3 ComminutionAlthough 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 P801) Explosive shattering: infinite 1 m2) Primary crushing: 1 m mm3) Secondary crushing: 100 mm 10 mm4) Coarse grinding: mm mm5) Fine grinding: mm 100 µm6) Very fine grinding: 100 µm 10 µm7) Superfine grinding: µm µmThe 80% passing size is used because it can be measured.
5 Comminution - Blasting Blasting practices aim to minimize explosives usePattern widened/explosive type limited to needsRequirements – maximum size to be loadedHowever, "Mine-to-Mill" studies show thatIncreased breakage by blasting reduces grinding costsBlasting energy efficiency ranges from 10-20%Crushing and grinding energy efficiencies are 1-2%Limitations in blasting relate toFlyrock controlVibration controlImprovements comes from reduced top-size & Wi
17 Secondary Crushing - Rolls Crusher Angle of NipStandard rollsHPGR forcesPacked-bed2a = bed thicknessNow applied to finecrushingCompetitive withSAG (or complementary)
18 Energy in Comminution Crushing and Grinding Very inefficient at creating new surface area (~1-2%)Surface area is equivalent to surface energyComminution energy is % of all energy usedA number of energy "laws" have been developedAssumption - energy is a power function of DdE = differential energy required,dD = change in a particle dimension,D = magnitude of a length dimension,K = energy use/weight of material, andn = exponent
19 Energy in Comminution Von Rittinger's Law (1867) Energy is proportional to new surface area producedSpecific Surface Area (cm2/g) inverse particle sizeSo change in comminution energy is given by:which on integration becomes:where Kr = Rittinger's Constant andfc = crushing strength of the material
20 Energy in Comminution Kick's Law (1883) Energy is proportional to percent reduction in sizeSo change in comminution energy is given by:which on integration becomes:where Kk = Kick's Constant andfc = 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 upHis analysis resulting in a value for n of 1.5:which on integration becomes:where Kb = Bond's Constant andfc = 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 µmRittinger applies to sizes < 100 µm
23 Size Reduction Different fracture modes Leads to different size distributionsBimodal distribution notoften seen in a crushedor ground product
24 Breakage in Tension All rocks (or brittle material) break in tension Compression strength is 10x tensile strengthKey issue is how a compression or torsion force is translated into a tensile forceAs well, the density and orientation of internal flaws is a key issue (i.e., microcracks, grain boundaries, dislocations)
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 crackwhereA = area of the elliptical plateE' = effective Young’s Modulus = strains = specific surface energya = half-length of the ellipse
28 Young's Modulus Also called Tensile Modulus or Elastic Modulus A measure of the stiffness of an elastic materialRatio of uniaxial stress to uniaxial strainOver the range where Hooke's law holdsE' 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 strength2. Yield strength3. Rupture4. Strain hardening region5. Necking regionA: Engineering stress (F/A0)B: True stress (F/A)
30 Griffith’s TheoryDifferentiating 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)1/2At fracture:KIC =Ysic(ai)1/2whereKIC =(EGIC)1/2GIC = Fracture ToughnessKI = 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'PD(a)qsk2a(b)si = sP( kcosq - sinq )KI=Y sP (kcosq - sinq ) a1/2At fracture KI=KIC. In theory there is a limiting average fine particle size:Dlimit ~ π(KIC/ksP) (where q = 0)
35 Impact EfficiencyKIC, P, and flaw orientation (θ) determine impact efficiencyImpact without fracture elastically deforms the particle with the elastic strain energy released as thermal energy (heat)Impact inefficiency leads directly to high-energy consumptionIn 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 HPGRSuch mills consume less energy and exhibit improved inter-particle separation in mineral aggregates (i.e., liberation via inter-phase cracking), particularly with diamond oresDiamond 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 testingSplit Hopkinson Bar testsPendulum testingMultiple Particle Breakage TestsBond Ball Mill testBond Rod Mill testComparison testHigh-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)
39 Split Hopkinson Bar Test Apparatus Method to obtain material properties in a dynamic regimeSample is positioned between two bars:- incident bar- transmission barA 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 PendulumImpact PendulumRock Particle
41 Bond Impact Crushing Test – Wi(C) Low-energy impact test pre-dates Bond “Third Theory” paper.Published by Bond in 1946Test involves 2 hammersstriking a 2"-3" specimensimultaneously on 2 sides.Progressively more energy(height) added to hammersuntil the specimen breaksDoll et al (2006) have shown that drill core samplescan 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 gravityWi(C) = _59.0·E_w·ρwhere 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 beclosing sieve size is 1180μm close to desired P80Multiply desired P80 by √2Stage crush 1250 ml of feedto pass 12.7 mm (0.5 in)Perform series of batchgrinds in standard Bondrod mill - 1' D x 2' L(0.305 m x m)Wave linersMill speed = 40 rpmCharge = 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" cycleRun level for 8 revs, then tilt up 5° for one rev, then downat 5° for one rev, then return to level and repeat the cycleScreen 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 beclosing sieve size is 150μm close to desired P80Multiply desired P80 by √2Stage crush 700 ml of feedto pass 3.35 mm (0.132 in)Perform series of batchgrinds in standard Bondball mill - 1' D x 1' L(0.305 m x m)Smooth liners / rounded cornersMill speed = 70 rpmCharge = 285 balls ( kg)
47 Bond Mill – to determine Wi(BM) Initial sample = 700 ml stage-crushed to pass 3.35 cmGrind initial sample for 100 revolutions, no "tilting" cycle usedScreen 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 HardBond Wi (kWh/t) > 20
51 Table of Materials Reported by Fred Bond1 Number TestedS.G.Work Index (kWh/t)All Materials1,211-15.90Andesite62.8420.12Barite74.506.32Basalt32.9118.85Bauxite42.209.68Cement clinker143.1514.95Cement (raw)192.6711.59Coke1.3116.73Copper ore2043.0214.03Diorite2.8223.04Dolomite52.7412.42Emery3.4862.50Feldspar82.5911.90Ferro-chrome96.668.42Ferro-manganese9.151 adjusted from short tons to metric tonnes
52 Hematite-specularite Table of Materials Reported by Fred Bond1MaterialNumber TestedS.G.Work Index (kWh/t)Ferro-silicon134.4111.03Flint52.6528.84Fluorspar3.019.82Gabbro42.8320.34Glass2.5813.57Gneiss32.7122.19Gold ore1972.8116.46Granite362.6616.59Graphite61.7548.02Gravel1517.70Gypsum rock2.697.42Iron ore – hematite563.5514.25Hematite-specularite3.2815.261 adjusted from short tons to metric tonnes
53 Table of Materials Reported by Fred Bond1 Number TestedS.G.Work Index (kWh/t)Hematite – Oolitic63.5212.49Magnetite583.8810.99Taconite553.5416.09Lead ore83.4512.93Lead-zinc ore1211.65Limestone722.6513.82Manganese ore3.5313.45Magnesite93.0612.27Molybdenum ore2.7014.11Nickel ore3.2815.05Oilshale1.8417.46Phosphate rock172.7410.93Potash ore2.408.87Pyrite ore4.069.84Pyrrhotite ore34.0410.551 adjusted from short tons to metric tonnes
54 Table of Materials Reported by Fred Bond1 Number TestedS.G.Work Index (kWh/t)Quartzite82.6810.56Quartz132.6514.96Rutile ore42.8013.98Shale92.6317.49Silica sand52.6715.54Silicon carbide32.7528.52Slag122.8310.35Slate22.5715.76Sodium silicate2.1014.88Spodumene ore2.7911.43Syenite2.7314.47Tin ore3.9512.02Titanium ore144.0113.59Trap rock172.8721.30Zinc ore3.6412.741 adjusted from short tons to metric tonnes
55 Histogram of Wi Values Reported by Fred Bond1 Average for 1055 tests = kWh/tF.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 GrindingEF1 = 1.3 for dry grinding in closed circuit ball mill2. Wet Open CircuitEF2 = 1.2 for wet open circuit factor for same product size3. Large Diameter MillsEF3 = (2.44/Dm)0.2 for Dm ≥ 3.81 m= for Dm < 3.81 m
58 Correction Factors for Bond Wi 4. Oversize FeedFo = Z ( 14.71/ [Wi (RM)]0.5where Fo = optimal feed size in mmZ = 16 for rod mills and 4 for ball millsIf actual F80 size (in mm) is coarser, then(adjusted to metric tonnes)EF4 = (Wi(BM)– 6.35)(F80 - Fo)/(Rr Fo)where Rr = F80 / P805. Reduction Ratio (only apply when product size is less than 75 microns)EF5 = (P ) / (1.145 P80) where P80 is in micronsWi (RM) Fo (mm)for a BM
59 Correction Factors for Bond Wi 6. High or Low Reduction Ratio for Rod Millswhere Rr - Rro is not between -2 and +2EF6 = 1 + (Rr – Rro)2 / 159where Rro = 8 + 5L/DL = rod length (m)D = inside mill diameter (m)7. Low Reduction Ratio for Ball MillEF7 = /(Rr ) if Rr < 6.0
60 Correction Factors for Bond Wi 8. Rod MillsRod Mill only circuitEF8 = 1.4 if feed is from open-circuit crushing= 1.2 if feed is from closed-circuit crushingRod Mill/Ball Mill circuitEF9 = 1.2 if feed is from open-circuit crushing= 1.0 if feed is from closed-circuit crushing9. Rubber Liners (due to energy absorption properties of rubber)EF9 = 1.07
61 Other Energy Indices MacPherson Autogeneous Mill Work Index Test SMC TestJK Rotary Breaker TestJK Drop Weight Test
62 Bond Abrasion Index - Ai Developed by Bond to predict wear rates of ball/rods and linersQuantifies the abrasiveness of an oreA 400g sample is stage-crushed & sized into the range mmA standard weighed test paddle and enclosure are usedPaddle is abraded by rotation with the sample for 15 min. at 632 rpmProcedure is repeated 4 times and paddle is re-weighedLoss in weight in grams is the Abrasion IndexSome representative Bond abrasion indices:Limestone 0.026QuartzMagnetite 0.250Quartzite 0.690TaconiteDoes not account for wear by corrosion in milling circuits
63 Comminution Energy Testing Mines today perform Bond Work Index Tests on multiple samplesA map of the drill core data is produced to show contours of ore with different Work Index RangesBall Mill, Rod Mill and Low Energy Crushing tests are doneThe mill will be designed based on Mine Production Schedule to allow the mill to achieve desired liberation on the hardest oreSome consideration is now being given to using these maps to do mine planning, so hard and soft ores can be blended toprovide 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 cascadeD Nc2 303 244 218 1512 12Nc =42.3(D-0.5)whereNc = 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 Africapioneered in N.A.variable speed drives