bulkSOHdS Volume 21 Number 1 January/February 2001 Design of Belt and Apron Feeders

An Overview of Feeder DesignFocusing on Belt and

Apron Feeders

A.w. Roberts, Australia

SummaryAn overview of feeder design and performance focussing on

belt and apron feeders is presented The importance of correct

hopper and feeder interfacing is stressed The objective is to

achieve uniform draw-down in the hopper and procedures for

achieving this objective are given For the belt and apron feeder,the required divergence angle for the interface zone to achieve

uniform draw-down in the hopper is determined Theories relat-

ing to the determination of feeder loads and correspondingdrive powers are reviewed Special attention is given to the re-

quirements of the interface zone geometry which ensures that

belt or apron slip is avoided and wear is minimised The need for

controlling feeder loads is stressed and procedures for reducingloads and power under start-up conditions are presented

1. Introduction

A feeder is a device used to control the gravity flow of bulk solids

from storage such as from a bin or stockpile While there are

several types of feeders commonly used, it is important that

they be chosen to suit the particular bulk solid and to providethe range of feed rates required It is also important that feedersbe used in conjunction with mass-flow hoppers to ensure both

reliable flow and good control over the feeder loads and drive

powers Correct interfacing of feeders and hoppers is essential

if performance objectives such as uniform draw of material over

the whole of the hopper outlet is to be achieved

Another aspect of hopper design and feeder interfacing con-

cerns the need to control feeder loads and minimise drive

torques and powers In the case of belt feeders, for example,the design of the hopper and feeder interface must take ac-

count of the need to prevent slip between the bulk solid and the

belt surface This is essential if belt wear is to be avoided

This paper presents an overview of relevant aspects of feeder

design which address the foregoing matters While the generalprinciples apply to all feeders, the paper focuses, mainly, on belt

and apron feeders A selection of references on this subject is

given at the end of the paper [1 -8]

A W Roberts Emeritus Professor and Director Centre for Bulk Solids and

Paniculate Technologies University of Newcastle University Drive CaHaghan,NSW 2308 Australia Tel +61 2 49 21 60 67, Fax +61 2 49 21 60 21.E mail engar@cc newcastle edu au

Details about the author on page 113

2. Basic Objectives for UniformDraw-Down

For unrform draw-down with a fully active hopper outlet, the ca-

pacity of the feeder must progressively increase in the direction

of feed It is important to note that the increase in feeder capac-rty cannot be arbitrary Rather, it must be pre-determined if uni-

form draw-down is to be achieved This may be illustrated with

respect to some of the more common types of feeders used in

practice commencing with the screw feeder

Fig 1 shows a screw feeder in which the screw and shaft diam-

eters are each constant, while the pitch progressively increases

from the rear to the front as illustrated This is not a satisfactoryarrangement, mainly due to the fact that the volumetric effi-

ciency of the feeder decreases with the expanding pitch in thedirection of feed The feeder will draw preferentially from the rear

as shown To overcome this problem, the screw requires both a

tapered shaft in addition to the expanding pitch as illustrated in

Fig 2

Time 0

AAAU A A A A A A i AI

V V V V V V v'v

Rg 1 Screw feeder with constant screw diameter constant shaft diameter and

expanding pitch Feed occurs preferentially from rear of hopper

Rg 2 Screw feeder with constant screw diameter tapered shaft diameter and

expanding pitch Results in unrform draw down in hopper

TTTnIncreasing Pitch

ConstantPitchN J

^Tapered Shafi

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Design of Belt and Apron Feedersbulk

Volume 21 Number 1 January/February 2001handling

In the case of vibratory feeders, there is a tendency for feed tooccur preferentially from the front. To overcome this problem, itis recommended that the slope angle of the front face of thehopper be increased by 5 to 8 as illustrated in Fig. 3. Alterna-

tively, the lining surface of the front face in the region of the out-let may be selected so as to have a higher friction angle than theother faces. Apart from providing flexible support, the springsassist in controlling the feeder loads.

In the case of belt and apron feeders, a tapered opening is re-

quired as illustrated in Fig. 4. The triangular skirtplates in thehopper bottom are an effective way to achieve the required di-

vergence angle X.. It is often stated that the angle X should rangefrom 3 to 5, but this leads to excessively wide belts or apronsin the case of feeders with large /_/S ratios. As will be shown, A,angles smaller than those stated lead to optimum performance.An important feature of the diverging skirts is the relief providedto skirtplate drag.The gate on the front of the feeder is a flow trimming device andnot a flow rate controller. The height of the gate is adjusted to

give the required release angle and to achieve uniform drawalong the slot. Once the gate is correctly adjusted, it should befixed in position; the flow rate is then controlled by varying thespeed of the feeder. An alternative arrangement is to use a di-

verging front skirt or brow as illustrated in Fig. 4. This has theadvantage of relieving the pressure at the feed end during dis-charge and forward flow.

3. Feeder PerformanceCharacteristics

The complexity of the shear zone of belt feeders has been high-lighted in a comprehensive study performed by Schulze andSchwedes [5]. They showed that the shear zone may be dividedinto three regions, the lengths of the regions being predicted on

the basis of the 'Coulomb principle of minimal safety'. This as-

sumes that the rupture surface in a consolidated bulk solid will

develop in such a way that the bearing capacity of the solid isminimised.

There will be a velocity gradient developed in the shear zone, as

indicated in Fig. 5. The characteristic shape of this profile de-

pends on the properties of the bulk solid, the feeder speed andthe geometry of the hopper/feeder interface.

Fig. 4: Belt and apron feeder

Fig. 3: Vibratory feeder

Under uniform hopper draw-down conditions, an 'idealised'shear zone may be assumed to exist as shown in Fig. 6. Theshear zone is assumed to be tapered or 'wedge-shaped' anddefined by the release angle tp. It is also assumed that the ve-

locity profiles are approximately linear as illustrated. In the ex-

tended skirtplate zone, the velocity profile is substantially con-

stant with the bulk solid moving at a average velocity equal to

the belt velocity. Since the average bulk solid velocity at the exitend of the hopper skirtplate zone is less than the average ve-

locity in the extended skirtplate zone, there will be a 'vena con-

tracta' effect with the bed depth y^ less than the bed depth /-/ at

the exit end of the feeder.

Shear Surface

Belt/Apron

Fig. 5: Velocity profile in shear zone

U U O O \O O O Q

Divergent Front Skirt or/Brow to RelievePressure at Feed End

ALTERNATIVE ARRANGEMENT

14

bulkVolume 21 Number 1 January/February 2001 Design of Belt and Apron Feeders

Velocity Distributions:

Shear Zone^-

v

Exit

VenaContracta'ffect

LhShear Zone

eExtended Zone

B

Fig 6 Bett/apron feeder - assumed shear zone and veloaty profiles

3.1 Feed Rate Distribution

Refemng to Fig 6, the mass throughput of the feeder will varyalong the feed zone At any location x, the throughput O(x) is

given by

x) (D

where

where

a, -

1 -

20-h+Xo)(6)

/A(x) = cross-sectional area

v^ = velocity of the belt or apron

t^(x) = volumetric efficiency

p = bulk density in feed zone (assumed constant)

2xtanX.)(y<. (2)

The volumetnc efficiency t^(x), which relates the actual through-put to the maximum theoretical throughput based on the bulk

solid moving forward with the belt or apron without slip, is givenby

(3)

where v,(x) = average feed velocity at location x, given by

v,(x)-(1+C)^ (4)

C = velocity distnbution coefficient at location x

Eq (4) assumes there is no slip at the belt or apron surface It

has been shown [6-8] that the throughput from Eq (3) is givenby the cubic equation

2(/_h +Xq) tamp

The parameters in Eq (6) are

y<. = clearance at rear of feeder

S, = width of opening at rear of feeder

X = divergence angle

tp = release angle

Xq = dimension defined in Fig 6

/_ = length of hopper shear zone

Cg = velocity distribution factor at x = L^

3.2 Feeder Throughput

At the discharge or feed end of the hopper the throughput is

given by

Q(x)

where

Also

where

= volumetnc efficiency at exit

= bulk density in extended zone

(7)

(8)

(5)It is noted that p^ < p since the consolidation pressures are

tower in the extended zone

15

Design of Belt and Apron Feeders Volume 21 Number 1 January/February 2001handling

Hence

1+C,(9)

It is desirable that the ratio of the gate height H to the width of

opening be such that < 1.0. Preferably ^ 0.75 in order

to ensure satisfactory flow in the extended skirtplate zone.

4. Optimum Interface Geometry

4.1 Conditions for Uniform Draw-Down

Draw-down in the hopper is related to the feed in the feed zone

by the continuity of the mass flow as illustrated in Fig. 7. Thecondition for uniform draw-down, which represents the opti-mum performance, is such that

dQ(x)dx

= constant (10)

That is, the gradient of the throughput along the feed zone isconstant.

4.2 Optimum Divergence Angle

Often the requirement of Eq. (10) is impossible to achieve. In thecase of a belt or apron feeder, for example, Eq. (5) for Q(x) iscubic in form and Q'(x) is quadratic, which means that Eq. (10)cannot be satisfied. To overcome this problem, an optimumperformance may be achieved by setting

Q"(x)dQ'(x)dx

= 0 at x =

2(11)

This is illustrated by the surface profile shown in Fig. 8.

Based on the foregoing analysis, it has been shown [6, 7], thatthe optimum divergence angle X is given by

etanX =

- I-0.5(12)

The influence of the feeder L^/ß ratio on the optimum values ofX for a range of clearance ratios is illustrated in Fig. 9. The opti-mum divergence angle X for uniform draw-down is shown todecrease with increase in L^/S ratio, the rate of decrease beingquite rapid at first but lessening as the L^/ß ratio increases.

* dQ(x)

Q(x) + dQ(x)Q(x)

Fig. 7: Contunuity of feed

Fig. 8: Condition for optimum draw-down

y a

Yc

L

1 ^JU dQ'(x) odx

+r^Vi

yc/H = 0yc/h =

yc/H = 0.2yc/H = 0.3

4 6RATIO UB

Fig. 9: Optimum divergence angle vs. Lyß ratio for a range of clearance ratios.ti = 0.75; C = 0.5

4.3 Use of Transverse Inserts

In the case of feeders employing long opening slots, that is

L^/S > 5, the use of transverse inserts, as illustrated in Fig. 10,can assist in promoting uniform draw of bulk solid from the hop-per along the length of the feeder. With reference to the latter,the inserts assist in establishing the required release angle along

Fig. 10: Use of transverse inserts in long feeder

16

Volume 21 Number 1 January/February 2001 Design of Belt and Apron Feeders

0.95

0.9

0.85

0.8

0.75

07

>

>-o

LU

FFILU

o

LU

D

d>

0.65

060 1 2 3 4 5 6

DISTANCE FROM REAR OF HOPPER x (m)

Fig 11 Throughput characteristics of bett feeder C, = 0 5 L,/8 = 5Case 1 optimum >. = 1 54 Case 2 >. = 3

the feeder The inserts also assist in reducing the loads on thefeeder The inserts may incorporate diverging brows as illus-trated in order to smooth the flow at the transitions

4.4 Belt Feeder Example

As an example, the case of a belt or apron feeder with L/S = 5is considered For convenience, the throughput O(x) and gradi-ent of the throughput O'(x) are expressed in normalised form as

follows

A/q(x) and /Vq'(x)d/Vp(x)dx

(13)

Fig 11 shows the volumetric efficiency r^(x), throughput para-meter A/q(x) and gradient /Vq'(x) for the case of y^/H = 0 1 and

Cg = 0 5 The full lines for A/q(x) and A/q'(x) correspond to the op-timum divergence angle X = 1 54 and, as shown, the gradientA/q'(x) is virtually constant indicating uniform draw-down in the

hopper The volumetric efficiency decreases from the rear to thefront of the feeder as is expected

Fig 12 Vertical pressure and load variations on a feeder

For comparison purposes, the performance of a feeder havingthe same feed rate as the optimum feeder but with a larger di-

vergence angle of 3 is also presented The relevant graphs are

shown by dotted lines In this case, the gradient A/q'(x) for thiscase increases toward the feed end which indicates that thehopper will draw down preferentially from the front

5. Feeder Loads - Basic Concepts

5.1 Stress Fields

The determination of feeder loads and dnve powers requires a

knowledge of the stress fields generated in the hopper duringthe initial filling condition and during discharge The relationshipbetween the vertical pressure p^, generated in a mass-flow bin

dunng both filling and flow and the feeder load O is illustrated in

Fig 12 Under filling conditions, a peaked stress field is gener-ated throughout the entire bin as illustrated Once flow is initi-ated, an arched stress field is generated in the hopper and a

much greater proportion of the bin surcharge load on the hop-per is supported by the upper part of the hopper walls Conse-quently, the load acting on the feeder substantially reduces as

shown in Fig 12

It is quite common for the load acting on the feeder under flowconditions to be in the order of 20% of the initial load Thearched stress field is quite stable and is maintained even if theflow is stopped This means that once flow is initiated and thenthe feeder is stopped while the bin is still full, the arched stressfield is retained and the load on the feeder remains at the re-

duced value The subject of feeder loads and performance is

discussed in some detail in Refs [1 -4]

5.2 Feeder Loads Design Equations

Consider the mass-flow hopper and feeder of Fig 13 It needsto be noted that the depth of the hopper Zg should be such that

Zg/D > 0 67 in order to ensure that the surcharge pressure Pgcan be adequately supported by the upper section of the hop-per walls The design equations used to determine the feederloads are summarised below

The loads acting on the feeder and corresponding power re-

quirements vary according to the stress condition in the storedbulk mass The general expression for the load 1/ is

y-Pvo^o (14)

where p^ = vertical pressure on feeder surface

>Aq = area of hopper outlet

Initial Filling Flow

Pv.

7

PeakedStressField

ArchedStressField

(a) Stress Fields

vof

FeederLoad 4 Filling

V

Time

(b) Feeder Loads

17

Design of Belt and Apron Feeders Volume 21 Number 1 January/February 2001handling

Fig 13 Loads on feeder

For convenience, following the procedure established byArnold et al [1], the load may be expressed in terms of a non-

dimensional surcharge factor as follows

\/ = qYL^-^ß^^ (15)

where q = non-dimensional surcharge factor

Y = p g = bulk specific weight

p = bulk density

/. = length of slotted opening

ß = width of slot or diameter of circular opening

m = hopper symmetry factor

= 0 for plane-flow hopper= 1 for conical hopper

It follows from Eqs (14) and (15) that

*" U) wBased on an analysis of the pressure distribution in the hopper,it may be shown that the vertical pressure acting at the hoppernutlet is

Pvo = + Ps"2(/-1)tana |/~ 2(/-1)tanaJLD

where Pg = surcharge pressure acting at the transition

The exponent 'y' in Eq (17) is given by

tan(j).tana

-1 (18)

where /^ is the ratio of normal pressure at the hopper wall to the

corresponding average vertical pressure

From Eqs (16) and (17) a general expression for the non-di-

mensional surcharge pressure may be obtained That is,

r2ps(/-1)tana[2(/-1)tana1 * [ D

(19)

Two cases are of importance, the initial filling condition and the

flow condition, are now discussed

6. Feeder Loads -

Initial Filling Condition

6.1 Design Equations

This applies when the feed bin is initially empty and then filledwhile the feeder is not operating Research has shown that the

initial filling loads can vary substantially according to such fac-

tors as

rate of filling and height of drop of solids as may produce im-

pact effects

uniformity of filling over the length and breadth of the feed

bin, asymmetric loading will produce a non-uniform pressuredistribution along the feeder

clearance between the hopper bottom and feeder surface

degree of compressibility of bulk solid

rigidity of feeder surface

For the initial filling condition, the stress field in the hopper is

peaked, that is, the major principal stress is almost vertical at

any location The determination of the initial surcharge factor q,can be made by using an appropriate value of 'y' in Eq (19) The

following cases are considered

a For a totally incompressible bulk solid and a rigid feeder withminimum clearance, the upper bound value of q, may be ap-proached The upper bound value corresponds to y = 0 forwhich the vertical pressure in the hopper is 'hydrostatic' In

this case the ratio of normal pressure to vertical pressure is

given bytana

/Ch, = (20)tana tan^

with y = 0, the upper bound value of q, is obtained from

Eq (19) which becomes

Q, - I 3 1 (21),2tana[ß y

This equation corresponds to the pressure at the outlet being'hydrostatic'

b For a very incompressible bulk solid and a stiff feeder, y = 0 1

c For a very compressible bulk solid and a flexibly supportedfeeder, y = 0 9

d For a moderately compressible bulk solid stored above a

flexibly supported feeder, y = 0 45

Recommended Value of q.

While the value of q, may be determined using an appropriatevalue of y in Eq (19), from a practical point of view, it has beenestablished that a satisfactory prediction of q, may be obtainedfrom

1^' Uy I 2tana I ß

The vertical load I/, is given by

D 2p,tana- + 1 (22)

(23)

6.2 Surcharge Load - Mass and Expanded-FlowBins - Initial Filling Condition

The computation of the initial vertical load acting on a feeder re-

quires a knowledge of the surcharge pressure Pg acting at the

transition of the feed hopper It is to be noted that the flow load

acting on a feeder is independent of the surcharge head The

determination of the initial surcharge pressure Pg depends on

the type of storage system employed

18

bulk$OMdS Volume 21 Number 1 January/February 2001 Design of Belt and Apron Feeders

Dc

Us

(a) Funnel-Flow (b) Expanded-Flow

Rg 14 Mass-flow and expanded-flow bins

Referring to Fig 14, the surcharge pressure Pg is given by theJanssen equation:

h- ? a, (24)

where = 'hydraulic' or effective radius defined as

D

2(1

2(1+mj

for mass-flow bin

for expanded-flow bin

(25)

m^ = 0 for long rectangular cylinder

= 1 for square or circular cylinder

/-/ = height of bulk solid in contact with cylinderwalls

Fig 15 Gravrty reclaim stockpile

K, = for cylinder Normally K = 0 4

<t> = wall friction angle for cylinder

It is noted that in the case of the expanded-flow bin, if the flowchannel is pre-formed, then the dimension D may replace D<. in

Eq. (25)

The effective surcharge head for the heap on top of the cylinderis given by

H.(26)

where

6.3

mg+2

Hg = surcharge head

mg = 1 for conical surcharge

= 0 for triangular surcharge

Surcharge Load - Gravity Reclaim Stockpiles -

Initial Filling Condition

The use of mass-flow reclaim hoppers and feeders under stock-

piles is illustrated in Fig 15 The initial load \/ on the reclaimfeeder is dependent on the effective surcharge head, while theflow load V, is independent of the head as illustrated.

The determination of surcharge head and pressure in the case

of stockpiles is somewhat uncertain owing to the significantvariations that can occur in the consolidation conditions existingwithin the stored bulk solid The state of consolidation of thebulk solid is influenced by such factors as

stockpile management and loading history

loading and unloading cycle times and length of undisturbedstorage time

variations in moisture content

degree of segregation

variations in the quality of bulk solid over long periods of time

compaction effects of heavy mobile equipment that may op-erate on the surface of the stockpile.

HydrostaticHead

Pre-formedRathole

SurchargePressure

Initial

Feeder-Load B

Effective Head

19

Design of Belt and Apron Feedersbulk

Volume 21 Number 1 January/February 2001 SOHdS

Case 1: Uniformly Consolidated Stockpile -

Highly Incompressible Bulk Solid

(27)

i e,the effective head is equal to the actual head This is the

most conservative solution and would rarely occur in practice A

less conservative solution may be applied through the use of the

Rankine pressure or head, i e,

*b (28)

where

Ps = Y ^s cos

<j) = angle of repose

Case 2: Pre-Formed Rathole or Flow Channel

Since, during the initial filling process, there will be some defor-mation of the bulk solid in the flow channel relative to the sta-

tionary material adjacent to the flow channel at the hopper inter-

face, the surcharge pressure will be significantly reduced

Furthermore, during subsequent filling and emptying, the

rathole that is formed acts as a pseudo bin and serves to reduce

the surcharge pressure In such cases, the effective head maybe estimated using the Janssen equation following the proce-dures described in Section 6 2 for an expanded flow bin In this

case the cylinder diameter is the actual rathole diameter Dj, and

the wall friction angle is estimated on the assumption that the

maximum shear stress occurs during flow On this basis, $ is

given by

= tan 1 (sin ö) (29)

where 6 = effective angle of internal friction

In many cases the H/ft ratio of the ratholes is such that the as-

ymptotic value of the Janssen pressure may be applied That is,

Ps =

K,tan<|>(30)

In this case f? is the effective radius of the rathole or flow channel

7. Feeder Loads - Flow Condition

Once flow has been initiated, an arched stress field is set up in

the hopper Even if the feeder is started and then stopped, the

arched stress field in the hopper is preserved In this case, the

hopper is able to provide greater wall support and the load on

the feeder, together with the corresponding drive power, is sig-nificantly reduced While Eq (19) may be applied by choosingan appropriate value of 'y', some difficulty arises due to the re-

distribution of stress that occurs at the hopper/feeder interface

A well-established procedure, based on Jenike's radial stress

theory has been presented in Refs [1, 3] This procedure has

some shortcomings inasmuch as the influence of the surchargepressure Pg, although small, is ignored While the hopper half-

Bangle is included in the analysis, the aspect ratio of the

hopper is not taken into account An alternative approach is

presented in Refs [7, 8] and is now summarised

The redistribution of the stress field in the clearance space be-

tween the hopper and the feeder is illustrated in Fig 16

7.1 Flow Load Equations

In this case the stress field in the shear zone is assumed to be

peaked with the vertical design pressure p^ being equal to the

major consolidation pressure a.. On this basis, the pressuremultiplier /Cp^ is introduced

+sm6Fm ~

1 -sin 6 cos 2 (ri + a)

Hence Pvod = ^Fm Pvof

p^ is given by Eq (17) Hence,

2(/-1)tana+ Ps- 2(/-1)tanaJLD

e

1 +tana

-1

Pvod ~

where

and

2-sin8(1

_

1 r

2 [ ^ sinö

(j)^ = wall friction anglea = hopper half-angle6 = effective angle of internal friction

The force acting at the outlet and is

2(1 +sinöcos2ri)

(31)

(32)

(33)

(34)

(35)

(36)

(37)

where /* = area of outlet -l-m)

m = 0 for plane-flow or wedge-shaped hopper

m = 1 for axi-symmetric flow or conical hopper

Alternatively, the non-dimensional surcharge factor q, is ob-

tamed from Eq (16)

Pvod(38)

Combining Eqs (33) and (38)

Q =/C Fm1

2(/-1)tana

1

- 1)tanaJ [D

Fig 16 Stress fields at hopper and feeder interface

ArchedStressField

Hopper

Shear Zone

FeederPnof

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bulksolids Volume 21 Number 1 January/February 2001 Design of Belt and Apron Feeders

7.2 Experimental Results

Fig 17 shows a comparison between the predicted and exper-imental results for the feeder test rig described in Refs [3 4]The flow load has been adjusted to allow for the weight of bulkmaterial in the shear and extended skirtplate zones In general,the results are in reasonable agreement

8. Belt and Apron Drive Resistances

The general layout of a belt or apron feeder is shown in Fig 18The components of the drive resistance are

i shear resistance of bulk solid

n skirtplate friction in the hopper zone and in the extendedzone beyond the hopper

in belt or apron support idler friction

iv elevation of the bulk solid

Details of the analysis of these various resistances are given in

Refs [2 4] Two particular aspects concerned with the hop-per/feeder interface are

the force to shear the bulk solid

the bulk solid and belt/apron friction to prevent slip

8.1 Force to Shear Bulk Solid

The forces acting in the feed zone are illustrated in Fig 18 Thevertical pressure distribution on the shear plane is shown dia-

grammatically and will change from the initial filling case to theflow case Under operating conditions, the resistance F parallelto the feeder surface is given by

F=ngl/ (41)

where (.i^ = equivalent friction coefficient

V = vertical force on shear surface

Rg 18 Hopper geometry for feeder load determination

as-

01-

a =15*

= 00 J

D=*0S3

w\

J//

'/o>

oii

O ? Experimental Values

RowQ, (Predicted)

01 0.2 0 3 0 4

HEAD h (m)

05 06 07

Fig 17 Comparison between predicted and experimental results feeder test ng[3 4] Bulk material plastic pellets

Starting or breakaway conditions are more difficult to predictand depend on such factors as the hopper and feeder interface

geometry skirtplate geometry feeder stiffness the compressibility of the bulk solid and whether any load control is applied Inthe absence of any of the foregoing information a reasonableestimate of the breakaway force F is

(42)

-COS0

SECTION 3-3

21

Design of Belt and Apron Feedersbulk

jMiVolume 21 Number 1 January/February 2001

An expression for ^ based on the geometry of the feed zone is,

[6-8],- smxp

cos (6 + xp) + HgSin(6 +(43)

where 6 = feeder slopexp = release angle

Hg = coefficient of internal friction on shear planeAssuming that the maximum shear stress corresponds to thefailure condition then

Hg = sin 8 (44)where 8 = effective angle of internal friction

By way of example, a set of design curves for j^ based on

Eq (43) is shown in Fig 19 As indicated, ^ is sensitive to boththe feeder slope angle 6 and the release angle ip, decreasingwith increase in both these angles

8.2 Skirtpiate Resistance

Assuming steady flow, the skirtplate resistance is determinedfor the hopper and extended sections (see Fig 18) as follows

Hopper Section

(2\/ + Wh) cos 0 (45)

Theta = -10 Deg.Theta = 0 Deg.Theta = 10 Deg.

2 4 6 8 10 12 14RELEASE ANGLES (Deg)

16

Fig 19 Equivalent friction for belt and apron feeder - S = 50

steady flow In the case of slow feed velocities, as in the case of

apron feeders, the value of K^ for flow may be in the middle

range

8.3 Load Slope Resistance

sine (50)

where

Extended Section (Section Beyond Hopper)

J

(46)

(47)

(48)where I/V^ = p g ß L^V = feeder load

p = bulk density

y^ = average height of material against skirtplatesfor hopper section

y^ = average height of material against skirtplatesfor extended section

Ky = ratio of lateral to vertical pressure at skirt-

platesg = acceleration due to gravity = 9 81 (m/s^)6 = slope angle

ß.^ = average width between skirtplates

jAg ^= equivalent skirtplate friction coefficient

Hgp = friction coefficient for skirtplates

L^ = length of skirtplates for hopper section

Lg = length of skirtplates for extended section

W^ = weight of material in skirtplate zone of hopper

Wg = weight of matenal in extended skirtplate zoneIt should be noted that in the hopper zone, the skirtplates are di-

verging Hence the fnctional resistance, and hence the normal

pressure on the skirtplates, will be less than in the case of par-allel skirts Referring to Fig 18, n-gph ^y be estimated from

^igp - tanXMsph =

^ rt (49)1 + tanX

where X = half divergence angle of skirtplatesThe pressure ratio /<^ is such that 0 4 s K^ 0 6 The lower limit

may be approached for the static case and the upper limit for

8.4 Belt or Apron Load Resistance

Hopper Section

Extended Section

(51)

(52)

where = idler friction

8.5 Empty Belt or Apron Resistance

fb = ^b^b (53)

where w^ = belt or apron weight per unit length

Lg = total length of belt a 2 (L + L^ + Xg) + 1 5 [m]

8.6 Force to Accelerate Material onto Belt or

Apron

(54)where Q = mass flow rate (given by Eq (8))

Vb = belt or apron speedUsually the force F^ is negligibleIt should be noted that for good performance, belt and apronspeeds should be kept low Generally ^sO5 m/s

8.7 Drive Powers

The power is computed from

P = 12 Resistances) (55)

where r| = efficiencyv, = average belt or apron speed

22

bulkSOlMS Volume 21 Number 1 January/February 2001 Design of Belt and Apron Feeders

For start-up, v^ ay be approximated as half the actual speedFor the flow condition, v^ will be the actual belt or apron speedduring running

9. Condition for Non-Slip

The condition for non-slip between the belt and bulk solid under

steady motion can be determined as follows

(56)VCOS (<l>s - v) + ßWj COS 8

= friction coefficient for bulk solid in contactwith the belt or apron

= total weight of bulk solid in the skirtplate zones

F= MgV= force to shear material at hopper outlet

(normally F, for flow is used)

^sp = ^sph "" ^spe = t^l skirtplate resistance

Fg = force to accelerate the bulk solidFor normal feeder speeds F^ - 0

V = feeder load acting on shear surface (normallythe flow load is relevant)

ß = cos (<(>s - 6 - v)

Neglecting Fg, alternative expressions for n^. and tan j^ are

Mt>sVcos (<|>s - u) + ßWV cos 8

(57)

or

cos(e, -)p(c, C,,,)co.e(58)

WW Wewhere C, - and C^ -

Also, for small clearances y^. - 0 5

Fig 20 Minimum belt/apron friction angle to prevent sip

^-5 '^.0 1 6-50- Ms -si6-0 76 OpdrrwnX-1 54-C,-0 5

Ü 35-

4 6 8 10 12

RELEASE ANGLE y (beg)

A more detailed analysis is given in Ref [8] As an example,Fig 20 illustrates the minimum belt or apron friction angle as a

function of release angle to prevent slip for the case when

50, m - smö - 0 76, C = 0 05-._Ü- 5, - 0, Ö

1+C,andThe volumetnc efficiency is such that Hv(^-

H^e"1-05 The graphs have been plotted for the feeder

slope angles, -10, 0, and 10 As indicated, the minimum belt

friction angle <t^ = tan ^|^ are shown to be sensitive to both

changes in feeder slope and release angles

10. Controlling Feeder Loads

The loads on feeders and the torque during start-up may be

controlled by ensunng that an arched stress field fully or partiallyexists in the hopper just pnor to starting This may be achieved

by such procedures as

cushioning in the hopper, that is leaving a quantity of mater-

lal in the hopper as buffer storage This preserves the arched

stress field from the previous discharge as illustrated in

Fig. 21

starting the feeder under the empty hopper before fillingcommences

using transverse, tnangular-shaped inserts

raising the feeder up against the hopper bottom during fillingand then lowering the feeder to the operating condition priorto starting In this way an arched stress field may be partiallyestablished

Rg 21 Application of load cushioning to control feeder loads

H

Hh

FeederLoad

non

No Cushioning

1 0

HAHh

23

Design of Belt and Apron Feedersbulk

Volume 21 Number 1 January/February 2001handling

Initial

JackingScrews

Clearance

Fig 22 Use of jacking screws to lower the feeder

The choice of mounting arrangement for a feeder can assist in

generating a preliminary arched stress field near the outlet suffi-cient to moderate both the initial feeder load and starting power.In some cases belt feeders are mounted on helical springs,where the initial deflection of the springs during filling of the bincan assist in generating an arched pressure field near the outletand reduce the initial load. An alternative arrangement is to in-

corporate a jacking system to lift the feeder up against the bot-torn of the hopper during filling. Before starting, the feeder is re-

leased to its operating position sufficient to cause some

movement of the bulk solid in order to generate a cushion ef-feet. The use of a slide gate or valve above the feeder is another

way of limiting the initial load and power. The gate is closed dur-

ing filling and opened after the feeder has been started.

For 'emergency' purposes, the provision of jacking screws as il-lustrated in Fig. 22 can be used to lower the feeder should a

peaked stress field be established on filling and there is msuffi-cient power to start the feeder. Lowering the feeder can induce,either fully or partially, an arched stress field and allow the feederto be started. This precaution is useful for feeders installedunder stockpiles where surcharge pressures as high as

1000 kPa may be experienced.

11. Concluding Remarks

An overview of feeder design and performance with specific ref-erence to belt and apron feeders has been presented. The

geometry of the hopper and feeder interface for optimum draw-down in the hopper has been examined. It has been shown thatthe required divergence angle for the hopper and feeder inter-face decreases with increase in feeder length to width ratio, ap-proachmg limiting values as the length to width ratio exceeds 5to 1. The influences of the release angle, divergence angle, as-

pect ratio of length to width of opening, volumetric efficiencyand bulk solids flow properties have been identified. Proceduresfor the determination of feeder loads and drive powers havebeen reviewed and the influence of the interface geometry on

the shear resistance and belt and apron slip has also been ex-

ammed. The advantages of the arched stress field in the hopperin controlling feeder loads and power have been highlighted andmethods for achieving load control in practice have been identi-fied.

References

[1] Arnold, P.C., McLean, A.G. and Roberts, A.W.: Bulk

Solids: Storage, Flow and Handling: TUNRA, The Univer-

sity of Newcastle, 1982

[2] Rademacher, F.J.C.: Reclaim power and geometry of bin

interfaces in belt and apron feeders; bulk solids handling,Vol. 2 (1982) No. 2, pp. 281-294.

[3] Roberts A.W., Ooms M. and Manjunath K.S.: Feeder load

and power requirements in the controlled gravity flow ofbulk solids from mass-flow bins; Trans. I.E.Aust., Mechan-

ical Engineering, Vol. ME9, No.1, April 1984, pp. 49 -61.

[4] Manjunath K.S. and Roberts, A.W.; Wall pressure-feederload interactions in mass-flow hopper/feeder combina-

tions; bulk solids handling, Part I Vol. 6 (1986) No. 4,pp. 769-775; Part II Vol. 6 (1986) No. 5, pp. 903-911.

[5] Schulze, D. and Schwedes, J.: Bulk Solids Flow in the

Hopper/Feeder Interface; Proc. Symposium on Reliable

Flow of Particulate Solids (RELPOWFLO II), Oslo, Norway,23-25 August, 1993.

[6] Roberts, A.W.: Interfacing Feeders with Mass-Flow Hop-pers for Optimal Performance; Proc. Intl. Conf. on Bulk

Materials Storage, Handling and Transportation, The Instn.

of Engrs Australia, Wollongong, pp. 459-468, 1998.

[7] Roberts, A.W.: Feeders and Transfers - Recent Develop-ments; Proc. Bulkex '99, Australian Society for Bulk Solids,The Instn. of Engrs, Australia and the Centre for Bulk

Solids and Particulate Technologies, Sydney, pp. 1-1 to

1-27, 29 June- 1 July, 1999.

[8] Roberts, A.W.: Feeding of Bulk Solids - Design Consider-

ations, Loads and Power; Course notes, Bulk Solids Han-

dhng (Systems and Design). Centre for Bulk Solids and

Particulate Technologies, The University of Newcastle,1998.

24

bulksolids

WVolume 21 Number 1 January/February 2001 Design of Belt and Apron Feeders

Appendix: Feeder Design Example

The case of a reclaim hopper and apron feeder for reclaimingbauxite in a gravity reclaim stockpile similar to that depicted in

Fig. 15 is considered The stockpile heightsumed that the surcharge pressure on the

is 25 m. It is as-

hopper is calcu-lated using Eq. (30). The data and calculated loads and pow-ers are given below.

Hopper Details

Hopper type - plane flow

Hopper half-angleHopper opening dimension S

Hopper width at transition, D

Height of hopper section, z

Length of hopper opening, L^Feeder Details

Length of hopper zone, /.,Length of extended zone, LgTotal length of feeder, L

Height of opening at exit, /-/

Release angle, ^Skirtplate half divergence angle, XVolumetric efficiency at exit

Bed depth in extended shirt zone, y^Width between skirtplates, ß,.Weight per metre of belt/apronBelt/apron idler friction, u^Feeder throughput, Q^,Feeder speed,l^Bulk Solid Details

Effective angle of internal friction

Wall friction angle for hopperWall friction angle for skirtplatesBulk density for hopper section, pBulk density for ext. skirtplate zone, p^>Hopper surcharge pressure, pgInitial surcharge factor, q,Flow surcharge factor, q,

Loads and Resistances, Initial Condition;

Feeder load, initial condition, V,Shear resistance, F^Resistance, hopper skirtplate zone, F^Resistance, extended skirt zone, F^Slope resistance, F^,Empty belt/apron resistance, F^Total initial resistance, FLoads and Resistances, Flow Conditions

Feeder load, flow condition VpShear resistance, F^,Resistance, hopper skirtplate zone, F^Resistance, extended skirt zone, F^Slope resistance, F^,Empty belt/apron resistance, F^Total flow resistance, FFeeder Power

Power, initial conditions, P,Power, flow conditions, P,

= 0m

= 25

= 1.25 m

= 5.5 m

= 4.5 m

= 6.25 m

= 6.25 m

= 1.5 m

= 8.5 m

= 0.8 m

= 6.4

= 1.54

= 0.8

= 0.64 m

= 1.3 m

= 3kN/m

= 0.05

= 1350t/h

= 0.3 m/s

= 50

= 30

= 30

= 1.7 t/nrv*= 1.5 t/nrv*= 133 kPa

= 4.42

= 1.05

= 830.6 kN

= 361.6 kN

= 198.1 kN

= 2.61 kN

= OkN

= 2.68 kN

= 595.5 kN

= 170.2 kN

= 102.5 kN

= 52.4 kN

= 2.6 kN

= OkN

= 2.7 kN

= 160.2 kN

= 40.0 kW

= 18.0 kW

0Centre for Bulk Solids &Participate TechnologiesThe Centre for Bulk Solids & Particulate Technolo-

gies is a joint activity of the Universities ofNewcastle and Wollongong, unifying two strongstreams of expertise in bulk solids handling.

The Centre is involved in industrial research in the

areas of:

* Bulk Solids Testing, Storage & Flow

* Bulk Handling Plant Design

Instrumentation & Control

Belt Conveying

Mechanical Handling

Pneumatic Conveying

Slurry Systems & Freight Pipelines

Dust & Fume Systems

Physical Processing

The Centre provides a Master of EngineeringPractice (Bulk Solids Handling) and associated

Professional Development Programs embracingthe above topics. Courses are offered throughoutthe year on a one week modular basis.

For further information regarding these events,other professional development programs, Master

of Engineering Practice degrees, or the Centre for

Bulk Solids and Particulate Technologies, can be

obtained by contacting:

Centre for Bulk Solids &

Particulate Technologies

University of Newcastle, University Drive,

Callaghan, NSW 2308, AUSTRALIA

Tel.:+61 2 492 160 67

Fax:+61 2 492 160 21

Email: engar@cc.newcastle.edu.au

URL: www.bulk.newcastle.edu.au/cbs/

25