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

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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