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SME Arizona Conference 2004Quarry Academy 2005
Cone Crusher Cone Crusher ModellingModelling
Magnus EvertssonApplied Mechanics
Chalmers University of TechnologyGöteborg, Sweden
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Background
Aggregate producers on the Swedish west-coast required
more knowledge aboutcrushing…
Modelling of cone crushers startedin December 1993.
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Cone Crushers
Cone Crushers=
Size Reduction
Mechanical mineral liberation - miningAggregate production - quarries
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Cone CrushersCrushing plant - Mining
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Cone CrushersCrushing plant - Aggregate
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History
1954 Fred Bond’s WI1954 Gauldie1970 Bill Whiten1991 Ted Bearman
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Objectives
FundamentalsPrediction of particle size distributionPrediction of crushing pressure distributionsPrediction of crushing forcesPrediction of power draw
Design considerationsUtilization of compressive size reduction in cone crushersEnergy efficient crushingRobust performance over total liner lifetime
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Product
Feed
Power
Cross-section of a cone crusher
Operating Principle
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Operating Principle
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Operating Principle
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Operating Principle
XFlow
XTemperature
Up/downL/R
Dependencies for a water tap...
Diagonal interdependency matrix – system is easy to control
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Operating Principle
Dependencies for a cone crusher...
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Crusher Model
Rock Material
CrusherDynamicsCrusher
Design Performance
Pressure
WearSizeReduction
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Crusher Model
The crushing process can be described with two functions.
Selection S – which?Breakage B – how?
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Crusher Model
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Rock Breakage Behavior
F
F
b
s
Form conditionedcompression-displacement controlled
( ),F F s σℵ ℵ=
ssbsize distribution widthσ
ℵ
ℵ
=
=
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Rock Breakage Behaviour
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Rock Breakage Behaviour
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Rock Breakage Behavior
( ) 2 2 2 2 21 2 3 4 5 6,p s a s a s a s a s a s a s
size distribution width
σ σ σ σ σ
σℵ ℵ ℵ ℵ ℵ ℵ ℵ ℵ ℵ ℵ ℵ ℵ
ℵ
= + + + + +
=
Multi (inter) particle-pressure response
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Rock Breakage Behavior
( ) ( )321 2, kF s d d k s k s
s compression ratiod particle size
ℵ ℵ ℵ
ℵ
= +
==
0 0.05 0.1 0.15 0.2 0.25 0.3 0.350
500
1000
1500
2000
2500
3000
3500
4000
quartzite 16-19o tests- simulations
Single particle-force response
s/b
F [N]
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Crushing Pressure and Power Draw
cα
OSS CSS
iα
iR( )p p α=
eω
Concave
Mantle( )( )
sintan
cosi
p d
p d
α α αα
α α α= ∫∫
( ) sin
sinii
p r dR
α α α
α= ∫
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Crushing Pressure and Power Draw
2 2 11 2
cos sincos( )
resres e
e
a eP Rh
ω ϕ αϕ ϕ
=+
Mechanical model of
spiderless cone crusher
SYMONS-type
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Crushing Pressure and Power Draw
Mechanical model of a top supported
cone crusher
HYDROCONE-type
1 22 2 1
1 2 1
sin sin cos sincos( ) cos
resw res e
e
a eP h Rh
ϕ ϕω ϕ α
ϕ ϕ ϕ⎛ ⎞
= −⎜ ⎟+⎝ ⎠
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Geometry
StdSH
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Geometry
Design drawings
FineCoarse
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Geometry
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Flow model
Material flow mechanics
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Flow model
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Flow model
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Interaction Flow-Size reduction
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Interaction Flow-Size reduction
Less confinement-mixed single and interparticle breakage
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Results
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Results - Particle size distributions
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Results - Particle size distributions
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Results - Particle size distributions
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Results - Compression ratio
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Results - Pressure
-only a small proportion of the crushing chamber is utilized
H3000-FCSS=10mmGneiss10-30mm
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Results - Crushing force
0 2 4 6 8 10 120
5
10
15
20
25
30
35
40
Crushing zone [No]
Cru
shin
g fo
rce
[kN
]
ID3F36010, H3000F, n=360, CSS=10.1, e0=15.2, td=0.01, #IP=2.5169
Total vertical force
188.3 kN
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Results - Crushing angle
0 2 4 6 8 10 1210
15
20
25
Crushing zone [No]
α [°
]
ID3F36010, H3000F, n=360, CSS=10.1, e0=15.2, td=0.01, #IP=2.5169
-very small crushing angles
[ ]α °
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Results - Crushing power
0 2 4 6 8 10 120
1
2
3
4
5
6
7
8
Crushing zone [No]
Pow
er [k
W]
ID3F36010, H3000F, n=360, CSS=10.1, e0=15.2, td=0.01, #IP=2.5169
Total power
47.5 kW
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Results
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Results
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Results
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H7800-Implementation of Results
Anglo American
Mantos Blancos
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H7800-Implementation of Results
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H7800-Implementation of Results
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3C-Implementation of Results
3C-teamCustomizedCrushingChambers
Fine Tuned Chambers
Recommended