bulk SOHdS
Volume 21
Design of Belt and Apron Feeders
January/February 2001
Number 1
An Overview of Feeder Design
Focusing
on
Belt and
Apron Feeders
A.w.
2. Basic Objectives for Uniform
Summary
Draw-Down
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
An
overview
Roberts, Australia
For unrform draw-down with
a
fully active hopper outlet, the
ca-
the hopper and procedures for
pacity of the feeder must progressively increase in the direction of feed It is important to note that the increase in feeder capac-
given For the belt and apron feeder, the required divergence angle for the interface zone to achieve
rty cannot be arbitrary Rather, it must be pre-determined if uniform draw-down is to be achieved This may be illustrated with
achieve uniform draw-down
achieving this objective uniform draw-down
in
are
in the hopper is determined
Theories relat-
feeder er loads and corresponding ing to the determination of feed drive 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 a nd procedures for reducing loads and power under start-up conditions are presented
respect to some of the more common types of feeders used practice commencing with the screw feeder 1 shows a screw feeder in which
Fig
eters
arrangement, mainly
progressively increases progressively is not a satisfactory
This
due to the fact that the volumetric effi-
To overcome this problem, the screw requires both
tapered shaft
Introduction
as illustrated
ciency of the feeder decreases with the expanding pitch in the direction of feed The feeder will draw preferentially from the rear as shown
1.
the screw and shaft diam-
are each constant, while t he pitch
from the rear to the front
in
in addition
to the expanding pitch
a
as illustrated in
Fig 2 A feeder
is a device used to control the gravity flow of bulk solids
from storage such
as
from
a
bin
or stockpile
several types of feeders commonly used, it
While there is
are
Time 0
important that
they be chosen to suit the particular bulk solid and to provide the range of feed rates required It is also important that feeders be used in conjunction with mass-flow hoppers to ensure both reliable flow and good control
over
the feeder loads and drive
of feeders and hoppers
powers Correct interfacing if performance objectives such the whole of the hopper outlet
is essential
as uniform draw of material over
is
to be achieved
AAAU A
Another aspect of hopper design and feeder interfacing cerns
the need to control feeder loads and
minimise
is essential if belt wear is
V V V
con-
A V
A
A
A V
V
AI
i
v'v
drive
torques and powers In the case of belt feeders, for example, the design of the hopper and feeder interface must take account of the need to prevent slip between the bulk solid and the belt surface This
A
Rg
1
constant shaft diameter and Screw feeder with constant screw diameter constant
expanding pitch Feed occurs preferentially from rear of hopper
to be avoided
Rg 2 Screw feeder with constant screw diameter tapered shaft diameter and This paper presents
an overview
of relevant aspects of feeder
design which address the foregoing matters While the general principles apply to all feeders, the paper focuses, mainly, on belt and apron feeders
A selection of references on this subject is
given at the e nd of the paper [1 -8]
expanding pitch Results
in unrform draw down in
hopper
TTTn Constant
Increasing Pitch A W
Pitch N
J
Roberts Emeritus Professor and Director Centre for Bulk Solids and
Paniculate Technologies University of Newcastle University Drive CaHaghan, +61 2 49 21 60 67, Fax +61 2 49 21 60 21. NSW 2308 Australia Tel E mail
engar@cc newcastle edu au
Details about the author on page 1 13
^
Tapered Shafi
13
bulk
Design
of Belt and Apron Feeders
Volume 21 Number
1
January/February 2001
handling
In the case of vibratory feeders, there is
a tendency for feed to preferentially from the front. To overcome this problem, it is recommended that the slope angle of the front face of the hopper be increased by 5 to 8 as illustrated in Fig. 3. Alternatively, the lining surface of the front face in the region of the out-
occur
let may be selected
so as
to have
a
higher friction angle than the
other faces. Apart from providing flexible support, the springs assist in controlling the feeder loads. In the case of belt and apron feeders,
quired
as
illustrated in
Fig.
4.
a tapered opening is reThe triangular skirtplates in the
hopper bottom are an effective way to achieve the required divergence angle X.. It is often stated that th e angle X should range from 3 to 5, but this leads to excessively wide belts or aprons in 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 t he diverging skirts
is the relief provided
to skirtplate drag.
The gate not
on
a flow
Fig.
the front of the feeder is
a flow
speed
position; the flow rate
is then controlled
of the feeder. An alternative
verging front skirt
or
brow
as
by varying the
arrangement is to
use a
di-
Under uniform hopper draw-down conditions, shear zone may be assumed to exist
as
shear zone is assumed to be tapered
or
'idealised'
an
shown in
Fig.
6. The
'wedge-shaped' and
defined by the release angle tp. It is also assumed that the
ve-
illustrated. In the
ex-
Fig.
4. This has the
locity profiles
at the feed
end during dis-
tended skirtplate zone, the velocity profile is substantially constant with the bulk solid moving at a average velocity equal to
illustrated in
advantage of relieving the pressure charge and forward flow.
Vibratory feeder
trimming device and
rate controller. The height of the gate is adjusted to
give the required release angle and to achieve uniform draw along the slot. Once the gate is correctly adjusted, it should be fixed in
3:
are
approximately linear
as
the belt velocity. Since the average bulk solid velocity at the exit end of the hopper skirtplate zone is less than the average ve-
3. Feeder Performance
locity
in the extended skirtplate zone, there will be
tracta' effect with the bed depth
Characteristics
a
'vena con-
y^ less than the b ed depth /-/
the exit end of the feeder.
The complexity of the shear zone of belt feeders has been high-
lighted in a comprehensive study performed by Schulze and Schwedes [5]. They showed that the shear zone may be divided into three regions, the lengths of the regions being predicted
the basis of the 'Coulomb principle of minimal safety'. This sumes
that the rupture surface in
develop in such
a
a
on
Shear Surface
as-
consolidated bulk solid will
way that the bearing capacity of the solid is
minimised. There will be
Belt/Apron
velocity gradient developed in the shear zone, as indicated in Fig. 5. The characteristic shape of this profile depends on the properties of the bulk solid, the feeder speed and the geometry of the hopper/feeder interface. Fig.
4:
a
Fig.
5:
Velocity profile
in shear zone
Belt an d apron feeder
U
U
O
O \O
O
O
Q
Divergent Front Skirt or /Brow to Relieve Pressure at Feed End
ALTERNATIVE ARRANGEMENT
14
at
bulk Volume 21 Number
Design of Belt and Apron Feeders
January/February 2001
1
Velocity Distributions: Exit
Shear Zone ^-
v
Vena
Contracta' ffect
e
Extended Zone
Lh Shear Zone
B
Bett/apron feeder
Fig 6
3.1
- assumed shear zone and veloaty
profiles
where
Feed Rate Distribution
a, -
Fig 6, the mass throughput of the feeder will vary At any location x, the throughput O(x) is the feed zone along given by
Refemng
to
1 -
20-h+Xo)
(D
x)
2(/_h +Xq) where
/A(x) v^
t^(x) p
= cross-sectional area
= velocity of th e belt =
=
or
The parameters apron
y<.
volumetric efficiency bulk density
in feed zone
S,
(assumed constant)
X
(2)
2xtanX.)(y<.
put to the maximum theoretical throughput based or
on
apron without slip,
Xq
the bulk is
given
by
(3)
where
v,(x)
=
average feed velocity at location x, given by
Eq (6)
in
=
= =
tamp
are
clearance at rear of feeder width of opening at rear of feeder
divergence angle
tp = release angle
The volumetnc efficiency t^(x), which relates th e actual through-
solid moving forward with the belt
(6)
=
/_
=
Cg
=
dimension defined
in
Fig 6
length of hopper shear zone
velocity distribution factor
at
x
=
L^
3.2 Feeder Throughput At the discharge or feed end of the hopper the throughput
is
given by
v,(x)-(1+C)^
(4)
(7) C =
velocity distnbution coefficient
at location
x
is no slip at the belt or apron surface It has been shown [6-8] that the throughput from Eq (3) is given
Eq (4) assumes there by the cubic equation
where
volumetnc efficiency at exit
Also
(8)
where
Q(x)
=
=
bulk density
< p since the consolidation pressures the extended zone
It is noted that p^
(5)
tower
in
in extended zone are
15
Design
of Belt and Apron Feeders
Hence
Volume 21
4.2 1+C,
(9)
opening be such that
1.0 Preferably
<
.
^
0.75 in order
Often the requirement of Eq. (10) is impossible to achieve. In the of
a
belt
or
apron feeder, for example, Eq. (5) for Q(x) is
cubic in form and Q'(x) is quadratic, which means that cannot be satisfied. To
performance
overcome
may be achieved
to ensure satisfactory flow in the extended skirtplate zone.
Q"(x)
this problem,
an
Eq. (10)
optimum
by setting
dQ'(x) =
0 at
x
(11)
=
dx
2
This is illustrated by the surface profile shown in Fig. 8.
Optimum Interface Geometry
4.
handling
Optimum Divergence Angle
case
It is desirable that the ratio of the gate height H to the width of
January/February 2001
Number 1
Based
the foregoing analysis, it has been shown [6, 7], that
on
the optimum divergence angle X is given by
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. The condition for uniform draw-down, which represents the optimum
e
tanX
(12)
=
-
performance, is such that
dQ(x)
= constant
dx
(10)
That is, the gradient of the throughput along the feed zone is constant.
I-0.5
The influence of the feeder L^/ß ratio on the optimum values of X for a range of clearance ratios is illustrated in Fig. 9. The optimum divergence angle X for uniform draw-down is shown to decrease with increase in L^/S ratio, the rate of decrease being
quite rapid
at first but lessening
as
the
L^/ß ratio increases.
yc/H yc/h yc/H yc/H
Q(x)
+
dQ(x)
4
Q(x) 7:
8:
= 0.2 = 0.3
6
RATIO
Contunuity of feed
Fig.
Optimum divergence angle
9:
ti
Fig.
0
dQ(x)
*
Fig.
= =
= 0.75; C
=
vs.
UB
Lyß ratio for a
range of clearance ratios.
0.5
Condition for optimum draw-down
L 1
U dQ'(x)
^J
dx
o
4.3
Use of Transverse Inserts
In the
case
L^/S
of feeders
5, the
employing long opening slots, that is
of transverse inserts,
as illustrated in Fig. 10, promoting uniform draw of bulk solid from the hopper along the length of the feeder. With reference to the latter, >
can assist
use
in
the inserts assist in establishing the required release angle along Fig.
y
a
Yc +r^Vi
16
10:
Use of transverse inserts in long feeder
Volume 21 Number
January/February 2001
1
Design
of Belt and Apron Feeders
For comparison purposes, the performance of a feeder having the same feed rate as the optimum feeder but with a larger divergence angle of 3 is also presented The relevant graphs are shown by dotted lines In this case, the gradient A/q'(x) for this
0.95
case increases >
0.9
toward the feed end which indicates that the
hopper will draw down preferentially from the front
>o
LU
0.85
FFI LU
0.8
5. Feeder Loads
5.1
- Basic
Concepts
Stress Fields
o
The determination of feeder loads and dnve powers requires LU
0.75
D
d
07
>
0.65
06
0
3
2
1
6
5
4
DISTANCE FROM REAR OF HOPPER
x
(m)
It
Fig
11
Throughput characteristics of bett feeder C, 1 54 Case 2 >. Case 1 optimum >. 3 =
0 5
L,/8
=
5
in
reducing the loads
on
as
the
illus-
flow field
in order
is stopped
the feeder is
is
for the load acting
in
arched stress field
The inserts may incorporate diverging brows to smooth the flow at the transitions
feeder
is quite common
conditions to be
=
the feeder The inserts also assist trated
=
a
knowledge of the stress fields generated in the hopper during the initial filling condition and during discharge The relationship between the vertical pressure p^, generated in a mass-flow bin dunng both filling and flow a nd the feeder load O is illustrated in Fig 12 Under filling conditions, a peaked stress field is generated throughout the entire bin as illustrated Once flow is initiated, an arched stress field is generated in the hopper and a much greater proportion of the bin surcharge load on the hopper is supported by the upper part of the hopper walls Consequently, the load acting on the feeder substantially reduces as shown in Fig 12 on
the feeder under flow
the order of 20% of the initial load
is
quite stable and
is maintained even
This means that once flow
stopped while the bin
retained and the load
on
is
is still full,
The if the
initiated and then
the arched stress
the feeder remains at the
re-
duced value The subject of feeder loads and performance discussed
in some detail in Refs
is
[1 -4]
4.4 Belt Feeder Example As
an
example, the case of
is considered
a
belt or apron feeder with L /S = 5
For convenience, the throughput O(x) a nd gradi-
ent of the throughput O'(x)
are
expressed
in normalised form as
follows
5.2 Feeder Loads Design Equations Consider the mass-flow hopper and feeder of Fig 13 It needs to be noted that the depth of the hopper should be such that
Zg/D can
and
A/q(x)
/Vq'(x)
d/Vp(x)
(13)
dx
11 shows the volumetric efficiency r^(x), throughput para-
Fig
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 1 54 and, as shown, the gradient timum divergence angle X meter
A/q(x)
=
=
0 67
Zg
order to ensure that the surcharge pressure Pg be adequately supported by the upper section of the hop>
in
per walls The design equations used to determine the feeder loads are summarised below
The loads acting
on
the feeder and
quirements vary according bulk mass The general expression for th e load 1/
y-Pvo^o
=
A/q'(x)
is
virtually constant indicating uniform draw-down
in
the
hopper The volumetric efficiency decreases from the rear to the front of the feeder as is expected Fig 12
Vertical pressure and load variations
corresponding power
re-
to the stress condition in the stored
where
p^
>Aq
= vertical
pressure
is
(14)
on feeder surface
= area o f hopper outlet
on a feeder
Initial Filling
Flow
Feeder Load 4 Filling
Peaked Stress Field
Arched
Pv.
Stress
7
V
Field
Time vof
(a) Stress Fields
(b) Feeder Loads
17
Design
of Belt and Apron Feeders
Volume 21 Number
1
January/February 2001
6. Feeder Loads Initial 6.1
handling
-
Filling Condition
Design Equations
This applies when the feed bin while the feeder initial filling loads tors
is
initially empty and then filled
not operating Research has shown that the
is
can
vary substantially according to such fac-
as
rate of filling and height of drop of solids
may produce
as
im-
pact effects
uniformity of filling over the length and breadth of the feed bin, asymmetric loading will produce a non-uniform pressure distribution 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 is, the major principal stress is almost vertical at
peaked, that Fig 13 Loads
on feeder
For convenience, following the procedure established by Arnold et al [1], the load may be expressed in terms of a nondimensional surcharge factor as follows \/ =
where
qYL^-^ß^^
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 a
Y =
p g
a
totally incompressible bulk solid and
proached
(15)
given by tana
/Ch,
=
tana
p = bulk density
of circular opening
= 1 for conical hopper
Based on it may
nutlet
an
c
w
analysis of th e pressure distribution
in
the hopper,
be shown that the vertical pressure acting at the hopper is
d
For
a
+
=
Pg
The exponent
=
'y'
surcharge pressure acting in
Eq (17)
is
very compressible bulk solid and feeder, y = 0 9 For
a
at the transition
a
satisfactory prediction of q,
Uy
tan(j).
may
D
2p,tana
-
+
I 2tana I
The vertical load
I/,
is
Eqs (16) and (17) a general expression for the non-dimensional surcharge pressure may be obtained That is, From
2(/-1)tana1 Two cases
are
flow condition,
18
[
discussed
(22)
(23)
6.2
Surcharge Load Bins
-
- Initial Filling
Mass and Expanded-Flow
Condition
The computation of the initial vertical load acting (19) D
of importance, the initial filling condition and the are now
1
given by
corresponding average vertical pressure
r2ps(/-1)tana
be obtained
ß
ratio of normal pressure at the hopper wall to the
*
a
(18)
tana is the
flexibly supported
q.
1
a
feeder, y = 0 1
from
given by
-1
a stiff
For a moderately compressible bulk solid stored above flexibly supported feeder, y = 0 45
^'
/^
(21)
While the value of q, may be determined using an appropriate value of y in Eq (19), from a practical point of view, it has been
Ps"
|/~ 2(/-1)tanaJLD
2(/-1)tana
y
very incompressible bulk solid a nd
established that
where
where
,2tana[ß
Recommended Value of
Pvo
obtained from
'hydrostatic' b
U)
is
This equation corresponds t o the pressure at the outlet being
Eqs (14) and (15) that
*"
(20)
1
Q, - I 3
= 0 for plane-flow hopper
It follows from
Eq (19) which becomes
= hopper symmetry factor
m
tan^
with y = 0, the upper bound value of q,
/. = length of slotted opening or diameter
rigid feeder with
which the vertical pressure in the hopper is 'hydrostatic' In this case the ratio of normal pressure to vertical pressure is
= bulk specific weight
ß = width of slot
a
the upper bound value of q, may be apThe upper bound value corresponds to y = 0 for
minimum clearance,
= non-dimensional surcharge factor
q
For
are considered
on a feeder re-
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 quires
a
bulk $OMdS
Volume 21 Number
1
January/February 2001
Design of Belt and Apron Feeders
K,
Dc
for cylinder
=
Normally
K
=
0
4
= wall friction angle for cylinder It
Us
is noted
channel
that
in
the case of the expanded-flow bin, if the flow
is pre-formed,
then the dimension D may replace D<.
in
Eq. (25) The effective surcharge head for the heap is
on
top of the cylinder
given by
H.
(26)
mg+2 where
Hg
=
mg
=
=
Rg
(b) Expanded-Flow The
14 Mass-flow an d expanded-flow bins
Referring
14, the surcharge pressure Pg
Fig
is
given by the
Janssen equation:
=
is
feeder
illustrated is
'hydraulic'
V,
a,
(24)
The initial load \/
on
the reclaim
the effective surcharge head, while the of th e head
is independent
of stockpiles
is somewhat
as
illustrated.
variations that
can occur in
is influenced
(25)
the case
significant
the consolidation conditions existing
The state of consolidation of the
by such factors
as
loading and unloading cycle times a nd length of undisturbed storage time
for expanded-flow bin
variations
in
moisture content
=
0 for long rectangular cylinder
degree of segregation
=
1 for square or circular cylinder
variations
in
in
stockpile management and loading history
for mass-flow bin
2(1
/-/ = height of bulk solid
uncertain owing to the
within the stored bulk solid
or effective radius defined as
D
m^
on
-
hoppers an d feeders under stock-
15
Fig
The determination of surcharge head and pressure ?
bulk solid
2(1+mj
in
dependent
flow load
hwhere
0 for triangular surcharge
use of mass-flow reclaim
piles to
1 for conical surcharge
Surcharge Load - Gravity Reclaim Stockpiles Initial Filling Condition
6.3
(a) Funnel-Flow
surcharge head
contact with cylinder
walls
in
the quality of bulk solid over long periods of time
compaction effects of heavy mobile equipment that may op on the surface of the stockpile.
erate
Fig 15 Gravrty reclaim stockpile
Hydrostatic Head
Pre-formed Rathole
Surcharge
Initial
Pressure
FeederLoad
Effective Head B
19
bulk
Design
of Belt and Apron Feeders
Uniformly Consolidated Stockpile
Case 1:
Volume 21 Number
1
January/February 2001
SOHdS
+sm6
-
Highly Incompressible Bulk Solid
Fm
(31)
~
1
-sin 6 cos 2
(ri
+
a)
(27) Hence i
e
,
the effective head
is
equal to the actual head This
most conservative solution and would rarely occur
in practice
less conservative solution may be applied through the
Rankine pressure
or
head,
Ps where
=
A
of the
,
Pvod
= Y ^s
*b
cos
Case 2: Pre-Formed Rathole
+
~
(28)
angle of repose
2(/-1)tana
Ps-
in
where
or
Flow Channel
1
-1
+
and
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
face,
2(1 +sinöcos2ri)
In such cases, the effective head may
in Section
6 2 for
an
expanded flow bin
1 r
2
In this
cylinder diameter is the actual rathole diameter Dj, and the wall friction angle is estimated on the assumption that the shear stress occurs during flow
On this basis, $
(36)
_
case the
maximum
(35)
2-sin8(1
be estimated using the Janssen equation following the procedures described
(34)
tana
the flow channel relative to the sta-
tionary material adjacent to the flow channel at the hopper inter-
the surcharge pressure
(33)
2(/-1)tanaJLD
Since, during the initial filling process, there will be some deformation of the bulk solid
(32)
^Fm Pvof
given by Eq (17) Hence,
is
p^
=
e
e
i
use
Pvod
the
is
(j)^ a
is
given by
[
^ sinö
= wall friction angle =
hopper half-angle
6 = effective angle of internal friction 1
= tan
where
(sin ö)
(29)
The force acting at the outlet and
is
(37)
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
In this case f?
is
where
/*
= area
m
= 0 for plane-flow
m
=
(30)
=
K,tan<|> or flow channel
the effective radius of the rathole
of outlet -
or
l-m)
wedge-shaped hopper
1 for axi-symmetric flow
or conical
hopper
Alternatively, the non-dimensional surcharge factor q,
Pvod
an
the hopper Even if the feeder
is started
arched stress field in the hopper
hopper
is able
arched stress field
is
is
set up
in
ob-
(38)
7. Feeder Loads - Flow Condition Once flow has been initiated,
is
tamed from Eq (16)
Combining Eqs (33) and (38)
and then stopped, the
to provide greater wall support and the load
the feeder, together with the corresponding drive power,
is
on
1
1
In this case, the
preserved
Q
=/C Fm
2(/-1)tana
-
1)tanaJ [D
sig-
nificantly reduced While Eq (19) may be applied by choosing an appropriate value of 'y', some difficulty arises due to the redistribution of stress that occurs at the hopper/feeder interface
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 surcharge A well-established
pressure Pg, although small,
is
ignored While the hopper halfB
angle
is
hopper
included is
presented
in
the analysis, the aspect ratio
not taken into account in
Refs [7, 8] and
An alternative
is now
The redistribution of the stress field tween the hopper
7.1
and the feeder
of the
in
is
the clearance space be-
is illustrated in
Fig 16
Field
Hopper Shear Zone
Flow Load Equations is
assumed to
peaked with the vertical design pressure p^ being equal major consolidation pressure a.. multiplier /Cp^ is introduced
Arched Stress
approach
summarised
In this case the stress field in the shear zone
20
Fig 16 Stress fields a t hopper and feeder interface
be
to the
On this basis, the pressure
Feeder
Pnof
bulk solids
Volume 21 Number
1
Design of Belt and Apron Feeders
January/February 2001
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 bulk material
in
the results
the shear and extended skirtplate zones In are in reasonable
D=*0S3
general,
agreement a
=15*
w \
as-
a belt or
apron feeder
The components of the drive resistance i
shear resistance of bulk solid
n
skirtplate friction zone
is shown in
iv
elevation of the bulk solid
or
in
01-
Details of the analysis of these various resistances
[2 4]
Two
are
given
in
are
the force to shear the bulk solid
01
the bulk solid and belt/apron friction to prevent slip
8.1
The forces acting in the feed zone
vertical pressure distribution
on
0.2
0 3
0 4
HEAD h
(m)
are illustrated in
the shear plane
is
Fig 18 The shown dia-
grammatically and will change from the initial filling case to the flow case Under operating conditions, the resistance F parallel to the feeder surface is given by
F=ngl/
Rg 18 Hopper geometry
on shear
06
07
(41)
Starting or breakaway conditions are more difficult to predict and depend on such factors as the hopper and feeder interface geometry skirtplate geometry feeder stiffness the compress ibility of the bulk solid and whether any load control is applied In the absence of any of the foregoing information estimate of the breakaway force F is
(.i^ = equivalent friction coefficient V = vertical force
05
Fig 17 Comparison between predicted an d experimental results feeder test ng [3 4] Bulk material plastic pellets
Force to Shear Bulk Solid
where
Experimental Values
RowQ, (Predicted)
particular aspects concerned with the hop-
per/feeder interface
J
00
O ?
Refs
ii
the extended
apron support idler friction
belt
o> o
are
in the hopper zone and beyond the hopper
in
=
Fig 18
/ /
'/
8. Belt and Apron Drive Resistances The general layout of
J
a
reasonable
(42)
surface
for feeder load determination
-COS0
SECTION 3-3
21
bulk
Design
of Belt and Apron Feeders
An expression for based ^
Volume 21 Number
jMi
January/February 2001
1
the geometry of the feed zone is,
on
[6-8], -
cos
where
(6
xp)
+
smxp
HgSin(6
+
(43) +
Theta
= -10 Deg.
Theta
=
0 Deg.
Theta
=
10 Deg.
6 = feeder slope xp = release angle
Hg
on shear
= coefficient of internal friction
plane
Assuming that the maximum shear stress corresponds to the failure condition then sin
Hg =
where
8 = effective
8
(44)
angle of internal friction
design curves for j^ based on As 19 indicated, ^ is sensitive to both Fig the feeder slope angle 6 and the release angle ip, decreasing
By way Eq (43)
of example,
a
set of
is shown in
with increase
in both these
2
8
6
4
10
RELEASE ANGLES
angles Fig 19 Equivalent friction for belt a nd apron feeder - S
12
14
16
(Deg) =
50
8.2 Skirt pi ate Resistance steady flow
Assuming steady flow, the skirtplate resistance is determined for the hopper and extended sections (see Fig 18) as follows
Hopper Section
case
of slow feed velocities,
apron feeders, the value of
K^
as in
for flow may be
in
the case of the middle
range
8.3 Load Slope Resistance (2\/
Wh)
+
cos 0
(46)
Extended Section (Section Beyond Hopper)
= p g ß
8.4
Belt
or
(50)
Apron Load Resistance
Hopper Section
J I/V^
sine
(45)
where
where
In the
(51)
(47)
(48)
L^
Extended Section
(52)
V = feeder load
where
p = bulk density
= idler friction
y^ = average height of material against skirtplates for hopper section
y^
Ky
=
8.5
Empty Belt
or
average height of material against skirtplates for extended section
= ratio
of lateral to vertical
pressure at skirt-
fb where
plates g = acceleration
due to gravity
=
Apron Resistance
9 81 (m/s^)
=
w^
= belt
Lg
= total length of belt
or
^b^b
(53)
apron weight per unit length a
2
(L
+
L^
+
Xg)
+
1 5
[m]
6 = slope angle
ß.^ jAg
^
Hgp
= =
8.6 Force to Accelerate Material onto Belt
average width between skirtplates
Apron
equivalent skirtplate friction coefficient
(54)
= friction coefficient for skirtplates
L^
=
length of skirtplates for hopper section
Lg
=
length of skirtplates
W^
=
weight of material
Wg
=
weight
of matenal
where
for extended section
in skirtplate zone
in extended
skirtplate
^igp
Msph
where
=
^
1
+
X = half divergence
^y
are
di-
rt
tanX
F^
is
apron speed
negligible
be noted that for good performance, belt and apron speeds should be kept low Generally ^sO5 m/s
8.7 Drive Powers The power
is
computed from
(49) P =
12
Resistances)
angle of skirtplates
The 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 22
Usually the force
or
(given by Eq (8))
be estimated from
- tanX
mass flow rate
It should
zone
verging Hence the fnctional resistance, and hence the normal pressure on the skirtplates, will be less than in the case of par-
Fig 18, n-gph
Q =
Vb = belt
of hopper
It should be noted that in the hopper zone, the skirtplates
allel skirts Referring to
or
where
r| = v,
=
efficiency average belt
or
apron speed
(55)
bulk SOlMS
Volume 21 Number 1 January/February 2001
Design
of Belt and Apron Feeders
analysis is given in Ref [8] As an example, 20 the minimum belt or apron friction angle as a illustrates Fig
For start-up, v^ ay be approximated as half the actual speed For the flow condition, v^ will be the actual belt or apron speed
A more detailed
during running
function of release angle to prevent slip for the
_Ü
-
- 0, Ö
5,
50,
m
- smö -
0 76,
C
=
9. Condition for Non-Slip The condition for non-slip between the belt and bulk solid under steady motion can be determined as follows
VCOS
(s
v)
-
ßWj
COS 8
is
when
0 05-.
1+C,
such that Hv(^-
and
H
^e"1-05
The graphs have been plotted for the feeder
slope angles, -10,
0,
and 10
As indicated, the minimum belt
^
angle
friction
for bulk solid in contact
= friction coefficient
with the belt
+
(56)
The volumetnc efficiency
case
or apron
10. Controlling Feeder Loads = total weight of bulk solid in the skirtplate zones
MgV
F=
controlled exists
= force to shear material at hopper outlet
(normally F,
^sp Fg
^sph
=
The loads
""
^spe
for flow
an arched stress field
fully
or
partially
the hopper just pnor to starting This may be achieved as
stress field from the previous
For normal feeder speeds F^ - 0
the flow load
by ensunng that
cushioning in the hopper, that is leaving a quantity of materlal in the hopper as buffer storage This preserves the arched
= force to accelerate the bulk solid
discharge
as
illustrated
in
Fig. 21
on shear surface (normally
V = feeder load acting
feeders and the torque during start-up may be
by such procedures
is used)
t^l skirtplate resistance
=
in
on
starting the feeder under the empty hopper before filling
is relevant)
commences
ß
cos
=
(<(>s
-
6
-
v)
Neglecting Fg, alternative expressions
Mt>s
Vcos
(<|>s
for
u)
-
+
n^. and tan
ßWV
using transverse, tnangular-shaped inserts
j^
are
raising the feeder up against the hopper bottom during filling
and then lowering the feeder to the operating condition prior to starting In this way an arched stress field may b e partially
(57) cos 8
established or
Rg
21 Application of load cushioning to control feeder loads
cos(e, -)p(c, C,,,)co.e (58)
We
W
where
C,
C^
and
-
-
Also, for small clearances y^.
-
0 5
H 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
Hh
non
No Cushioning
Feeder Ü
35-
Load
HA 4
6
8
RELEASE ANGLE y
10
(beg)
12
1 0
Hh
23
bulk
Design
of Belt and Apron Feeders
Volume 21 Number
1
January/February 2001
handling
Initial
Jacking Screws
Clearance Use o f jacking screws to lower the feeder
Fig 22
The choice of mounting arrangement for
a feeder can
assist
in
generating a preliminary arched stress field near the outlet sufficient 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 bin can assist in generating an arched pressure field near the outlet and reduce the initial load. An alternative arrangement is to incorporate a jacking system to lift the feeder up against the bottorn of the hopper during filling. Before starting, the feeder is released to its operating position sufficient to cause some movement of the bulk solid in
feet.
The
use
of
order to generate
a
cushion ef-
a slide gate or valve above the feeder is another
way of limiting the initial load and power. The
gate is closed durand after feeder the started. has been opened ing filling For 'emergency' purposes, the provision of jacking screws as illustrated in Fig. 22 can be used to lower the feeder should a
peaked stress field be established on filling and there is msufficient power to start the feeder. Lowering the feeder can induce, either fully or partially, an arched stress field and allow the feeder to be started. This precaution
is
useful for feeders installed
under stockpiles where surcharge pressures 1000 kPa may be experienced.
as
high
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 of bulk solids from mass-flow bins; Trans. I.E.Aust., Mechanical
Engineering,
Vol. ME9, No.1, April 1984, pp. 49 -61.
[4] Manjunath K.S. and Roberts, A.W.; Wall pressure-feeder load 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.
as
[5] Schulze,
D.
and Schwedes, J.: Bulk Solids Flow
Hopper/Feeder Interface; Proc. Symposium
on
in
the
Reliable
Flow of Particulate Solids (RELPOWFLO II), Oslo, Norway,
11.
Concluding Remarks
An overview o f feeder design erence
in
and performance with specific ref-
to belt and apron feeders has been
geometry down
23-25 August, 1993.
presented.
The
of the hopper and feeder interface for optimum draw-
the hopper has been examined. It has been shown that
the required divergence angle for the hopper and feeder interface decreases with increase in feeder length to width ratio, ap-
proachmg limiting values
as
the length to width ratio exceeds 5
to 1. The influences of the release angle, divergence angle,
as-
pect ratio of length to width of opening, volumetric efficiency and bulk solids flow properties have been identified. Procedures for the determination of feeder loads and drive powers have
been reviewed and the influence of the interface geometry
on
the shear resistance and belt and apron slip has also been exammed. The advantages of the arched stress field in the hopper in controlling feeder loads and power have been highlighted a nd methods for achieving load control in
fied.
24
practice have been identi-
[6] Roberts, A.W.: Interfacing Feeders with Mass-Flow Hoppers for Optimal Performance; Proc. Intl. Conf.
on
Bulk
Materials Storage, Handling and Transportation, T he 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.
bulk solids
Volume 21 Number
January/February 2001
1
W
Appendix:
Design
of Belt and Apron Feeders
0
Feeder Design Example
hopper and apron feeder for reclaiming bauxite in a gravity reclaim stockpile similar to that depicted in Fig. 15 is considered The stockpile height is 25 m. It is assumed that the surcharge pressure on the hopper is calculated using Eq. (30). The data and calculated loads and pow-
The case of
ers
are
a reclaim
given below.
Hopper Details Hopper type
plane flow
-
=
Hopper half-angle
=
Hopper opening dimension
Hopper width
Centre for Bulk Solids &
25
= 1.25
S
at transition, D
Height of hopper section,
0m
z
Length of hopper opening, L^
m
=
5.5
m
=
4.5
m
=
6.25
m
Length of hopper zone, /.,
= 6.25
Length of extended zone, Lg
=
1.5
m
Total length of feeder, L
=
8.5
m
Height of opening
=
0.8
m
=
6.4
at exit, /-/
^
Skirtplate half divergence angle, X
=
0.8
=
Bed depth in extended shirt zone,
= 0.64
y^
m
1.54
Volumetric efficiency at exit
=
Weight per metre of belt/apron
= 3kN/m
Belt/apron idler friction,
=
Feeder throughput,
u^
1.3
is
speed,l^
=
areas
*
Bulk Solids Testing, Storage & Flow
*
Bulk Handling Plant Design
Belt Conveying
0.05
Mechanical Handling
0.3 m/s
Effective angle of internal friction
=
50
Wall friction angle for hopper
=
30
Bulk density for ext. skirtplate zone, p^>
Hopper surcharge pressure, pg
=
Initial
= 4.42
Flow surcharge factor, q,
=
Shear resistance,
V,
133 kPa
1.05
Resistance, extended skirt zone,
F^
F^
=
Total initial resistance,
=
595.5 kN
=
170.2 kN
Shear resistance,
Practice (Bulk Solids Handling) and associated Professional
OkN
= 102.5 kN =
52.4 kN
=
2.6 kN
Slope resistance, F^,
=
OkN
Empty belt/apron resistance, F^
=
2.7 kN
Total flow resistance,
= 160.2 kN
Resistance, hopper skirtplate zone, Resistance, extended skirt zone,
F
F^
F^
Feeder Power
Power, initial conditions, P, Power, flow conditions, P,
on a
are
offered throughout
one week modular basis.
of Engineering Practice degrees,
or
the Centre for
Bulk Solids and Particulate Technologies,
can
be
obtained by contacting:
Centre for Bulk Solids &
Flow Conditions
F^,
Development Programs embracing
198.1 kN
= 2.61 kN
2.68 kN
Vp
of Engineering
For further information regarding these events,
=
Feeder load, flow condition
Master
other professional development programs, Master
Empty belt/apron resistance, F^
and Resistances,
a
361.6 kN
=
Loads
provides
830.6 kN
Slope resistance, F^,
F
The Centre
the year =
Resistance, hopper skirtplate zone,
Physical Processing
the above topics. Courses =
F^
Systems
1.5 t/nrv*
Loads and Resistances, Initial Condition;
Feeder load, initial condition,
Dust & Fume
1.7 t/nrv*
=
=
Conveying
Slurry Systems & Freight Pipelines
30
Bulk density for hopper section, p
surcharge factor, q,
of
Instrumentation & Control
m
Pneumatic
=
the Universities
of:
Bulk Solid Details
Wall friction angle for skirtplates
of
joint activity
The Centre is involved in industrial research in the
= 1350t/h
Q^,
a
Newcastle and Wollongong, unifying two strong streams of expertise in bulk solids handling.
m
Width between skirtplates, ß,.
Feeder
The Centre for Bulk Solids & Particulate Technolo-
gies
Feeder Details
Release angle,
Participate Technologies
Particulate Technologies
University of Newcastle, University Drive,
Callaghan,
NSW 2308, AUSTRALIA
Tel.:+61 2 492 160 67
Fax:+61 2
492
160 21
Email: [email protected] =
40.0 kW
= 18.0 kW
URL:
www.bulk.newcastle.edu.au/cbs/
25