1

BELT CONVEYORS II

Mechanical Engineering Department

Carlos III University

BELT CONVEYORS

TRANSPORTATION

BELT CONVEYORS II

INTRODUCTION

A belt conveyor is rubber or textile structure with a belt shape closed ring, with a vulcanized or metallic joint, used for material transportation.

• Belt conveyors are the mostused for transport of solidobjects and bulk materials at great speed, covering greatdistances (up to 30 km)

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BELT CONVEYORS II

COMPONENTS

Drivingpulley Belt

Unloading Carryingidlers

Return idlers

Tailpulley

Take up weight

Structuralsupport

Snubpulley

Scraper

Bin or hopper

Work run

Free/return run

BELT CONVEYORS II

BELT

Textile belts or smooth textiles

•Definition (UNE 18 025):

–The width, expressed in mm.

–The quality of the cover (standard UNE 18 052).

–The number of plies.

–The quality of the fabric (standard UNE 18 052).

–The thickness of the top cover (tenths of mm).

–The thickness of the bottom cover (tenths of mm).

–The length of the belt (metres).

500 / A – 4 L / 35 – 15 des 50 UNE 18025Width of the belt (mm)

Highly resistant to abrasion

Consists of 4 light plies (L type)

Thickness of the top cover (tenth mm)

Thickness of the bottom cover (tenth mm)

Length (m)

3

BELT CONVEYORS II

BELT

Textile belts or smooth textiles

•Quality of the covers (UNE 18 052)

•Quality of the fabric (UNE 18 052)

3501050C

5002000B

5502500A

Elongation at rupture (%)Tensile strength

(g/mm2)Quality of the cover

352075P

302070LS

252060L

Elongation at rupture

(%)

Tensile strength

(kgf/cm)

Weft

Tensile strength (kgf/cm)

WarpQuality of the

fabric

BELT CONVEYORS II

BELT

Textile belts or smooth textiles

• Number of plies:

1100

mS TzB R

⋅=⋅ ⋅

Safety factor

131211Safety factor (S)

More than 9from 6 to 9from 3to 5Number of plies (z)

Safety Factors for textile Carcass Belts (DIN 22101 standard)

Belt width

(metres)

Maximum stress

work of the belt (kgf )

Nominal tensile

strength of each

textile ply (kgf/m)

• It depends on the time the belt

finishes its travel, which depends on:

– The number of flexures on the

pulleys.– The load impacts.

• If time travel is above 5 minutes⇒⇒⇒⇒ - 2 plies

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BELT CONVEYORS II

BELT

Belt conveyors for vertical or inclined transport

• Drawback of smooth textile belt:

– Grade limit : 18º - 20º

• Different solutions:

– Profile belts:

• Herringbone profile.

• Nasta, Nappula, Ripa and Pyramid profile.

• Grip Top profile.

• Ripro profile.

– U-cleats and V-cleats profiles.

– Corrugated edge belt.

BELT CONVEYORS II

PULLEYS

Bigger angle Bigger force transmitted

Driving pulley

Entrusted of transmiting movement by means of the motor-speed reducer.

• Guarantee maximum adherence ⇒⇒⇒⇒ Low slip.

Simple pulley

ϕ = 180ºSimple plulley with snub

pulley

210º ≤ ϕ ≤ 230º

Tandem motor

350º ≤ ϕ ≤ 480º

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BELT CONVEYORS II

TENSION

• The tension varies along the belt length.

• Depends on:

– Belt conveyor arrangement.

– The number and arrangement of the drive pulleys.

– The drive and brake features.

– The type and tension devices arrangement.

– Operation phase (start-up, normal operation, braking, etc.).

BELT CONVEYORS II

TENSION

One drive pulley

•Most common situation.

• Operation conditions:

– Peripheral forces applied to the drive pulley have to be transmitted to the

belt by friction without slippage.

– The applied tension to the belt has to be adequate to avoid an important sag

(between two pulleys).

Roll angle

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BELT CONVEYORS II

TENSION

One drive pulley

• Euler-Eytelwein (without slip) equation:

1

2

Te

T

µ ϕ⋅=

1 2 uT T F= +

1 2

2

1T T

eT

µ ϕ⋅− = − 1 22 2

1uFT T

eT T

µ ϕ⋅− = = −

2 1

1

( 1)u T uT F C F

eµ ϕ⋅= ⋅ = ⋅

−

11

u TS u

eT F C F

e

µ ϕ

µ ϕ

⋅

⋅= ⋅ = ⋅−

BELT CONVEYORS II

PULLEYS

Pulley diameter

0.8tail pulley tensioning pulley driving pulleyD D D= ≅

0.65snub pulley driving pulleyD D≅

2.0001.8001.6001.4001.2501.000800630500400320250200

Standard pulley diameter s/DIN 22101

min

360 FD

p Bπ ϕ⋅=

⋅ ⋅ ⋅

Minimum drivingpulley diameter

proposed for fabricbelts (m)

Action force (kg)

Angle contact

(degrees)

Belt width (m)

Transmission capacity pulley/belt:

1.600÷2.000 Kg/m²

In underground, up to 3.500 kg/m²

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BELT CONVEYORS II

MOBILE COMPONENT WEIGHT

( )T B R BM kg M M M= + +

Mobile component weight (kg):

Mobile component weight per unit length (kg/m):

TT

MP

L=

Belt length (m)

Belt weight(kg):

Idler rollerweight (kg):

Pulley weight(kg):

BELT CONVEYORS II

MOBILE COMPONENT WEIGHT

2191772200

2051682100

1781441800

1601321001650

143121911500

12710782701350

1109571631200

948264521050

79705545900

63574637750

49453629600

332523450

Steel cable belt

Rollers 152 mm

Heavy belt

Rollers 152 mm

Moderate belt

Rollers 127 mm

Lightweight belt

Rollers 102 mm

Mobile component weight per unit length (kg/m)Belt width

(mm)

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BELT CONVEYORS II

MOBILE COMPONENT WEIGHT PER UNIT LENGTH

0,278 [kg/m]3,6

G

Q Qq

v v= = ⋅

⋅

Belt capacity(t/h)

Belt speed (m/s)

BELT CONVEYORS II

RESISTANCE TO MOVEMENT

• Classification (UNE 58-204-92):1. Principal resistances, FH2. Secondary resistances, FN3. Special principal resistances, FS14. Special secondary resistances, FS25. Resistances due to inclination, FSt

1 2u H N S S StF F F F F F= + + + +

In every installation (1) y (2)

In some installations (3) y (4)

Act in all the belt length (1) y (3)

Act in certain regions (2) y (4)

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BELT CONVEYORS II

RESISTANCE TO MOVEMENT

•Turning resistance due to the load idlers rollers, due to friction in the

bearings and joints in rollers.

•Belt friction resistance due to the rolling of the belt over the idlers rollers.

Principal resistance

[ ](2 ) cosH RO RU B GF f L g q q q q δ= ⋅ ⋅ ⋅ + + ⋅ + ⋅Friction coefficient

Work run roller weight per unit length(kg/m)

Return rollers weight per unit length(kg/m)

Belt weight per unitlength (kg/m)

Load weight perunit length (kg/m)

Angle of theincline

0,050Friction

0,023 – 0,030Unfavourable

0,020Normal

0,018Favourable

Roller

Bearing

fStateType of

bearing

BELT CONVEYORS II

•Inertia resistance and friction due to material acceleration in the loading

point:

Material density(kg/m3)

RESISTANCE TO MOVEMENT

Secondary resistances

Material flux (m3/s)

0( )ba vF I v vρ= ⋅ ⋅ −

Belt speed (m/s)

Feed-in speed (m/s)

•Resistance due to material friction with feed-in chute sidewalls.

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BELT CONVEYORS II

•Resistance of pulley bearings safe drive pulleys:

– For fabric belts:

–For metallic belts:

RESISTANCE TO MOVEMENT

Secondary resistances

•Resistance due to rolling belt effect over the pulleys:

1 9 (140 0.01 )F d

F BB D

= ⋅ ⋅ + ⋅ ⋅

1 12 (200 0.01 )F d

F BB D

= ⋅ ⋅ + ⋅ ⋅

Belt width(m)

Mean belt stress (N)

Belt thickness (m)

Pulley diameter(m)

00.005t Td

F FD

= ⋅ ⋅Pulley applied forces (N)

Drive axle diameter (m)

BELT CONVEYORS II

•When L > 80 m ⇒⇒⇒⇒ FN < FH:

RESISTANCE TO MOVEMENT

Secondary resistances

[ ][ ]

(2 ) cos

(2 ) cos

H N L RO RU B G

C RO RU B G

F F f C L g q q q q

f L g q q q q

δδ

+ = ⋅ ⋅ ⋅ ⋅ + + ⋅ + ⋅ =

= ⋅ ⋅ ⋅ + + ⋅ + ⋅

Friction coefficient Load weight perunit length (kg/m)

Incline angle

Belt weight per unitlength (kg/m)

Return run idler rollers weight per unitlength (kg/m)

Work run idler rollers weight per unitlenght (kg/m)

Corrected belt length (m)

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BELT CONVEYORS II

LENGTH CORRECTION FACTOR

Shorter belts need more power to overcome friction resistances than longer belt conveyors.

Corrected belt length (m):

c LL C L= ⋅

1.051.11.21.31.41.51.61.71.822.2CL

500400320250200160125100806350Belt length(m)

2.42.62.93.23.644.55.15.96.65.69CL

4032252016131086543Belt length (m)

Correction factor

BELT CONVEYORS II

RESISTANCE TO MOVEMENT

Special principal resistance

•Toe resistance due to oblique belt position because of the loading rollers:

– 3 roller picking idler of the same length in the work run:

–

– 2 roller picking idler for the return run:

( ) coso B GF C L q q g senµ δ∈ ∈ ∈= ⋅ ⋅ ⋅ + ⋅ ⋅ ⋅ ∈

cos coso BF L q g senµ λ δ∈ ∈= ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ∈

Value:

- 0,4 for an angle of 30º

- 0,5 for an angle of 45º

Friction coefficient between

the belt and the idler rollers : 0,3 – 0,4

Longitud de la instalación con rodillos

portantes convergentes (m)

Belt weight per unit length(kg/m)

Load weight per unitlength (kg/m)

Toe angle (degrees)

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BELT CONVEYORS II

RESISTANCE TO MOVEMENT

Special principal resistance

•Resistance due to friction with feed-in chute sidewalls, or with the

longitudinal guide rails, when they take place along the total belt length:

2

2

2 2

1

vgL

I e g lF

v b

µ ⋅ ⋅ ⋅ ⋅=⋅

Friction coefficientbetween the material andthe guides: 0,5 – 0,7

Transported flux (m3/s)

Weight volume not tared(kg/m3)

Transport length betweenguide rails (m)

Belt width between guide rails (m)

BELT CONVEYORS II

RESISTANCE TO MOVEMENT

Special secondary resistances

•Resistance due to friction between the cleaning systems and the belt:

•Resistance due to the friction between the chute sidewalls or with guide

rails when they only take place over a limited belt length :

Contact surface between thebelt and the cleaning system

(m2)

3rF A p µ= ⋅ ⋅

Pressure between the cleaningsystem and the belt (N/m2)

Friction coefficient between thecleaning system and the belt

a aF B k= ⋅

Belt width (m)Scraping factor = 1500 N/m

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BELT CONVEYORS II

RESISTANCE TO MOVEMENT

Resistance due to slopes

St GF q H g= ⋅ ⋅

Load weight per unitlenght (kg/m)

Installationheight (m)

BELT CONVEYORS II

POWER OF THE DRIVE PULLEY

Drive pulley power

Force opposed to movement (N)

Belt speed (m/s)

A uP F v= ⋅

• For powered belts:

1

Am

PP

η=

14

BELT CONVEYORS II

TRANSPORT CAPACITY

3600Q v A kγ= ⋅ ⋅ ⋅ ⋅Transport capacity(t/hora)

Speed (m/s)

Cross section of material over the belt (m2)

Material specificweight (t/m3)

Reduction capacity coefficient due to incline

0,810,850,890,910,930,950,970.,980,991,0k

2018161412108642Incline

(degrees)

BELT CONVEYORS II

Depends on: - material fluidity

- transport conditions

TRANSPORT CAPACITY

•Cross section of the material over the belt depends on:

– Effective width (b) of the belt is function of the real width B:

•

•

– The number, arrangement and dimensions of the rollers.

– The dynamic built-in shape of the material over the belt is limited by a

parabolic curve, characterised by a dynamic slope angle θθθθ.

0.9 0.05 for B 2 mb B= ⋅ − ≤0.2 for B> 2 mb B= −

One roller Two rollers Three rollers

1 2S S S= +( )21 3 3( ) cos

6

tgS l b l

θλ= + − ⋅ ⋅

( )332 3

( ) 1sin

2 cos 2

b lb lS l λ

λ− − = + ⋅ ⋅ ⋅

Pickingangle

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BELT CONVEYORS II

TRANSPORT CAPACITY

• Uniform material size (cereals, granules or milled stones) do not influence

belt width.

• Non classified materials (materials obtained in quarries or mines)

influence on belt width:

–Maximum material size.

– Fine and coarse-grain percentage.

• It may occur that for little capacities the belt width is big ⇒⇒⇒⇒ not economic

• Belt width as a function of the maximum grain size:

53θ ≤ 20º

10620º ≤ θ ≤ 30º

100 % coarse10 % coarse, 90 % finesDynamic slope angle

BELT CONVEYORS II

TRANSPORT CAPACITY

• The belt speed has to be as big as possible so that width is short.

• Speed depends on material properties:

– Fluidity. Dust risk.

– Abrasion. Belt cut risk.

– Friable. Material split risk.

– Size. Great impacts on the belt take place for big sizes and heavy ones, thus

weakening the belt.

1,05 – 1,68Any widthNon abrasive

2,09

3,35

4,19

5,24

500

650 a 1000

1200 a 1200

1400 a 2400

Coal, clay pan, soft

minerals and soils, grinned

stones of little size

2,62

3,35

4,19

5,24

500

650 y 800

1000 y 1200

1400 y 2400

Grains and other materials

that have a good fluidity

and are not abrasive

V (m/s)B (mm)Material

0,3 a 0,6Any width

Discharge belts, flat or picking

for fine non abrasive materials

or medially abrasive

1,31 a 2,09Any widthPrepared cast-iron sands or

compacted

1,68

2,09

3,35

500

650 y 800

1000 a 2400

Minerals with sharp edge, hard

and heavy, grinned stones of

little size

V (m/s)B (mm)Material

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BELT CONVEYORS II

TRANSPORT CAPACITY

900

0,2536

878

0,2467

840

0,2368

798

0,2240

738

0,2071

680

0,1903

351

0,09801400

654

0,1828

638

0,1777

610

0,1705

580

0,1612

537

0,1491

494

0,1370

255

0,07101200

445

0,1236

434

0,1205

415

0,1152

394

0,1094

365

0,1013

336

0,0933

173

0,04801000

276

0,0766

269

0,0747

258

0,0716

244

0,0677

227

0,0630

208

0,0577

108

0,0300800

176

0,0488

172

0,0477

164

0,0455

156

0,0433

144

0,0400

133

0,0369

69

0,0191650

98

0,0272

95

0,0263

91

0,0252

87

0,0241

80

0,0222

74

0,0205

38

0,0105500

1190

0,3355

45º

1160

0,3264

40º

1110

0,3134

35º

1055

0,2965

30º

1600

B\λ

464

0,1294

0º

976

1055

25º

898

0,2519

20º

Capacity in m3/hourfor v = 1 m/s

Cross section in m2

5,244,193,352,622,091,681,311,050,840,66

• Standard speeds in m/s (DIN 22101)

• For horizontal belt conveyors:

BELT CONVEYORS II

TRANSPORT CAPACITY

Belt geometry:

• L = 805 m, vertical extent = 150 m, incline = 10,73º

• For the previous incline, the capacity reduction coefficient k = 0,95

• Picking angle = 35º

Capacity to be transported: 1500 T/hour

EXAMPLE

Limestone

•Specific weight = 1,4 T/m3

•Particle size:

•10% of coarse, maximum size: 250 mm

•Dynamic slope angle: 15º

•Not abrasive, friable but no reduction in

price, due to a needed later grinding

¿Speed?

¿Belt width?

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BELT CONVEYORS II

TRANSPORT CAPACITY

EXAMPLE

53θ ≤ 20º

10620º ≤ θ ≤ 30º

100 % coarse10 % coarse, 90 % fineDynamic slope angle

θ=15θ=15θ=15θ=15º

Maximum grain size 250 mm:

B = 3 ⋅⋅⋅⋅ Maximum size = 3 ⋅⋅⋅⋅ 250 = 750 mm

B=800 mm

0,810,850,890,910,930,950,970.,980,991,0K

2018161412108642Slope angle

(degrees)

BELT CONVEYORS II

TRANSPORT CAPACITY

EXAMPLE

900

0,2536

878

0,2467

840

0,2368

798

0,2240

738

0,2071

680

0,1903

351

0,09801400

654

0,1828

638

0,1777

610

0,1705

580

0,1612

537

0,1491

494

0,1370

255

0,07101200

445

0,1236

434

0,1205

415

0,1152

394

0,1094

365

0,1013

336

0,0933

173

0,04801000

276

0,0766

269

0,0747

258

0,0716

244

0,0677

227

0,0630

208

0,0577

108

0,0300800

176

0,0488

172

0,0477

164

0,0455

156

0,0433

144

0,0400

133

0,0369

69

0,0191650

98

0,0272

95

0,0263

91

0,0252

87

0,0241

80

0,0222

74

0,0205

38

0,0105500

1190

0,3355

45º

1160

0,3264

40º

1110

0,3134

35º

1055

0,2965

30º

1600

B\λ

464

0,1294

0º

976

1055

25º

898

0,2519

20º

800 mmB =

35ºλ =

Qv1 = 258 m3/s

For 1 m/s:

18

BELT CONVEYORS II

TRANSPORT CAPACITY

EXAMPLE

[ ]3

3600 t/h

3600 m /hv

Q v A k

QQ v A k

γ

γ

= ⋅ ⋅ ⋅ ⋅

= = ⋅ ⋅ ⋅

– Because Av1 = Av2:

312 2 2

1 1

2 2

2583,35 0,95 821m /hou

< 1500 t/ho

r1 1

1150 t/ho rur u

vv

v

QQ v k

v k

Q Qγ

= ⋅ ⋅ = ⋅ ⋅ =⋅ ⋅

= ⋅ =

1,05 – 1,68Any widthNon abrasive

2,09

3,35

4,19

5,24

500

650 a 1000

1200 a 1200

1400 a 2400

Coal, clay pan, soft

minerals and soils, grinned

stones of little size

2,62

3,35

4,19

5,24

500

650 y 800

1000 y 1200

1400 y 2400

Grains and other materials

that have a good fluidity

and are not abrasive

V (m/s)B (mm)Material

BELT CONVEYORS II

TRANSPORT CAPACITY

EXAMPLE

• We select B = 1000 mm

900

0,2536

878

0,2467

840

0,2368

798

0,2240

738

0,2071

680

0,1903

351

0,09801400

654

0,1828

638

0,1777

610

0,1705

580

0,1612

537

0,1491

494

0,1370

255

0,07101200

445

0,1236

434

0,1205

415

0,1152

394

0,1094

365

0,1013

336

0,0933

173

0,04801000

276

0,0766

269

0,0747

258

0,0716

244

0,0677

227

0,0630

208

0,0577

108

0,0300800

176

0,0488

172

0,0477

164

0,0455

156

0,0433

144

0,0400

133

0,0369

69

0,0191650

98

0,0272

95

0,0263

91

0,0252

87

0,0241

80

0,0222

74

0,0205

38

0,0105500

1190

0,3355

45º

1160

0,3264

40º

1110

0,3134

35º

1055

0,2965

30º

1600

B\λ

464

0,1294

0º

976

1055

25º

898

0,2519

20º

19

BELT CONVEYORS II

TRANSPORT CAPACITY

EXAMPLE

• We select B = 1000 mm

5,244,193,352,622,091,681,311,050,840,66

• Standard speeds in m/s (DIN 22101)

v=3,35 m/s

So as not to over design

1,05 – 1,68Any widthNon abrasive

2,09

3,35

4,19

5,24

500

650 a 1000

1200 a 1200

1400 a 2400

Coal, clay pan, soft

minerals and soils, grinned

stones of little size

2,62

3,35

4,19

5,24

500

650 y 800

1000 y 1200

1400 y 2400

Grains and other materials

that have a good fluidity

and are not abrasive

V (m/s)B (mm)Material

BELT CONVEYORS II

TRANSPORT CAPACITY

EXAMPLE

• Selecting B = 1000 mm⇒⇒⇒⇒ Qv1 = 415 m3/h y v2 = 3,35 m/s

312 2 2

1 1

2 2

4153,35 0,95 1320,7m /hora

1 1

1849 t/hour

vv

v

QQ v k

v k

Q Qγ

= ⋅ ⋅ = ⋅ ⋅ =⋅ ⋅

= ⋅ =

OK

B = 1000 mm and v = 3,35 m/s