Comminution

(Size reduction)

COMMINUTION

external forces

– smashing– breaking – attrition – pealing – cutting– crushing– other

special forces

– thermal shock– pressure change– bombing with photon and other elemental particles– other

chemical forces

– roztwarzanie– rozpuszczanie– spalanie– bioługowanie– inne

MECHANICAL CHEMICAL

h

a

b

Special forces

Outer forces

Mechanical comminution

a

b

Chemical comminution

biological

acid

Leaching and disssolution

Ways of size reduction

breaking attrition smashing

splitting cutting crunching

Size reduction

CRUSHING dry, + 50 mm

GRINDINGwet, - 50 mm

Types of intergrowths of minerals

regular vein coating oclusion

Methods of separation and optimum particle size in feed

screens (wet)classifiers (wet)hydrocyclones drums jigsshaking tables spiralesconespinched sluiceMozley tablesmagnetic separators (LI*) magnetic separators (HI**)magnetic separators ( HG***) oil agglomertionflotation flocculationDRY SEPARATION screens (dry) air cyclones pneumatic separationair tables magnetic separators (LI*)magnetic separators (HI**)elektrostatic separa tors

1 10 100 1000

particle size in feed, m

0

1 10 100 1000

F < F F = F

FF

F

kr krF << Fkr

rr

s

Splitting of brittle particles

F < F F = Fkr kr

Bending metals

Comminution is a separation process

Feed

Product B

Product A

ordering forces

splitting forces

Feed

modified feed

ordering forces

Indices of comminution

I = degree of reduction = D/d

L = Degree of liberation = L

Mass of free particles of a given component

Mass of a given component in feedL =

Physicomechanical delineation of particle breaking

Er = 0.5G2 V/E + S

Er - breaking energyG - stress at the moment of breakingV - particle volume S - surface area of particle - surface energy of particle E - Young’s modulus

Er = En + Ep + Einne

Er = 0.5G2 V/E + S

Energy of surface formation

Energy of stress formation

Noice, heat, etc.

The Young modulus and surface energy as two principal parameters of comminution.The Young modulus after Lipczyński and co-workers (1984) and www, surface energy after Drzymala (1994)

MaterialYoung modulus

GN/m2 = 109 Pa=GPaSurface energy* mN/m = 10–3 J/m2

Water ~0 72.8

Ice 9.5 (at 268K)*** 90–120

KCl (silvinite) 29.6*6 97(780 °C)

CaF2 (fluorite) 75.8*6 450 (plane 111)

CaCO3 (calcite) 56.5(marble) 230 (100)

Al2O3 ( corundum) 390**** 580 (2050 °C)

C (diamond) 1050-1200** ~3700

Ag 83 923 (995 °C)

Au 78***** 1128 (1120 °C)

Cu 120 1120 (1140 °C)

Pb 16,2 442 (350 °C)

SiO2 50–78 (glass) 230 (1400 °C)

Granite 51.5–61.4 –

Sand stone 34–50 –

Diabase 61–69 –

Empirical delineation of size reduction

dEo = - C dd/df(d) Hukki, 1975

dEo = - C dd/dn

or in a simplified version:

Walker, 1937

dEo - increase of specific (per mass unit) energy of comminution

C - constant

f(d) - function dependent on particle size

dd - change of partcie size

10-04

10-02

1000

1002

1004

1006

1008

particle size d, m

10-03

10-01

1001

1003

1005

1007

1009

En

erg

y co

nsu

mp

tio

n,

Eo

, kW

h/M

ggrinding crushing

f(d) = n = 1

n = 4n = 2

n = 1.5

dE = –Cdd/d f(d)o

Kick

Bond

Rittinger

Specific solutions of the Waker equation

n=1

KK ln(D/d) = Eo = Er/m = Er /V

d - average size of particles after size reduction, m

KK - constant - density of particle, Mg/m3

V - volume of particle, m3

Eo - specific energy of size reduction, J/kgEr - comminution energy, Jm -mass of particle, kg

Kick, 1885

(Energy of comminution is proportional to the volume of the particle)

D - average size of particles before size reduction, m

n=1.5

Eo = KB (1/d0.5 -1/D0.5)

Bond, 1952

i i

i

d

gd

1

i i

i

D

gD

1

(Energy of size reduction depends on both volume and surface area of particle)

Specific solutions of the Waker equation

n =2

Eo = KR (1/d -1/D)

That is Er = KR*(Sd - SD)

S - surface area of particle

Rittinger, 1857

(Comminution energy is proportional to the surface area of particles)

Eo = Er /V

Specific solutions of the Waker equation

10 100 1000

particle size, µm

20

30

40

50

60

70

Fe

con

ten

t in

co

nce

ntr

ate,

%

liberation starting point

full liberation

Comminution equipment: crushers and mills

a b c

d e f

Rys. 3.15. Wybrane urządzenia do rozdrabniania: a – kruszarka walcowa, b – młyn kulowy,c – młyn wah adłowy, d – kruszarka młotkowa, e – łamacz szczękowy, f – kruszarka stożkowaSelected devices for size reduction.a) crushing rolls, b) tumbling mills,

c) pendular mill, d) hammer mill, e) jaw crusher, f) gyratory crusher

http://www.retsch-technology.com/

jaw crusher

Ball mills

http://ball-mill.fam.de/english/Products

Ball mills

http://ball-mill.fam.de/english/Products

http://ball-mill.fam.de/english/Products

Rod mills

Impact hammer mills

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Impact crushers