Wear in chutes

8/22/2019 Wear in chutes

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2.2 CHUTE DESIGN CONSIDERATIONS FOR FEEDING AND TRANSFER A.W. Roberts

Emeritus Professor and Director.

Centre for Bulk Solids and Particulate Technologies,University of Newcastle, NSW, Australia.

SUMMARY

Chutes used in bulk handling operations are called upon to perform a variety of operations. For instance, accelerating

chutes are employed to feed bulk materials from slow moving belt or apron feeders onto conveyor belts. In othercases, transfer chutes are employed to direct the flow of bulk material from one conveyor belt to another, often via athree dimensional path. The importance of correct chute design to ensure efficient transfer of bulk solids withoutspillage and blockages and with minimum chute and belt wear cannot be too strongly emphasised. The importance is

accentuated with the trend towards higher conveying speeds.

The paper describes how the relevant flow properties of bulk solids are measured and applied to chute design. Chuteflow patterns are described and the application of chute flow dynamics to the determination of the most appropriatechute profiles to achieve optimum flow is illustrated. The influence of the flow properties and chute f low dynamics in

selecting the required geometry to minimise chute and belt wear at the feed point will be highlighted.

1. INTRODUCTION

Undoubtedly the most common application of chutes occurs in the feeding and transfer of bulk solids in belt conveyingoperations. The importance of correct chute design to ensure efficient transfer of bulk solids without spillage andblockages and with minimum chute and belt wear cannot be too strongly emphasised. These objectives are

accentuated with the trend towards higher conveying speeds.

While the basic objectives of chute design are fairly obvious, the following points need to be noted:

chute should be symmetrical in cross-section and located central to the belt in a manner which

directs the solids onto the belt in the direction of belt travel

in-line component of the solids velocity at the exit end of the chute should be matched, as far aspossible, to the belt velocity. This is necessary in order to minimise the power required toaccelerate the solids to the belt velocity, but more importantly to minimise abrasive wear of thebelt

normal component of the solids velocity at the exit end of the chute should be as low as possible inorder to minimise impact damage of the belt as well as minimise spillage due to particle re-bounding

slope of the chute must be sufficient to guarantee flow at the specified rate under all conditions and

to prevent flow blockages due to material holding-up on the chute bottom or side walls. It is implicitin this objective that the chute must have a sufficient slope at exit to ensure flow which means that

there is a normal velocity component which must be tolerated

adequate precautions must be taken in the acceleration zone where solids feed onto the belt inorder to minimise spillage. Often this will require the use of skirtplates

in the case of fine powders or bulk solids containing a high percentage of fines attention needs tobe given to design details which ensure that during feeding aeration which leads to floodingproblems, is minimised. For this to be achieved, free- fall zones or zones of high acceleration in thechute configuration should be kept to a minimum.

Chute design has been the subject of considerable research, a selection of references being included at the end of this

paper [1-29]. However, it is often the case that the influence of the flow properties of the bulk solid and the dynamicsof the material flow are given too little attention. The purpose of this paper is to focus on these aspects, indicating thebasic principles of chute design with particular regard to feeding and transfer in belt conveying operations.

2. BOUNDARY FRICTION, COHESION AND ADHESION

2.1 Boundary or Wall Yield Locus



For chutethe intera

loading c

The deterFigure 1(

boundary

The Jenikcompressparticularallow lowshear rinFigure 1(

betweenunder low

300mm i

The bounshape an

character

= tan-1 [ where τw

The WYL

axis at τo which shsurfaces.which is

the bulk

The naturof the phgenerally

design, wall oction between

ndition and e

mination of w). The cell di

yield locus, S

e test was oriive. In the casly where adhecompressiveand lid which) was develo

he bulk solidcompressive

order to allo

dary or wall yi, as usually i

istics. This ch

τw ]

σw = shear stres

for cohesive b

The Wall Frictws the wall friIt is to be notn upper boun

olid will fail b

e of adhesionsics and cheincrease as th

r boundary suthe relevant

vironmental

ll or boundarmeter is 95m

versus V, or

Fig

inally establise of chute dession occurs duressures to bforms part of ed at the Uni

nd the sampland even tens

more repres

eld loci (WYL)the case, eac

racteristic is r

(1) at the wall; σ

Figure 2.

ulk solids is of

ion Angle, , wiiction angles f ed that the wa

limit for . Th

internal shea

Figure 3. Fri

and cohesion iistry of bulk se wall surface

rface friction hroperties of t

arameters su

friction is usu. The shear f

ore usually s

ure 1. Bounda

hed for hopperign, the presse to the cohesapplied since

the normal loersity of New

of the liningile stresses. T

ntative size d

for most bulkh WYL interse

eproduced in F

w = pressure

all or Bounda

en convex up

ll then decreasr a representll friction angls, for very lo

r rather than

ction Angles f

is quite complolid and surfabecomes smo

as the major ie bulk solid a

h as temperat

ally performerce S is meas

ear stress τ v

ry or Wall Fric

design for whres are norm

ive nature of tthere is alwad. To overcoastle. The she

material. In the inverted sh

istributions of

solids and linits the wall sh

igure 2. The w

cting normal

ry Friction an

ard in shape

e with increastive cohesivecannot be larnormal pres

y boundary s

r a Particular

x; a study of e contact. It ither relative

nfluence. It had lining surfa

ure and moist

using the Jenured under va

ersus normal s

tion Measure

ich the normally much lowe

he bulk solid.s the weight oe this shortco

ar cylinder is r

is way, it is poar cell has be

bulk solids to

g materials tear stress axis

all or boundar

o the wall

Adhesion Ch

and, when ext

e in normal prcoal in contactger than the eures where th

ear, leaving a

Coal on Mild S

his subject ws known, for eo the mean p

s been showne, with extern

ure having a s

ike direct sherying normal f

tress σ is plot

ent

l stresses or pr than in hopphe Jenike tesf the bulk soliming, the invetracted so as

ssible to meaen manufactur

be tested.

nd to be slighindicating coh

y friction angl

racteristics

rapolated, int

essure. This iswith a dull anffective anglee friction angl

layer of mate

teel Surfaces

uld require axample, that crticle size of t

that friction dal factors suc

ignificant influ

r test as illustorce V and the

ed.

ressures are aers, and oftenof Figure 1(ain the shear

rted shear testo maintain c

ure the sheared with a dia

ly convex upwesion and adh

e is defined by

rsects the she

illustrated ind polished milof internal fric

4 can be qui

rial on the sur

detailed underohesion and ahe adjacent b

pends onas

ence.

rated inwall or

lwaystensile,) does notcell, theter of ontact

stresseter of

ard inesion

:

ar stress

igure 3d steelion δ e large,

ace.

standinghesionlk solid.



Also adhevery smocause sercarbon st

also serio

2.2 Type

In order tmass to

can occur

The bodyin dynam

flow pro

2.3 Mec

When thestrengthScott [29

(a) Failur

In this cafailure enthe boun

(b) Failur

In casesconsolidaboundary

build soli

Often sucthe fines

may thenconveyor

sion and coheoth surfaces.ious flow bloceel surfaces.

usly aggravat

s of Adhesio

hat build-up ae sufficient to

.

forces are noric systems suc

otion aid.

anisms of F

body forces aersus shear c

], the followin

e Envelopes -

se the shear svelope at theary surface r

e Envelopes -

f high moistuion stresses o. This is depic

adhering to t

h problems ariand moisture

be transferrebelts is transf

sion generallyo doubt, in suage problemshe bonding ac

the behavior

Problems nd hence blocovercome the

S = S

mally those dh as in the ca

ilure

re sufficient toonditions exist

failure condit

General Case

ress versus noundary. Thisther than inte

Special Case

re content cohr pressures toed in Figure 6

he chute surfa

ise in cases wigrating to th

to chute surf erred to chute

increase as mch cases, surf when corrosivtion can occur

due to adhesi

ages can be aforces due to

Figurehear Force; B

e to the weige of belt conv

cause failureing at the bouions are consi

rmal stress fais illustrated i

rnally within t

Figure 5 Failu

esive bulk soligive lower int.5. The body f

ce. This layer

Figure 6. Fail

ere the bulk se belt surface

aces. Other casurfaces.

oisture contenace tension hae bonding occafter relativel

n and cohesi

voided, it is nadhesion and

. Build-Up on= Body Force;

t componenteyor discharge

and, hence, flndary surfaceered:

ilure envelopen Figure 5. Foe bulk solid.

re Envelopes

s it is possiblrnal strengthrces may the

may then buil

re Envelopes

olid is transpoas the belt m

ses occur whe

of the bulk ss a significanturs, such as w

short contac

n.

cessary for thshear. Figure

SurfacesFo = Adhesiv

of the bulk solor, in other c

w, the modeand internally

for a cohesivr such cases, i

General Case

for the failurthan the correcause failure

up progressi

- Special Case

rted on belt coves across th

n the very coh

lid increase,influence. Cohhen moist coaltimes. Impur

e body forcesillustrates th

Force

id but may alsses, when vib

f failure will dwithin the bul

bulk solid isis expected t

envelope of sponding streby internal sh

ely over a pe

nveyors leadiidlers. The s

esive carry-ba

articularly in tesion and adhl is in contactities such as cl

generated in te types of buil

o include inertrations are ap

epend on thek solid. As disc

lways greaterhat failure will

he bulk solidgth condition

ear leaving a l

iod of time.

g to segregatigregation con

ck material fr

he case of esion canith

ay can

he bulk-up that

ia forcesplied as a

relativeussed by

than theoccur at

t lowerat the

ayer of

on withdition

m



(c) Failur

For free flfailure en

condition.

The foreg

within th

2.4 Exa

Considercontact wFigure 8.

5, the sta

hb = ρ g

where a

Without vTo reducamplitud

example i

3. FEEDI

Figure 9 i

conveyorsection ocurved se

As a com

are high

3.1 Free

For the fr

_

vi = √ Equationaccount,

Envelope - F

lowing, dry buvelope. In this

oing cases ind

bulk solid ne

ple

the case of aith mild steel,A vibrator is p

ble build up,

σo

( 1 +a

) g

(2 π f) Xf =

ibration (thathb to say 10to achieve th

indicates the d

NG OR LOAD

llustrates the

belt. The bulkthe feed chutction of the fe

ment, the alte

aintenance d

Fall of Bulk

ee fall section,

_________ fo + 2 g h

(3) neglects aihe relationshi

ree Flowing Bu

lk solids withcase, adhesio

Figur

icate that for f

r the boundar

ohesive coal oa typical valuroposed as a

enoted by the

mplitude of a

is a = 0), hb =m, an acceler

is. For instanc

ifficulty of ove

ING CONVEY

pplication of

solid is assue. Since, nored chute will b

rnative to the

evices and stil

olid , the velocity v

ir resistance, wp between hei

lk Solids.

o cohesion, thn of the bulk s

e 7. Failure En

ailure and, he

y must lie abo

f bulk density. The coal is aeans of remo

hb , is given b

Figure

(2)

plied accelera

0.1 m = 100ation a = 9.2e, a frequency

rcoming adhe

OR BELTS gravity feed

ed to fall vertially, the belte, essentially,

use of an acce

l require head

i may be esti

(3)

hich in the caht of drop an

e boundary suolid to a chut

velopes - Free

ce, flow to oc

ve the failure

ρ = 1 t/m whittached to theving the coal.

y

8. Adhesion P

tion

mm, a substag is required.of f = 151 Hz

ion problems.

hute to direct

cally throughr apron speedin the vertical

lerating chute

room. Feed c

ated from

se of a chute,velocity Vi (F

rface failure esurface will n

Flowing Bulk

cur, the shear

envelope.

ch has a measunderside of

Assuming a fa

roblem

tial amount.here are manand amplitud

the discharge

height 'h' bevf ≤ 0.5 m/s,direction. is to employ a

utes may be r

is likely to beigure 9) is,

nvelope is higot occur. Figur

Solids

stress versus

ured adhesiveild steel surf

ilure condition

y combinationof X = 0.1m

from a belt or

ore making cthe velocity o

short acceler

egarded as th

mall. If air re

er than the be 6.6 illustrat

normal stress

stress of σo =ce as illustratas depicted b

s of frequencywould suffic

apron feeder

ntact with theimpact vi wit

ting conveyor

better propo

sistance is tak

lk solids this

state

1 kPa fored in

Figure

and. This

to a

curvedthe

. These

ition.

n into



h =

v∞ -----

g where v∞

vfoVi

3.2 Flow

The caseThe relev

The drag

FD = E N

where E =surface, t

E = [ 1 +

whereKv H

B

For conti

ρ A v = C

where ρ A

It follows

E = [ 1 +

loge [ 1 - vfo

v∞ --------

1 - vi v∞

= terminal ve

= vertical co = velocity cor

of Bulk Soli

of 'fast' flow aant details are

force FD is du

equivalent frihe stream cro

Kv H/B ]

actual frictio= pressure ra= depth of fl

= width of ch

uity of flow, onstant

bulk densitycross-sectio

, therefore, th

C1 ]v

] - ( vi - vo

)------- g

locity

ponent of velresponding to

around Cur

round curved

to Coulomb f

(5) ction which tass-section and

(6) n coefficient f tio. Normallywing stream

ute

al area of flo

t equation (6

(8)

v∞

ocity of bulk sdrop height 'h

Figure 9.

ed Chute of

hutes is depic

riction, that is

kes into accouthe internal s

r bulk solid in~ = 0.4 to 0.t a particular

(7) ing stream can also be w

Figure

(4)

lid dischargin' at point of i

eed Chute Co

Constant Ra

ted by the chu

nt the frictionear of the bul

contact with c.

location

ritten as

10. Chute Flo

g from feederpact with chu

nfiguration ius te flow model

coefficient betk solid. E is ap

hute surface

Model

e.

of Figure 10.

een the bulkproximated by

solid and the hute



For a chu

C1 =Kv

where vo

Ho

Analysing

dv + Ev

dθ If the curstream, it

θ.

v = √ For v = v

K = { vo

Special C

When θo

Equation

v =

√ 4 TRANS

The foreg

solid andtransfers,

an inverttransfer.streamlinof the lin

4.1 Inve

te of rectangul

o Ho B = initial veloci

= initial strea

the dynamic

g R (cos θ

v ved section of may be show

___________

2 g R

4 E + 1 at θ = θo,

-2 g R

[(4 E + 1

ase:

0 and v = v

(11) becomes

___________

2 g R [4 E + 1

FER CHUTES oing discussio

the chute surf it is common

d curve. Thishe lining is di

ed flow. The crs to be carri

rted Curved

lar cross-secti

(9) ty at entry to

m thickness equilibrium co

- E sin θ)

the chute is on that the sol

___________

[( 1 - 2 E) sin

1 - 2 E) sin θo

, K=vo -6 E

1 +

, ___________

( 1 - 2 E) sin θ

n has focused

ace is alwaysto employ chu

is illustrated ivided into twooncept of remd out without

Fig

hute Sectio

n

hute

ditions of Fig

constant radition of equati

__________

θ + 3 E cos θ ]

+ 3 E cos θo ]

g R

4 E

__________

+ 3 E cos θ ]

on curved chu

ssured by grates of multiple

Figure 11 inzones, one fovable impactinterrupting t

ure 11. Transf

s

re 10 leads to

(10)

us R and ~E isn (10) leads t

________

+ K e-2

Eθ

} e-2Eθo

(13)

___________

+ K e-2Eθ [vi -

es of concave

vity plus centrgeometrical s

hich the user the impact rplates, used ine production.

er Chute Show

the following

assumed cono the equation

(11

(12)

________

6 E R g4 E + 1

upward form

ifugal inertia f ections in whi

of curved impgion under loconjunction w

ing Impact Pl

differential eq

stant at an avbelow for the

)

(14

in which conta

orces. In the ch the zone of

ct plates is eimpact angl

ith spares allo

tes

uation:

rage value fovelocity at an

ct between th

ase of conveyfirst contact a

ployed in a cs, and the othws ready mai

they location

bulk

rnd flow is

nveyorer for thetenance



The methillustrate

-dv

+ E dθ

For a con

v = √ For v = v

K = {vo -

Special C

K = {vo -

and

v =

√

Equations

v≥ si

R g

The miniFigure 13

4.2 Conv

On someadhesion

od outlined inin Figure 12.

v =g R

(cosv

stant radius a

___________

2 g R

4 E + 1 at θ = θo, th

2 g R

[ 31 + 4 E

ase: v = vo at

2 g R[ 2

1 + 4 E

___________

2 g R

4 E + 1

(16) to (19)

θ

um bulk soli. ex Chute Se

occasions, iteffects and as

Section 3.2 foNoting that FD

θ + E sin θ)

d assuming E

___________

[ sin θ (2 E -

n cos θo + (2 E

θo = π /2 E - 1]} e-

Eπ

___________

[ sinθ (2 E -

pply during p

(20)

Figure

velocities for

tions ay be desirab

sist the discha

r curved chute= E N , it ma

(15)

is constant at

__________

1) + 3 E cos

- 1) sin θo ]}

Figure 12. In

__________

1) + 3 E cosθ

ositive contact

13. Minimum

chute contact

le to incorporarge process.

s may be readbe shown th

an average va

___________

θ ] + K e2Eθ

e-2Eθo

verted Curve

(18)

___________

] + e-E(π - 2θ) [v

, that is, when

Velocities for

as a function

te a convex c

ily adapted tot the different

lue for the str

(

Chute Model

___________

o -2 R g (

4 E

mpact Chute

f contact angl

rve as illustra

inverted curvial equation is

am, the soluti

(14)

7)

_________

2 E + 1)]

+ 1

ontact e for three cur

ted in Figure 1

d chute sectiogiven by

ion of equation

(1

ve radii are pr

4 in order red

n as

(15) is

9)

esented in

uce the



For FD =

dv - E v

dθ This hold

sinθ

· ≥

It is notevelocity f

For a con

v = √ For v = v

K = {vo -

Special C

K = {vo -

and

v = √ 5. WEAR

Chute we

mechanic

5.1 Abra

In casesmay be d

N ,it may be

g R (cosθ -

v for

v

g that Figure 1

r chute conta

stant radius a

___________

2 g R

4 E + 1 at θ = θo, th

2 g R

[(1 + 4 E

ase: v = vo at

2 g R[1

1 + 4 E

__________

2 g R[(

4 E + 1 IN CHUTES

ar is a combin

s of chute flow

sive Wear Fa

here the buletermined as

shown that th

E sinθ)

3 also appliesct. d assuming E

___________

[ (1 + 2 E

n 1 + 2 E) sin θo

θo = π /2 + 2 E]} e-

Eπ

___________

1 + 2 E) sinθ

ation of abrasi

as will be no

ctor of Chute

solid movesollows:

Figure 14. C

differential e

(22)

in this case wi

is constant at

__________

sin θ - E cos θ

- E cos θo ]} e

___________

E cosθ ] + e

ve and impact

described.

s

s a continuou

nvex Curved

quation is give

(21)

th the vertical

an average va

___________

] + K e2Eθ

-2Eθo

(25)

__________

(2θ - π) [vo -

wear. Abrasiv

stream unde

Chute Section

n by

axis now repr

lue for the str

(

__________

2 R g

4 E + 1

e wear may b

'fast' flow co

esenting the

am, the soluti

(23)

24)

analysed by

ditions the ab

aximum valu

ion of equation

(26)

considering th

rasive or rubb

of the

(21) is

ing wear



(a) Wea

Considerabrasive

Wc =Qm

Wc has u

NWR is th

NWR =R

The vario

= chutKc = rati

Qm = thrv = av

θ = ch

The factoreduce. T

chutes. (i) Straig

In this ca

Wc =Qm

On the as

velocity v

(ii) Const

In this ca

of Chute Bo

the general caear factor Wc

g Kc tan NWR

B its of N/ms non-dimensi

+ sin θ

g us parameters

e friction anglo vs /v

ughput kg/srage velocityte slope angl

r Kc < 1. For 'f wo particular

t Inclined chu

se R = ∞ and

Kc tan g sinθ B

sumption that

ariation. ant Radius Cu

se R is consta

ttom

se of a curvedexpressing th

nal abrasive w

are B =vs =

R =at section conmeasured fro

ast' or accelerhute geometri

tes equation (27)

Kc is nominall

ved Chutes t and the wea

Figure

chute as showe rate of rubbi

(27)

ear number a

(28)

chute width (velocity of slid

radius of curidered (m/s)m the vertical

ated thin streaies are of prac

reduces to (29)

y constant, th

r Wc is given

(a)

15. Chute Flo

n in Figure 15ng against the

nd is given by

)ing against ch

ature of the c

m flow, Kc ~/ical interest,

n the wear is

y equations (

Velocity Varia

Model

, the chute bechute bottom

,

ute surface

hute (m)

0.6. As the straight incline

constant alon

7) and (28).

tion

ing of rectanghas been deri

tream thickned chutes and

the chute an

ular cross-sectved as follows

ss increases Konstant radius

d independent

ion. An:

, willcurved

of the



Figure 1

The veloc16(a) shoangular pincreases

to be self

(b) Chut

It is to bewill be m

pressurewear on t

Wcsw =

Kc and Kv the chute

5.2 Imp

Impact w

is causedimpact d

6. WEAR

An impor

problem i

The prim

6.1 Abra

. Velocities an

ity variation aws the variatiosition for con, the increase

cleaning is in

e Side Walls noted that thch less, varyi

to increase linhe side walls

c Kv Kc

are as previobottom surfa

ct Wear in C

ear may occur

when impingmage occurs

OF BELT AT

ant applicatio

s illustrated in

ry objectives

mat

redukept

load

ensu

sive Wear Pa

d Wear in Chu

round a constn of velocity,

stant curvaturin NWR becom

icated.

e wear plottedng from zero a

early from zeran be estimat

(

sly defined. If e wear. hutes at points of e

ment angles at steep impin

FEED POINT n of feed and t

Figure 17.

are to h the horizont

ce the verticalwithin accept

the belt centr

re streamlined

rameter

(

tes of Constan

nt radius curvand Figure 16e chutes of ras progressivel

in Figure 16 at the stream s

at the streaed from 0) , for example,

try or points

re low, that isement angles

ransfer chutes

Figure 17

al component

component of ble limits

lly so that the

flow without

) Abrasive W

t Curvature Q

= 30 ed chute is gi(b) the corresii 1m, 2 m, 3y smaller. In

pplies to the curface to a m

surface to a

Kc = 0.8 and

f sudden cha

in the order o, that is angle

is to direct th

Feeding a Co

of the exit vel

the exit veloc

load is evenl

pillage or blo

ar =30 t/h; vo =

en by equatioonding abrasim and 4 m. Itigure 16(a), t

hute bottom sximum at the

maximum valu

Kv = 0.4, then

ge in directio

15 to 30. Fors in the vicinit

e flow of bulk

veyor Belt

city vex as clo

ity vey so that

distributed in

kages

0.2m/s; ρ = 1

s (11-14). Byve wear numbis interestinge limiting cut

urface. For thchute bottom.

e at the botto

the average s

. For ductile

hard brittleof 90.

solids onto bel

se as possible

abrasive wear

order to avoi

t/m; b=0.5m;

way of examer as functionto observe thaoff angle for t

side walls, thAssuming the

m, then the a

ide wall wear i

aterials, grea

aterials, great

t conveyors. T

to the belt sp

due to impact

belt mistrack

E = 0.6;.

le, Figureof

t as Rhe chutes

e wearside wall

erage

s 25% of

test wear

est

he

ed

may be

ing



An abrasi

Impact p

where ρ

Abrasive

Wa = b ρ

Where b

The wear

Equation

Wa = b ρ

where Kb

θe = chut

Kb is a no

As indicat

For the cbulk solid

α ≥ tan-1

6.2 Acce

The accel

La =vb -

2 g

7. WEAR

The abra

illustrate

ve wear para

essure pvi = ρ

bulk density,

wear paramet

vey (vb - vex)

friction coeffi

will be distrib

(32) may be a

ve Kb

= cosθe (vb /ve

e slope angle

n-dimensional

ed, the wear i

ute to be self on the chute

(E) + 5o

leration Len

eration length

vey mb MEASUREM

ive wear of ch

in Figure 19.

eter expressi

vey (

, t/m; vey = ve

r (kPa

icient between

ted over the

lso expressed

(33

- sinθe)

ith respect to

wear parame

s quite severe

Figure 18.

cleaning, thesurface. It is r

th La over which

(3

NT ute lining and

g the rate of

kPa)

rtical compon

m/s)

the bulk solid

cceleration le

as )

(34)

vertical at exi

er. It is plotte

at low chute a

on-Dimensio

lope angle of commend tha

slip occurs is

6)

conveyor belt

Figure 1

ear for the b

(31)

nt of the exit

(32) and conveyor

gth La.

t d in Figure 18

ngles but red

al Wear Para

the chute at et

(35)

iven by

samples may

9. Wear Test

lt may be est

velocity, m/s

belt; vb = bel

for a range of

ces significan

eter versus S

xit must be gr

be determined

pparatus

blished as foll

speed

ve /vb values.

ly as the angl

lope Angle θ ater than the

using the we

lows:

θe increases.

angle of repo

r test apparat

e of the

us



As illustrdelivers aheld in punder the

is appliedbucket elmeasureconverte

Thickness

where MA

ρ

Tests havtypical tea wear ra

due to lo

8. CONV

8.1 Gen

Figure 21The bulktransitionspreading

profile mtrajectori

ted, the rig incontinuous ssition by a retsample to a

by weights ovator and chent of the teto loss in thi

Loss =M.10 A ρ

= Mass loss (gContact Sur

Test Sample

e been condust result for ate of approxi

ding of coal o

EYOR BELT D

ral Discussio

shows the trasolid will also. The amountis also more

y develop as is

corporates a spply of the buaining bracketepth of sever

top of the sate. The appart sample's weikness using t

mm

)ace Area (m)

Density (kg/

ted on samplnormal pressuately 1.3 m/h

n this type of

ISCHARGE C

n nsition of a coave the tend

of spreading ispronounced at

illustrated in Fi

(b) Sec

Figure 21.

urge bin to colk material atsecured to lol millimetres

ple holding btus is left to r

ight and surfae relationship

(37)

)

Figure

s of solid wovre of 2 kPa anour. This infor

onveyor belt.

ARACTERIS

nveyor belt wncy to spreadmore pronoulower belt spe

igure 22. As a

(a)

ion X at Idler

Conveyor Bel

Figure 22

tain the bulka required veld cells that my the wedge

racket. The bun for extende roughness igiven in equa

20. Wear Test

n PVC conveya velocity of ation may b

ICS

ich may causlaterally as thced for free fleds. Once the

result of the v

onveyor Disc

Set (c) Sec

Transition G

Belt Conveyor

material, whiccity to the sa

onitor the shection of the in

lk material isd periods interequired. Theion (37).

Results or belt using0.285 m/s is gused to esti

some initial lie belt troughinowing bulk solbulk solid on

elocity profile

arge

ion Y at Disch

ometry and L

Transition

feeds onto aple of materir load. The b

clined belt. Th

cycled back torrupted at intmeasured we

lack coal as tiven in Figureate the wear

ft of the bulkg angle decreids than for che belt reach

here will be a

arge Drum

ad Profiles

belt conveyoral to be testedlk material ise required nor

the surge binrvals to allowight loss is th

e abrading ag20. The graphxpected to ta

olid prior to dses through thesive bulk sos the drum, a

spread in the

. The belt, which isdrawnmal load

via a

n

ent. Aindicatese place

ischarge.helids. Thevelocity

discharge



There will also be a variation in the adhesive stress across the depth of the stream. In most cases, however, thesegregation that occurs during the conveying process will result in the moisture and fines migrating to the belt surfaceto form a thin boundary layer at the surface. This layer will exhibit higher adhesive stresses than will occur for theremainder of the discharging bulk solids stream. The magnitude of the adhesive stresses at the interface of the

boundary layer and the belt surface will determine the extent of the carry-back on the belt 8.2 Profile of Bulk Solid on Belt The conveyor throughput is given by

Qm = ρ A vb (38) Referring to Figure 21(b), the cross-sectional are at Section X is given by A = U b (39) where U = non-dimensional cross-sectional area factor

b = contact perimeter Assuming a parabolic surcharge profile, for a three-roll idler set, the cross-sectional area factor is given by U =

1{r sinβ +

r sin2β +

tanλ [1 + 4 r cosβ + 2 r (1 + cos2β)]} (40)

(1 + 2 r)

2

6

where r = C/B β = troughing angle λ = surcharge angle 8.3 Height of Bulk Solid on Belt at Idlers

a. Overall Height H (Figure 21(b))

H = C sin β + (B + 2 C cos β) tan λ(41)

4

b. Mean height ha

ha = C sin β + (B + 2 C cos β) tan λ

(42)6

8.4 Cross-Sectional Profile at Drive Drum The profile shape at the drive drum, Figure 21(c), is difficult to determine precisely. It depends on the conveyor speed,

cohesive strength of the bulk solid and the troughing configuration. The mean height h may be assumed to be h =

A(43)

(B + C) where A = cross-sectional area determined from equation (39). 8.5 Angle at which Discharge Commences In order that the conditions governing discharge may be considered, the model of Figure 23 is considered. In general,slip may occur before lift-off takes place. Hence, the acceleration ·/v and inertia force ∆m ·/v are included in the

model, v being the relative velocity. However, it 15 unlikely that slip will be significant so it may be neglected.



For an ar

v = g co

r where ∆

σo

8.6 Mini

In most c

the dischwill be focontact is

vb =

Figure 24point of b= 1 kPa.indicates

be remov

8.7 Disc

In most c

The equa

y = x tan

The bounfrom equ

9. CURV

itrary radius

s θ +FA

∆m

= ρ ∆A (h -= adhesive

um Belt Sp

ases, the spe

rge drum. Inthe belt surf __________

R g (cos α +

illustrates theelt contact ishe need for h

the difficulty o

ed by belt cle

arge Trajec

ases the influ

ion of the pat

θ + 1 g

2 v

ds for the trajtion (45). D IMPACT P

, the conditio

(44

∆r) = mass of tress

ed for Disch

d of the conv

this case θ =ce, that is, wh

_____ σo

) ρ g h

Figure 24

application of lotted againstigher belt spef removing th

ners. ories nce of air dra

h is x

os θ ctories may b

LATES

Figure 23

for discharge

element F ρ

rge at First

yor is such th

α, where α =en ∆r = 0. Th

elt Speed for

R=0.5m, ρ

equation (45)bulk solids lads to achievethin layer of

is negligible.

e determined

onveyor Disc

will commenc

= σo∆A = ad= bulk densit

Point of Dru

t discharge w

slope of the bminimum bel

(45)

Discharge at F

=1 t/m, α = 0

. The minimuer thickness 'lift-off as thecohesive bulk

Hence the eq

(46)

or the two ra

arge Model

e when the no

esive forcey

Contact ill commence

elt at contactlt speed for dis

irst Point of Dr

, σo = 1kPa. belt velocity

'. The graphlayer thicknessolid that beco

ations of moti

ii (R + h) and

rmal force N b

s soon as the

oint with thecharge at the

um Contact

for dischargepplies to thedecreases is

mes the carry

on simplify.

R for which th

ecomes zero.

belt makes co

drum. The critfirst point of d

o occur at thease when α =highlighted. T-back that is r

e angle θ is o

ntact with

ical caserum

first0 and σo is

equired to

tained



Section 4of the dis

Rc =

[1

--

For contapoint of c

Rc ≥ R

where Rc

Example

Considerhorizonta

The curvcontact.

10. CHU

Although

extendedexpressetransfer c

Problem

Bulk MatBulk densthroughpBelt spee

Belt speeSurchargConveyorEffectiveIdler incli

Receiving

.1 presented acharge traject

( g x

vb cosθ ---------------

g

vb cosθ

ct to be madeontact must b

= chute radiu

the case of al distance 'x' i

d impact plathis is illustrat

ES OF THRE

this paper has

to the three din the most

hute for the r

pecification: rial - Bauxiteity as loadedt Qm = 2500

d, delivery bel

d, receiving bangle of bau

inclination α drive drum dination angle β

belt at right

n analysis of f ory is given by

) ]1.5 ----

with a curvedsuch that,

(48)

onveyor dischshown in Fig

Figure

may be positd in Figure 2

Fig

E DIMENSIO

concentrated

imensional caonvenient co-ceiving conve

= 1.3 t/m /hvb = 5 m/s

lt, vb = 5 m/sxite on belt λ

10meter = 1.2= 35

ngle to delive

low around cu

(47)

impact plate o

arge in whichre 25.

25. Radius of

ioned so that t.

ure 26. Impac

AL GEOMET

on chutes of t

e. Using the lordinate systeyor at 90 to th

;25

y belt

ved impact pl

f constant rad

vb = 4 m/s, θ

urvature of P

he chute radi

t Plate and Tr

Y wo dimension

mped paramrelevant to

e delivering c

ates. Referring

ius, the radius

= 0 The radius

ath Vb = 4 m/

s matches the

jectory Geom

l geometry, t

ter model apphe particularnveyor is sum

to Figure 22,

of curvature

of curvature

; θ = 0 radius of cur

etry

e concepts pr

roach, the eqhute profiles.marised.

the radius of

f the trajector

c as a functio

ature at the p

esented may b

ations of motiThe example

urvature

y at the

of

oint of

e readily

on mat bef a



Referring

Impact

Feed Chm/s 11. CON

An overviattentionthese pro

flow dyna

illustrate

12. REFE

to Figure 26

hute: Rc1 = 2

te: Rc2 = 3.0

LUDING RE

ew of chute dhas been direperties into th

mics to the d

. RENCES

1. CHAChut

2. CHAGran

3. CHATranof S

4. CHI

of G

5. CHIGran

6. CHIProfiandU.S.

7. ChutAfric

8. "Chu

Afric

9. LONMat

244.

10. MARBulk

11. ROBandNov

12. ROBDisc196

nd 27, the de

.8m; Contact

; ve = 5.57

ARKS sign with speted at the ne

e chute design

termination of

RLTON, W. H.,es: Optimising

RLTON, W. Hular Materials

RLTON, W. H.sit Time". Paplids, Chicago,

RELLA, C. and

anular Materi

RELLA, C., CHular Materials:

RELLA, C., CHles for MinimuHandling in Ch.

e Design, Firsa, 1991.

te Design Pro

a, February 19

E, K.W., "Therials Storage,

CUS, R.D., BASolids Handlin

ERTS, A. W., "Chemical Engimber 1967.

ERTS, A. W., "arge Chutes".

Figure 27.

ign parameter

angle θc = 74.

/s at cut off a

ial reference td to measureprocess. Chut

the most app

CHIARELLA,Flow Properti

nd ROBERTS,. Jnl. Agric. E

and ROBERTS,r No. 72, MH-U.S.A., Septe

CHARLTON,

ls". Jnl. Agric.

ARLTON, W. H: A Discrete Se

ARLTON, W. Hm Transit Timemical Proces

International

lems and Cau

92.

Design of ConHandling and

LLER, W.J. andg, Vol. 16, No

The Dynamicseering Transa

An InvestigatiTransactions

Transfer Chu

s are: 2; vc = 5.12

ngle θ = 55;

o belt conveyithe relevant fle flow pattern

ropriate chute

. and ROBERes". Jnl. Agric.

A. W., "Chutegng. Res., Vo

A. W., "Gravi33, A.S.M.E.,ber 1972)

. H., "Chute

Engng. Res.,

. and ROBERgment Solutio

. and ROBER". Paper PresIndustries',

Conference, B

ses", Seminar,

veyor Transferansportation

BARTHEL, P..3, July/Septe

of Granular Mctions, Institu

n of the Graviof A.S.M.E., J

e Example /s; xc = 0.23

ex = 4.57 m/s

ng operationsow propertiess have been d

profiles to ach

S, A. W., "GraEngng. Res.,

Profile for Mal. 15, 1970.

y Flow of Gra(presented at

rofile for Mini

Bol. 17, 1972.

S, A. W., "Optn Method": Pa

S, A. W., "Granted at SympIChE, 77th Na

ionic Research

, Bionic Resear

Chutes". Pap, Newcastle, N

"The Design aber 1996. (p

aterials Flow tion of Engine

ity Flow of Nol. of Eng. in I

m; yc = 1.96

; vey = 3.12m

has been presof the bulk solescribed and t

ieve optimum

vity Flow of Gol. 20, 1975,

imum Exit Vel

ular Materials2nd Symposiu

um Transit T

imum Chute Pper No. 73, M

vity Flow of Gosium on 'Solitional Meeting

Institute, Joh

ch Institute, J

r Reprints, 3rSW, Australia,

nd Operationp.405-409).

rough Curvedrs, Australia,

-cohesive Gradustry, Vol. 9

; vd = 6.75m

s; Wear Wa =

ented. Particulid and to integhe application

flow has been

anular Materipp. 39-45.

ocity in Gravit

: Analysis of Pm of Storage

ime in the Gra

rofiles in Gravi-A, A.S.M.E.,

anular Materis and Slurry

, June 1974, P

annesburg, So

ohannesburg,

d Int Conf on, June 1989, p

f the Weber C

Chutes". MecVol. MC3, No.

nular Material1, Series B, N

/s 2.26 kPa

arrateof chute

ls in

y Flow of

articlend Flow

vity Flow

ity Flow of 1972.

ls: Chutelow of ittsburg,

uth

South

ulk240-

hute".

hanical2,

through. 2, May



13. ROBERTS, A.W., "Bulk Solids Handling : Recent Developments and Future Directions". Bulk SolidsHandling, 11(1), 1991, pp 17-35.

14. ROBERTS, A.W., OOMS, M. and WICHE, S.J., "Concepts of Boundary Friction, Adhesion and Wear inBulk Solids Handling Operations". Bulk Solids Handling, 10(2), 1990, pp 189-198.

15. ROBERTS, A.W., SCOTT, O.J. and PARBERY, R.D., "Gravity Flow of Bulk Solids through TransferChutes of Variable Profile and Cross-Sectional Geometry". Proc of Powder Technology Conference,Publ by Hemisphere Publ Corp, Washington, DC, 1984, pp 241-248.

16. ROBERTS, A.W. and CHARLTON, W.H., "Applications of Pseudo-Random Test Signals and Cross-Correlation to the Identification of Bulk Handling Plant Dynamic Characteristics". Transactions of A.S.M.E., Jnl. of Engng. for Industry, Vol. 95, Series B, No. 1, February 1973.

17. ROBERTS, A. W., CHIARELLA, C. and CHARLTON, W. H., "Optimisation and Identification of Flow of Bulk Granular Solids". Proceedings IFAC Symposium on Automatic Control in Mining, Mineral andMetal Processing, Inst. of Engrs., Aust., Sydney, 1973.

18. ROBERTS, A. W. and ARNOLD, P. C., "Discharge Chute Design for Free Flowing Granular Materials".Transactions of A.S.A.E., Vol. 14, No. 2, 1971.

19. ROBERTS, A. W. and SCOTT, 0. J., "Flow of Bulk Solids through Transfer Chutes of VariableGeometry and Profile". Proceedings of Powder Europa 80 Conference, Wiesbaden, West Germany,January 1980.

20. ROBERTS, A. W. and MONTAGNER, G. J., "Identification of Transient Flow Characteristics of Granular Solids in a Hopper Discharge Chute System". Paper presented at Symposium on Solids

and Slurry Flow and Handling in Chemical Process Industries, AIChE, 77th National Meeting, June2-5, 1974, Pittsburg, Pa., U.S.A.

21. ROBERTS, A. W. and MONTAGNER, G. J., "Flow in a Hopper Discharge Chute System". Chem. Eng.Prog., Vol. 71, No.2, February 1975.

22. ROBERTS, A. W., SCOTT, O. ,J. and PARBERY, R. D., "Gravity Flow of Bulk Solids through TransferChutes of Variable Profile and Cross-Sectional Geometry". Proceedings of International Symposiumon Powder Technology, Kyoto, Japan, September 1981.

23. ROBERTS, A. W. and SCOTT, O. J., "Flow of Bulk Solids through Transfer Chutes of VariableGeometry and Profile". Bulk Solids Handling, Vol. 1, No. 4, December 1981, pp. 715.

24. ROBERTS, A.W. "Basic Principles of Bulk Solids Storage, Flow and Handling", TUNRA Bulk Solids,The University of Newcastle, 1998.

25. ROBERTS, A.W. and WICHE, S.J. "Interrelation Between Feed Chute Geometry and Conveyor Belt

Wear". Bulk Solids Handling, Vol. 19, NO.1 January, March 1999

26. ROBERTS, A.W. "Mechanics of Bucket Elevator Discharge During the Final Run-Out Phase". Lnl. of Powder and Bulk Solids Technology, Vol. 12, No.2, 1988. (pp.19-26)

27. SAVAGE, S. B., "Gravity Flow of Cohesionless Granular Materials in Chutes and Channels". J. FluidMech. (1979), Vol. 92, Part 1, pp. 53-96.

28. SAVAGE, S.B., 'The Mechanics of Rapid Granular Flows". Adv Appl Mech, 24, 1984, pp 289.

29. SCOTT, O.J., "Conveyor Transfer Chute Design, in Modern Concepts in Belt Conveying and HandlingBulk Solids". 1992 Edition. The Institute for Bulk Materials Handling Research, University of Newcastle, 1992, pp 11.11-11.13.

Documents

Wear in chutes