Design and Application of Feeders

8/11/2019 Design and Application of Feeders

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i. 3ravity -low 4opper The hopper geometry and internal wall friction characteristics in conjunction withthe flow properties of the bulk solid establishes the type of discharge flow pattern and maximumpotential rate of discharge.

-igure ' 4opper/-eeder combinations for loading conveyor belts

ii. -eeder The feeder controls and meters the flow of bulk material from the hopper to meet the specified

discharge flow rate. The importance of the hopper and feeder to be designed as an integral unit cannotbe too greatly emphasised. ! well designed hopper may be prevented from functioning correctly if thefeeder is poorly designed, and vice versa.

iii. 5hute %hile primarily a flow directing device, the chute, when properly designed, can control thevelocity of material entering the belt in a way which ensures uniform distribution of bulk material on thebelt with minimum belt wear, spillage and power losses. In view of their obvious simplicity feed chuteshave all too often received little attention to their design. There have been many instances where feedchutes are the 6weakest link in the chain7 in that lack of attention to design detail has led to majorproblems such as flow blockages, spillage7s and accelerated belt wear.

$ver recent years considerable advances have been made in the development of theories and associated designprocedures for gravity flow storage and feeding systems for bulk solids handling. ! selection of relevantreferences &*"8) are included at the end of this paper. The purpose of the paper is to review the overallrequirements for designing gravity flow feeding systems for bulk solids handling with particular emphasis on thefeeding operations in association with belt conveying. The paper outlines the characteristics of gravity flowstorage/feeder systems, presents an overview of the more common types of feeders used and discusses the

determination of feeder loads and power requirements. 9rief mention is made of the role of chutes and skirtplatesin directing and containing the motion of bulk solids.

/. GRAVITY FLOW OF BULK SOLIDS

%hile the general theories and design requirements for gravity storage and feeding systems are welldocumented, &*':) it is useful to review those aspects of particular relevance to the design and operation offeeding systems for belt conveying operations.

/. Ge!era' Des&(! P%&'osop%*

The design of gravity flow storage bin/feeder combinations for controlling the flow of bulk solids onto conveyorbelts involves the following basic steps

;etermination of the strength and flow properties of the bulk solids for the worst likely conditionsexpected to occur in practice.

;etermination of the bin geometry to give the desired capacity, to provide a flow pattern with

acceptable characteristics and to ensure that discharge is reliable and predictable.

+election of most appropriate type of feeder and determination of feeder geometry to achieve a

satisfactory flow pattern with a fully live hopper outlet.


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;esign and detailing of the bin structure and feeder components.

It is important that all bin and feeder design problems follow the above procedures. %hen investigating therequired bin geometry, it should be assumed that gravity will provide a reliable flow from storage. =ot until it hasbeen demonstrated that the gravity forces available are insufficient to provide reliable flow should moresophisticated reclaim methods be investigated.

/./ B&! F'o+ Patter!s

-ollowing the definitions of >enike, there are two basic modes of flow, massflow and funnelflow. These areillustrated in -igure ?.

-igure ? 9in -low 5haracteristics

In massflow the bulk material is in motion at substantially every point in the bin whenever material is drawnfrom the outlet. The material flows along the walls with the bin and hopper 0that is, the tapered section of thebin1 forming the flow channel. #assflow is the ideal flow pattern and occurs when the hopper walls aresufficiently steep and smooth and there are no abrupt transitions or inflowing valleys.

-unnelflow 0or coreflow1, on the other hand, occurs when the bulk solid sloughs off the surface and dischargesthrough a vertical channel which forms within the material in the bin. This mode of flow occurs when the hopperwalls are rough and the slope angle @ is too large. The flow is erratic with a strong tendency to form stable pipeswhich obstruct bin discharge. %hen flow does occur segregation takes place, there being no remixing duringflow. It is an undesirable flow pattern for many bulk solids. -unnelflow has the advantage of minimising bin wear.

#assflow bins are classified according to the hopper shape and associated flow pattern. The two main types areconical hoppers, which operate with axisymmetric flow, and wedgeshaped or chiselshaped in which planeflowoccurs. In planeflow bins the hopper half angle @ will usually be, on average, approximately 'AB larger than thatfor the corresponding conical hoppers. Therefore, they offer larger storage capacity for the same head room thanthe conical bin but this advantage is somewhat offset by the long slotted opening which can cause feed problems.

The limits for massflow depend on the hopper half angle @, the wall friction angle C and the effective angle ofinternal friction D. The relationships for conical and wedgeshaped hoppers are shown in -igure E. In the case ofconical hoppers the limits for massflow are clearly defined and quite severe while the planeflow or wedgeshaped hoppers are much less severe. 5onsider, for example, a conical hopper handling coal with D F "8B. If thehopper is of mild steel it is subject to corrosion, the angle C is likely to be approximately EAB. $n this basis, from-igure E, the limiting value of @, F 'EB. ! margin of EB is normally allowed making @ F 'AB which is a very steephopper. If the hopper is lined with stainless steel, the friction angle C is likely to be approximately ?AB. $n thisbasis @ F ?GE F ?EB. This results in a more reasonable hopper shape. The corresponding angles for planefloware @ F ??B for C F EAB and @ F E8B for C F ?AB.
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i. variation in hopper half angle @ at a function of opening hopper dimension 9 and

ii. the corresponding variation in flow rate for unrestricted discharge.

The full lines refer to a conical axisymmetricshaped hopper while the chain dotted lines refer to a planeflowwedged shape hopper. In the latter case the flow rate is given in tonnes/hr x 'AEper metre length of slot. Thegraphs indicate the following

The hopper half angle @, for massflow increases initially with increase in opening sie 9 and then

approaches a constant value.

The hopper half angle for a planeflow hopper is approximately '?B larger than that for a conical hopper

for the same outlet dimension 9,

The potential flow rate depending on the outlet dimension is quite significant. %hile with train loading

operations where flood loading is required there is a need for high discharge rates, for the majority ofcases the potential flow rate may be excessive rendering the need to employ feeders as flow controllingdevices.

-igure G #ass-low hopper geometry7s and flow rates for typical coal

0. FEEDERS FOR BULK SOLIDS HANDLING

0. Ge!era' Rear2s

-eeders for controlling the flow of bulk solids onto conveyor belts require certain criteria to be met

;eliver the range of flow rates required.

4andle the range of particle or lump sies and flow properties expected.

;eliver a stable flow rate for a given equipment setting. Kermit the flow rate to be varied easily over the

required range without affecting the performance of the bin or hopper from which it is feeding.

-eed material onto the belt in the correct direction at the correct speed with the correct loading

characteristic and under conditions which will produce minimum impact, wear and product degradation.$ften a feed chute is used in conjunction with the feeder to achieve these objectives.

-it into the available space.

It is important that the flow pattern be such that the whole outlet of the feed hopper is fully active. This is offundamental importance in the case of massflow hoppers. %hen feeding along slotted outlets in wedge shapedhoppers the maintenance of a fully active outlet requires the capacity of the feeder to increase in the direction offeed. To achieve this condition special attention needs to be given to the design of the outlet as vertical skirts and
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control gates can often negate the effect of a tapered outlet. 3ates should only be used as flow trimming devicesand not as flow rate controllers. -low rate control must be achieved by varying the speed of the feeder.

=oting the foregoing comments, the salient aspects of the various types of feeders commonly used to feed bulksolids onto belt conveyors are now briefly reviewed.

0./ V&brator* Fee3ers

0./. Ge!era' Rear2s

Vibratory feeders are used extensively in controlling the discharge of bulk solids from bins and stockpiles anddirecting these materials onto conveyor belts. They are especially suitable for a broad range of bulk solids, beingable to accommodate a range of particle sies and being particularly suitable for abrasive materials. 4oweverthey are generally not suited to fine powders under '8A to ?AA mesh where flooding can be a problem. !lso7sticky7 cohesive materials may lead to buildup on the pan leading to a reduction in flow rate.

9ulk solids are conveyed along the pan of the feeder as a result of the vibrating motion imparted to the particlesas indicated in -igure :.

-igure : #ovement of particles by vibration

The pan of the feeder is driven in an approximate sinusoidal fashion at some angle theta to the trough.

The conveying velocity and throughput depend on the feeder drive frequency, amplitude or stroke, drive angleand trough inclination, coefficient of friction between the bulk solid and the pan as well as the bulk solidparameters such as bulk density, particle density and general flow properties.

0././ T*pes o" )&brat&!( Fee3ers

In general vibrating feeders are classified as 7brute force7 or 7tuned7 depending on the manner in which the drivingforce imparts motion to the pan.

!s the name implies 7brute force7 type feeders involve the application of the driving force directly to the pan asillustrated in -igure (. These feeders have the following characteristics.

Hower initial cost but higher operating costs.

3reater forces to be accommodated in the design.

Impact loads on the pan are transmitted to bearings on which outofbalance weights rotate.

;elivery rates are dependent an the feeder load due to bulk solids.

3enerally confined to applications requiring only one feed rate.

$n the other hand 7tuned7 vibrating feeders are more sophisticated in their operation in as much as the drivingforce is transmitted to the pan via connecting springs as indicated in -igure *. In this way they act essentially as
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a two mass vibrating system and employ the principle of force magnification to impart motion to the pan. Theprimary driving force is provided by either an electromagnet or by a rotating outofbalance mass system.

-igure ( 79rute7 force type vibratory feeders Lef. &'()

-igure * Tuned type vibratory feeders Lef. &'()

-ollowing the work of Lademacher &'*) some general comments may be made. =ormally the trough mass is

designed to be ?.8 to E times as large as the exciter mass. -igure 'A shows typical magnification curves for thetuned feeder for two damping ratios M'and M?. =ormally the feeders operate below the resonance frequency withN/NAF A.* where N F driving frequency and NAF natural frequency of the system. It is often claimed that the7tuned7 feeder maintains its feed rate when the head load varies. The validity of this claim may be examined byreference to -igure 'A. The increased head load effectively increases the pan mass lowering the naturalfrequency NAand increasing the frequency ratio N/NA. This corresponds to a shift from ! to 9 in the diagram. !tthe same time, the damping increases due to the increased load resistance causing a shift from 9 to 5. Thus theclaim that the feeder maintains its performance regardless of the head load, basically, is not true. 4owever inmany instances the negative effect of the increase in damping approximately compensates for the change inmagnification factor. This means that points ! and 5 in -igure 'A are approximately of the same magnificationfactor so that the trough stroke is kept approximately constant.

-igure 'A Typical magnification curve for a tuned two mass system


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! similar analysis in the case of the over critical operation with N/NAP ' indicates that increases in N/NAand Mleads to a smaller, magnification factor corresponding to a smaller stroke. -or this reason over critical operation ofthis type of feeder must be avoided.

0./.0 Hopper4Fee3er Co!"&(-rat&o!s

There are several aspects to note when designing feed hoppers for use with vibrating feeders. These are

discussed at some length by 5olijn and 5arroll &?A). +ome important aspects are noted here.

-igure '' shows a typical vibrating feeder arrangement. The effectiveness of the feeder, as with all feeders,depends largely on the hopper which must be capable of delivering material to the feeder in an uninterruptedway.

-or a symmetrical hopper there is a tendency for the feeder to draw material preferentially from the front of thehopper. niform draw can be achieved by making the hopper outlet asymmetrical with the back wall at thecorrect hopper half angle @ and the front wall at an angle of @ Q 08B to (B1.

0The angle @ is obtained from -igure E1. !lternatively a symmetrical hopper may be made to feed approximatelyuniformly by using a rougher lining material on the front face. $ther recommendations include

;imension < to be at least '8A cm.

9 to be large enough to prevent arching or ratholing.

+lope R to be sufficient for the required flow rate

3ate height 4 to be chosen primarily to achieve an acceptable flow pattern rather than to vary the

flowrate.

-or high capacity feeders skirtplates extending to the outlet of the trough may be required as in -igure

'?.

-igure '' Typical arrangement for vibratory feeder

In the case of wedgeshaped planeflow bins problems arise when it is necessary to feed from the long slottedoutlets. It is always theoretically better to feed across the slot as in -igure 'E0a1 but the cost of wide feeders toachieve this goal often becomes prohibitive. ! better solution may be to use a multioutlet arrangement as in

-igure 'E0b1 and employ several narrower vibrating feeders to feed across the slot as shown.
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-igure '? Tapered skirts Lef. &?A)

%here it is necessary to feed along the slot as in -igure '" 0a1 , then tapering of the outlet in the direction of thefeed is required as indicated in -igure '"0b1. $nce again it is reiterated that the adjustable gate is a flowtrimming device rather than a flow rate controlling device.

-igure 'E !lternative arrangements for feeding across the slot wedgeshaped hopper

-igure '" !rrangement for feeding along slot of wedgeshaped hopper Lef. &'()

0.0 Be't Fee3ers

9elt feeders are used to provide a controlled volumetric flow of bulk solids from storage bins and bunkers. Theygenerally consist of a flat belt supported by closely spaced idlers and driven by end pulleys as shown in -igure '8.In some cases, hoppers feed directly onto troughed conveyors as in the case of dump hoppers used inconjunction with belt conveyors.

+ome particular features of belt feeders include

+uitable for withdrawal of material along slotted hopper outlets when correctly designed.

5an sustain high impact loads from large particles.

-lat belt surfaces can be cleaned quite readily allowing the feeding of cohesive materials.
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+uitable for abrasive bulk solids.

5apable of providing a low initial cost feeder which is dependable on operation and amenable to

automatic control.

%ith respect to the first point, the hopper and feeder geometry for long slots are critical if uniform draw is to be

obtained. %hile normally feeders are installed horiontally, on some occasions a feeder may be designed tooperate at a low inclination angle 8. The outlet should be tapered as shown in the plan view of -igure 'G.Lesearch &?'?") has shown that the taper angle R and downslope angle S together with the gate opening 4 arevery sensitive as far as obtaining efficient performance is concerned. In particular, as stated previously, the gateopening 4 should be used to train the flow pattern and not to control the flow rate. !s has been demonstrated byexperiment &?E), incorrect setting of the gate will cause non uniform draw with funnelflow occurring either downthe back wall or down the front wall. In one series of experiments using a free flowing granular type material,merely increasing the gate setting 4 causes the flow to move progressively towards the front. The final gatesetting needs careful adjustment if uniform draw is to be achieved. Thus in belt feeders flow rate variations mustbe achieved by varying the belt speed. This requirement places some limitations on belt feeders when very lowflow rates are required, especially if the bulk solid is at all cohesive or contains large lumps.

-igure '8 !rrangement for belt feeder

Karticular care is needed with the design of the hopper/feeder arrangement when handling fine powders in orderto ensure that problems of flooding are avoided. If the bulk material tends to stick to the belt, spillage may be a

problem with belt feeders. Therefore if sufficient headroom is available, it is desirable to mount the feeder abovethe belt conveyor onto which it is feeding material in order that any material falling from the return side of thebelt will automatically fall onto the conveyor belt.

-igure 'G 9elt feeder sited above conveyor to minimise spillage Lef. &*)

9elt feeders can also have applications where a short speedup belt is used to accelerate the material at theloading point of a high speed conveyor as illustrated in -igure ':. The accelerating conveyor avoids wear thatwould otherwise occur to the cover of the long conveyor.
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-igure ': 9elt feeder as acceleration conveyor Lef. &?8)

0.5 Apro! Fee3ers

!pron feeders are a version of belt feeders and are useful for feeding large tonnages of bulk solids beingparticularly relevant to heavy abrasive ore type bulk solids and materials requiring feeding at elevatedtemperatures. They are also able to sustain extreme impact loading. The remarks concerning the need foruniform draw and gate settings applicable to belt feeders are also applicable to apron feeders. -igure '(0a1 showsan apron feeder with parallel outlet which is inducing funnelflow down the rear wall of the hopper. !part from theobvious flow problems, the funnelflow pattern developed will accelerate the wear down the rear wall. Thetapered outlet of -igure '(0b1, when correctly designed will induce uniform draw, minimising segregation andminimising hopper wall wear.

-igure '( !pron feeders

0.6 P'o-(% Fee3ers

Lotary plough feeders are generally used in long reclaim tunnels under stockpiles where they travel along thetunnel as in -igure '* or fixed under stockpiles and large storage bins, as shown in -igure ?A.

In the case of the stockpile slot reclaim system of -igure '*, it is necessary for the diagonal dimension of the slotto be at least equal to the critical rathole diameter ;fof the bulk solid in order to prevent ratholes from formingunder the high storage pressures &'8). In this way the gravity reclaim efficiency is maximised. The tie beamsbetween slots should be steeply capped. -urthermore the slot width 9 fmust be large enough to prevent arching.

-igure '* Typical stockpile with paddle feeder reclaim system
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-igure ?A -ixed plough feeder

The basic concept of the traveling plough feeder is to allow bulk solids to flow by gravity onto a stationary shelfand then remove the solids from the shelf either with a linear drag plough or a traveling rotary plough. it isimportant that high penetration of the plough is achieved and that there is a small vertical section behind theplough to prevent material buildup on the sloping back wall. ! high penetration rotary plough feeder is shown in-igure ?'.

-igure ?' 4igh penetration plough feeder

5olijn and Vitunac &?G) have reviewed the application of plough feeders in some detail. They recommend thefollowing limiting values for plough feeders

a. Lotary Klough

o Tip speed O ?A m/s

o Tip diameter range '.( to " m

o 5arriage speed A.A' to A.A( m/s0does not contribute significantly to capacity1.

b. Hinear ;rag Klough

o Traversing speed A.'E to A.:G m/s

o 5ut width '." to ?.E m.

0.7 Rotar* Tab'e Fee3ers

The rotary table feeder can be considered as an inverse of the plough feeder. It consists of a power driven circularplate rotating directly below the bin opening, combined with an adjustable feed collar which determines thevolume of bulk material to be delivered. ! typical rotary feeder arrangement is shown in -igure ??. The aim is to
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permit equal quantities of bulk material to flow from the complete bin outlet and spread out evenly over the tableas it revolves. The material is then ploughed off in a steady stream into a discharge chute.

-igure ?? Lotary table feeder

This feeder is suitable for handling cohesive materials which requirelarge hopper outlets, at flow rates between 8 and '?8 tonnes per hour. -eed rates to some extent are dependenton the degree to which the material will spread out over the table. This is influenced by the angle of repose of the

material which varies with moisture content, sie distribution and consolidation. These variations prevent highfeed accuracy from being obtained.

Lotary table feeders are suitable for bin outlets up to ?.8 m diameter2 the table diameter is usually 8A to GAJlarger than the hopper outlet diameter. %ith some materials a significant dead region can build up at the centreof the table. This can sometimes be kept from becoming excessive by incorporating a scraping bar across thehopper outlet. It is important to ensure that the bulk material does not skid on the surface of the plate, severelycurtailing or preventing removal of the bulk material.

0.8 S$re+ Fee3ers a!3 D&s$%ar(ers

0.8. S$re+ Fee3ers

+crew feeders are widely used for bulk solids of low or ero cohesion such as fine and granular materials whichhave to be dispensed under controlled conditions at low flow rates. 4owever, as with belt feeders, design

difficulties arise when the requirement is to feed along a slotted hopper outlet, -igure ?E, !n equal pitch,constant diameter screw has a tendency to draw material from the back of the hopper as in -igure ?E0a1. Tocounteract this, several arrangements are advocated for providing an increasing screw capacity in the direction offeed as in -igure ?E0b1 to 0f1. The arrangements shown are

+tepped pitch

Variable pitch

Variable pitch and diameter

Variable shaft diameter.

Kitch variation is generally limited to a range between A.8 diameters minimum to '.8 diameters maximum. Thislimits the length to diameter ratio for a screw feeder to about six, making them unsuitable for long slots.
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-igure ?E +crew feeding along a slot

The section of the screw leading from the hopper to the feeder outlet is fundamental in determining the quantityof material discharged per revolution of the screw. !t the point where the screw leaves the hopper, it is essentialfor control purposes to cover the screw, normally by a 7choke7 section having the same radial clearance as thetrough. This choke section should extend for at least one pitch to prevent material cascading over the flights.

!s a screw feeder relies on friction to transport material it has a very low efficiency in terms of the energyrequirements. -urthermore, the volumetric efficiency is impaired somewhat due to the rotary motion imparted tothe bulk material during the feeding operation &?:).

+ince screw feeders are generally fully enclosed, relatively good dust control is achieved. 4owever due to thehigh frictional losses abrasive type bulk solids can effectively reduce the life of the feeder due to abrasive wear.-ine powders that tend to flood are difficult to control in a screw feeder in flooding situations.

0.8. S$re+ D&s$%ar(ers

+crew dischargers are variations of the normal screw feeder. Two of the more commonly used versions are shownin -igure ?". -igure ?"0a1 shows a single screw which is forced to circle slowly around the bottom of a flat bottomstorage silo. The screw rotates at the same time and slices the bulk material, transferring it to a central dischargechute. In -igure ?"0b1 the whole floor of the silo rotates about a fixed axis. The bulk material is forced againstthe rotating screw as the silo bottom rotates.

-igure ?" Various screw discharge arrangements

+crew discharges have been used successfully with some wet, sticky, bulk solids which have not been handledeffectively using other means. In addition to providing the necessary flow promotion, these devices also controlthe feed rate. Kroblems could arise when devices of this type suffer breakdown need careful investigation when

considering a screw discharge device for use in a particular application.

!n alternative application of screw discharges is in the


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Lotary feeders 0also known as drum, vane, star and valve feeders1 are generally used for the volumetric feedingof fine bulk solids which have reasonably good flowability.

! rotary drum feeder, -igure ?80a1, might be considered an extremely short belt feeder. The drum prevents thebulk material from flowing out but discharges it by rotation. This feeder is only suitable for materials with goodflowability which are not prone to aeration. +imilar considerations apply to the rotary vane feeder, -igure ?80b1,which might be considered as an extremely short apron feeder2 -igure ?80c1 shows some modifications to thevane. The rotary valve feeder, -igure ?G0a1, is completely enclosed and aims at preventing powders or fine

grained materials from flooding. The star feeder, -igure ?G0b1, provides a means for obtaining uniform withdrawalalong a slot opening.

These feeders are not suitable for abrasive bulk materials as clearances cannot be maintained and the feederstend to lose control especially when handling aerated powders. 5ohesive powders will tend to clog the rotorpockets and reduce feeder capacity.

-igure ?8 Lotary drum and vane feeders with various rotating elements Lef &'()

-igure ?G Lotary valve star feeders

0.: Fee3er Se'e$t&o!

The selection of a feeder for a particular situation is not always simple, especially if more than one satisfactorysolution appears possible. The type and sie of feeder for a given application is primarily dictated by thecharacteristics of the bulk material to be handled and the required capacity. +ome general guidelines on feederselection are given in Leferences &'(,'*).

5. FEEDER LOADS AND POWER RE;UIRE#ENTS

5. Ge!era' Rear2s

-rom a design point of view it is important to be able to determine with some accuracy the loads acting onfeeders in hopper/feeder combinations and the corresponding power requirements. Uet the stateoftheart has,in the past, been such that the loads and power requirements could not be estimated with any degree ofprecision. -or instance %right &?*) has observed that the majority of formulae published are empirical in natureand derived to predict loads and corresponding power requirements for feeders used in conjunction with funnelflow bins. These formulae are inadequate when applied to massflow bins since, in such cases, the loads andpower requirements are often greatly underestimated. This is largely due to the fact that in massflow bins thefull area of the hopper outlet is presented to the feeder.
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The loads acting on feeders can vary considerably. There are many reasons for this, some more obvious thanothers. !s indicated by Leisner and Lothe &'(), the shape of the hopper outlet will influence the load on a feederas illustrated in -igure ?:. In -igure ?:0a1, the full load 0not equal to the hydrostatic head1 acts on the feeder. In-igure ?:0b1 the load is partly reduced by changing the shape of the hopper. In -igure ?:0c1, the load iscompletely removed from the feeder and only acts on the hopper wall. !lthough the advantages of -igure ?:0b1and 0c1 appear obvious, the solution may not be as simple as that depicted. It is clear that the flow patterndeveloped in the feeding operation must be such that uniform, nonsegregated flow is achieved at all times.

The loads acting on feeders and corresponding power requirements are influenced by several factors. Theseinclude the following

4opper flow pattern, whether massflow or funnelflow

-low properties of the bulk solid

The chosen hopper shape which in the case of massflow includes axisymmetric or conical, planeflow

or transition 0combination of conical and planeflow1

The actual hopper geometry

The wall friction characteristics between the bulk solid and hopper walls and skirtplates

The type of feeder and its geometrical proportions

The initial filling conditions when the bin is filled from the empty condition and the flow condition when

discharge has occurred.

The most efficient and reliable feeding performance is achieved by using a massflow hopper/feeder combination.-or a given bulk solid and hopper/ feeder geometry the load acting on a feeder varies considerably between theinitial load, when the bin is first filled, and the load either during flow or after flow has stopped. Leisner &'() hasindicated that the initial load can be ? to " times the flow load. 4owever, research &?',??,?") has shown that thevariation is much greater than this with the initial loads of the order of " to ( times that of the flow load.Theoretical predictions show that circumstances can arise whereby the initial/flow load variations can be muchhigher than those indicated.

! procedure for estimating feeder loads for massflow/feeder combinations has been established &'E,EA). Thegeneral procedure is now reviewed.

-igure ?: Varying the load on the feeder by varying the hopper configuration &'()

5./ Press-re D&str&b-t&o!s &! #ass1F'o+ B&!s

It is first necessary to examine the pressures acting in massflow bins under both initial filling and flowconditions. The pressures in massflow bins are discussed in some detail in Leferences &'E,E'E:).
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-igure ?( shows the bin stress fields and corresponding pressure distributions for the initial filling and flow cases.In each case, pnrepresents the pressure acting normal to the bin wall while pvrepresents the average verticalpressure.

-igure ?( Kressures acting in massflow bins

5./. I!&t&a' F&''&!( Case 1 F&(-re /9anssen equation with an initial surcharge pressure term included.

pnFL

&'eWXjh/L

) Q pnoe

WXjh/L

0'1W

where L F ; F 4ydraulic radius 0?1?0'Qm1

Y F 9ulk +pecific %eight ; F 5ylinder diameter or width m F ' for axisymmetric or circular bin m F A for long rectangular planeflow bin W F tanR F coefficient of wall friction R F wall friction angle KnoF initial pressure at top contact point with wall due to natural surcharge of material caused by filling.

The coefficient Xjrelates the normal pressure pnto the average vertical pv. That is

XjF pn/pv 0E1

The value of Xjvaries depending on the cylinder geometry. -or parallel sided cylinders with slight convergence7s>enike suggests

XjF A." 0"1

-or continuously diverging or stepwise diverging cylinders without convergence7s, the theoretical value of Xjmaybe used
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XjF'sinD

081'QsinD

%here D F effective angle of internal friction for the bulk solid

-or continuously converging cylinders Xjis approximated by

XjF '

The initial surcharge pressure pnomay be estimated by

pnoF Xj hs 0G1

%here hsF effective surcharge.

hsdepends on the bin shape and manner in which the bin is loaded. !ssuming central loading, then for an axisymmetric bin a conical surcharge is assumed2 for a planeflow bin in which the length is greater than the width,an approximate triangular shape would occur if a travelling feeding arrangement, such as a tripper, is used. %iththese two limits

hsF 4s 0:1msQ?

where msF A for triangular surcharge msF ' for conical surcharge 4sF actual surcharge

-or a plane flow bin, some rounding of the ends of the top surface of material is likely to occur so that anapproximate intermediate value of mscan be used.

The >anssen curves for the cylinder are shown in -igure ?(0a1.

0ii1 4opper

-ollowing >enike &E:), the normal pressure acting against the wall is related to the average vertical pressure by aparameter X such that

X FKn

0(1pv

-rom an equilibrium analysis for the hopper the following differential equation is obtained.

dpn Q

npnF X 0*1

d 0ho1

+olution of this equation leads to

pnF X Z0ho

1 Q &hc ho

)&ho

)n[ 0'A1n' n' ho

where n F 0mQl1 ZX 0' Q W

1 '[ 0''1tan@

@ F hopper half angle

hcF surcharge head acting at transition of cylinder and hopper

hoF distance from apex to transition


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hcis given by

hcF\c

0'?1!c

where\c

is derived from the >ansen


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where Xmaxis given in graphical form in Leference &E:) or else may be computed using equationsderived in Leference &'E). That is

XmaxF &]w

/q0"

1m) 0'(19 ^

%here]w

FU0'QsinD cos?S1

0'*19 ?0x'1sin@

and q F 0 ^ 1m ' Z?0 ]w 10tan@ Q tanC1 ' [ 0?A1E "tan@ 9 'Qm

%here S F _&C Q sin'0sinC

1) 0?'1sinD

x F?m sinD

&sin0?SQ@1

Q ') 0??1'sinD sin@

y F&?0'cos0SQ@11)m 0SQ@1 'm sin@ Q sinS sin'Qm 0SQ@1

0?E10'sinD1sin?Qm0SQ@1

C F tan'W where C F wall pressure angle D F effective angle of internal friction m F ' for axisymmetric flow F A for planeflow.

In equation 0??1 the planeflow numerate term 0@QS1 must be in radians.

5.0 T%eoret&$a' Est&ate o" Fee3er Loa3s a!3 Po+er

The theoretical prediction of the surcharge load acting at the outlet of a massflow hopper requires considerationof both the initial and flow consolidation pressures acting on the bulk material. -igure ?* shows diagrammaticallythe loads acting in a hopper feeder combination.

-igure ?* -eeder loads in hopper/feeder combination

-ollowing the approach adopted by #cHean and !rnold &EA) the surcharge \ acting at the hopper outlet is givenby

\ F q H'm9?Qm 0?"1

where q F nondimensional surcharge factor F specific weight of bulk solid at hopper outlet F `g ` F bulk density at outlet g F acceleration due to gravity H F hopper outlet length 9 F hopper outlet width or diameter m F A for planeflow or wedgeshaped hopper m F ' for axisymetric or conical hopper

5.0. A!a'*t&$a' E>press&o! "or I!&t&a' No!1D&e!s&o!a' S-r$%ar(e Fa$tor

The load acting on the feeder may be estimated by assuming the average vertical pressure Kvacts over the wholearea of the hopper outlet. -rom +ection ".?.', the average vertical pressure is given by equation 0'G1, whenmultiplied by the hopper outlet area and combined with equation 0?"1 yields the following expression for theinitial nondimensional surcharge factor qi
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qiF 0^

1m '

&;

Q?\ctan@

') 0?81? ?0mQ'1tan@ 9 !c9

where ; F bin width 9 F hopper opening dimension @ F hopper half angle m F A for planeflow m F ' for axisymmetric flow

#cHean and !rnold &EA) considered the surcharge at the outlet as being the difference between the weight of thematerial in the hopper section plus the surcharge \ cat the transition minus the vertical wall support. They usedthe original >enike method &'E) for the initial normal wall pressures in the hopper. The expression obtained is

qiF 0^

1m '

&;

Q?\ctan@

') 0?G1? ?0mQ'1tan@ 9 !c;

It will be noted that equations 0?81 and 0?G1 are identical except for the denominator of the middle term of thesection contained within the square bracket2 in 0?81 the denominator includes 9 while in 0?G1 it is ;.

press&o! "or F'o+ No!1D&e!s&o!a' S-r$%ar(e Fa$tor

-ollowing #cHean and !rnold &EA) the flow nondimensional surcharge factor q fis given directly by equation 0?A1.That is

qfF 0^

1m '

& y

0'sinD cos?S

10tan@ Q tanC1 '

) 0?:1E tan@ x' sin@ 'Qm

where S, x and y are given by equations 0'*1, 0?A1 and 0?'1 respectively.

5harts for qfare also presented in Leference &'E).

5.5 Ep&r&$a' Approa$%es "or Est&at&!( Fee3er Loa3s

In this section the empirical approaches of Leisner &'(), 9ruff &E() and and >ohanson &E*) are given.

".".' Leisner7s #ethods

i. -low Hoad 9ased on ]'

Leisner postulates that, faced with higher experimental values of feeder loads, one shouldconsider the possibility that the stress field shifts and rotates above the feeder causing adifferent vertical stress condition. The highest value would occur when the major consolidationpressure 0]'1 acts downward. ]'is given by

]'F

9 ff

0?(140@1

where ff F flow factor. 5harts for ff and 40@1 are given in &'E). %hile Leisner suggests thatthis value should be used for vibratory feeders to predict feeder loads during flow, recentresearch &?',??,?") suggests that the prediction is also applicable to belt feeders.

ii. -low Hoad 9ased $n ]%


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Leisner suggests that the normal wall pressure at the hopper outlet 0]%1 0which is less than ]'but greater than the mean consolidation stress ]1 provides a good approximation for belt,apron and table feeders during flow. 0+ee comment at end of 0i1 above.1

]%/9 is available in chart form &'E) or can be calculated from the equation 0':1 which isrepeated below

]% F y0'QsinD cos?S1 0?*19 ?0x'1sin@

x and y are given by equations 0??1 and 0?E1 respectively. -or both the above approaches \fiscalculated from

\fF ]'0or ]%1 x 4opper $utlet !rea.

iii. Initial Hoads

Leisner indicates that initial loads are ? to " times higher if the bin is filled from completelyempty and only '.' to '.? times higher if the bin is not completely emptied before refilling.

5.5./ Br-""?s #et%o3

9ruff &E() suggests that \ for flow conditions be approximated by taking the weight of a block of bulksolid of height F " x L 0where L F hydraulic radius1 above the hopper outlet, -igure EA.

L Fcrosssectional area of outlet

0EA1perimeter of outlet

L for a circular outlet F 9/" 0E'1

L for slotted outlet F H9

including end effects 0E?1?0HQ91

F9/? neglecting effects 0EE1

\ for flow and initial conditions can then be calculated from the following equations

-or circular outlet \ F ^/" 9 s 0E"1

-or slotted outlet including end effects

\ F?H9

s 0E81HQ9

-or slotted outlet neglecting end effects

\ F ?H9 s 0EG1

where sF " for initial filling conditions

F ' for flow conditions.

5.5.0 @o%a!so!?s #et%o3

>ohanson &E*) suggests a similar empirical approach to 9ruff, for flow conditions, except that he useshalf 9ruff7s values and always neglects the end effects for a long slotted outlet, -igure E'. >ohansonmakes no recommendations for initial filling conditions.

5.6 Po+er to S%ear B-'2 So'&3 &! Hopper


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Xnowing the load acting on the feeder, the force required to shear the bulk solid tangentially at the hopper outletmay be estimated. -or a belt or apron feeder, the force to shear the material is approximated by

- F W'\ 0E:1

Various authors assume different values of W'. -or instance

-igure EA 9ruff7s approximation for \f

-igure E' >ohanson7s approximation for \f

Leisner and 9ruff assume W F A."

#cHean and !rnold, and >ohanson assume

W F sinD 0E(1

where D F effective angle of internal friction.

The power required to the shear bulk at the hopper outlet is

p F -v 0E*1

%here v F belt or apron speed.

It is to be noted that depending on the feeder type, additional forces may be exerted on the feeder. -or example

force due to material contained within skirtplates

additional load due to material on a belt, trough or table.

It may also be necessary to determine the resistances and powers due to other factors such as

+kirtplate resistance

belt resistance

These aspects are discussed in more detail in +ection 8.

5.7 E>ap'e

5.7. Prob'e Des$r&pt&o!

It is required to determine the loads exerted at the outlet of the planeflow wedgeshaped bin of -igureE?.
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-igure E? %edgeshaped planeflow bin for feeder load example

The relevant details are as follows

i. 9in

$pening ;imension 9 F '.8 m

4eight 4 F (.A m

%idth ; F 8.A m

+urcharge 4s F '.8 m

4eight of hopper 4h F ?.'G m4alf angle @ F E*B

Karallel section of bin F mild steel

4opper section F Hined with stainless steel type EA"?9

Hength of opening H F 8 m

ii. 9ulk +olid Type F coal


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F "A.8E kKa

-rom 0?G1 with m F A for planeflow

qiF '

& 8

Q?x"A.8EtanE*

') F ?.E''x?xtanE* '.8 A.*8x*.('x8

ii. -low +urcharge -actor-rom 0?'1

S F _&'( Q sin'0sin'(

1) F ?A.(*sin8A

iii. -rom 0??1 and 0?E1

x F sin8A

&sin0?x?A.(*QE*1

Q ')'sin8A sinE*

iv. F (."'

y F'.A"8sinE*Qsin?A.(*xsin0?A.(*QE*1

0'sin8A1sin0?A.(*QE*1

v.

F 8.8?

vi. -rom 0?:1

qfF '

&8.8?

0'Qsin8Asin"'.(10tanE*Qtan'(1 ')"tanE* :."'

vii. F A.E"

viii. -eeder Hoads

sing 0?"1

Initial \iF ?.E' x A.*8 x *.(' x 8 x '.8

F ?"?.? k=

-low \fF A.E" x A.*8 x *.(' x 8 x '.8

F E8.*E k=

ix.


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9ruff Incl.


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-igure E8 Variations in feeder loads with hopper geometry planeflow bin of example ".G.'

4owever there is a further advantage2 the material left in the hopper as a cushion, having previously been inmotion, will preserve the arched stress field. The new material being deposited in the bin will initially have apeaked stress field. This will provide a surcharge load an the arch field, but the load at the outlet will be of lowerorder than if the bin is totally filled from the empty condition. The stress condition and reduced loading isillustrated in -igure EG.

-igure EG 5ushioning in hopper to reduce feeder load

6. FEEDING OF BULK SOLIDS FRO# BIN ONTO BELT CONVEYOR

In the handling of bulk solids, belt feeders with skirtplates are commonly used. In other cases dump bins areused in combination with belt conveyors as illustrated in -igure E:. -or design purposes it is necessary todetermine the belt loads under initial filling and flow conditions and the corresponding drive powers &'').

-igure E: +chematic arrangement of dump bin and belt conveyor

6. Des&(! E-at&o!s

6.. B&! a!3 Hopper S-r$%ar(e a!3 Correspo!3&!( Po+er

These are determined in accordance with the methods described in +ection ".

6../ S2&rtp'ate Res&sta!$e

!ssuming steady flow, the skirtplate resistance may be determined as follows

i. 4opper +ection

-sphF W?Xv0?\ Q `g9Hy1 y/9 0"A1
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ii.


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K F 0 Lesistances1. v/ 0":1

%here F efficiency and v F belt speed.

The condition for nonslip between the belt and bulk solid under steady motion can be determined asfollows

WE0\fQ w1 P 0-fQ -sp1 0"(1

%hereWEFcoefficient of friction between belt and bulk solid\fFflow surcharge at hopper outlet% F weight of bulk material between skirtplates in hopper section of conveyor-fFforce to shear material at hopper outlet-spF skirtplate resistance.

6./ E>ap'e

6./. Prob'e Des$r&pt&o!

!s an extension of the example of section ".G.', consider the bin being used in conjunction with a beltconveyor. referring to -igure EG the relevant details are

i. 9in

$pening ;imension 9 F '.8 m

4eight 4 F (.A m

%idth ; F 8.A m

+urcharge 4+ F '.8 m

4eight of 4opper 4h F ?.'G m

4alf angle @ F E*B

Hength of bin H F 8 m

5ylinder F #ild steel

4opper lining F +tainless steel

ii. 9ulk +olid

Type F coal


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F '.'( 0k=/m1

-bF '.'( x ? x ?A x A.AG F ?.(E 0k=1

0!ctual belt weight will need to be checked after final belt selection is made1.

viii. !cceleration Lesistance

\mF A.*8 x '.8 x A.( x A.8 F A.8: t/s

-!F A.8: x A.8 F A.?(8 0k=1

ix. 5hecking =on+lip

-rom 0"(1

WEP-fQ -sph0f1 Q -spe0f1

\fQ w

P ?:.8 Q '".* Q '*.8"E8.*E Q A.*8 x *.(' x ?A x '.8 x A.(

P A.?"

-or nonslip WEP A.?". -or coal on rubber belting this condition is easily satisfied.

x. Total Kower

!ssume F *AJ

Initial case KiF 0'(8.G Q "?.A Q 'E.A Q ':.* Q 'A.' Q ?.(E1x A.8/A.* F '8' k%

-low case KfF 0?:.8 Q '".* Q '*.8 Q 8.8 Q 'A.' Q ?.(E Q A.?*1x A.8/A.*

F "".( k%

The value of Kfwill be larger if the Leisner value of \fis used.The total initial power is based on the assumption that the total initial load acts with beltvelocity v during startup from the initial filling condition. In practice, the initial power is mostlikely to be less due to the starting characteristics of the drive. -urthermore, once flowconditions have been established, and the bin is kept nominally full, then startup from astopped condition will most likely occur at a much lower power corresponding to the flowcondition.

6.0 Be't Fee3ers 1 #ore R&(oro-s A!a'*s&s

In order to obtain satisfactory draw of material uniformly distributed over the full hopper outlet, as previouslydiscussed, it is usually necessary to taper the hopper bottom in the direction of feed. ! detailed study of theforces and power requirements for belt feeders has been presented by Lademacher &'*,"A).

6.5 A$$e'erate3 F'o+ &! S2&rtp'ate o!e

The skirtplate analysis presented in the example of +ection 8.? is based on the assumption of uniform flow. %hendirecting bulk solids onto conveyor belts through feed chutes, it is necessary to accelerate the solids to beltspeed. The motion is resisted by the drag imposed by the skirtplate. This problem has been analysed by Lobertsand 4ayes &?,'').!s material accelerates, the depth h of the bed decreases as indicated in -igure E(.


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In view of the shallow bed conditions, it may be assumed that the lateral pressure distribution is proportional tothe hydrostatic pressure distribution. -or each wall the average pressure is Xv`gh/?, where Xvis the pressureratio coefficient at the walls of skirtplates. 4ence for the two walls the total average lateral pressure is `gh Xv.

4ere h is the depth of the material and within the acceleration one varies inversely with the velocity vs. That is,for a constant throughput \m0kg/s1, it follows that

h F 0 \m 1 ' 0"*1`b vs

where ` is density of the material 0kg/m1, b is width between skirtplates 0m1, and v sis velocity at sectionconsidered 0m/s1. 4ere 0\m/`b1 F constant.

-igure E( +kirtplates in acceleration one

! dynamic analysis of the motion of the material in contact with both the belt and skirtplates shows that theacceleration of the material is nonuniform and that the velocity vsas a function of distance l is nonlinear inform. 4owever for simplicity in this case it will be assumed that the average height of the material is inverselyproportional to the average velocity based on l inearity. That is, from equation 0"*1,

havF 0\m

1 0 ?

1`b vvo

4ence the drag force due to side plate friction can be obtained as follows

-!F W?`g bXv0hav1

or

-aF"W?g b'\m

08A1` b Xv0vvo1

where W?is friction coefficient between material and skirtplates F A.8 to A.:, b'is the acceleration length.

!ssuming, for simplicity, a blocklike motion of the bulk solid, an analysis of the forces due to the belt driving thematerial forward and the skirtplates causing a resistance to forward motion shows that the acceleration of thebulk solid is

a F W'g W?g Xvh/b 08'1

where W'F belt friction

W?F skirtplate friction

It is to be noted that the component W'g in 08'1 is the acceleration in the absence of skirtplates. +ubstituting forh from 0"*1 gives

a F g0W'W?Xv\m

1 08?1`bvs

where vsF bulk solid velocity at distance s from point of entry to belt.
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content 0d.b.1 on stainless steel, polished mild steel and rusted mild steel for the instantaneous condition as wellas the polished mild steel surface after :? hour storage. The increase in friction in the latter case is quiteconsiderable. It has been found that

-igure E* -eed 5hute for 9elt 5onveyor

-igure "A %all yield loci for coal at '*Jmoisture content 0d.b.1

certain coals, for example, will build up on mild steel surfaces even after a short contact time of a few hours. Thetype of behavior found to occur in practice is illustrated in -igure "'. #oist coal from a screen has been found toadhere to vertical mild steel surfaces as indicated, particularly where the initial velocity of the coal in contact withthe surface is low.

-igure "' 9uild up of cohesive material on chute surfaces

!s indicated by -igure "?, the wall yield loci are normally slightly convex upward in shape. !lso, depending on thesurface 6roughness6 or rather 6smoothness6, moisture bulk solids may exhibit an adhesion component adhesionoften occurs with a smooth surface. The effect of the adhesion and/or the convexity in the wall yield locus is tocause the wall friction angle to decrease as the consolidation pressure increases. This is illustrated in -igure "E.

The variation of friction angle with consolidation pressure must be taken into account when determining chuteslope angles. +ince bed depth on a chute surface is related to consolidating pressure it is useful, for designpurposes, to examine the variation of friction angle with bed depth. -igure "E shows, for a range of moisturecontents, the considerably high friction angles that can occur at low bed depths, the decrease in friction anglebeing significant as the bed depth increases.

-igure "? %all yield locus and wall friction angles
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-igure "E %all friction versus bed depth

-or a chute inclined at an angle R to the horiontal, the relationship between bed depth and consolidationpressure at the chute surface is

h F ]'

08G1 cos R

The slope of the chute R should be at least 8B larger than the maximum friction angle measured. $ften moistbulk solids will adhere initially to a chute surface particularly if the initial velocity tangential to the chute surfaceis low. 4owever, as the bed depth increases, the corresponding decrease in friction angle will cause flow to be

initiated. In such cases flow usually commences with a blocklike motion of the bulk solid. This is depicted in-igure "".

-igure "" 9locklike flow of bulk solid

9y far the greatest component of the drag force in a chute occurs along the chute bottom2 the side wallscontribute to a lesser extent. %here possible the side walls should be tapered outward or flared as indicated in

-igure "8 with gussets in the corners to prevent, or at least reduce, the buildup of material in the corners.

-igure "8 Lecommended chute configuration

8. CONCLUDING RE#ARKS

This paper has focused attention on the interactive role of storage bin, feeders and chutes in providing efficientand controlled feeding of bulk solids onto conveyor belts. Various types of feeders have been reviewed andmethods for determining feeder loads and power requirements have been presented. The theoretical expressions

given by equations 0?"1 and 0?G1 appear to provide a good estimate of the initial feeder load while thecombinations of equations 0?"1 and 0?:1 give a theoretical prediction based on the radial flow stress theory forthe flow loads. 4owever the flow loads tend to be underestimated by this procedure and accordingly the methoddue to Leisner based on the major consolidation stress ]'as given by equation 0?(1 is recommended as providinga more realistic estimate. It is clear that more research is necessary to validate the predictions proposed.

!s a general comment it is worth noting that the modern theories of storage and feeding system design havebeen developed over the past EA years with many aspects still being subject to considerable research anddevelopment. It is gratifying to acknowledge the increasing industrial acceptance, throughout the world, of themodern materials testing and design procedures. These procedures are now well proven, and while much of theindustrial development has, and still is, centered around remedial action to correct unsatisfactory design features
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of existing systems, it is heartening that in many new industrial operations the appropriate design analysis andassessment is being performed prior to plant construction and installation. It is more important that this trendcontinue.

1. Loberts, !.%., 4ayes, >.%. and +cott, A.>., 6.%. and +cott, A.>., 6$ptimal ;esign of 5ontinuous 5onveyors6, 9ulk +olids4andling, ' 0?1, l*('.

4. Loberts, !.%., 6enike, !.%., 6+torage and -low of +olids6, 9ul. '?E, tah uly '*(?.


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15. Loberts, !.%., !rnold, K.5., #cHean, !.3. and +cott, $.>. 6The ;esign of 3ravity +torage +ystems for9ulk +olids6, Trans. Institution of ., 6;esign 5riteria for 9in -eeders6, Trans. +oc. of #ining


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32. >enike, !.%., >ohanson, >.L. and 5arson., >.%., 69in Hoads Kart ? 5oncepts6, >ournal of ohanson, >.L., 6+torage and -low of +olids6, E ;ay %orking +eminar =otes, !ustralian #ineral-oundation, !delaide, >uly '*:G.

40. Lademacher, -.>.5., 6Leclaim Kower and 3eometry of 9in interfaces in 9elt and !pron -eeders6, 9ulk+olids 4andling., Vol. ?, =o. ?, pp.?(',?*", >une '*(?.

41. Loberts, !.%., 6The ;ynamics of 3ranular #aterials -low through 5urved 5hutes6, #echanical and5hemical

Documents

Design and Application of Feeders