1. Energy Use in Comminution
Lecture 7
MINE 292

2. 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

3. 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

4. Comminution and Sizes Effective Range of 80% passing sizes by Process
Process F P80
1) Explosive shattering: infinite 1 m
2) Primary crushing: 1 m mm
3) Secondary crushing: 100 mm 10 mm
4) Coarse grinding: mm mm
5) Fine grinding: mm 100 µm
6) Very fine grinding: 100 µm 10 µm
7) Superfine grinding: µm µm
The 80% passing size is used because it can be measured.

5. 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

6. Primary Crushing Jaw crusher < 1,000 tph Underground applications
Gyratory crusher > 1,000 tph
Open-pit and In-pit

7. 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

8. Secondary Crushing Symons Cone Crushers Standard and Shorthead
Secondaries Tertiaries
CSS (mm)
Can process up to 1,000 tph
Mech. Availability = 70-75%

9. Secondary Crushing Plants
Fully-configured Plant

10. Secondary Crushing Plants
No Internal Surge Bins

11. Secondary Crushing Plants
No Screen Bin

12. Secondary Crushing Plants
Open Circuit – gravity-flow

13. Impact Crushers Used in small-scale operations Coarse liberation sizes
Hammer velocities (50mps)
Screen hole size controls
product size
High wear rates of
hammers and screen

14. Impact Crushers Barmac Crusher Invented in New Zealand
Impact velocity = mps
High production of
fines by attrition
Used in quarries &
cement industry

15. Impact Crushers Barmac Crusher Invented in New Zealand
Impact velocity = mps
High production of
fines by attrition
Used in quarries &
cement industry

16. Secondary Crushing - Rolls Crusher

17. 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)

18. 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 % 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

19. Energy in Comminution 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

20. Energy in Comminution Kick's Law (1883)
Energy is proportional to percent reduction in size
So change in comminution energy is given by:
which on integration becomes:
where Kk = Kick's Constant and
fc = crushing strength of the material

21. Energy in Comminution Bond's Law
Energy required is based on geometry of a crack expansion as it opens up
His analysis resulting in a value for n of 1.5:
which on integration becomes:
where Kb = Bond's Constant and
fc = crushing strength of the material

22. Energy in Comminution 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 µm
Rittinger applies to sizes < 100 µm

23. Size Reduction Different fracture modes Leads to different size
distributions
Bimodal distribution not
often seen in a crushed
or ground product

24. Breakage in Tension All rocks (or brittle material) break in tension
Compression strength is 10x tensile strength
Key issue is how a compression or torsion force is translated into a tensile force
As well, the density and orientation of internal flaws is a key issue (i.e., microcracks, grain boundaries, dislocations)

25. Griffith’s Crack Theory

26. Griffith’s Crack Theory
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)

27. Griffith’s Crack Theory
Based on force (or stress) needed to propagate an elliptical plate-shaped or penny-shaped crack
where
A = area of the elliptical plate
E' = effective Young’s Modulus
 = strain
s = specific surface energy
a = half-length of the ellipse

28. Young's Modulus Also called Tensile Modulus or Elastic 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 tensile test conducted on a sample of the material

29. 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)

30. Griffith’s Theory
Differentiating with respect to 'a' gives: Rearranging derives the fracture stress to initiate a crack as well as the strain energy release rate, G: where G = energy/unit area to extend the crack

31. Compression Loading Fracture under point-contact loading
D. Tromans and J.A. Meech, "Fracture Toughness and Surface Energies of Covalent Materials: Theoretical Estimates and Application to Comminution", Minerals Engineering 17(1), 1–15.

32. Induced stresses-compressive load P
KI =Ysi(ai)1/2
At fracture:
KIC =Ysic(ai)1/2
where
KIC =(EGIC)1/2
GIC = Fracture Toughness
KI = Stress intensity (at fracture KI = KIC, si = sic)
si = Tensile stress, ai = crack length Y = Geometric factor (2 π -½)
E = Young's modulus, GIC = critical energy release rate/m2

33. Schematic of particle containing a crack (flaw) of
radius 'a' subjected to compressive force 'P' P D
(a) q s k 2 a
(b)
si = sP( kcosq - sinq )
KI=Y sP (kcosq - sinq ) a1/2
At fracture KI=KIC. In theory there is a limiting average fine particle size:
Dlimit ~ π(KIC/ksP) (where q = 0)

34. Impact Efficiency

35. Impact Efficiency
KIC, P, and flaw orientation (θ) determine impact efficiency
Impact without fracture elastically deforms the particle with the elastic 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/steel interactions, 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 attributable to the high KIC of diamond relative to that of the host rock

36. 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

37. Drop Weight Test 2 to 3 inch pieces of rock are subjected to different
drop weight energy levels to establish Wi(C)

38. Split Hopkinson Bar Test Apparatus

39. 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 the incident 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.

40. Pendulum Test – twin pendulum
Rebound Pendulum
Impact Pendulum
Rock Particle

41. Bond Impact Crushing Test – Wi(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 hammers
until the specimen breaks
Doll et al (2006) have shown that drill core samples
can be used to establish range of energy requirements

42. Bond Impact Crushing Test – Wi(C)
Values measured are:
E = Energy applied at breakage (J)
w = Width of specimen (mm)
ρ = Specific gravity
Wi(C) = _59.0·E_
w·ρ
where Wi(C) = Bond Impact Crushing Work Index (kWh/t)
F.C. Bond, "Crushing Tests by Pressure and Impact", Transactions of AIME, 169,
A. Doll, R. Phillips, and D. Barratt, "Effect of Core Diameter on Bond Impact Crushing Work Index", 5th International Conference on Autogenous and Semiautogenous Grinding Technology, Paper No. 75, pp.19.

43. Bond Impact Crushing Test – Wi(C)
Some example results:
A. Doll, R. Phillips, and D. Barratt, "Effect of Core Diameter on Bond Impact Crushing Work Index", 5th International Conference on Autogenous and Semiautogenous Grinding Technology, Paper No. 75, pp.19.

44. Bond Mill – to determine Wi(RM)
For a Wi(RM) test, the standard Closing screen size should be
closing sieve size is 1180μm close to desired P80
Multiply 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 m)
Wave liners
Mill speed = 40 rpm
Charge = 8 rods (33.38 kg)

45. 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 down
at 5° for one rev, then return to level and repeat the cycle
Screen on selected ‘closing’ screen to remove undersize. Add back 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.

46. Bond Mill – to determine Wi(BM)
For a Wi(BM) test, the standard Closing screen size should be
closing sieve size is 150μm close to desired P80
Multiply 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 m)
Smooth liners / rounded corners
Mill speed = 70 rpm
Charge = 285 balls ( kg)

47. 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. Add back 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 250% circulating load.
Repeat at least 7 times until undersize produced per mill rev reaches equilibrium. Average net mass per rev of last 3 cycles to obtain ball mill grindability (Gbp) in g/rev.
Determine P80 of final product.

48. Effect of Circulating Load on Wi(BM)
From S. Morrell, "A method for predicting the specific energy requirement of comminution circuits and assessing their energy utilization efficiency", Minerals Engineering, 21(3),

49. Bond Mill – Wi(BM) or Wi(RM)
Procedure: use lab mill of set diameter with a set ball or rod charge and run several cycles (5-7) of grinding 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)

50. Size Ranges for Different Comminution Tests
Property Soft Medium Hard Very Hard
Bond Wi (kWh/t) > 20

51. Table of Materials Reported by Fred Bond1
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
1.31
16.73
Copper ore
204
3.02
14.03
Diorite
2.82
23.04
Dolomite 5
2.74
12.42
Emery
3.48
62.50
Feldspar 8
2.59
11.90
Ferro-chrome 9
6.66
8.42
Ferro-manganese
9.15
1 adjusted from short tons to metric tonnes

52. Hematite-specularite
Table of Materials Reported by Fred Bond1
Material
Number Tested
S.G.
Work Index (kWh/t)
Ferro-silicon 13
4.41
11.03
Flint 5
2.65
28.84
Fluorspar
3.01
9.82
Gabbro 4
2.83
20.34
Glass
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
17.70
Gypsum rock
2.69
7.42
Iron ore – hematite 56
3.55
14.25
Hematite-specularite
3.28
15.26
1 adjusted from short tons to metric tonnes

53. Table of Materials Reported by Fred Bond1
Number Tested
S.G.
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
11.65
Limestone 72
2.65
13.82
Manganese ore
3.53
13.45
Magnesite 9
3.06
12.27
Molybdenum ore
2.70
14.11
Nickel ore
3.28
15.05
Oilshale
1.84
17.46
Phosphate rock 17
2.74
10.93
Potash ore
2.40
8.87
Pyrite ore
4.06
9.84
Pyrrhotite ore 3
4.04
10.55
1 adjusted from short tons to metric tonnes

54. Table of Materials Reported by Fred Bond1
Number Tested
S.G.
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
2.10
14.88
Spodumene ore
2.79
11.43
Syenite
2.73
14.47
Tin ore
3.95
12.02
Titanium ore 14
4.01
13.59
Trap rock 17
2.87
21.30
Zinc ore
3.64
12.74
1 adjusted from short tons to metric tonnes

55. Histogram of Wi Values Reported by Fred Bond1
Average for 1055 tests = kWh/t
F.C. Bond, "Work Indexes Tabulated", Trans. AIME, March, 194,
F.C. Bond, "The Third Theory of Comminution", Trans. AIME, May, 193,

56. Wi versus S.G.
Average Wi for 1055 tests = kWh/t and 3.10 for S.G.
F.C. Bond, "Work Indexes Tabulated", Trans. AIME, March, 194,
F.C. Bond, "The Third Theory of Comminution", Trans. AIME, May, 193,

57. Correction Factors for Bond Wi
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)0.2 for Dm ≥ 3.81 m
= for Dm < 3.81 m

58. Correction Factors for Bond Wi
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 = (Wi(BM)– 6.35)(F80 - Fo)/(Rr Fo)
where Rr = F80 / P80
5. Reduction Ratio (only apply when product size is less than 75 microns)
EF5 = (P ) / (1.145 P80) where P80 is in microns
Wi (RM) Fo (mm)
for a BM

59. Correction Factors for Bond Wi
6. High or Low Reduction Ratio for Rod Mills
where 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 = /(Rr ) if Rr < 6.0

60. Correction Factors for Bond Wi
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

61. Other Energy Indices MacPherson Autogeneous Mill Work Index Test
SMC Test
JK Rotary Breaker Test
JK Drop Weight Test

62. Bond Abrasion Index - Ai
Developed by Bond to predict wear rates of ball/rods and liners
Quantifies the abrasiveness of an ore
A 400g sample is stage-crushed & sized into the range mm
A standard weighed test paddle and enclosure are used
Paddle is abraded by rotation with the sample for 15 min. at 632 rpm
Procedure is repeated 4 times and paddle is re-weighed
Loss in weight in grams is the Abrasion Index
Some representative Bond abrasion indices:
Limestone 0.026
Quartz
Magnetite 0.250
Quartzite 0.690
Taconite
Does not account for wear by corrosion in milling circuits

63. Comminution Energy Testing
Mines today perform Bond Work Index Tests on multiple samples
A map of the drill core data is produced to show contours of ore with different Work Index Ranges
Ball Mill, Rod Mill and Low Energy Crushing tests are done
The mill will be designed based on Mine Production Schedule to allow the mill to achieve desired liberation on the hardest ore
Some consideration is now being given to using these maps to do mine planning, so hard and soft ores can be blended to
provide a more consistent mill feed

64. Nc =42.3(D-0.5) Critical Speed Equation for Mills
Critical speed defines the velocity at which steel balls will centrifuge in the mill rather than cascade
D Nc
2 30
3 24
4 21
8 15
12 12
Nc =42.3(D-0.5)
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.

65. 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

66. Grinding Mills
Ball Mills

67. Grinding Mills
Ball Mills – grate-discharge

68. Grinding Mills
Ball Mills – rubber-lined

69. Grinding Mills
Ball Mills – conical mill (Hardinge mill)

70. Grinding Mills
Ball Mills

71. Grinding Mills
Ball Mills – Mufulira Mine Grinding Aisle

72. Grinding Mills
Rod Mills

73. Grinding Mills
Semi-Autogenous Mills

74. Grinding Mills Semi-Autogenous Mills
End-plate Liners in an overflow SAG Mill

75. Grinding Mills Semi-Autogenous Mills
Elements in a Grate-Discharge SAG Mill

76. Grinding Mills
Semi-Autogenous Mills

77. Grinding Mills
SAG Mill – Ball Mill Circuit (Lac des Iles)

78. Grinding Mills
Grinding Control Diagram

79. 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.

80. Grinding Mills
Stirred Mills

81. Grinding Mills
Horizontal Stirred Mill with Pin Stirrers

82. Grinding Mills
Vertical Stirred Mill (ultra-fine grinding)

83. Grinding Mills
Micronizer Jet Mill (ultra-fine grinding)

84. Grinding Circuits
One Stage Ball Mill Circuit

85. Grinding Circuits
Two Stage Ball Mill Circuit

86. Grinding Circuits
Rod Mill / Ball Mill Circuit

87. Grinding Circuits
SAG/AG – Crusher - Ball Mill Circuit (ABC)