peated crushing is a valid method for reducing flakiness. Appar-

ently the particle shape also depends on the material

characteristic (Bouquety et al., 2007). This work could be useful

for determining strategies for improving cone crushers in future.

4. Cone crusher optimization

Based on the analysis and modeling above, it is possible to carry

out the optimization of the cone crusher parameters to improve

the performance of the crusher.The objective of cone crusher optimization is the maximal out-

put of the cone crusher, as shown in Eq. ( 7). The product quality

including particle size and particle shape are taken as constraints

of optimization, as shown in Eq.(8).PCSS is the product weight per-

centage passing CSS, and it is a key parameter for estimating prod-

uct size.PCSSminis the expectation of minimalPCSS and FITOTALmax is

the expectation of maximalFITOTAL.

Qn;c;h;a; l ! max 7

PCSSP PCSSmin

FITOTAL6 FITOTALmax

8

The cone crusher performance mainly depends on some key

parameters. In this work rotational speed n, eccentric angle c,height of pivot point h, base angle of cone a and parallel strip

lengthl, which are controllable parameters in the cone crusher de-

sign, are taken as the design variables in cone crusher optimiza-

tion. To ensure the outcome is applicable to practical designs,

boundary constraints on the design variables had to be included

in the cone crusher optimization as shown in Eq.(9).

nmin 6 n 6 nmax

cmin

6 c 6 cmax

hmin 6 h 6 hmax

amin 6 a 6 amax

lmin 6 l 6 lmax

8>>>>>>>>>>>:

9

To verify the validity of the cone crusher chamber optimization,we cooperated with the Shanghai Jianshe Luqiao Machinery Co.,

Ltd. to redesign the PYB1750 cone crusher according to the

outcome of the optimization process. To improve the power draw

the previous 160 kW motor was replaced by the 220 kW motor.

The corresponding prototype was manufactured and used in a

quarry in YueYang, China. The material is quartz.

As shown inTable 1, the performance of the improved PYB1750

is better than the previous one, although it did not reach our

expectations. Several factors such as the cone crusher operating

condition, feeding condition, assumptions of those models and

cone crusher manufacturing deviations, may have led to those dis-

crepancies. On the other hand, the test revealed the fact that an

optimization which only involves key design parameters cannot

greatly improve the performance of a cone crusher. For future cone

crusher optimization some other factors, such as the crushing

chamber geometry, should be taken into account. However, thevalidity of the cone crusher optimization process was basically ver-

ified by the corresponding full-scale test.

5. Conclusions

In this paper the model for predicting the cone crusher output

was obtained. Previous research on the analysis and modeling of

the crushing process was reviewed. By combining the empirical

model for predicting particle shape with the size distribution mod-

el, a flakiness prediction model was proposed. With this model the

percentage of flakiness of the discharged material of each crushing

zone was calculated and the variation of the flakiness percentage in

the process of crushing was analyzed.

Based on the analysis and modeling above, the optimization ofthe cone crusher was achieved and the validity of the optimization

of the cone crusher was basically verified with this full-scale

test.

References

Bouquety, M.N., Descantes, Y., Barcelo, L., 2007. Experimental study of crushedaggregate shape. Constr. Build. Mater. 21, 865872.

European Standard, 1997. EN 933-3. CEN European.Evertsson, C.M., 1997. Output prediction of cone crushers. Miner. Eng. 11, 215

231.Evertsson, C.M., 2000. Cone Crusher Performance. Ph.D. Thesis. Chalmers University

of Technology, Gothenburg, Sweden.Gauldie, K., 1953. Performance of jaw crushers. Engineering (October 9), 456458

(October 16, 1953, 485486).Lang, Baoxian, 1998. Cone Crusher. Mechanical Industry Publishing Company,

Beijing. pp. 212236 (in Chinese).Magnus, B., Evertsson, C.M., 2006. An empirical model for predicting flakiness in

cone crushing. Int. J. Miner. Process. 79, 4960.

Table 1

The outcome of optimization and full-scale test.

Type of parameters Structural and working parameters Performance parameters

n(r min1) c(deg) h(mm) a(deg) l (deg) Q(t h1) PCSS (%) FITOTAL(%)

Initial parameters 245 2 577 40 150 280 20 35

Parameters optimized 300 1.8 734 45 100 336 32.4 29.8

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