Department of Mining, Dressing and Transporting Machines ... · 1 © [email protected], [email protected] Department of Mining, Dressing and Transport Machines AGH

1

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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.

- [email protected]

( 12617 30 92

B-2 ground-floor room 6

consultations: Mondays 11.00 - 12.00

Conveyors

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Belt drives - history

2

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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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Follow-up Device

izl

M

0 MNmax MHmax

S2

S2

11

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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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Bibliography

Kulinowski, wykłady „Transport przenośnikowy”,

www.kmg.agh.edu.pl

http://www.kmg.agh.edu.pl/

Documents

Department of Mining, Dressing and Transporting Machines ... · 1 © [email protected], [email protected] Department of Mining, Dressing and Transport Machines AGH