Chapter 6. Roll Crushers

6. INTRODUCTION

Roll crushers consist of two or more adjacent rolls placed parallel to each other and rotated inopposite directions. Single roll crushers are also available which rotate a single roll against afixed breaker plate. Mineral or rock particles placed between the rolls are nipped and thencrushed as they pass between the rolls. Rolls are held against each other by springs. Radicalchanges to the design of roll crushers have been introduced by Schonert, [1,2] as a result offundamental work on breakage mechanisms. These roll crushers have large forces ofcompression and are called High Pressure Grinding Rolls (HPGR). The present tendency is toreplace secondary cone crushers by HPGR. The work at Polysius [3] and described byFriedrich and Baum [4], and Otte [5] indicate considerable metallurgical advantage in theextraction of minerals like gold and copper by the use of high pressure grinding rolls. In thischapter these two types of roll crushers are described.

6.1. Design of Roll CrushersTwo types of roll crushers are generally designed. In the first type both rolls are rigidly fixedto a frame with provision for adjusting the lateral position of one of the rolls to control the gapbetween them. Once set these rolls are locked into place. One roll is attached to the drivingmechanism while the other rotates by friction. Single roll crushers are also available whichrotate a single roll against a fixed breaker plate. In the second type, at least one roll is springmounted which forms the driving roll, the other roll rotates by friction (Fig. 6.1). The nest ofsprings helps to provide uniform pressure along the length of the rolls. The springs are helicaland pressure varies with the size of crusher and could be as high as 6 t/meter (about 8300kPa). In some roll crushers the rolls are individually driven. The drive is either by gears orbelt. Both rolls usually rotate at the same speed but some crushers are designed such that oneroll could rotate faster than the other. For fine grinding both rolls are rigidly fixed to the baseand therefore they do not permit any movement of the rolls during operation. The surfaces ofthe rolls are either smooth, corrugated or ribbed. Heavy duty toothed rollers are sometimesused as primary crushers but the use of such rollers in the metallurgical industry is verylimited.

Some rollers are toothed. The shape of the teeth is generally pyramidal. The roll surfacesplay an important part in the process of nipping a particle and then dragging it between therolls. The corrugated and ribbed surfaces offer better friction and nip than smooth surfacedrolls. The toothed surfaces offer additional complex penetrating and compressive forces thathelp to shatter and disintegrate hard rock pieces.

The distance between the rolls is adjusted by nuts at the end of one of the rolls. The nipangle is affected by the distance between the rolls. The nip angle is defined as the angle that istangent to the roll surface at the points of contact between the rolls and the particle. It dependson the surface characteristics of the rolls. Usually the nip angle is between 20° and 30° but insome large roll crushers it is up to 40°.

143143

Feed

spring loaded roll

Fig. 6.1. Schematic Diagram of Roll Crusher

6.1.1. Roll Crusher Sizes and DesignThe usual crusher sizes and power ratings for different types of roll faces as described byvarious manufacturers' literatures are summarised in Table 6.1.

Table 6.1Roll Crusher sizes.

Crusher Surface

Plain RollsToothed RollsStudded Rolls

Min750750

Size,

WidthMax8608601400

mm

DiameterMin3501500

Max210017202400

Roll crushers are arbitrarily divided into light and heavy duty crushers. The diameters ofthe light duty crushers vary between 228 mm and 760 mm with face lengths between 250 mmand 460 mm. The spring pressure for light duty rolls varies between l.l.kg/m and 5.6 kg/m.The heavy duty crusher diameters range between 900 mm and 1000 mm with face lengthbetween 300 mm to 610 mm. In general the spring pressures of the heavy duty rolls rangesbetween 7 kg/m to 60 kg/m. The light duty rolls are designed to operate at faster speedscompared to heavy duty rolls that are designed to operate at lower speeds.

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6.1,2. Roll DesignFor a particular operation where the ore size is known, it is necessary to estimate the diameterof rolls required for a specific degree of size reduction. To estimate the roll diameter it isconvenient to assume that the particle to be crushed is spherical and roll surfaces are smooth.Fig. 6.2 shows a spherical particle about to enter the crushing zone of a roll crusher and isabout to be nipped. For rolls that have equal radius and length, tangents drawn at the point ofcontact of the particle and the two rolls meet to form the nip angle (28). From simplegeometry it can be seen that for a particle of sizs d, nipped between two rolls of radius R:

COS0 =

where Ris the roll radius and L the distance between the rolls.

Simplifying Eq. (6.1), the radius of the roll is given by:

L - d cosG

(6.1)

R =2 (cos 6-1)

(6.2)

Eq. (6.2) indicates that to estimate the radius R of the roll, the nip angle is required. Thenip angle on its part will depend on the coefficient of friction, u,, between the roll surface andthe

F sin 6

Fig. 6.2. Roll crusher geometry.

145

0

100

200

300

400

500

600

700

800

0 20 40 60 80

Feed particle size, mm

Ro

ll ra

diu

s, m

m

17o

11o

145

particle surface. To estimate u consider a compressive force, F, exerted by the rolls on theparticle just prior to crushing, operating normal to the roll surface, at the point of contact, andthe frictional force between the roll and particle acting along a tangent to the roll surface atthe point of contact. The frictional force is a function of the compressive force F and is givenby the expression, Fu. If we consider the vertical components of these forces, and neglect theforce due to gravity, then it can be seen that at the point of contact (Fig. 6.2) for the particle tobe just nipped by the rolls, the equilibrium conditions apply where:

F sin G = F u cos 0 or

JJ, = tan 9 or 0 ^ (6.3)

As the friction coefficient is roughly between 0.20 and 0.30 the nip angle has a value ofabout 11°-17°. However, when the rolls are in motion the friction characteristics between theore particle will depend on the speed of the rolls. According to Wills [6] the speed v, isrelated to the kinetic coefficient of friction of the revolving rolls, UK, by the relation:

(1 +1.12 V),(6.4)

Eq. (6.4) shows that the ^K values decreases slightly with increasing speed. For speedchanges between 150 and 200 rpm and u ranging from 0.2 to 0.3, the value of UK changesbetween 0.037 and 0.056. Eq. (6.2) can be used to select the size of roll crushers for specificrequirements. For nip angles between 11° and 17°, Fig. 6.3 indicates the roll sizes calculatedfor different maximum feed sizes for a set of 12.5 mm.

E

</f

rad

iilo

ll i

u_

800

700

600

500

400

300

200

100

0

1

/

/ .

/ .L //

11°

V/

20 40 60

Feed particle size, mm

80

Fig. 6.3. Roll radius for different maximum feed sizes, calculated from a set of 12.5 mm at nip anglesof 11 and 17 degrees (solid lines). The points correspond to industrial roll crusher data.

146146

The use of the above expressions to determine the size of rolls to be used for a particularoperation is illustrated in Example 6.1.

Example 6.1

The maximum particle size of a limestone sample received from a cone crusher was 2.5 cm.It was required to further crush it down to 0.5 cm in a roll crusher with smooth rolls. Thefriction coefficient between steel and particles was 0.25, if the rolls were set at 6.3 mm andboth revolved to crush, estimate the diameter of the rolls.

SolutionStep 1

Estimate the nip angle using Eq. (6.3)

Substituting friction coefficient n = 0.25, tan 6 = 0.25 or 6 = 14.03°

Step 2Substituting in Eq. (6.2)

_ (6.3-25 x 0.97)

2 x (0.97-1)

= 300 mm

and hence the roll diameter = 600 mm

It is generally observed that rolls can accept particles sizes larger than the calculateddiameters and larger nip angles when the rate of entry of feed in crushing zone is comparablewith the speed of rotation of the rolls.

6.1.3. Roll Crusher Circuit DesignRoll crushers are generally not used as primary crushers for hard ores. Even for softer ores,like chalcocite and chalcopyrite they have been used as secondary crushers. Choke feeding isnot advisable as it tends to produce particles of irregular size. Both open and closed circuitcrushing are employed. For close circuit the product is screened with a mesh size much lessthan the set.

Fig. 6.4 is a typical set up where ore crushed in primary and secondary crushers are furtherreduced in size by a rough roll crusher in open circuit followed by finer size reduction in aclosed circuit by roll crusher. Such circuits are chosen as the feed size to standard rollcrushers normally do not exceed 50 mm.

147

Feed

Primary crusher

Secondary crusher

Screen #1

Coarse roll crusher

Final roll crusher

Screen #2

Product

147

Feed

Coarse roll crusher

Screen #1

Product

Fig. 6.4. Roll Crusher Design Circuit.

6.2. Operation of Roll CrushersThe feed to roll crushers is usually dry. Moisture tends to clog the crusher and could result

in the formation of hard crust, which impairs operation. Hence dry crushing is preferred.Sometimes, water is added between the rolls, which help to prevent formation of the crust andalso to remove the hard cake that tends to form on the roll surface. Wet grinding is usuallycarried out when fine grinding is required.

Rock particles are usually fed through a chute designed to distribute the charge evenlyalong the width (length) of the roll. About two-thirds of a roll-width is active. As in anycrusher, particle sizes less than the distance between the rolls tend to pass through uncrushed.Particles that are larger than the opening is nipped and crushed. The maximum size of particlethat is nipped without slippage depends on friction, distance between rolls and roll size.

The size of the product depends on the crusher set, the distance between the rolls. Due tosingle pass operation it is evident that no middlings or over-size is produced.

The normal speed of operation of commercial light duty rolls is 130-300 rpm compared toheavy duty rolls whose operating speeds are in the region of 80-100 rpm. Regulated slow rateof feeding spread over evenly across the width of rolls is preferred when closed circuitoperation is adopted for finer product size.

148148

6.3. Capacity of Roll CrushersThe capacity Q, of roll crushers is directly proportional to its width, W, diameter, D and

speed of revolution of rolls [6]. Under continuous and steady feeding conditions the capacityis given by:

Q = 7i60DWtoLpB

= 188.5 DWmLpB t/h (6.5)

where D = diameter of roll, m,W = width of roll, m,co = speed, rpm,L = set or distance between rolls, m,PB = bulk SG of the mineral, t /m3 .

In deriving the expression it is assumed that the particles are continuously fed from aheight and that the rolls are kept full all the t ime, that is the rolls are choke fed. Further it isassumed that the product is in the form of a continuous ribbon having the width of the roll andthickness equal to the set. This would give the theoretical production. The actual productionwill depend on the "ribbon factor, R F " given by the expression:

RF = 0 . 0 0 9 5 3

where Q = Feed rate, t/h,vp = peripheral speed of the roll, m/s.

The ribbon factor is defined as the ratio of the actual tonnage passing through the crusherto the tonnage of the theoretical solid-rock ribbon [7]. In practice, the actual capacity can beas little as 25 % of this calculated capacity, Q. This correction is required due to voidsbetween particles and the increase in bulk density of the particles as it passes through thecrushing chamber. When the feed rate is irregular, the capacity would decrease [8].

Eq. (6.5) has been modified by Otte [5] by introducing an efficiency factor, s andexpressing capacity as:

Q = 3600 E W vP pB L (6.7)

where ps = bulk density of the feed material, t/m3,e = efficiency factor which has a value between 0.15 and 0.30, depending on

the roll gap or product size.

The product of (E pa) has been termed by Otte as the operational density, that is, thedensity of the product, which is in the form of a continuous ribbon or cake. Otte observed thatthe operational density of roll crushers are low (0.25 to 0.6 t/m3).6.4. Power Consumption of Roll Crushers

Within the same reduction ratio the power consumption of roll crushers vary widely. Thepower required could be expressed by the general equation:

149149

P = Capacity x Reduction Ratio x work index (6.8)

In industry the low pressure smooth surfaced rolls are designed to draw 8-50 kW of powerunder dry conditions. The heavy duty rolls draw between 40 and 550 kW depending on sizeand low moisture conditions. Sufficient data are not available for toothed rolls where crushingforces are complex and crushers often are operated under wet conditions.

6.5. High Pressure Grinding Rolls (HPGR)In a roll crusher comminution primarily involves individual particles nipped between

converging roller surfaces. The forces of compression and friction between the rolls andparticles are responsible for size reduction provided the combined forces exceed thecompressive strength of the particle. When a large quantity of rock is held between the rollsand subjected to high pressure then comminution could take place by compressive forces aswell as by interparticle breakage, provided again that the total applied pressure was greaterthan the crushing strength of the rock pieces. The product again is a continuous "ribbon" ofcrushed material in the form of a compacted cake.

While studying the specific energy of breakage due to impact and by compressive forces,Schoenert [9,10] observed that the utilisation of the specific energy of breakage as a result ofimpact was much less than with compressive forces. Thus during high pressure grindingwhere large compressive forces were applied to a bed of ore, the total energy required wouldbe relatively less compared to comminution systems where impact forces predominate.Schoenert also observed that with decreasing particle size the energy utilisation increased.Several workers [5,11-13] have confirmed Schonert's observations. These observations weredeveloped and finally resulted in the high pressure grinding roll (HPGR) by Krupp-Polysius[14] in conjunction with Schonert. The HPGR are being used with considerablesuccess in the cement, iron ore and diamond industries [4,5,15] and increasingly in the generalmineral industry.

Fig. 6.5 illustrates the manner of comminution in HPGR. This figure shows that during theinitial stages when the feed size is greater than the gap between the rolls, breakage of particlesis due to conventional forces applicable to roll crushers. In such a case, the edge effects of therolls are significant. As the feed descends, some of the particles that are larger than the gap,experience high compressive forces and therefore reduced in size.; these particles occupy thevoid spaces between large particles. Interparticle contact therefore increases resulting intransference of more interparticle compressive forces that further crushes the particles. Due tohigh compressive forces the crushed particles compact forming a continuous productresembling a cake or ribbon. Some plastic deformation also takes place the extent of whichdepend on the characteristics of the ores and rocks. The compacted particles are subsequentlydispersed by a second operation in a grinding mill. It is found [5] that the total energyrequirement for the combined operation of HPGR and ball mill is less than the conventionalcomminution processes.

To perform the operation, pressure is applied hydraulically through four cylinders to theroll that is designed to move laterally. The second roll is immovable. A crushing pressure ofthe order of 200 MPa is applied. The dimensions of the rolls used in the mineral industry are[5] 0.7- 2.8 m diameter with a Length/Diameter ratio between 0.2 - 0.6. The roll speeds are85-105 m/min. The roll faces are either studded or have Ni-hard liners. The studs are madeof tungsten carbide to combat heavy abrasion but softer studs have better life as they are lessbrittle.

150150

Feed

Fig. 6.5. Schematic diagram of a High Pressure Grinding Roll (HPGR).

Both dry and wet crushing and grinding is possible. Crushing rates up to 450 t/h in SouthAfrican diamond mines and about 400 t/h for hard taconite ores in the USA have beenreported by Krupp-Polysius [14]. Design capacities up to 757 t/h are available.

Due to the fact that fine product sizes can be obtained, the HPGR has been used both forcrushing and grinding. In a crushing circuit it can replace secondary or tertiary crushers likecone crushers. In grinding circuits it can replace tertiary crushing and installed before a ballmill. In some cases it is installed after the ball mill, as in Kudramukh in India in an iron orecircuit, where the product from the HPGR is fed directly to a pelletising plant [16].

6.5.1. Circuit Design and HPGRAs the product size from HPGR is fine, the present tendency is to replace the conventionalsecondary and tertiary crushers with a single HPGR unit. Thus liberation size is moreeconomically achieved and the product acceptable for down stream operations such asflotation. In some flow sheets HPGR is placed before the roll crusher in order to inducecracks and fissures in the ore particles. In such cases ball mill grinding is facilitated. Severalalternate circuits have been suggested by Baum et al [17] and Patzelt et al, [11,15]. A typicalflow sheet for coarse grinding is illustrated in Fig. 6.6. Allers and Blasczyk [18] claims greatenergy savings when HPGR is used in closed circuit as combined pre-grinder and finishinggrinding mill.

6.6. Operation of HPGRFor the operation of High Pressure Grinding Rolls it is necessary to determine the chief

operating parameters. That is:

151

Gyratory crusher

ScreenO/S

U/S

Secondary crusher

HPGR

Storage bin

De-agglomeration

Product

151

Gyratory crusher

Secondary crusher

HPGR

De-agglomeration

Product

Fig. 6.6. High Pressure Grinding Roll flowsheet.

1. operating pressure,2. nip angle,3. gap,4. roll speed and5. ore size.

6.6.1. Estimation of Operating PressureTo operate the HPGR Polycom grinding mill the pressure required is applied hydraulicallythrough four cylinders to the roll that is designed to move laterally. The second roll isimmovable. The crushing pressure applied is generally of the order of 200 MPa. but for hardores, higher pressures are required. For example, in Cyprus Sierrita, a pressure of 340 MPa isused.

The pressure required for crushing should be in excess of 50 MPa [19]. Battersby,Kellerwessell and Oberheuser [20] states that the force required was in the range of 100 kNper linear meter of roll width. Schonert [2] has estimated theoretically the specificcomminution pressure on mineral particles trapped between the rolls as:

P = F (L D)"1 N/m2 (6.9)

152152

where F = Grinding force, kN,L = Length (width) of roll,D = Diameter of roll, m.

The maximum pressure on particles is inversely proportional to the interparticle angle ofnip and is expressed as:

PMAX = F (K D L 8IP)-' MPa (6.10)

K is a material constant with values between 0.18-0.23 and 6n> is the angle of nip forinterparticle comminution, defined in Eq. (6.12). It is difficult to use Eq. (6.10) due to thedifficulty in determining K. Klymowsky, et al [21] therefore uses average pressure on theparticles which is described as:

PAVE = F (1000 L R Gjp)"1 (6.11)

where R is the radius of the rolls and 9n> the angle of nip of the interparticle particles definedby Eq. (6.13).

6.6.2. Estimation of Nip AngleThe mechanism of breakage in HPGR has been recognised by Klymowsky et al [21] whoconcludes that in the high pressure region comminution is due to:

1. Interparticle forces acting between particles that are less than the gap,2. Combination of interparticle plus single particle breakage when the single particles are

larger than the gap and being nipped directly by the rolls and crushed before enteringthe compression zone.

The larger particles are broken prior to entering the compression zone. In the compactionzone the bulk density of the ore is reduced to the bulk density of the cake. These concepts canbe visualised in Fig. 6.7.

The angle of nip for the two situations involving single particle breakage was derived as[21]:

0sp = arccosLT JlOOOD

(6-12)

and for interparticle breakage, the nip angle Gip, is:

Pr . LT0IP = arccos - T

pB(F) 11000 D(6.13)

where dMAX = maximum size of particle, mm,LT = thickness of cake, mm,D = diameter of roll, m,pc = density of compacted cake, t/m3,PB(F) = bulk density of feed,

153

Feed

Compression zone

Breakage zone

θ SP

θ IP

153

Feed

Breakage zone

Compression zone

Fig. 6.7. Mechanism of crushing in HPGR [21].

6,6.3. Estimation of the Roll GapAs the gap determines the product size distribution, it is helpful to predict the gap opening ofHPGR. Morrell et al [22] expressed the dimensionless working gap as the ratio of theworking gap, LG, to roll diameter, D. This ratio varies linearly with the logarithm of thespecific grinding force and can be expressed by Eq. (6.14) as:

D(6.14)

where LQ = working gap,vP = peripheral speed of rolls, m/s (normalised),g = acceleration due to gravity (9.81 m/s2 )D = diameter of rolls, m,Fg = specific grinding force, N/mm

ki- Lj = material constants.

Eq. (6.14) shows that as the log (Fs) increases LQ fD ratio decreases. The working gap willbe affected by the surface characteristics of the roll, moisture content in the ore and the largestsize of ore pieces. To evaluate Eq. (6.14), the material constants are determined by laboratorytest work.

6.6.4. Roll SpeedThe choice of roll speed affects the production rate. However, the choice is between fasterand narrower rolls which are easier to operate or slower and wider rolls where control of the

154154

gap across the width could be a problem. Excessive speed is to be avoided as the rolls tend todeflect particles away from the crushing zone reducing the throughput.

Roll speeds are related to the diameter of the rolls. Klymowsky [21] suggests the followingperipheral speed for different roll diameters:

1. For roll diameters < 2 m, peripheral speed vP < 1.35 V D2. For roll diameters > 2 m, peripheral speed Vp < D

6.6.5. Feed and Product SizeThe feed size and the working gap should be compatible as neither too large nor too smallpieces are acceptable. However the hardness of the rock and the type of roll surface alsoaffect the feed size. The recommended feed size therefore depends on the ratio of feedsize/working gap. Expressing this ratio as y the recommendations of Klymowsky [21] issummarised in Table 6.2.

Table 6.2HPGR feed sizes for different ore types [21].

Rock type Compressive strength Feed size/working gapSoft Ores < 100 MPa up to 1.5Hard rock > 250 MPa £J

For hard faced rolls with a smooth surface profile, the feed size can be up to 3 times theworking gap. For rolls with studded surface the feed size should be less than or equal to theworking gap.

The feed size to the HPGR in some Brazilian mines is 90 % passing 1 mm [3] but the useof coarser feed sizes (16-50 mm) has been reported by Patzelt et al. [15]. At Argylediamonds, (Australia), Maxton [23] reports charging feed size of 80% passing 75 mm withlumps up to 750 mm.

Product SizeThe product size from HPGR can be much finer than the corresponding ball or rod mill

products. As an example, the results by Morsky et al [12] is given in Fig. 6.8 where, for thesame net input energy (4 kWh/t) the product sizes obtained from HPGR, ball and rod mills areplotted. It can be seen that the fraction below 100 microns is much greater from HPGRcompared to that produced by the rod mill operation. Other workers have observed similarresults [12,15].

6.7. Capacity of HPGRThe production capacity of HPGR can be taken as the volume of material passing through

the gap between two rolls. It therefore depends on the width of the rolls, the working gap andthe velocity of material through the gap. The mass flow rate through the gap will therefore be:

Q = Roll width x working gap x velocity of material x density of solids in the gap, or

Q = 3.6 WLG v p s t/h (6.15)where the roll width is in m, LG is in mm and v is in m/s.

155

1

10

100

10 100 1000 10000

Size (microns)

Cu

mu

lati

ve %

Pas

sin

g

Feed

Rod Mill

Ball Mill

HPGR

155

100

10

3

d

y

f

r

<

• '

f 3

^ P

-• -F• C

— • — h

fc=i

^ r1

eed

od Mill

all Mill

PGR

•it

—}

10 100 1000

Size (microns)

Fig. 6.8. Particle size of product from ball mill and HPGR [12].

10000

A popular way to describe capacity is to express it in terms of specific throughput rate.Seebach and Knobloch [24] and later Morrell [22] have expressed it in dimensionless form as:

Q = Qs D W v p p s t/h (6.16)

where Qs = specific throughput rate,D = diameter of roll, m,W = width of roll, m andPs - material density.

Otte (1988) expressed the capacity of HPGR, in terms of the distance between the rolls andthe operational density of the ore, as:

Q = W LG vP pop t/h

where pop = operational density, t/m3, (discharge cake density)

(6.17)

From laboratory experiments Morrell indicates that the specific throughput was related tothe specific grinding force, Fs, by a linear function of the form;

Qs = k ( l + C l o g F s )

where Fs = specific grinding force,k = a factor dependant on roll speedC = a material constant

(6.18)

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The factor for roll speed, k y was evaluated experimentally and is a function of roll speed,vp, according to the polynomial equation:

k = Civ?2 +C2vp + C3 (6.19)

where &1-C3 are material constants. Eq. (6.19) is evaluated experimentally.

The specific throughput rate can then be computed by combining Eqs. (6.18) and (6.19).Thus:

Qs = (1 + C log Fs) (dvP2 + C2 vP + C3) (6.20)

This relation needs to be fully tested.

Lubjuhn and Schonert [25], working with a laboratory model HPGR (diameter 200 mm xlength 100 mm ) using limestone feed sizes, 0.25-1.0 mm and 1.6-6.3 mm, concluded that:

1 When milling forces varied between 1-6 N/m2, little effect on throughput was observed,,2. When the specific forces of breakage was constant, speed has low significance on

breakage,3. Corrugated roll surface has greater throughput.

6.8. Power Consumption of HPGRAs a general rule, motor power is the product of capacity and energy input. For HPGR we

have seen that the energy input is defined as the specific energy input, hi conventional work,Bond's work index is usually accepted as the measure of the net specific energy required forcomminution. Klymowsky and Liu [13] found that Bond's work index was not quiteapplicable in the case of the HPGR as it was determined using a tumbling mill where repeatedimpact and grinding forces were responsible for size reduction. Further in a tumbling millcascading particles dropped on a bed of particles, which cushioned the impact and thereforeaffected the specific energy of size reduction. Klymowsky[14] et al. indicated that the Bondwork index was not exactly a constant factor for a given ore. Otte [5] reported an increase ofWi from 13.9 kWh/t to 15.6 kWh/t for a copper ore and 9.4 kWh/t to 15.6 kWh/t for a goldore. Similar observations were made by Patzelt et al. [11]. Klymowsky et al. advocate that inthe case of the HPGR, RMnger's law (see Chapter 2) was more appropriate than Bond'swork index.

To determine the power draw, Morrell et al [21] applied the basic laws of physics. Theyconsidered the angular velocity of the roll initiated by a given torque of the roller shaft.According to basic principles of dynamics, the power required at the roll shaft will be:

2 Torque x Angular velocity _ 2 Tro t< _T.Diameter of roll D

where T = Torque (Nm), andto = Angular velocity, (rad/s)

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The torque is generated by the angular displacement B of the horizontal force F between thematerials, that is:

T = (3 F D (6.22)

or

D = — (6.23)FB

Note that F is the horizontal component of the grinding force applied by the movable roll andtransmitted to the material between the two rolls. F is equal to the specific grinding forcetimes the roll diameter times the roll length. Substituting the value of the diameter D fromEq. (6.23) in Eq. (6.21) gives:

P = 2 T ( 0 F P = 2COFP (6.24)

The angular velocity, co, will be affected by the specific grinding forces. Morrell et al [22]found experimentally that the angular displacement P, was related to the specific grindingenergy by the relation,

B = (avP2 +bv P + c ) ( l+kF s ) (6.25)

where a, b, c and k are constants.

Substituting the value of P in Eq. (6.24) the power required to operate a high-pressure roll willbe:

P = 2 co F (a vp2 + b vP + c) (1 + k Fs) (6.26)

Quantitative analysis by Morrell et al [22] verified the validity of this equation.

6.9. Problems

6.1A smooth surfaced roll crusher had a roll diameter of 910 mm. Its suitability to crush an oreat 10.0 t/h was being examined. Preliminary examination showed that the kinetic frictionfactor was 0.36 when the speed of revolution was 33 rpm. The average diameter of particlesfed to the crusher was 200 mm and the S.G. of the ore was 2.8.

Estimate:

1. the distance between the rolls,2. the angle of nip,3. the width of the rolls.

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6.2Establish a relation between the diameter of roll and maximum size of ore when the reductionratios were 2.0, 3.0 and 4.0 and nip angle was held at 15°.

6.3A roll crusher was installed as a primary crusher to crush rocks of 7.0 cm maximum size. Thedistance between the rolls was set at 1.5 cm, the diameter of the rolls was 110 cm and thewidth 100 cm. The particle size distribution of the feed was:

Size , mm Wt. % Size, mm Wt. %retained retained

+7.0 0.0 +0.8 5.3+3.5 80.0 +0.4 3.2+1.7 106 -04 0.9

2 100.0

If the S.G. of the rock was 2.8, and the bulk density was 1.68 t/m , determine:

1. the relation between the capacity and the peripheral speed velocity when it varied from6 m/min to 22 m/min in steps of 4 m/min,

2. the change in the ratio of the coefficient of kinetic friction to static friction between theroll and the particles and the peripheral speed,

3. the ratio of tangential force at the points of contact to the radial forces at the same pointof contact between the roll and the nipped particle.

6.4The roll size of a roll crusher was 30.5 cm x 90.1 cm. Gypsum rock (S.G.= 2.7, bulk density= 1.7 t/m3) is to be crushed.

Determine:

1. the set in order to crush at the rate of 12 t/h and 10 rpm speed of the rolls.2. the ratio between capacity and peripheral speed if the set was 2.5 cm,3. the nip angle when the crusher feed size is 10 cm,4. the coefficient of friction between roll and gypsum particles.

6.5At a nip angle of 30°, an approximate relation between peripheral speed Vp (m/min), diameterof rolls D (cm) and sieve size, d (cm) through which 80 % of ore passes is given by therelation:

vP=1.8D^K)d+128

Establish the relation when the nip angle is changed to 35 and then to 40 degrees. Draw anomogram relating these variables of a roll crusher.

159159

6.6A set of rolls was required to crush limestone delivered from a secondary cone crusher at therate of 52 t/h. The product size from the cone crusher was less than 24 mm. The product sizefrom rolls was expected to be less than 8 mm. The shape factor of the feed was determined tobe 1.5. Using the data given below, estimate:

1. the diameter of rolls,2. the width of the rolls.

Data: The bulk density of limestone =1.6 t/m3

Speed of rotation = 75 rpm,Nip angle = 25°

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