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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
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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.
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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
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(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
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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
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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
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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
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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
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(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
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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
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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
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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
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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.
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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
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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
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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
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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.