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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:[email protected](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:[email protected]://www.sciencedirect.com/science/journal/08926875http://www.elsevier.com/locate/minenghttp://www.elsevier.com/locate/minenghttp://www.sciencedirect.com/science/journal/08926875mailto:[email protected] -
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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.
1092 D. Gang et al. / Minerals Engineering 22 (2009) 10911093
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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
D. Gang et al./ Minerals Engineering 22 (2009) 10911093 1093