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© [email protected], [email protected] Department of Mining, Dressing and Transport Machines AGH tel/fax +48126335162
Department of Mining, Dressing and Transporting Machines AGH
Belt Conveyor
Theory
Piotr Kulinowski, Ph. D. Eng.
Piotr Kasza, Ph. D. Eng.
( 12617 30 92
B-2 ground-floor room 6
consultations: Mondays 11.00 - 12.00
Conveyors
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© [email protected], [email protected] Department of Mining, Dressing and Transport Machines AGH tel/fax +48126335162
Belt drives - history
2
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© [email protected], [email protected] Department of Mining, Dressing and Transport Machines AGH tel/fax +48126335162
Euler-Eytelwein formula
Rb
a
Sn
Sz
P
zn SSP
Euler-Eytelwein
a eS
S
z
n
PRM bn
zzmax SeSP a
a – angle of wrap [rad]
– friction coefficient
P – driving force[N]
Sz,n – belt tension [N]
M – driving torque [Nm]
Rb – radius of pulley [m]
)1e(SRM zbmax a
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© [email protected], [email protected] Department of Mining, Dressing and Transport Machines AGH tel/fax +48126335162
Ways to increase the maximum driving force
)1e(SP zmax a
zS
a
Increasing and stabilizing tension force
- take-up devices
Increasing and stabilizing the friction coefficient
Increasing the angle of wrap
3
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© [email protected], [email protected] Department of Mining, Dressing and Transport Machines AGH tel/fax +48126335162
Tandem drive
aI
SnI
SzII
PI
aII
SzI
SnII
PII
II I
zInII SS
necessary condition!
a – angle of wrap [rad]
– friction coefficient
P – driving force[N]
Sz,n – belt tension [N]
M – driving torque [Nm]
Rb – radius of pulley [m]
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© [email protected], [email protected] Department of Mining, Dressing and Transport Machines AGH tel/fax +48126335162
Zasada sprzężenia ciernego napędu wielobębnowego
aI
SnI
SzII
PI
aII
SzI
SnII
PII
II I
IeS
S
zI
nI aIIe
S
S
zII
nII a
=
IIIIII eeeS
S
zII
nI aaaa
nIIzII SSe II a
Ie
SS nI
zI a
4
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© [email protected], [email protected] Department of Mining, Dressing and Transport Machines AGH tel/fax +48126335162
Zasada sprzężenia ciernego napędu wielobębnowego
aI
SnI
SzII
PI
aII
SzI
SnII
PII
II I
zIInIzIInIIzInIIII SSSSSSPPP
IIIeS
S
zII
nI aa
1eSP IIIzmax
aa
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© [email protected], [email protected] Department of Mining, Dressing and Transport Machines AGH tel/fax +48126335162
Static Characteristics of the Tensioning Device
• Belt sag
• Drive
u
2gut
minf8
lmmgS
S1N
S2N Rb
α
MN 1
2
S1H
S2H
MH 1
2
1eSRM N2bN a a
aa
e
1eSR1eSRM H2bH1bH
- driving - braking
5
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© [email protected], [email protected] Department of Mining, Dressing and Transport Machines AGH tel/fax +48126335162
c
u
2
gut
2f8
lmmS
a
1eR
eMS
b
HH2
a
a
b
1eR
MS
b
NN2
a
Static Characteristics of the Tensioning Device
set of prohibited values of force S2
A Z
B D` C
0 MNmax MHmax
S2
Stop
Braking
Stationary work
Starting
Driving torque
Minimum force value in the belt coming off the drive pulley
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© [email protected], [email protected] Department of Mining, Dressing and Transport Machines AGH tel/fax +48126335162
Types of take-up devices used in belt conveyors
Fixed take-up
Moveable take-up:
Gravity weight
Hydraulic, pneumatic
Regulated take-up winch
Follow-up
Those with a fixed position of the tensioning pulley during conveyor operation – so
called fixed take-up device;
Those with a changing position of the tensioning pulley during conveyor operation
6
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© [email protected], [email protected] Department of Mining, Dressing and Transport Machines AGH tel/fax +48126335162
Fixed Take-up Device – with a constant position of the tensioning pulley during conveyor operation.
S2
M
0 MNmax MHmax
S2
Must
force caused by the action of the tensioner
required tensioning force
With a tensioning pulley periodically
moved during conveyor stoppage.
Elastic elongations of a belt loaded
with a longitudinal force cause a
reduction of forces in the zone where
the belt comes off the drive pulley .
This necessitates causing much
greater forces of preliminary belt
tensioning. Permanent deformations of
the belt are periodically compensated
by moving the tensioning pulley during
conveyor stoppages.
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© [email protected], [email protected] Department of Mining, Dressing and Transport Machines AGH tel/fax +48126335162
0
50
100
150
200
250
300
350
400
0 10 20 30 40 50 60 70 80
Rozruch Hamowanie
0
50
100
150
200
250
300
-50 0 50 100 150 200 250 300
P [kN]
S [kN]
0 MNmax MHmax
S2
Fixed Take-up Device
S1
S2
MN 1
2
7
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© [email protected], [email protected] Department of Mining, Dressing and Transport Machines AGH tel/fax +48126335162
Gravity Weight
S2
M
0 MNmax MHmax
S2
In conditions of a variable load of output on the belt, weight (gravity) devices stabilise the belt tension forces within limits conditional on the efficiency of the tackle and rope system. In non-steady-state operation of the conveyor, tensioning force changes are observed due to inertia forces and longitudinal vibrations of the belt.
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© [email protected], [email protected] Department of Mining, Dressing and Transport Machines AGH tel/fax +48126335162
0
50
100
150
200
250
300
350
400
0 10 20 30 40 50 60 70 80
t [s]
S [kN]Rozruch HamowaniePraca ustalona
0
50
100
150
200
250
300
-50 0 50 100 150 200 250 300
P [kN]
S [kN]
0 MNmax MHmax
S2
Gravity Weight
S1
S2
MN 1
2
8
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© [email protected], [email protected] Department of Mining, Dressing and Transport Machines AGH tel/fax +48126335162
0
10
20
30
40
50
60
70
-20 0 20 40 60 80 100 120 140 160 180 200
Driving force [kN]
Tensio
nin
g forc
e [
kN
]
=0.3 =0.5
Measured Static Characteristics of the Gravity Weight
15
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© [email protected], [email protected] Department of Mining, Dressing and Transport Machines AGH tel/fax +48126335162
Hydraulic or pneumatic take-up devices with a limited tensioning path
Tensioners with linear cylinders may
employ various solutions: the so-called
constant tension ones are connected to
a trunk line with a pressurised liquid or
ones with their own drive and a
controlled pressure range. The
characteristic feature of this type of
devices is that the length of the
tensioning path is limited by the length
of stroke of the cylinder piston; the
speed of tensioning is also limited.
0 MNmax MHmax
S2
Tensioning cart motion blocking
9
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© [email protected], [email protected] Department of Mining, Dressing and Transport Machines AGH tel/fax +48126335162
Automatic take-up devices with a periodic operation
Tensioners in which the
tensioning cart is pulled by
the rope from a winch driven
by an electric motor. They are
controlled by three-position
controllers, sometimes with
the ability to change the force
adjustment range for the
duration of the conveyor start-
up.
0 MNmax MHmax
S2
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© [email protected], [email protected] Department of Mining, Dressing and Transport Machines AGH tel/fax +48126335162
Model of follow-up, mechanical take-up devices
10
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Follow-up, mechanical take-up devices
izl
A B
0 MNmax MHmax
S2
Tensioning cart A motion
blocking
Mechanical tensioners receiving their power from
the main drive of the conveyor. Two tried and tested
solutions are worth mentioning here.
The first has a tilting drive system suspended from
the pulley shaft hanging from a system of ropes and
tackle connecting it to the tensioning cart. The
tensioning force of this device is the sum of a part
of the weight of the driving system and the reaction
to the driving torque.
The second type of tensioners with a similar
solution are those with two tensioning carts
installed before and after the drive pulley in the
main drive zone and connected with a rope system
of a constant ratio ensuring that the friction contact
between the drive pulley and the belt is correct .
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© [email protected], [email protected] Department of Mining, Dressing and Transport Machines AGH tel/fax +48126335162
Follow-up Device
izl
M
0 MNmax MHmax
S2
S2
11
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© [email protected], [email protected] Department of Mining, Dressing and Transport Machines AGH tel/fax +48126335162
Follow-up Device
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Centering belt run - Causes of belt mistracking
12
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Centering belt run
vt
vp
Ft
Fc
Fo
Axis
Vt – Belt speed
Vk – Circumferential idler speed
Vp – Slip speed
Ft – Friction force
Fo – Resistance of centering
Fc – Centering force
Belt vt
vk
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© [email protected], [email protected] Department of Mining, Dressing and Transport Machines AGH tel/fax +48126335162
Bibliography
Kulinowski, wykłady „Transport przenośnikowy”,
www.kmg.agh.edu.pl