1
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Department of Mining, Dressing and Transport Machines AGH
Belt Conveyors Calculations
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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m
δ mgcosδ
mgsinδ
mg
P v
DIN 22101
Stationary work(v=const) → Pu = WC
v Pu
Gravity Force
Friction Force
δ singmδ cosgmWP
Belt conveyor:
μ → f m → mi [N] δ singmδ cosgmfWP iiCu
2
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Length related mass of moving parts
Length related mass of the material handled :
or
Length related mass of the rotating parts of the idlers in a conveyor section :
Length related mass of conveyor belt :
v6.3
Qml
[kg/m] l
m
l
mm
kd
'
zkd
kg
'
zkg'
k
[kg/m] m1000
Bm tjt
v.
Qm
Stj
l
63
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Theoretical volume flow Qj (in m3/h) (v = 1 m/s)
3
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Motional Resistances
1. rolling resistances of the idlers
2. flexing resistance of the belt
3. flexing resistances of the bulk material
4. acceleration resistance and frictional resistance
between material handled and belt
5. chute frictional resistance
6. scraper resistance
7. deflection resistance due to belt bending
8. gradient resistance of conveyed material
WS - Secondary Resistances
WH - Gradient Resistance
WG - Primary Resistances
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Friction value f for top and bottom run together
Note:
Higher safety in the design of the drive units is achieved
– with motor-operated drive units by selecting a higher f value,
– with generator-induced operation of the drive units by selecting a smaller f value.
4
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Secondary Resistances - Coefficient C(L)
The total secondary resistances FN result from the sum of locally limited motional
resistances in the top run and return run, particularly at the head and tail of a belt
conveyor system:
Bulk material feed
• acceleration resistance and frictional resistance
between material handled and belt
• chute frictional resistance
Belt cleaner
• scraper resistance
Pulleys (not driven)
• deflection resistance due to belt bending
• resistance of the pulley bearings
80 100 200 300 500 1000 2000 5000
1,01,031,05
1,1
1,2
1,3
1,4
1,5
1,6
1,7
1,8
1,9
2,0
Wsp. długości C
Długość przenośnika L [m]
C(L)
Conveying length[m]
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Motional Resistances
[N] gmmHgδ cosmmmLfCW '
lt
'
lt
'
kggg
[N] gmHgδ cosmmLfCW tt
'
kddd
DHSGC WWWWW
Total primary resistances :
[N] gδ cosmm2mLfW '
lt
'
kG
Total secondary resistances.
[N] W1CW GS
Total gradient resistances :
[N] gmHW '
lH
5
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Power Required
WC - total of the motional resistances in top run/return run in a steady
state operation
v - belt speed
N - total as a result of loading conditions in a steady operating state
of necessary power at the periphery of the driving pulley
[kW] v1000
WN C
[kW] ηNNor η
NN CC
Rodzaj napędu napęd jednobębnowy
η+
napęd wielobębnowy
η+
napęd hamujący
η-
Elektrobęben 0,96
Electromechanical 0,94 0,92
Electromechanical + Hydrodynamic
Coupling 0,9 0,85 0,95 ÷ 1,0
Hydraulic 0,86 0,80
(generator operated drive) (motor operated drive)
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Tension calculations
1e
kWS
pc
2
d23 WSS
34 SS
g41 WSS
Tensions correction (belt sag) Smax = MAX(S1; S2; S3; S4) [N]
S1
S2
S4
S3
10 kN
5
5’
1
2
4
3
6
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Sections pf belt conveyor
1
2
R R
3 4
5 6 9 7
10
8
11
12 13 14 15 16
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Si
i+1
i Si+1
P
WGSD
WHnt mzra
S [kN]
100
200
300
400
500
0 v
)ii()ii(zr)ii(Ht)ii(Hn)ii(GSDii PamWWWSS 111111
7
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Belt Type
– Coefficient of belt splicing rp,
– Maximum belt tension – stationary work Smax,
– Safety factor – stationary work u,
[kN/m] B
S
r1K max
p
uN
Carcass Splicing Coefficientrp
B – cotton
P – poliamid
E – poliester
Cold Vulcanisation 1/z
Hot Vulcanisation 0
Cold Vulcanisation – 1 ply 0,3
Mechanical Splice > 0.4
St – steel 2 0
3 0,5(n - 2)
Carcass Work
conditions
Stationary work
u
Cotton,
Poliamid, Poliester,
Steel
good 6,7
average 8,0
poor 9,5
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Guide Values for Top and Bottom Cover Gauges for Textile Carcass and Steel Cord Conveyor Belts for different Uses (in mm)
8
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Minimum Pulley Diameters
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9
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Bibliography
Continuous handling equipment – Nomenclature, ISO 2148-1974
Kulinowski, wykłady „Transport przenośnikowy”,
www.kmg.agh.edu.pl
Phoenix Conveyor Belts Design Fundamentals