MINE292 Lecture7 Energy Used in Comminution 2013

7/27/2019 MINE292 Lecture7 Energy Used in Comminution 2013

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Energy Use in Comminution

Lecture 7

MINE 292


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COMMINUTION

MECHANICAL CHEMICAL

External Special Chemical

forces forces forces

- smashing - thermal shock - digestion

- blasting (chemical) - microwaves - dissolution

- breaking - pressure changes - combustion

- attrition - photon bombardment - bioleaching

- abrasion

- splitting or cutting

- crushing

- grinding


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Comminution

Although considered a size-reduction process,

since minerals in an ore break preferentially,

some upgrading is achieved by size separation

with screens and/or classifiers


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Comminution and Sizes

Effective Range of 80% passing sizes by Process

Process F80 P801) Explosive shattering: infinite 1 m

2) Primary crushing: 1 m 100 mm

3) Secondary crushing: 100 mm 10 mm

4) Coarse grinding: 10 mm 1 mm

5) Fine grinding: 1 mm 100 m

6) Very fine grinding: 100 m 10 m7) Superfine grinding: 10 m 1 m

The 80% passing size is used because it can be measured.


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Comminution - Blasting

Blasting practices aim to minimize explosives use Pattern widened/explosive type limited to needs

Requirements maximum size to be loaded

However, "Mine-to-Mill" studies show that Increased breakage by blasting reduces grinding costs

Blasting energy efficiency ranges from 10-20%

Crushing and grinding energy efficiencies are 1-2%

Limitations in blasting relate to Flyrock control

Vibration control

Improvements comes from reduced top-size & Wi


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Primary Crushing

Jaw crusher < 1,000 tph

Underground applications

Gyratory crusher > 1,000 tph Open-pit and In-pit


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Primary Crushing

Product size = 10 4 inches (250 100 mm) Open Side Setting (OSS) is used to operate

Mantle and bowl are

lined with steel plates Spider holds spindle

around which the

mantle is wrapped


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Secondary Crushing

Symons Cone Crushers Standard and Shorthead

Secondaries Tertiaries

CSS (mm) 25-60 5-20

Can process up to 1,000 tph

Mech. Availability = 70-75%


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Secondary Crushing Plants

Fully-configured Plant


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No Internal Surge Bins


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No Screen Bin


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Open Circuit gravity-flow


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Impact Crushers

Used in small-scale operations

Coarse liberation sizes

Hammer velocities (50mps)

Screen hole size controlsproduct size

High wear rates of

hammers and screen


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Impact Crushers

Barmac Crusher Invented in New Zealand

Impact velocity = 60 -90 mps

High production offines by attrition

Used in quarries &

cement industry


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Impact Crushers

Barmac Crusher Invented in New Zealand

Impact velocity = 60-90 mps

High production offines by attrition

Used in quarries &

cement industry


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Secondary Crushing - Rolls Crusher


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Secondary Crushing - Rolls Crusher

Angle of Nip Standard rolls

HPGR forces

Packed-bed

2a = bed thickness

Now applied to fine

crushing

Competitive with

SAG (or complementary)


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Energy in Comminution

Crushing and Grinding

Very inefficient at creating new surface area (~1-2%) Surface area is equivalent to surface energy Comminution energy is 60-85 % of all energy used

A number of energy "laws" have been developed Assumption - energy is a power function of D

dE = differential energy required,

dD = change in a particle dimension,

D = magnitude of a length dimension,

K = energy use/weight of material, and

n = exponent

nDK

dD

dE


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Von Rittinger's Law (1867)

Energy is proportional to new surface area produced Specific Surface Area (cm2/g) inverse particle size So change in comminution energy is given by:

which on integration becomes:

where Kr= Rittinger's Constant and

fc= crushing strength of the material

2

cr DfKdDdE

)D

1

D

1(fKE

fp

cr


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Kick's Law (1883)

Energy is proportional to percent reduction in size So change in comminution energy is given by:


where Kk= Kick's Constant and

fc

= crushing strength of the material

1

ck DfKdD

dE

p

feckDDlogfKE


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Bond's Law

Energy required is based on geometry of a crackexpansion as it opens up

His analysis resulting in a value forn of 1.5:


where Kb = Bond's Constant and

fc

= crushing strength of the material

5.1

cb DfKdDdE

)D

1

D

1(fKE

fp

cb


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Where do these Laws apply?

Hukki put together the diagram below (modified on right) Kick applies to coarse sizes (> 10 mm) Bond applies down to 100 m

Rittinger applies to sizes < 100 m


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Size Reduction

Different fracture modes

Leads to different size

distributions

Bimodal distribution not

often seen in a crushed

or ground product


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Breakage in Tension

All rocks (or brittle material) break in tension

Compression strength is 10x tensile strength

Key issue is how a compression or torsionforce is translated into a tensile force

As well, the density and orientation of internalflaws is a key issue (i.e., microcracks, grain

boundaries, dislocations)


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Griffiths Crack Theory


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Three ways to cause a crack to propagate:

Mode I Opening (tensile stress normal to the crack plane)

Mode II Sliding (shearing in the crack plane normal to tip)

Mode III Tearing (shearing in the crack plane parallel to tip)


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Based on force (or stress) needed to propagatean elliptical plate-shaped or penny-shaped crack

where

A = area of the elliptical plate

E' = effective Youngs Modulus

= strain

s = specific surface energy

a = half-length of the ellipse

s

222

a42

A

'E

a

'E2

AU


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Young's Modulus

Also called Tensile Modulus orElastic Modulus

A measure of the stiffness of an elastic material

Ratio of uniaxial stress to uniaxial strain

Over the range where Hooke's law holds

E'is the slope of a stress-strain curve of a tensiletest conducted on a sample of the material


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Young's Modulus

Low-carbon steel

Hooke's law is valid from the

origin to the yield point (2).

1. Ultimate strength

2. Yield strength

3. Rupture

4. Strain hardening region

5. Necking region

A: Engineering stress (F/A0)

B: True stress (F/A)


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Griffiths Theory

Differentiating with respect to 'a' gives:

Rearranging derives the fracture stress to initiate acrack as well as the strain energy release rate, G:

where

G = energy/unit area to extend the crack

0'E

a2a4

2

s

'E

aG

2


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Compression Loading

Fracture under point-contact loading

D. Tromans and J.A. Meech, 2004. "Fracture Toughness and Surface Energies of Covalent Materials:

Theoretical Estimates and Application to Comminution", Minerals Engineering 17(1), 115.


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Induced stresses-compressive load P

P

P

P

a2

a1

2a3

2a4

a51

2 3

4

5

KI=Yi(ai)1/2

At fracture:

KIC=Yic(ai)1/2

where

KIC=(EGIC)1/2

GIC

= Fracture Toughness

KI= Stress intensity (at fracture KI= KIC, i= ic)

i= Tensile stress, ai= crack length Y= Geometric factor (2 -)

E= Young's modulus, GIC= critical energy release rate/m2

Schematic of particle containing a crack (flaw) of


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P

P

D

(a)

q

P

kP kPP

kP kP

2a

(b)

2a

P

P

D

P

kP kPP

kP kP

Schematic of particle containing a crack (flaw) of

radius 'a'subjected to compressive force 'P'

i= P( kcosq - sinq)KI=YP(kcosq - sinq) a

1/2

At fracture KI=KIC. In theory there is a limiting average fine particle size:

Dlimit~

(KIC/k

P)2

(where q= 0)


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Impact Efficiency


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Impact Efficiency KIC, P, and flaw orientation () determine impact efficiency

Impact without fracture elastically deforms the particle with theelastic strain energy released as thermal energy (heat)

Impact inefficiency leads directly to high-energy consumption

In ball and rod mills with the random nature of particle/steelinteractions, a wide distribution of "P" occurs leading to very

inefficient particle fracture. A way to narrow this distribution

is to use HPGR

Such mills consume less energy and exhibit improved inter-particle separation in mineral aggregates (i.e., liberation via

inter-phase cracking), particularly with diamond ores

Diamond liberation without fracture damage is attributableto the high KICof diamond relative to that of the host rock


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Comminution Testing

Single Particle Breakage Tests Drop weight testing

Split Hopkinson Bar tests

Pendulum testing

Multiple Particle Breakage Tests Bond Ball Mill test

Bond Rod Mill test Comparison test

High-velocity Impact Testing


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Drop Weight Test

2 to 3 inch pieces of rock are subjected to different

drop weight energy levels to establish Wi(C)


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Split Hopkinson Bar Test Apparatus


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Split Hopkinson Bar Test Apparatus

- Method to obtain material properties in a dynamic regime- Sample is positioned between two bars:

- incident bar

- transmission bar

- A projectile accelerated by compressed air strikes theincident bar causing an elastic wave pulse.

- Pulse runs through first bar - part reflected at the bar end,

the other part runs through sample into transmission bar.

- Strain gauges installed on surfaces of incident and

transmission bars measure pulse strain to determine

amplitudes of applied, reflected, and transmitted pulses.


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Pendulum Test twin pendulum

Rebound Pendulum

Impact Pendulum

Rock Particle


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Bond Impact Crushing TestWi(C)

Low-energy impact test pre-dates Bond Third Theory paper.

Published by Bond in 1946

Test involves 2 hammers

striking a 2"-3" specimen

simultaneously on 2 sides.

Progressively more energy

(height) added to hammersuntil the specimen breaks

Doll et al (2006) have shown that drill core samples

can be used to establish range of energy requirements


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Values measured are:

1. E = Energy applied at breakage (J)

2. w = Width of specimen (mm)

3. = Specific gravity

Wi(C) = _59.0E_

w

where Wi(C) = Bond Impact Crushing Work Index (kWh/t)

F.C. Bond, 1947. "Crushing Tests by Pressure and Impact", Transactions of AIME, 169, 58-66.

A. Doll, R. Phillips, and D. Barratt, 2010. "Effect of Core Diameter on Bond Impact Crushing

Work Index", 5th International Conference on Autogenous and Semiautogenous

Grinding Technology, Paper No. 75, pp.19.


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Some example results:

A. Doll, R. Phillips, and D. Barratt, 2010. "Effect of Core Diameter on Bond Impact Crushing

Work Index", 5th International Conference on Autogenous and Semiautogenous

Grinding Technology, Paper No. 75, pp.19.


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Bond Mill to determine Wi(RM)For a Wi(RM) test, the standard Closing screen size should be

closing sieve size is 1180m. close to desired P80Multiply desired P80 by 2

Stage crush 1250 ml of feed

to pass 12.7 mm (0.5 in)

Perform series of batch

grinds in standard Bond

rod mill - 1' D x 2' L

(0.305 m x 0.610 m)

Wave liners

Mill speed = 40 rpm

Charge = 8 rods (33.38 kg)


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Bond Mill to determine Wi(RM)

Initial sample = 1250 ml stage-crushed to pass 12.7 cm (0.5 in) Grind initial sample for 100 revolutions, applying "tilting" cycle

Run level for 8 revs, then tilt up 5 for one rev, then downat 5 for one rev, then return to level and repeat the cycle

Screen on selected closing screen to remove undersize. Addback an equal weight of fresh feed to return to original weight.

Return to the mill and grind for a predetermined number of

revolutions calculated to produce a 100% circulating load. Repeat at least 6 times until undersize produced per mill rev

reaches equilibrium. Average net mass per rev of last 3 cycles

to obtain rod mill grindability (Gbp) in g/rev.

Determine P80 of final product.


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Bond Mill to determine Wi(BM)For a Wi(BM) test, the standard Closing screen size should be

closing sieve size is 150m. close to desired P80Multiply desired P80 by 2

Stage crush 700 ml of feed

to pass 3.35 mm (0.132 in)

Perform series of batch

grinds in standard Bond

ball mill - 1' D x 1' L

(0.305 m x 0.305 m)

Smooth liners / rounded corners

Mill speed = 70 rpm

Charge = 285 balls (20.125 kg)


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Bond Mill to determine Wi(BM)

Initial sample = 700 ml stage-crushed to pass 3.35 cm Grind initial sample for 100 revolutions, no "tilting" cycle used

Screen on selected closing screen to remove undersize. Addback an equal weight of fresh feed to return to original weight.

Return to the mill and grind for a predetermined number ofrevolutions calculated to produce a 250% circulating load.

Repeat at least 7 times until undersize produced per mill rev

reaches equilibrium. Average net mass per rev of last 3 cyclesto obtain ball mill grindability (Gbp) in g/rev.

Determine P80 of final product.


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Effect of Circulating Load on Wi(BM)

From S. Morrell, 2008. "A method for predicting the specific energy requirement of

comminution circuits and assessing their energy utilization

efficiency", Minerals Engineering, 21(3), 224-233.


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Bond MillWi(BM) or Wi(RM)Procedure: use lab mill of set diameter with a set ball or

rod charge and run several cycles (5-7) ofgrinding and screening to recycle coarse

material into next stage until steady state

(i.e., recycle weight becomes constant).

Formula:

where Wi = work index (kWh/t);P = 80% passing size of the product;

F = 80% passing size of the feed;

Gbp = net grams of screen undersize per mill revolution;

P1 = closing screen size (mm)


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Size Ranges for Different

Comminution Tests

Property Soft Medium Hard Very Hard

Bond Wi (kWh/t) 7 - 9 9 -14 14 -20 > 20


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Material Number Tested S.G.

Work Index

(kWh/t)All Materials 1,211 - 15.90

Andesite 6 2.84 20.12

Barite 7 4.50 6.32

Basalt 3 2.91 18.85

Bauxite 4 2.20 9.68

Cement clinker 14 3.15 14.95

Cement (raw) 19 2.67 11.59

Coke 7 1.31 16.73

Copper ore 204 3.02 14.03

Diorite 4 2.82 23.04

Dolomite 5 2.74 12.42Emery 4 3.48 62.50

Feldspar 8 2.59 11.90

Ferro-chrome 9 6.66 8.42

Ferro-manganese 5 6.32 9.15

Table of Materials Reported by Fred Bond1

1 adjusted from short tons to metric tonnes


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Work Index

(kWh/t)Ferro-silicon 13 4.41 11.03

Flint 5 2.65 28.84

Fluorspar 5 3.01 9.82

Gabbro 4 2.83 20.34

Glass 4 2.58 13.57Glass 4 2.58 13.57

Gneiss 3 2.71 22.19

Gold ore 197 2.81 16.46

Granite 36 2.66 16.59

Graphite 6 1.75 48.02

Gravel 15 2.66 17.70Gypsum rock 4 2.69 7.42

Iron ore hematite 56 3.55 14.25Hematite-specularite 3 3.28 15.26




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Work Index

(kWh/t)Hematite Oolitic 6 3.52 12.49

Magnetite 58 3.88 10.99

Taconite 55 3.54 16.09

Lead ore 8 3.45 12.93

Lead-zinc ore 12 3.54 11.65

Limestone 72 2.65 13.82

Manganese ore 12 3.53 13.45

Magnesite 9 3.06 12.27

Molybdenum ore 6 2.70 14.11

Nickel ore 8 3.28 15.05

Oilshale 9 1.84 17.46Phosphate rock 17 2.74 10.93

Potash ore 8 2.40 8.87

Pyrite ore 6 4.06 9.84

Pyrrhotite ore 3 4.04 10.55




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Work Index

(kWh/t)Quartzite 8 2.68 10.56

Quartz 13 2.65 14.96

Rutile ore 4 2.80 13.98

Shale 9 2.63 17.49

Silica sand 5 2.67 15.54

Silicon carbide 3 2.75 28.52

Slag 12 2.83 10.35

Slate 2 2.57 15.76

Sodium silicate 3 2.10 14.88

Spodumene ore 3 2.79 11.43

Syenite 3 2.73 14.47Tin ore 8 3.95 12.02

Titanium ore 14 4.01 13.59

Trap rock 17 2.87 21.30

Zinc ore 12 3.64 12.74



Histogram of W Values Reported by Fred Bond1


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Histogram of Wi Values Reported by Fred Bond1

F.C. Bond, 1953. "Work Indexes Tabulated", Trans. AIME, March, 194, 315-316.

F.C. Bond, 1952. "The Third Theory of Comminution", Trans. AIME, May, 193, 484-494.

Average for 1055 tests = 14.85 kWh/t

W S G


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Wi versus S.G.

F.C. Bond, 1953. "Work Indexes Tabulated", Trans. AIME, March, 194, 315-316.

F.C. Bond, 1952. "The Third Theory of Comminution", Trans. AIME, May, 193, 484-494.

Average Wi for 1055 tests = 14.85 kWh/t and 3.10 for S.G.

C i F f B d W


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Basic Assumption for Bond Equation: Mill Size = 2.44m C.L. = 250%

1. Dry Grinding

EF1 = 1.3 for dry grinding in closed circuit ball mill

2. Wet Open Circuit

EF2 = 1.2 for wet open circuit factor for same product size

3. Large Diameter Mills

EF3 = (2.44/Dm)0.2for Dm 3.81 m= 0.914 for Dm < 3.81 m

Correction Factors for Bond Wi

C ti F t f B d W


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4. Oversize Feed

Fo = Z (14.71/ [Wi(RM)]0.5

where Fo = optimal feed size in mm

Z = 16 for rod mills and 4 for ball mills

If actual F80 size (in mm) is coarser, then

(adjusted to metric tonnes)

EF4 = 1 + 1.1(Wi(BM) 6.35)(F80 - Fo)/(RrFo)

where Rr = F80 / P80

5. Reduction Ratio (only apply when product size is less than 75 microns)

EF5 = (P80 + 10.3) / (1.145 P80) where P80 is in microns


Wi (RM) Fo (mm)

for a BM

10 4.85

12 4.43

14 4.10

16 3.83

18 3.6220 3.43

22 3.27

24 3.13

26 3.00

28 2.90

30 2.80

C ti F t f B d W


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6. High or Low Reduction Ratio for Rod Millswhere Rr - Rro is not between -2 and +2

EF6 = 1 + (Rr Rro)2 / 159

where Rro

= 8 + 5L/D

L = rod length (m)

D = inside mill diameter (m)

7. Low Reduction Ratio for Ball Mill

EF7 = 1 + 0.013/(Rr - 1.35) if Rr < 6.0


C ti F t f B d W


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8. Rod Mills

Rod Mill only circuit

EF8 = 1.4 if feed is from open-circuit crushing

= 1.2 if feed is from closed-circuit crushing

Rod Mill/Ball Mill circuit

EF9 = 1.2 if feed is from open-circuit crushing

= 1.0 if feed is from closed-circuit crushing

9. Rubber Liners (due to energy absorption properties of rubber)

EF9 = 1.07


Oth E I di


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MacPherson Autogeneous Mill Work Index Test

SMC Test

JK Rotary Breaker Test

JK Drop Weight Test

Other Energy Indices

B d Ab i I d A


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Developed by Bond to predict wear rates of ball/rods and linersQuantifies the abrasiveness of an ore

A 400g sample is stage-crushed & sized into the range -19+12.7 mm

A standard weighed test paddle and enclosure are used

Paddle is abraded by rotation with the sample for 15 min. at 632 rpmProcedure is repeated 4 times and paddle is re-weighed

Loss in weight in grams is the Abrasion Index

Some representative Bond abrasion indices:

Limestone 0.026Quartz 0.180

Magnetite 0.250

Quartzite 0.690

Taconite 0.700

Does not account for wear by corrosion in milling circuits

Bond Abrasion Index -Ai

C i ti E T ti


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Mines today perform Bond Work Index Tests on multiple samples

A map of the drill core data is produced to show contours of orewith different Work Index Ranges

Ball Mill, Rod Mill and Low Energy Crushing tests are done

The mill will be designed based on Mine Production Scheduleto allow the mill to achieve desired liberation on the hardest ore

Some consideration is now being given to using these mapsto do mine planning, so hard and soft ores can be blended to

provide a more consistent mill feed

Comminution Energy Testing

C iti l S d E ti f Mill


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Nc =42.3(D-0.5)

Critical Speed Equation for Mills

where

Nc = critical speed (revolutions per minute)

D = mill effective inside diameter (m)

Typically , a mill is designed to achieve 75-80% of critical

speed. SAG and AG mills operate with variable speed. Ball

and rod mills have not in the past , but this is changing.

Critical speed defines the velocity at which steel balls will

centrifuge in the mill rather than cascade

D Nc

2 30

3 24

4 218 15

12 12

Grinding Mills


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Grinding Mills

Ball Mills

Rod Mills

Autogenous Mills

Pebble Mills

Semi-Autogenous Mills

- limited to 20' (6m) ft. by rod length (bending)

- cascade mills for iron ore

- pioneered in Scandinavia, South Africa

- pioneered in N.A.

variable speed drives

Grinding Mills


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Grinding Mills

Ball Mills

Grinding Mills


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Grinding Mills

Ball Mills

grate-discharge

Grinding Mills


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Grinding Mills

Ball Mills

rubber-lined

Grinding Mills


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Grinding Mills

Ball Mills

conical mill (Hardinge mill)

Grinding Mills


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Grinding Mills

Ball Mills

Grinding Mills


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Grinding Mills

Ball Mills

Mufulira Mine Grinding Aisle - 1969

Grinding Mills


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Grinding Mills

Rod Mills

Grinding Mills


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Grinding Mills


Grinding Mills


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Grinding Mills


End-plate Liners in an overflow SAG Mill

Grinding Mills


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Grinding Mills


Elements in a Grate-Discharge SAG Mill

Grinding Mills


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Grinding Mills


Grinding Mills


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Grinding Mills

SAG Mill

Ball Mill Circuit (Lac des Iles)

Grinding Mills


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Grinding Mills

Grinding Control Diagram

Secondary Crushing


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Secondary Crushing

Hydroset Control

Automatic change

in closed-side setting

(C.S.S.)

Motor load can be

used to adjust feed

tonnage and/or C.S.S.

Grinding Mills


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Grinding Mills

Stirred Mills


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Grinding Mills


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Grinding Mills

Vertical Stirred Mill (ultra-fine grinding)

Grinding Mills


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Grinding Mills

Micronizer Jet Mill (ultra-fine grinding)

Grinding Circuits


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g

One Stage Ball Mill Circuit

Grinding Circuits


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g

Two Stage Ball Mill Circuit

Grinding Circuits


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Rod Mill / Ball Mill Circuit

Grinding Circuits


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SAG/AG

Crusher - Ball Mill Circuit (ABC)

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MINE292 Lecture7 Energy Used in Comminution 2013

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