Chapter 3. Size Reduction and Energy Requirement 3. INTRODUCTION In nature, minerals exist in physical and chemical combinations with each other. To separate minerals of commercial interest from the host rock both physical and chemical methods are employed. Most minerals are mined in the form of large rocks. Others like the ilmenite, rutile, zircon, leucoxene, heavy minerals or alluvial placer deposits of gold are found decimated amongst sand in beaches or in riverbeds. To access the minerals in the host rocks, they have to be crushed and even ground. When a maximum amount of the mineral of interest is separated by comminution from the parent rock, that size is usually known as the liberation size. The aim of comminution is to maximise the liberation of the mineral from the host rock. Usually the concentration of useful minerals in host rocks are low, therefore large tonnages of host rocks have to be mined to recover sufficient quantities of the useful mineral to make the operation commercially viable. The first step in the recovery process of minerals from the host rocks therefore is to reduce the size of rock by crushing and grinding. The equipment used and their operation are discussed in subsequent chapters. 3.1. Design of Size Reduction Processes The process of size reduction is normally designed to take place in single stage open circuit, single stage closed circuit or multiple stage open or closed circuit In some cases a combination of these methods are adopted. In a single stage, single pass, open circuit size reduction operation, the product consists of a range of particle sizes which seldom achieves the desired degree of liberation. Hence second or even third stages of size reduction are often necessary to progressively reduce the remaining particle size to liberate mineral particles to an acceptable degree (Fig. 3.1). In closed circuit, the product from the stage of size reduction is separated into relatively fine and coarse fractions. The coarser fraction is then collected and recrushed in the same unit as seen in Fig. 3.2. In so doing the load on the equipment for size reduction is increased and a circulating load is established, but the total number of units required for obtaining the same degree of size reductio is less. Several options in design exist in closed circuit grinding set-ups. The two most commonly used devices for size reduction are the crushers and grinding mills. The crushers are normally fed with rocks, up to about 1 meter in size, while the grinders are usually fed with rocks crushed down to a maximum size of about 50 mm. Larger rocks produced at the mines are initially separated by grizzlies, broken by hammers and then fed to the crushers The mechanisms of size reduction during crushing and grinding are different. The chief difference being that in crushing operations the size reduction is more by compression and impact and less by attrition while in grinding, the forces of attrition are much greater. The grinding operation is rather complex and its complexity can roughly be illustrated by Fig. 3.3. Spherical balls or cylindrical rods are mostly used as the grinding media. These media cascade within a mill and impinge on the ore thus providing a crushing action. As the balls and rods tumble within tubular mills, they provide a grinding action and forces of attrition, all
Transcript
Chapter 3. Size Reduction and Energy Requirement
3. INTRODUCTION
In nature, minerals exist in physical and chemical combinations with each other. To separateminerals of commercial interest from the host rock both physical and chemical methods areemployed. Most minerals are mined in the form of large rocks. Others like the ilmenite, rutile,zircon, leucoxene, heavy minerals or alluvial placer deposits of gold are found decimatedamongst sand in beaches or in riverbeds. To access the minerals in the host rocks, they have tobe crushed and even ground. When a maximum amount of the mineral of interest is separatedby comminution from the parent rock, that size is usually known as the liberation size. Theaim of comminution is to maximise the liberation of the mineral from the host rock. Usuallythe concentration of useful minerals in host rocks are low, therefore large tonnages of hostrocks have to be mined to recover sufficient quantities of the useful mineral to make theoperation commercially viable. The first step in the recovery process of minerals from the hostrocks therefore is to reduce the size of rock by crushing and grinding. The equipment used andtheir operation are discussed in subsequent chapters.
3.1. Design of Size Reduction ProcessesThe process of size reduction is normally designed to take place in single stage open
circuit, single stage closed circuit or multiple stage open or closed circuit In some cases acombination of these methods are adopted. In a single stage, single pass, open circuit sizereduction operation, the product consists of a range of particle sizes which seldom achievesthe desired degree of liberation. Hence second or even third stages of size reduction are oftennecessary to progressively reduce the remaining particle size to liberate mineral particles to anacceptable degree (Fig. 3.1).
In closed circuit, the product from the stage of size reduction is separated into relativelyfine and coarse fractions. The coarser fraction is then collected and recrushed in the same unitas seen in Fig. 3.2. In so doing the load on the equipment for size reduction is increased and acirculating load is established, but the total number of units required for obtaining the samedegree of size reductio is less.
Several options in design exist in closed circuit grinding set-ups. The two most commonlyused devices for size reduction are the crushers and grinding mills. The crushers are normallyfed with rocks, up to about 1 meter in size, while the grinders are usually fed with rockscrushed down to a maximum size of about 50 mm. Larger rocks produced at the mines areinitially separated by grizzlies, broken by hammers and then fed to the crushers
The mechanisms of size reduction during crushing and grinding are different. The chiefdifference being that in crushing operations the size reduction is more by compression andimpact and less by attrition while in grinding, the forces of attrition are much greater. Thegrinding operation is rather complex and its complexity can roughly be illustrated by Fig. 3.3.
Spherical balls or cylindrical rods are mostly used as the grinding media. These mediacascade within a mill and impinge on the ore thus providing a crushing action. As the ballsand rods tumble within tubular mills, they provide a grinding action and forces of attrition, all
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Feed
Grizzley screen
Primary Jaw crustier
Secondary cone crusher
Tertiary cone crusher
Fig. 3.1. Open circuit crushing
Feed
Product
P ri ma ly J aw crustier
Screen Oversize
Product
Fig. 3.2. Closed circuit crushing
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abrasion
Fig. 3.3. A Ball Mill; abrasion; impact breakage;B Rod Mill; rods preferentially grind the coarse particles
of which result in further reduction of the size of the rock particles. Impact breakage occursas balls or rods drop into the toe of the charge and abrasion or attrition occurs as the layer ofballs or rods slides over each other or against the mill liner.
In designing a plant for size reduction the two main features of interest are:
1.2.
The power required for size reductionThe choice of crushers and grinders
The power or energy required is the sum of the work required to crush or grind the rock aswell as rotate the mill. The power required depends on the hardness of the rock, the initialsize and the final product size required to achieve reasonable liberation of the mineral ofinterest, from the host rock.
3.2. Energy for Size Reduction - Work IndexOver the years several workers [1-12] have attempted to determine the energy required for
crushing rocks. For a metallurgist this study is of interest where it is necessary to liberate themineral embedded in the rock. It had been generally observed that in the process of sizereduction, as the size of the particles diminishes the surface area of the particles increases. Soa measure of size or surface area before and after size reduction would indicate the extent ofenergy expended in the comminution process. Hence if E was the energy used for a desiredsize reduction, which resulted in a change in surface area S, it has been found that [13-17]:
dE =k[S ndS] (3.1)
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where k is a constant and a function of the crushing strength of the rock. Different workershave determined the value of the exponent n, as:
n =n =n =
- 2- 1-1.5
(Rittinger)(Kick)(Bond)
It has been found that Rittinger's expression, n = - 2 , is more applicable for coarse sizereduction while that of Kick, n = - 1, is more appropriate for finer size reductions in theregion where large surface areas of particles are exposed as in the case of grinding operations.Bond's intermediate value of 1.5 covers almost the entire range of particles.
Substituting n = - 1.5 in equation 3.1 and integrating between feed particle size, F, andproduct particle size, P, yields Bond's general expression for the energy required in sizereduction as:
E = 2k 4 = - - j = (3-2)LVP V F J
where k is a constant and a function of ore characteristics. For size reduction of ore in aclosed circuit reduction process Bond derived the specific energy for grinding as:
EG=10Wj - T = — 7 = kWh/t (3.3)p V*1
Eq. (3.3) is the result of fundamental work by Bond. It has now been accepted universally.In practice instead of a specific size of feed, a spread of particle sizes is generated at themines, as a result of blasting, and is charged to the size reduction process. As a result of thecrushing operation, a spread of smaller product size is obtained and fed to the grinding mill.To use Eq. (3.3) therefore, Bond considered the work as the energy required for the reductionof feed particles that passed 80% of a particular sieve to a product particle size that passed80% of a sieve opening.
The final form of Bond's equation for size reduction of a mass of feed, MF, in closedcircuit grinding is now written as:
EG = 1 0 W i [ ^ - ^ ] M F kWh (3.4)
where F = 80% passing size of the feed in microns, (written as Fgo)P = 80% passing size of the product in microns (written asWi = A constant for the ore
Wj is known as the Bond Work Index and represents the work required to reduce the orefrom an infinite size to 100 um.
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The value of Wi can be considered to be independent of any classifier placed in the circuit.The terms F and P are usually written as Fgo and Pgo, the subscripts denoting the sieve size offeed and product respectively through which 80% of the feed and product passes. The terms
—P= and -7= are dimensionless, as the number 10 represents VlOO microns.VP VF
By definition the specific grinding energy is the energy required per unit mass of the rock.The specific grinding energy of a particular mineral is written as:
E o = 101 1
kWh/t (3.5)
NOTE: 1. kWh/t x 3600 = Joules/t2. While 80% passing a particular sieve is accepted as standard for determining
the Work Index, as recommended by Bond, some use 75% instead.
In Bond's equation, (Eq. (3.3)), the grinding energy, EG, required for size reduction of rocksin industrial tumbling mills was based on mill shaft power, PM, and on mill capacity (Q). Therelationship between these parameters is:
E Mill Power *M ^3 QE ^ Q
^ Mill capacity Q
For any rock therefore the energy required for comminution may be determined, providedthe Work index Wj is known.
During manual crushing and disintegration of a rock with a hammer, or during mechanicalcrashing operations, the size reduction of large sized rocks and ores is mostly by sharp impactaction, and less so by the impact and attrition experienced in tumbling mills. The equationused by Bond is inappropriate to determine the energy required for crushing. To cover thisdiscrepancy Oka and Majima [9] found that in such cases the exponent of n (1.5) in equation3.1 should be replaced by (l+[6/B]). This equation reverts to the Bond equation (equation 3.3)by taking the value of B as 12 and integrating, thus;
(3-7)
which in effect is the Bond equation.Bond's original work on establishing the energy for size reduction was established in a 2.44
m (8 foot) internal diameter wet grinding overflow type ball mill. Doubt is now expressedwhether the derived empirical equation is applicable to high pressure roller crushers whereone stage open circuit takes place. According to Klymowsky and Lin [18] indications are thatthe Rittinger expression, E = K (1/P —1/F), is more applicable for size reduction by highpressure rolls.
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hammer hammer
specimen
wheel
413 mm
762 mm 279 mm radius
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3.3. Estimation of Work Index for crushers and grinding millsThe standard laboratory procedures for estimating work index can be divided into two
categories. The first category involves tests on individual particles of rock and the secondcategory deals with bulk rock material. A number of tests are required to get an idea of therock strength. The standard laboratory procedures adopted in industry are:
• Bond Pendulum test• Narayanan and Whitens rebound pendulum test• JKMRC drop test• Bond ball mill grinding test• Bond rod mill grinding test
3.3.1 Bond Pendulum TestIn this test the energy required to crush a dry ore particle by the impact of two swinginghammers is determined. The standard method adopted by Bond is as follows [5]:
Two equal hammers, 13.6 kg each, (Fig. 3.4), about 0.7 m in length and the striking face 50x 50 mm are suspended from two (bicycle) wheel rims. The hammers are raised to a knownheight and when released strike simultaneous blows on opposite sides of a dry test piece (-7.6cm + 5.0 cm). The test piece is suspended or supported with its smallest dimension betweenthe hammers. The hammers are initially raised to make an angle of 10° with the vertical thenreleased. After the impact the test piece is examined for fracture and the number of piecesbroken is recorded. If the piece is not completely broken, the hammers are raised a further 5°and the process repeated till the piece is completely shattered. The heights of the hammers arerecorded each time. At least 10 rock samples should be used per test but 20 is preferred.
279 mm radius
413 mm
•—I hammer
Fig. 3.4. Bond's Impact Test at the point of impact with the specimen
The impact crushing strength (I) is calculated after each operation from the expression:
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2 x Mass of one hammer x Final height of hammer , , ,„ „.1= - kg.m/mm (3.8)
dwhere d = thickness of sample in mm
The value of I is usually averaged over the ten to twenty tests. The impact crushing strengthof rocks so determined is used to calculate the Bond crushing work index using theexpression:
Relative Density of samplekWh/t (3.9)
where C is a constant which converts the impact crushing strength, numerically anddimensionally to the work index,C = 2.59 in the original Bond equation where I is in ft-lb/in and W( in kWh/shortton; C = 53.49 for I in Joules/mm and Wi in kWh/t (metric tonne).
The Bond impact test is considered to be inaccurate in that it consistently underestimatesthe actual operating crushabilities of most materials studied [19].
In a slightly modified apparatus by Metso, the bicycle wheels are replaced by slotted arcs ina fixed circle where notches are calibrated to indicate the energy released by hammers frompre-determined heights or notches. Results from this apparatus require careful evaluationbefore acceptance.
It should be noted that Bond's Grinding Work Index and Bond's Crushing Index are notthe same though in the literature both are referred to as Wj.
3.3.2 Narayanan and Whiten's Rebound Pendulum TestA slightly different test for measuring the crushing strengths of rocks was developed byNarayanan and Whiten [20]. In this test, the specimen is shattered against a suspendedpendulum by an impact pendulum (Fig. 3.5). On impact, part of the energy is absorbed in theshatter of the sample, and part transmitted to the anvil block, which is displaced by the forceof impact and commences oscillating. The remaining energy is dissipated as sound, heat etc.
Two sizes of anvil-blocks are used depending on the size of the sample and the size of theimpact pendulum. The pendulum characteristics both types are summarised in Table 3.1.
Table 3.1Alternative rebound pendulum masses
Sample Size, microns Mass of rebound pendulum Mass of striking(anvil - block) pendulum
-3150+1120 40.35 kg 19.86 kg-1120 + 475 6.364 kg 4.441 kg
The swing of the pendulum is recorded by a computer, which receives signals from a laserbeam impinging on fins fixed to the rebound pendulum. From simple geometry it can be seen
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that the displacement, D, of the input pendulum from the rest position is given by:
D = L sin a (3.10)
where L is the length of cord of suspension and a the angle subtended with the vertical fromthe position of rest. Similarly, the horizontal displacement of the rebound pendulum afterimpact is given by L sin 9, where 0 is the angle subtended from the vertical from the positionof rest of the rebound pendulum. The angle 8 is determined from the period of oscillation,Pos, of the pendulum from the swing using the expression:
Pos=A + B8 2 (3.11)
To determine the value of 8, the value of the constants A and B have to be determined.This is carried out by raising the pendulum to at least three heights and the Pos for the firstswing of the pendulum determined. The height, H, to which the pendulum is raised, is givenby the relation:
H = L ( l - c o s a ) (3.12)
The velocity, vs°, of the striking pendulum at the point of impact before collision is:
vs° =(2gH)0-5 = 2gL(l-cosa)]0 5 (3.13)
Reboundpendulum
Striking pendulum
sample
Fig. 3.5. Rebound pendulum device
and the energy of the striking pendulum from the point of release to the point of impact is:
Es = MSH = Ms L(l-cosa) (3.14)
where Ms is the mass of the striking pendulum.
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After the strike by the striking or input pendulum, when the block or anvil or reboundpendulum swings away from its position of rest, the velocity of the rebound pendulum wouldbe:
VB1 = (2gHB)a5 (3.15)
where HB = the vertical height attained by the block pendulum andVB1 = the velocity of the block or rebound pendulum after impact,
and the corresponding energy of rebound will be:
E B = M B H B (3.16)
where MB = the mass of the block or rebound pendulum.
After the impact, the velocity of the striking pendulum decreases, and vs°now will be givenby:
v s°-vB°=
where e = the coefficient of restitutionVB° = the velocity of the block before impactvs1 = the velocity of the striking pendulum after impact
As the initial velocity of the rebound block pendulum is zero, applying Newton's Law ofconservation of energy, the coefficient of restitution will be:
(3-18)
The energy for crushing, E, is the difference between the energy of the input pendulum andthe energy of the rebound pendulum and is computed from the following expression:
E = Es(l-ea)f MB 1 (3.19)
Units: Energy terms (E) = kWh/t = 3600 kJ/tMass = kgThe value of E = 0 - 0 . 2
The results obtained with the larger anvil block have been found to agree well with theenergy consumed in Autogenous and Semi-Autogenous Grinding (SAG) mills, while resultsfrom the smaller anvil agree more with ball and rod mill comminution systems. Theestimation of energy for crushing by this method could be lengthy and tedious.
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3.3.3 JKMRC-Drop Weight Crushing TestAttempts at a much simpler and direct method of estimating the energy required for crushingrocks have been attempted by several workers like Gross [16], Piret [21], Hoffler and Herbst[22]. The method developed by Brown [23] is now accepted.
Fig. 3.6 is a schematic diagram of the apparatus developed by Brown. Rock is placed on arigid heavy base-plate and crushed by weights falling from predetermined heights. The fall ischannelled by guide rails. Conditions of the test include:
• Weights range vary from 20 kg to 50 kg• Drop height vary from 0.5 to 1.0 m
Specific gravity of rocks should lie between 2800 kg/m3 and 4000 kg/m3. The energy ofcrushing ranges from to 0.01 to 50 kWh/t on a 10 to 50 mm particle size.
The rock sample is usually screened between close size ranges and the average mass ofparticles determined. The height from which the weight is released to affect breakage ismeasured.
The energy of breakage per unit mass is calculated from the expression:
_0.0272Mc
M(3.20)
= 97.9M
Joules/t
sample
guide rails
weight
steel plate
Fig. 3.6. Drop weight test
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where E = Input energy per tonne, Joules/t,H = Height, cm,Me = Mass of crushing weight, kg,M = Mean mass of sample.
After the crushing operation, the weight comes to rest on the broken particles. Thus theactual distance travelled by the weight is therefore less than the measured height, A correctionin the actual distance travelled by the crushing weight has to be made by replacing H by(H-HR) where HR is the initial distance from the base plate to the position of rest of the leadweight after crushing. The rebound energy after impact, if present, has been claimed to bevery small with respect to the input energy and is therefore neglected [24].
The usual practice is to use a 20 kg block for crushing. The number of particles rangesbetween 20-50 per size/energy combination totalling 500 to 1300 with a corresponding massof 50 - 100 kg. If the mass is insufficient, it is increased. The energy of breakage is regulatedby the ratio of the mass of the block and the height from which it is dropped. The breakageenergy determined by this method agree well with the energy required by commercial crushersand AG/SAG mills. It is used as a useful guide for designing crushers and plant flowsheets.
3.3.4 Bond Ball Mill Standard TestThe method for determining the energy consumptions for tumbling mill conditions has moreor less been standardised by laboratory tests and adopted after Bond.
The conditions of the tests are:
Mill Size = 305 mm (internal diameter) x 305 mm (internal length)
Material Dry mineralSize - reduced to 100 % < 3350 um (6 mesh) and about 80% < 2000 urnQuantity - 700 cm3 (tapped down to give a reproducible bulk density)
Mill Charge-Steel Balls - Total mass =20.125 kgTotal No =285Ball diameters made up as:
43x3.7 cm, 9.094 kg67x3.0 cm, 7.444 kg10x2.5 cm, 0.694 kg71x1.9 cm, 2.078 kg94x1.55 cm, 0.815 kg
Mill Rotation - 70 rev/min
Procedure:Step 1 Ball plus ore charge is ground for 100 revolutions.Step 2 Ground charge is screened (classified) at the desired test mesh size (D), which is
usually 106 um (150 mesh).Step 3 Under size is removed and replaced by an equivalent mass of original feed
forming a new mill feed.Step 4. The new mix is ground again as above by the number of revolutions calculated to
produce a circulating load of 250%, That is, 28.6% (1/3.5 of total charge) will
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pass the required chosen screen at the end of the cycle.
Step 5 The process is continued till the net mass of the undersize produced per revolutionis constant. When this is achieved, then the mass, in grams, of the undersizeproduced per revolution is equivalent to a 250% circulating load.
Step 6 A size analysis is performed on the screen undersize and the original mill feed.
The average of the last three constant net mass of undersize per revolution in grams (G) is themeasure of the ball mill grindability.
The ball mill work index, Wj Test> is calculated from the expression:
WlTest = ^ ,- kWh/t (3.21)
D ° 2 3 G 0 8 2 1 0 1 - ' '„ . .0 V F 8 0 J
where ¥so = Feed size (microns) through which 80% of the feed will pass,P8o = Product size (microns) through which 80% of the product will pass.D = Aperture (microns) of the classifying screen andG = net mass (grams) of undersize product per unit revolution of the mill.
Note: Bond had used short tons to determine work index. To convert to metric tons thefactor 1.1 has been used here, (44.5 x 1.1 = 48.95).
Due to its extensive use, details of the procedure is given in appendix.B-2, B-3.Instead of 80% passing a certain selected screen size some workers in Australia use 75 %
passing. It is therefore imperative that the screen size be mentioned when work index isreported.
The Wj jest value measured corresponds to the motor output power Bond correlated to anaverage overflow discharge ball mill of 2.44 m internal diameter, wet grinding in closedcircuit with a 250% circulating load.
Eqs. (3.21) and (3.5) are used extensively to calculate the work index and energy forcomminution from data collected in operating plants. To distinguish the work index valuedetermined under laboratory conditions from that required at the plant the concept of the plantoperating work index (WoO was developed by Rowland [25] and described by Rowland andKjos [10], in terms of the energy requirements in the test mill and the commercial mill.According to Rowland, the ratio of the work indices equals the ratio of energies required inthe test and the plant mills. That is:
Woj _ Energy required at Plant MillW; ~ Energy at Test Mill
(3.22)
To calculate the operating work index the work input is obtained from the mill powerwhich, if obtained from the motor power, has to be the power at the mill pinion shaft. That is,if adjustments were coupled directly to the pinion shaft, then motor output power is the millpinion shaft power. Work input is then obtained from the mill power (kW) by dividing it bythe circuit throughput (t/h).
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W,mill power
Oi
tonnage 101 _ 1
VP VF
(3.23)
In the Bond equation, the feed F is the feed to the grinding circuit and the product P, is theproduct from the grinding circuit. In an open circuit this is straightforward but in a closedcircuit mill, where a classifier is installed to return the course fraction to the mill, the workindex is based on the work done in reducing the size of the "new feed", that is, the originalfeed plus the coarse fraction from the product separated at the classifier and returned to themill feed.
The operating work index is used for:
1. Recording mill performance on a regular basis (hourly, daily etc.)2. Comparing current performance with historical data3. Comparing circuits in multi-circuit plants
Since the operating work index includes motor, drive and grinding inefficiencies, it is notdirectly comparable to the work index obtained from laboratory grindability tests. If motor anddrive losses are taken into account, then the operating index divided by the laboratorygrindability work index test can be used as a measure of grinding efficiency in the plant.
WGrinding efficiency = 1 0 0 — ^ - (3.24)
where Woic = operating work index, corrected for non-standard conditions and non-optimum feed,
= laboratory grindability work index.
3.3.5 Bond Rod Mill Standard TestStandard conditions for determining the work index of rod mills under laboratory conditionsare:
Mill Size = 305 mm (internal diameter) x 610 mm (internal length) with wave type lining
Material Dry mineralSize - reduced to 100 % < 13200 urnQuantity - 1250 cm3 (tapped down to give a reproducible bulk density)
Mill Charge-Steel Rods - 6 x 38.1 mm dia x 0.53 m long steel rods plus2 x 44.5 mm dia x 0.53 m long steel rodstotal mass = 33.38 kg
Procedure: (a detailed procedure is given in the appendix)
Step 1 To equalize the charge segregation at the ends of the mill, the mill is rotated in thelevel position for 8 revolutions then tilted up 5° for 1 revolution, tilted down 5° for1 revolution then returned to the level position for 8 revolutions and the cyclerepeated throughout the test.
Step 2 At the completion of the grind, the mill is tilted at 45° for 30 revolutions todischarge the contents.
Step 3 Ground charge is screened at the desired test mesh size (D).Under size is removed and replaced by an equivalent mass of original feedforming a new mill feed.
Step 4 The new mix is ground again as above by the number of revolutions calculated toproduce a circulating load equal to the new feed (1250 cm3), i.e. 100% circulatingload.
Step 5 The process is continued till the net mass of the undersize produced per revolutionis constant.
Step 6 A size analysis is performed on the screen undersize and the original mill feed.
The average of the last three constant net mass of undersize per revolution in grams (G) isthe measure of the rod mill grindability.
The work index is given by:
WlTest = ^ . kWh/t (3.25)D0.23 G0.625 1 Q 1 _ 1
Note: 1. Bond had used short tons to determine work index. To convert to metric tons thefactor 1.1 has been used here, (62 x 1.1 = 68.2).
2. Wj conforms to the motor output on an average overflow rod mill of 2.44 minternal diameter, wet grinding in open circuit.
3.3.6 Factors affecting the Work IndexThe Wj TEST values calculated from Eqs. (3.21) and (3.25) are based on Bond's work using alaboratory size tube mill. It is claimed that the Wi values obtained from a 2.44 m internaldiameter tube mill, operating under closed circuit wet grinding conditions agree well with thelaboratory sized test mill. However, the Bond Work Index (TEST) so determined has to becorrected for conditions encountered in industry that differ from the above conditions. Bonddefined eight correction factors.
1. Correction factor: Fl For conversion of Wj obtained under wet grinding conditions todry grinding:
Wj(Dry) = 1.3xWi(Wet) (3.26)
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1.0
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
50 60 70 80 90 100% passing sieve control size
Mu
ltip
lyin
g F
acto
r, F
2
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2. Correction factor; F2 For conversion to wet open circuit grinding index from wetclosed circuit grinding;
For open circuit grinding, the correction factor depends on the degree of control requiredon the product. Table 3.2 gives the multiplying factors against different sieve sizes used forcontrolling product size in closed circuit grinding.
Wi (wet open Circuit) = Wj ( wet closed circuit) x Multiplying factor
For example if Bond's work index Wj = 12.40 for wet closed circuit grinding where an 80%passing control screen was used, then the corresponding value for wet open circuit grindingaccording to Table 3.2 would be:
Wi open (wet) grinding = W, x 1.2 (closed) at 80% passing a size control= 12.4x1.2 = 14.8
For convenience of calculation, Table 3.2 is plotted in Fig. 3.7.
Table 3.2Multiplying factor for converting wet closed circuit Work Index to wet open circuit WorkIndex [26].
That is, greater than 1.5/(V W; Test) cm for a ball mill. In this situation the correction factor Fosis given by Eq. (3.28):
Fso ^ I-10- 1 (3.28)
4. Correction factor: F4 For extra fineness of grind: FQWhen the required product size is less than 75 microns and greater than 15 microns, it
implies that the product size has to be ground to an extra fine size. In such cases, the workindex will depend on the product size. The work index correction required is given by Eq.(3.29):
FG = ^ ^ (3.29)1 145P
5. Correction factor: F5 For low reduction ratio R, for ball mills: FRThis correction is applicable when the reduction ration, i.e., ratio of feed size to product
size is less than 6.The multiplying factor for different values of Fso/Pso is determined from the expression:
2(R-1.35)+0.26R 2(R-1.35)
( 3 3 0 )F80-1.35P80
6. Correction factor: F6 High or Low Reduction Ratio, Rod Milling:There is an optimum ratio of reduction for each rod mill due to the natural preference to
grind the coarser sizes by a rod charge. For higher throughputs leading to a coarser grind dueto lower residence times in the mill, the coarser particles spread the rods apart, disrupting thenormal grinding action. If the feed to the mill is reduced to attempt a finer grind, thereduction ratio increases, trying to produce a product finer than the rod mill should be capableof producing. For both cases of abnormal reduction ratios, a correction factor, F6, is appliedto the Bond Work Index, where:
F 6 = 1 +(R~RRo) ( 3 3 1 )
150
where RRO = optimum reduction ratio for the mill size = 8+5 —
L = Rod lengthD = Mill diameter (internal).
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This efficiency factor is only used when R is outside the range RRO ± 2.
7. Correction factor: F7 Mill Diameter:The grinding efficiency changes with mill diameter. The change arises from the change in
power drawn by the mill and the change is mill capacity with diameter. The correction factoris given as:
2 44Y"2
=^\ for D<3.81m
F7 = 0.914 for D £ 3.81m (3.32)
where the mill diameter, D, is in meters. It has been shown by Bond that for mills larger than3.81 m, the reduction in grinding energy resulting from mill diameter ceases and thecorrection factor is constant at the 3.81 m value of 0.914.
8. Correction factor: F8 Rod Milling:The correction factor for rod milling is complex and depends on the feed preparation. Bond
suggests two conditions:
1. For a rod mill only application, use an efficiency factor of 1.4 when the feed isproduced by open circuit crushing, and use a factor of 1.2 when the mill feed isproduced by closed circuit crushing.
2. For a rod mill-ball mill circuit, do not apply a mill diameter correction for the ball mill.If the rod mill feed is produced by open circuit crushing, use a factor of 1.2 for the rodmill stage only. If the rod mill feed is 80% passing 12 mm or less (e.g. from a closedcircuit crusher) do not apply a rod mill efficiency factor. Other correction factors suchas mill diameter and reduction ratio however do apply.
The uncertainty in this correction factor means that it has little value in calculating,and the efficiency of plant rod mill performance. Thus the test work index value multipliedby the product of the correction factors will provide an estimate of the true (plant) work indexvalue.
Wi = WiTEsT x F l x F 2 x ... xF7xF8 (3.33)
Factors for condition not applicable should be taken as 1.The Bond Work Index value changes with the sieve size chosen during a particular test. For
example, instead of choosing the screen size through which 80% of the ore passes, the screensize through which 75% of the ore passed may be chosen to suit a particular condition of milloperation. Bond's original expression for the work index is based on 80% of the materialpassing a screen size. This has now been adopted as the standard. Any deviation from thisstandard would require the determination of a corresponding equivalence. The method ofdetermining the equivalence may be explained by the following example.
8080
Example 3.1A gold ore was crushed and screened so that 99% passed 9.5 mm size screen. Laboratorymeasurement showed that the product size of gold was 75% minus 63 microns. A standardball-mill Bond test indicated that the grindability was 2.28 grams per revolution at a testscreen size of 106 microns. The ore was ground in a wet closed circuit ball mill at athroughput rate of 150 t/h. Estimate the work index for a mill of I.D. 2.0 m.
SolutionStep 1.Establish the Fso by referring to Table 3.3.Feed size (F80) equivalent from Table 3.3 = 6000 urn
Step 2.Next establish the Pgo from a Gaudin-Schuhmann plot of the sieve analysis, if available. If thesieve analysis was not available then use the relation:
Size 2 =_ [Percent Pas sing Size 2 |
Percent passing Sizel Jx Sizel
Table 3.3Feed size and approximate 80 % passing sizes (in mm)
Optimum feed top size = 1.5/(V Wj Test) = 1.5/V8.10 = 0.53 cm = 5300 microns. The feedsize is greater than this hence a coarse feed correction factor needs to be applied.
Thus the overall correction factor, F = 1.0005 x 1.016 x 1.041 = 1.058 and the correctedwork index is given by:
= 8.10x1.058 = 8.57 kWh/t
3.3.7 Effect of the Test Screen Size on the Work IndexThe Bond Work Index is not solely a material constant but is influenced by the grindingconditions. For example, the finer the grind size desired, the higher is the kWh/t required togrind to that size. Magdalinovic [27] measured the Bond Work Index of three ore types usingdifferent test screen sizes. He produced a correlation between the mass of test screenundersize per revolution, G, and the square root of the test screen size, D:
G = K , V D (3.35)
The constant Ki is dependent on the ore type. Magdalinovic also produced a relationshipbetween the test screen size and the 80% passing size of the test screen undersize where:
8282
D = K2 Pso (3.36)
The constant K2 is also dependent on ore type and ranged from 1.4 to 1.5. A regression ofMagdalinovic's data including the feed 80% passing size gives an average value of 1.485 forK2. If we extend this relationship to any sample of screened material then this gives anapproximate estimate of the 80% passing size as 67.3% of the top size. This compares with avalue of 66.7% of the 99% passing size obtained from data in Table 3.3.
Using Magdalinovic's method, from the results of a Bond Work index test at a single testscreen size, the constants Ki and K2 can be calculated and from these values, the Work Indexat any test screen size can be estimated.
3.3.8 Approximation methods for Work IndexThe Bond method of measurement of the grindability of ores in rod mills and ball mills is longand tedious and requires a standard set of grinding conditions; mill size, ball charge etc. Anumber of approximate methods have been reported that shorten or approximate the workindex estimation.
1. Magdalinovic Method:The method proposed by Magdalinovic [27] reduces the number of grinds required fromapproximately five to two. The first grind is to determine the grinding rate of screenundersize. This grinding rate is then used to adjust the number of mill revolutions in thesecond grind to give 250% circulating load.
The method uses the standard Bond Mill (305 mm diameter x 305 mm length) and the Bondball charge. A summary of the procedure is as follows:
1. The ore is crushed to the same size (-3.35 mm) as in the Bond method and a subsample taken to determine the size analysis of the new feed (include a screen equal tothe test screen in the size analysis to make later calculations easier). From the sizeanalysis, the 80% passing size of the feed, Fgo, is determined.
2. A mass, M, of 700 mL of the crashed ore is measured which represents the mill chargemass.
3. The "new feed" material is riffle split into two equal portions of mass (M/3.5).4. Approximately 4 kg of the ore is screened on the test screen (the separating size of the
closed circuit screen/classifier) and the undersize is discarded.5. The oversize is riffle split into two masses equal to (2.5M/3.5). This mass, Me,
represents the circulating mass at 250 % circulating load.6. One portion of (2.5M/3.5) from step 5 is combined with one portion of (M/3.5) from
step 3 to give a combined mass of M, the charge to the first grind.
7. The two remaining portions are combined to give a second mass of M, the charge tothe second grind. Thus the feed to each of the two grinds should be identical in termsof mass and size.
8. The first sample is placed into the ball mill and ground for 100 revolutions at a millspeed of 70% of the critical speed.
9. After the grind, the entire sample is screened at the test screen size and the mass of the
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oversize is recorded. This mass Mos should be equal to the mass Me at a circulatingload of 250%.
10. The oversize grinding rate constant, k, is calculated using the equation:
= n ( l n M 0 - l n M 0 S )
N k ' '
where n = number of mill revolutions per minuteN = number of mill revolutions in the first testMos - mass of test screen oversize after grindingMo = mass of test screen oversize at the beginning of the grinding test
11. The total number of mill revolutions for the second grinding test (N2) is calculated fromthe equation:
= n / . ( l + 0.4mo)
k
where m0 = fraction of test screen oversize in the new feed (obtained from step 1).
12. The mill is loaded with the second charge and grind for N2 revolutions.13. After grinding, the entire mill charge is screened on the test screen and the oversize
and undersize weighed. The oversize should be approximately equal to (2.5M/3.5) andthe mass of the undersize, Mus, should be approximately equal to M/3.5.
14. The size analysis of the test screen undersize is determine and the 80% passing size(Pso) of the product calculated.
15. The new undersize per mill revolution, G, in the second grind is then determined usingthe equation:
Mus--Ul(l-mJG = ^ (3.39)
N 2
16. The ore Work Index is then calculated using the Bond formula (Eq. 3.21).
This method reduces the time of measurement and where the ore is homogeneous, giveswork index values within 7% of the Bond method. However, where the ore contains soft andhard components, a true Bond test will have a recirculating load which is composedpredominantly of the harder component and hence will give a higher Work Index valueconsistent with closed circuit grinding. Since the Magdalinovic method uses the same feed toeach grinding step, this harder material in the circulating load is not simulated and hence themethod will give a lower Work Index value.
2. Methods using a non-standard mill and charge
If a standard Bond mill is not available then an approximate Work Index value can beobtained if a sample of ore of known Work Index is available [28], The non-standard mill can
8484
be "calibrated" using the ore of known Work Index as follows:
1. A sample of known mass of the unknown ore is ground for a known period of time toproduce the desired grind. Berry and Bruce use 2 kg of -1.7 mm (10 mesh) feed groundwet.
2. The same mass of the ore of known Work Index is ground in the same mill under thesame conditions of feed size, mill and charge size and grind time.
3. The size analysis of the feed and products is determined from each grind, and hence theFgo and Pso values are evaluated.
Since the mill conditions in both grinds are the same, the energy used to grind the unknownore should be approximately the same as the energy used to grind the reference ore of knownBond Work Index. This can be calculated using Bond's Eq. (3.5). The Bond Work Index ofthe unknown ore can then be estimated from the equality given in Eq. (3.40).
F - W iREF I ̂ = ^ — ^ = I (3.40)
where Wnj = Bond Work Index of the unknown ore,WJREF = Bond Work Index of the reference ore,Fu, Pu = Fgo and Pso of the unknown ore,FREF, PREF = FsoandPsoof the reference ore.
Horst and Bassarear [29] used a similar —1.7 mm (10 mesh) feed in a non-Bond laboratorymill according to the following procedure:1. The size distribution of the reference ore feed is measured.2. A 1 kg sample of a reference ore (known Bond Work Index) is ground for a period of
time to achieve the desired grind.3. Three samples of the unknown ore under the same grinding conditions are ground for
different periods of time that include times shorter and longer than in step 2.4. The size analysis results from products from the three grinds from step 3 are fitted to a
simple first order rate equation:
him, = In m01 - kj t (3.41)
where mi = cumulative mass fraction retained on the ith sieve,nioi = cumulative mass fraction retained on the ith sieve at zero time,kj = comminution coefficient of the fraction coarser that the i* sieve,t = time.
5. From the values of kj, the product size distribution of the unknown ore is calculatedfrom the same feed size distribution as the reference ore, which has been ground for thesame time and using Eq. (3.41).
6. From step 5, the 80% passing size of the grind product for the unknown ore is estimated.7. The Work Index of the unknown ore is then determined from Eq. (3.40).
8585
This method has been shown to be more accurate that the method of Berry and Brucehowever the procedure is just as lengthy as the standard Bond test and not all ores follow thesimple first order breakage of Eq. (3.41).
3. Simulation methodsAn algorithm for the simulation of the Bond grindability, G, was developed by Kapur [30].The mass of the test screen oversize, MQS, after the first grind of the Bond Test is given by:
Mos = MoM^t) (3.42)
where Mo = mass of test screen oversize at the beginning of the grind,M = mass of mill charge,J(t) = a function of grind time, t.
Kapur showed that it was possible to estimate the grindability and the Work Index from thefirst two cycles of the Bond test. He obtained the following empirical expression for thegrindability;
GbP = -Mo Mi G K (3.43)
where GbP = mass of the undersize per mill revolution (g/rev),Mi = mass of new feed in the first grind,G = batch grinding parameter, related to the grinding rate of the fresh feed,
K =3
G' = grinding parameter of the circulating load.
In practice, K is assumed to be equal to unity. The work index is calculated by anempirical equation:
Wi = 2.648 Pi0406 (-G2)-°-810(RoM,)-"53(l-Ro)-0099 (3.44)
where Gj = grinding parameter from the second grind,Pi = 80% passing size of the product from the first grind.
The calculated values of G (g/rev), using Kapur's method, were higher than the measuredvalues for softer ores and lower than the measured values for harder ores.
Austin et al. [26] has shown that batch grinding can be simulated by using the size-massbalance grinding equations. It should be possible then to simulate the Bond test by computersimulation, provided that the breakage distribution function, By, and the breakage ratefunction, Si, are known. Lewis et al. [31] back calculated these breakage functions from thefirst cycle of a Bond grinding test, Yan and Eaton [32] went further and measured thebreakage parameters for two ore types (one hard and one soft) and simulated the Bond test.Their results gave work index values of 13.1 and 5.6 kWh/t compared to measured values of14.0 and 6.6 kWh/t respectively. The test work involved in determination of the breakage
86
0
5
10
15
20
25
30
0 10 20 30
Bond Work Index (kWh/t)
Ten
sile
Str
ng
th (
MP
a)
0
50
100
150
200
250
300
350
0 5 10 15 20 25 30
Bond Work Index (kWh/t)
UC
S (
MP
a)
86
parameters can be even longer that that required for a Bond test. However potentially muchmore information can be obtained from the data and further computer simulations.
Subasinghe and Kanau [33] evaluated the breakage distribution function and the ratefunction of a 1 kg charge of a single size interval (-3.35 + 2.36 mm). The breakage rate andbreakage distribution functions were used to simulate the Bond batch grinds using theapproach of Lewis et al [31], however, the simulated grindabilities deviated considerably fromthe measured results.
Subasinghe and Kanau found that the zero order fines production rates, corresponding to(By Sj), for the 150 and 106 micron sizes correlated well with the Bond grindabilities. TheBond grindabilities corresponding to the observed gradients evaluated from the regressionlines showed a superior correlation compared to those obtained from Kapur's method.
4. Work Index from Rock MechanicsEverell [34] believed that the mechanism of breakage of particles in a grinding mill wasanalogous to the slow compression loading of irregular particles and that the specific rate ofbreakage for a particular size of fragment is an inverse function of the average failure load ofthe particles. Everell et al [35] developed a model to describe the relationship between thegrinding selection function (breakage rate) and the physio-mechanical properties of the rocks.The advantage in such a relationship lies in the wealth of rock strength data determined ondrill core during mine development being available to predict energy demands in thecomminution circuits.
Briggs [36] measured the tensile strength, using the Brazil tensile test, and the point loadcompressive strength of four rock types of different grindabilities. These results werecompared to the Bond Work Index of the ores as measured by the Magdalinovic method [27].The results in Fig. 3.8 show that there is a good correlation between the Bond Work Index andthe tensile strength and the Equivalent Uniaxial Compressive Strength (EUCS). Some of thescatter in the graphs are due to the structure of the rock. For example one rock type was abanded iron, heavily mineralised with sulphides with numerous planes of weakness on amacro scale. This affected the mechanical properties when tested on large specimens.However when the grinding tests were carried out at relatively small particle sizes, the planesof weakness were no longer present and the ore became more competent.
350
300
250
200
150
100
010
0
MP
a)rn
gth
(le
Si
snsi
i-
30
25
20
15
10
5
0
•
•/
•
D
/D
•
/
y
10 20
Bond Work Index (kWh/t)
30 5 10 15 20 25Bond Work Index (kWh/t)
30
Fig. 3.8. Bond Work Index vs tensile strength and the EUCS; • Briggs [36] D Yan [37].
8787
The correlation between Bond Work Index and tensile strength is an indication that thegrinding mechanism in the work index test favours abrasion type breakage given that tensilestrength is a fair indication of the abrasiveness of a rock.
Briggs also measured the breakage rate and breakage distribution function of the ores andcompared the breakage rate and Bond Work Index. There was a good correlation between therock strength data and the breakage rate with higher strength rocks having a lower breakagerate. However the data set for these tests was small and further work needs to be done toconfirm the relationship.
Bearman et al [38] measured a wide range of rock strength properties and correlated theseto the JKMRC drop weight test data. Conclusions were that this technique will enable thedata required for comminution plant design to be obtained from mechanical tests on drill coresamples.
5. Chakrabarti's Statistical MethodChakrabarti [39] has advanced a simple statistical correlation method of estimating workindex using the Rosin-Rammler and Gaudin-Schuhmann size distribution parameters.Chakrabarti considered the Rosin-Rammler and Gates-Gaudin-Schuhmann functions of 35data sets covering work indices between 5.36 and 23.93. The best correlation was found withthe Rosin-Rammler parameters.
According to Chakrabarti, the work index of an unknown rock material can be obtained byfirstly crushing the rock to less than 3327 microns, avoiding over crushing by using lowenergy impact or compression and by closing the circuit with a 3327 micron screen. Thecrushed product is sized using a Tyler standard sieve nest set between 3350 and 75 micronsand the Rosin-Rammler distribution parameters determined. The work index is then calculatedfrom the statistical power relation:
Wj = a + Axi + cx2 + dxi2 + ex22+fxi x2 (3.45)
where xj is the size parameter, x1, of the Rosin-Rammler equation of 3327 micron feed and x2
is the distribution parameter, b, of the Rosin-Rammler distribution of the same feed material(see Chapter 2.2).
Chakrabarti suggests that a modified form of the Rosin-Rammler equation gives a better fitto the experimental size distributions. The constants a, b, c, d, e and/were found to have thevalues of:
a = 7.581733618, b = 0.003845, c = -14.83865521, d= -6.165619037 x 10"7,e = 15.15586454,/= 0.000789264
The correlation between experimental and calculated work indices is shown in Fig. 3.9based on the unmodified and modified Rosin-Rammler function.
Whilst Fig. 3.9 shows that there is a trend, the equation requires further refinement fromlarger data sets before it can be adopted.
3.3.9 Work Index of Ore BlendsThe blending of different ore types is common practice to provide a consistent feed to aprocess in terms of uniform hardness or assay. When several different ore deposits of varying
88
0
5
10
15
20
25
0 5 10 15 20 25
Wi (calc)
Wi (
exp
)
25
20
15
10
s
•
•
DEl
_ JP •• mi /
•
•
m
y
s
10 15Wi (calc)
20 25
Fig. 3.9. Comparison between calculated and experimental Bond work index values of a range of oretypes based on Chakrabarti's correlation ( • modified; • unmodified Rosin-Rammler equation)
grindabilities are blended prior to closed circuit grinding, the work index of the ore is not anaverage or even a weighted average of the work indices of the components. The reason forthis is that the circulating load will consist predominantly of the harder component and if thecirculating load is high then the mill charge will also consist of mostly the harder components.Thus the work index of the blend will be weighted towards the harder components [32]. Fig.3.10 shows the Bond Work Index of a blend of hard and soft ores as a function of the volumefraction of the softer ore in the blend. The dotted line between the two extremes indicates theweighted average work index based on volume fraction. The work index values of theMagdalinovic method agrees with this average Bond Work Index because the method doesn'tsimulate the recycling of harder components into the mill charge. On the other hand, theWork Index obtained using the standard Bond test shows the weighting of the Work Indextowards the harder component as a result of the circulating load.
Yan and Eaton [32] also measured the breakage rates and breakage distribution functionsof the different ore blends in order to predict the Work Index of the blend by simulation of theBond batch grinding test. Qualitative analysis of the breakage properties suggests that there isan interaction between the components of the blend that affect their individual breakage rates.The breakage properties of the harder material appears to have a greater influence on theoverall breakage properties and the Bond Work Index of the blend than the softer material.
Table 3.4Experimental and simulated Work Indices of ore blends [32],Ore type
Hard50:50 blendSoft
Bond Work Index (kWh/t)Measured
14.012.06.6
Simulated13.111.15.6
89
02468
10121416
0 0.2 0.4 0.6 0.8 1
Volume fraction of soft ore in blend
Bon
d W
ork
Inde
x, k
Wh/
t
Bond Method
Magdalinovic Method
89
IIiI•ocom
161412108642
—•_
n
—•—Bond Method
D Magdalinovic Method
\
f11
0.2 0.4 0.6 0.8 1Volume fraction of soft ore in blend
Fig. 3.10. Bond Work Index of a blend of hard and soft ore [32].
Table 3.4 shows the simulated Work Index of the blend of hard and soft ore types. Thecomputer simulation under estimated the value of the Work Index by approximately 1 kWh/t.
3.3.10 Work Index and AbrasionSize reduction in a tubular mill is also caused by abrasion and attrition. The forces of abrasionact between:
1. the grinding media and the mineral particles,2. the mineral particles themselves, and3. between the grinding media themselves.
Separate evaluation of these parameters is difficult. Bond [13] while measuring the wear ofthe grinding media in tubular mills attempted to measure the attrition between the media andthe charge and arbitrarily defined an Abrasion Index by the loss of mass of a standard spindlerotating in a drum on which standard sized minerals are continuously impinging for a set time.Bond's method is now generally accepted as the attrition of metals by minerals.
Bond's Abrasion Test (also known as Allis Chalmers Abrasion Test)Bond's abrasion test consists of an hardened Cr-Ni-Mo alloy steel paddle (hardness 500
Brinell), 7.62 cm x 2.54 cm x 2.54 cm with 2.54 cm of its length sitting inside a rotor, 11.43cm diameter. The rotor is covered by a concentric steel drum 11.43 cm in length and 30.54 cmin diameter. Both the rotor and the outside drum are mounted on an horizontal shaft. Therotor rotates at 632 rpm while the drum is rotates in the same direction at 70 rpm. The initialcharge mass is 400 grams of -19.0 mm + 12.7 mm size material. The rotors are runsimultaneously for 15 minutes. Next, the charge is removed and the process repeated fourtimes. That is, the spindle is exposed to abrasion for 1 hour. The charge recovered each timeis collected, mixed, sieved dry and the Pso determined. The spindle is also weighed. The lossin mass (in grams) of the spindle gives the attrition index, Ai. The total power used in rotationis noted. The Attrition Index thus determined is included in Table 3.5 for selected minerals.Mathematical correlation with the Work Index has not been reliably established.
9090
Table 3.5Average Abrasion and Work Index of selected minerals [41].
JKMRC Abrasion TestJKMRC has developed a slightly different method of estimating abrasion. Their method issimilar to the standard laboratory Trommel Test applied for testing the abrasion of iron orepellets and coke. In this test 3 kg of dry ore, size -55 mm + 38 mm is charged into ahorizontal cylindrical steel drum ID 0.30 m x 0.30 m with lifter bars 2.54 cm in height Thedrum is rotated for 10 minutes at 53 rpm. The sample is then removed and screened to -38am. The cumulative mass percent passing each screen size is plotted. The mass percentpassing 1/10 (Tio) of the original size is taken as the "abrasion parameter".
The concept and use of the factor, TIQ, has been promoted by Weedon et al, [40] to developa relation between crushing strength and specific comminution energy. Tio is defined as thepercent ore passing 1/10* of the original particle size. The meaning of the subscripts can beextended as:
T2 = % passing 1/2 of the original particle sizeT4 = % passing 1/4 of the original particle size
Tio= % passing 1/10 of the original particle size
TN = % passing 1/N of the original particle size
TN is the cumulative mass % passing a size dot* where dGM is the geometric mean of thesize interval between sieves. A plot of particle size against TN where N = 1.2.... N yields thevalue of Tio. The relation between Tio and specific breakage energy due to crushing has beenestablished as [24]:T1 0=A(l-e-B E o) (3.46)
91
0
10
20
30
40
50
60
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Specific Comminution Energy
T10
0.5
B = 2.0
0.7
A
1.0
91
where A and B are ore specific constants and EG is the specific comminution energy. Theparameter A represents the theoretical limiting value of Tio (see Fig. 3.11). For hard ores thevalue of A approximates 50. The value of A.B (the impact parameter) is the slope of theTio-E curve at zero input energy.
The Tio-mass distribution curve is useful as it is a description of the product sizedistribution and the Tio can be considered an index of the degree of breakage. The harder theore, the lower the Tio value for a given input energy. Knowing the Tio value resulting from agiven input energy, the complete product size distribution can be calculated. According toNapier-Munn et al [24]:
For crushing - Tio is usually between 10-20% andFor grinding - Tio ranges between 20-50%.
Fig. 3.11.
,_r 30 -
0.5 1.0 1.5 2.0 2.5
Specific Comminution Energy
3.0
Relationship between Tlo and specific comminution energy (Eq. (3.46))
Napier-Munn et al [24] indicate a possible correlation between the impact parameter (A.B)and the Bond ball mill work index given by the equation:
A.B = -3.5 Wi + 117 (3.47)
The determination of the Tio value and its use in determining the specific breakage energyis illustrated in the following Example 3.2.
92
0
10
20
30
40
50
60
70
80
90
100
0 2 4 6 8 10 12 14 16 18 20 22 24
Size (mm)
Cu
m. m
ass
% p
assi
ng
Y/10
92
Example 3.2
Sample size = 1000 kg, Particle size = -26.5 mmmm). The sieve analysis after crushing is given by:
Size analysis of crushed sample
25.0mm (geometric mean = Y = 25.7
Size,passing mm
25.012.56.33.31.41.0
(X) Size,retained mm
12.56.33.31.41.00
Massretained
102.0124.0216.0280.0180.098.0
1000.0
% massretained
10.212.421.628.018.09.8100
Cum. mass %passing89.877.455.827.89.80
1/N = X/Y
1.00.690.340.180.08
From a plot of geometric mean size against cumulative mass percent passing shown below,we find that the Tio equals 47 and A can be taken as 50 and the value of B as 2.2. Substitutingthese values into equation 3.46, the energy of crushing is calculated to be 1.28 kWh/t (4604kJ/t).
100 -i
90
an
70
fin
50_
40
30
20
10
--
\j*\l|JT
f\
0
f
2 I
__A
1—
/
4
/
e
,
8
'
10
*--
12 14 16
SB—
18 20
——
22 24
Y/10 Size (mm)
Product size distribution - plot of the size vs. cumulative % passing the lower screen size.NOTE: the value of Tio in this case is high. Usually the value is less than 20.
3.4. Problems
3.1Dry samples of quartz, galena and limestone ores were ground separately in a standardlaboratory size ball mill 305 x 305 mm with a total ball load of 20.1 kg. After 100 revolutions
9393
they were screened through a 150 micron sieve. The amount retained was returned to the milltogether with equal amount of fresh ore. The process was repeated till the net mass of thesamples were: Quartz = 169.4 grams, Galena = 481.2 grams, Limestone = 192.10 grams. Theaverage feed size, Fgo, (2000 micron ) was the same for each mineral and the final productsizes were Quartz: 75 % passing 93.2 microns, Galena: 75 % passing 72.9 microns andLimestone: 75 % passing 84.4 microns.Estimate and compare the Work Indices taking that of limestone as the standard.
3.2The feed size (FM) of a sample of limestone was 3200 urn. The Work Index of the sample wasdetermined in two laboratories and was found to be 11.61 kWh/t (41.8 MJ/t) and 15.0kWh/t(54 MJ/t) respectively. The product size (Pso) was found to be 140 and 219 micronsrespectively.
Estimate:1. The size of screen used in each case if the grindabilities (g/rev) were the same in both
cases,2. The constant masses of the samples obtained in each case (g/rev) if the same test sieve
size of 350 am was used.
3.3Bond's pendulum method was used to determine the crushing strength of a dry sample ofgypsum 76 mm x 24 mm x 24 mm. The mass of each hammer was 13.6 kg each. They werereleased simultaneously from a position making 15° with the vertical. The relative density ofgypsum is 2.32.
Estimate:1. Crushing Strength of the gypsum sample,2. Bond's crushing work index of gypsum,
3.4A sample of granite passing a 7.5 cm square opening screen was suspended in a Bond'spendulum test. The length of the pendulum was 413 mm and the mass of hammers 13.6 kgeach. The sample was completely crushed when the initial position of the pendulums made anangle of 30° with the vertical. The specific gravity of granite is 2.70.
Estimate:1. The total energy required and energy consumed per cm to crush the sample,2. The work index.
3.5A standard Bond laboratory ball mill test was commissioned to estimate the grinding powerrequirements in the design of an alumina refinery. The size analysis of the R.O.M. ore afterpreliminary screening was:
Size, mm% by mass
-20 +1025
-10+540
-5+2.515
-2.5+112
.0 -1.0+0.4205
0.42+0.2102
-0.2101
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The required product size specification was 80% passing 75 um. Tests were conducted underdry conditions but the commercial mill was expected to operate under dry conditions. Themass of screen undersize per revolution was found to be 1.25 g/rev.
Estimate:1. The work index using a 106 urn sieve,2. The work index of the commercial mill,3. The power required by the commercial mill per tonne of dry bauxite.
3.6A dry nickel ore was crushed and screened when 99 % of the ore passed 12.5 mm screen .Acomplete screen analysis showed that the liberation size was 75 um. Bond's grindabilitystandard rod mill test showed a constant 12.6 grams per revolution. The ore had to be groundin wet rod mills at the rate of 2400 t/day.
Estimate the work index if the :1. Internal diameter of rod mill was 2 m,2. Internal diameter of rod mill was 6 m,3. If a wet rod mill of 2 m I.D. was used instead, what would be the difference, if any, in the
power required?
3.7Bond's work index of a manganese ore (SG. 3.7) was estimated at 12.31 kWh/t when anunknown screen size was used. The ore was charged and ground in a standard ball mill. Thefeed and product size (80% passing sizes) in the test was 300 microns and 90 micronsrespectively.The grindability test was then repeated using a test screen size 20% of that used in the firsttest.
Estimate:
1. The change in grindability in the second test2. The test screen sizes at which the work indices were determined in the two tests.
Data: Work index in the second test = 11.26 kWh/tGrindability in the second test = 3.03 g/rev.
3.8To estimate the work index of a quartzite sample, two tests were performed. The first usedBond's pendulum method, the second Narayanan and Whiten's method, hi both cases, themean particle size of feed was 12.5 mm. Indicate the height to which the pendulum has to beraised in order to give the same work index.
Data: Feed size = 11.2 mm, Product size = 1200 um, S.G. of ore = 2.65Coeff. of restitution, 8 = 0.20
95
Crusher Rod Mill Ball Mill
Product
classifier
ROM
95
3.9The average size analysis of an iron ore after preliminary crushing showed a Pgo value of 1173microns This was fed to a wet rod mill which produced a product 80 % of which passed 150microns. This was then charged continuously to a ball mill, which was required to produce aproduct of-34 microns for the purpose of pelletising the ore.
The flowsheet considered was dry open circuit crushing and wet rod and closed circuitgrinding ball mill grinding.
The internal diameters of both rod and ball mills were 2.5 m and a throughput of 100 t/hwas initially expected. Estimate the total energy and power required for grinding by the rodand ball mills. The standard laboratory work index of the ore was 12.5 kWh/t.
ROM
iCrusher Rod Mill Ball Mill
Product
classifier
3.10A representative sample of ore (-37.5+31.5 mm) was crushed in an impact test and the productscreened. The screen analysis is given below:
Geom Meanparticle size mm
25.717.68.94.61.1
Cum. mass %passing
99.284.655.128.016
Estimate:1. The values of Tio,T2s, T50 and T75,2. The specific comminution energy for the ore if A equals 35 and B is 2.
3.11An ore sample weighing 1.2 kg and particle size -35.5 mm +31.5 mm was crushed in alaboratory impact crasher. The result was noted and is given below. The work index of theore was 13.2 kWh/t and the limiting value of the impact breakage parameter A was equal to50 and B is 1.85. Estimate the T10 value and determine the energy required in thecomminution process.[Hint: Assume Napier-Munn's Eq. (3.46) is applicable.]
3.12The masses of four different ores and their initial sizes are given in the table below. Alsogiven are their breakage characteristics as obtained from an impact crusher. The work indexof ores were 11.8, 13.2, 12.2 and 12.8 kWh/t. Assuming that the impact breakage parameterswere the same and the limiting value of the breakage parameter, A, was equal to 50 and Bequals 2. Determine:
1. the specific comminution energy in each case,2. the energy required to crush the entire amounts of each ore sample.
Initial sample size of four ore types
Ore Mass of Initial sizeType sample, kg of sample, mm
1 10002 12503 15004 1300
Product sizes after breakage (
Sieve Size,mm I
MeanDarticle
-37.5+26.5-25.0+22.4-45.0+37.5-37.5+26.5
)f four ore types
Cum.i mass %
size (GM), passing
-26.5+22.5-22.5+11.2-11.2+5.6-5.6+2.8-2.8+1.4
-1.4+0.710-0.710 + 0.355-0.355 + 0.180
mm24.315.87.94.02.01.00.500.25
Orel100.088.053.028.012.05.82.01.0
Cum.mass %passing
Ore 298.087.076.053.027.013.09.05.0
Cum.mass %passingOre 3
100.087.051.022.011.18.05.02.0
Cum.mass %passingOre 4
100.080.042.020.0
8.03.02.01.0
9797
3.13In the Nayayanan/Whiten test, the Ti0 (%) values of the product and the correspondingspecific comminution energies (E) were determined for an ore. The results are given in thefollowing table.
Determine:1. The impact parameters A and B2. The work index (Wi) of the ore3. If the cost of crashing 10001 of ore if power cost is $ 2.50/GJ
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