Μathematical Modeling of the Conveyor Belt Capacity

athematical modeling of the conveyor belt capacity

Tsakalakis K.G.*and Michalakopoulos Th. National Technical University of Athens (NTUA)-Greece School of Mining and Metallurgical Engineering * [email protected]

CHoPS 2015, The 8th International Conference for Conveying and Handling of Particulate Solids Tel-Aviv, Israel, 3-7 May 2015 1

Objective of the work In this work we try to formulate and present a

new poly-parametric empirical model, which can be used for the prediction of the conveyor belt capacity Q, facilitating the whole mathematical work, especially for design purposes of mining industry treatment plants.

It is performed also an assessment of the accuracy and the adequacy of the proposed model.


Outline of the presentation Belt conveyor applications Aggregates processing plant layout Belt Conveyor Advantages Conveyor belt design Physical properties and features of solid bulk materials affecting

their handling Angle of repose (a) and angle of surcharge (b) During material transport Cross Sectional Area / Comparison for Various Forms of Troughing

configurations Geometrical calculation of the cross-sectional area (profile) of a

conveyed load

CHoPS 2015, The 8th International Conference for Conveying and Handling of Particulate Solids Tel-Aviv, Israel, 3-7 May 2015

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Outline of the presentation Equation for the capacity factor CF in three roll equal-length trough

idlers belt designation Capacity factor CF (Data given compared to computed values) Relationship of the cross-sectional area S and the belt width W Assessment of the cross sectional area S model Integrated model for the calculation of the conveyor belt capacity

Q (m3/h) Remarks-suggestions referred to the model Assessment of the proposed model using CEMA data RESULTS CONCLUSIONS Acknowledgement


Belt conveyor applications

Belt conveyors play a major role in bulk materials handling operations (especially in the extractive industry).

They may be used effectively for the transportation of bulk materials over both short and long distances.

In the latter case, the adaptability of their design and construction permits them to operate over undulating terrain.

http://www.bulksolids.com.au/beltconveying.html


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Aggregates processing plant - layout

After Pathak K., Belt Conveyors


Belt Conveyor Advantages Belt conveyors are used throughout the world for the conveying of bulk materials

and have many advantages over other types of bulk material handling equipment Capable of handling a wide range of bulk materials from very fine (cement

powder) to large lump sizes (coarse lumps of coal) Capable to handle capacities for any operation (e.g. from 10,000 tons/h to a

small amount of material between processes) Longer distances can be covered more economically than any other

transportation system by means of a single or a series of belt conveyors Can be configured to fit almost any application (horizontal material convey, on

an incline or a combination of both) Can be used to stock-pile or reclaim bulk materials from large stockpiles Require less horsepower to operate than other types of conveyors, due to the

fact that the carried bulk materials are on top of the belt and remain static Reliable method of conveying bulk materials.


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Conveyor belt design The proper design of a belt conveyor requires: an understanding of the characteristics (bulk density, PSD, etc. ) of

the material to be conveyed The material behavior, during transportation, affects the conveyor's

capacity and design. A conveyor is described by its rated capacity Q in m3/h or t/h, which is

a function of: Q = f (W, , dyn)

Where: W (belt width), (lamda,troughing angle of the idlers), dyn (the surcharge angle of the carried material) and

v the belt speed and the bulk density of the material (t/m3) if they are different from 1 (m/s or t/m3)

Any change of these factors, affects the capacity of the conveyor.


Physical properties and features of solid bulk materials affecting their handling :

1. Bulk Density 2. Lump-Size 3. Particle size (mean, max, min) 4. Particle size distribution (PSD) of the conveyed material 5. Particle shape 6. Moisture content 7. Flowability 8. Temperature 9. Coefficient of friction on solid surfaces 10. Abrasiveness 11. Corrosiveness 12. Miscellaneous Characteristics

CHoPS 2015, The 8th International Conference for Conveying and Handling of Particulate

Solids Tel-Aviv, Israel, 3-7 May 2015 9


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Particle size distribution (PSD) of the conveyed material

Boddington Gold Mine (Australia) 11.5 kilometres conveyor belt , after FLSmidth


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Inclined conveyor belt fully loaded

Angle of repose (a) and angle of surcharge (b)

st = angle of repose (static angle) of a material or angle of natural friction dyn = angle of surcharge or dynamic angle of a moving material

Approximately dyn = (0.5 - 0.9)st CHoPS 2015, The 8th International Conference for Conveying and Handling of Particulate

Solids Tel-Aviv, Israel, 3-7 May 2015 12

During material transport 1. Settling of the material (range 10-15%) 2. Material rearrangement on the moving belt 3. Increase of the bulk density of the conveyed material,

due to external forces 4. Changes in the cross-sectional area (profile) of the

conveyed load


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Thus, for capacity and equipment calculations necessary to know

1. The angles of repose and surcharge of the conveyed material related to belt configuration (number of idlers, belt width W, usable belt width b, troughing angle/-s )

2. The variation in bulk density in loose and packed states 3. The particle size distribution (PSD) of the material and 4. The moisture content of the material greatly influencing

the above factors

Material properties affecting material flowability and conveyor belt capacity after CEMA


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Cross Sectional Area S / Comparison for Various Forms of Troughing configurations

The number of idler rolls in a carrying idler set and the troughing angle (-s) determine the cross sectional area of the load stream and thus the conveying capacity

The area of the section S may be calculated geometrically adding the area of a circle segment A1 to

that of the trapezoid A2 or mathematically

(Cross-sectional area, S) Material moving on a conveyor belt supported on

three equal-length roll idlers


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Geometrical calculation of the cross-sectional area (profile) of a conveyed load

Equation for capacity factor CF in three roll equal-length trough idlers belt designation


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Applying multiple linear regression analysis to the 30 sets of data (surcharge angle dyn, idler troughing angle lamda, Table) yields:

CF = (-0,0002*+0,0219)*dyn + 0,0408*0,7903

Capacity factor CF Data given compared to computed values


19

0

0,2

0,4

0,6

0,8

1

1,2

1,4

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

Com

pare

d va

lues

(dat

a vs

com

pute

d)

Number of pairs compared (data vs computed values)

Relationship of the cross-sectional area S and the belt width W


S = 0,1084W2,1473 R = 0,9997

0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0 0,5 1 1,5 2 2,5

Cro

ss-s

ectio

nal a

rea

S of

the

load

, m2

Conveyor belt width W, m


21

-6

-5

-4

-3

-2

-1

0

1

2

3

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

% d

iffer

ence

bet

wee

n gi

ven

and

com

pute

d S

valu

es

Number of data values used for model derivation

Assessment of the cross sectional area S model

All % differences (except one), between the given and the computed S values, vary from about -3 to 2 %

Comparison of the given and the computed S values for 18 pairs

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7

1

3

5

7

9

11

13

15

17

Cross sectional area S (data vs computed), m2

Num

ber o

f dat

a va

lues

(pai

rs) c

ompa

red

Integrated model for the calculation of the conveyor belt capacity Q (m3/h)

But, since Q = Sv (m2m/s) = 3600 Sv (m3/h) Multiplying the two models, derived previously, yields:

The model gives the conveyor belt capacity Q (

)as a function of:

Q = f(W, , dyn)

Where: W Belt width (m), the troughing angle and dyn the angle of surcharge (thus, taking into account the capacity factor CF for

different conveyor configuration)


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= , , , + , + , ,

Remarks-suggestions referred to the model


23

= , , , + , + , ,

Q values refer to horizontal conveyor belts,

moving at speed v = 1 m/s and loaded with a material of bulk density = 1000 kg/m3 (1 tonne/m3)

Under different operating conditions (belt speed, material bulk density, belt inclination)

Use correction factors !!!

given in the technical literature by the belt conveyor manufacturers


-4

-2

0

2

4

6

8

10

12

14

0 20 40 60 80 100 120

Perc

ent d

iffer

ence

in c

apac

ity, %

pu

blis

hed

vs p

redi

cted

val

ues

Conveyor belt width W, inches

0

10000

20000

30000

40000

50000

60000

70000

80000

90000

1 2 3 4 5 6 7 8 9 10 11 12 13

Conv

eyor

cap

acity

Q (f

t3/h

)

Number of pairs compared (data given vs computed values)

Assessment of the proposed model using CEMA data

Only belt conveyors wider than 84 inches (2.1 m)

present differences greater than 4%, all other from

-2 to 4%

Conveyor Equipment Manufacturers Association (CEMA)

RESULTS

A new polyparametric empirical model, predicting the horizontal conveyor belt capacity as a function of:

1. The idler troughing angle 2. The surcharge angle dyn of the carried material 3. The belt width W 4. The belt speed v 5. The material bulk density,


25

CONCLUSIONS

With the help of the proposed model:

not only accurate prediction of the conveyor belt capacity Q under various operating conditions, but

use it for design purposes of belt conveyor systems


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This work was supported by the LIFE+ financial instrument of the European Community in the context of LIFE RECLAIM Landfill mining pilot application for recovery of invaluable metals, materials, land and energy (www.reclaim.gr), Grant: LIFE12 ENV/GR/ 000427. The coordinating beneficiary is ENVECO S.A. and the associated beneficiaries are the Municipality of Polygyros, School of Mining & Metallurgical Engineering NTUA and HELECTOR S..

Acknowledgement

athematical modeling of the conveyor belt capacityObjective of the workOutline of the presentationOutline of the presentationBelt conveyor applicationsSlide Number 6Belt Conveyor AdvantagesConveyor belt designPhysical properties and features of solid bulk materials affecting their handling :Slide Number 10Slide Number 11Slide Number 12During material transportSlide Number 14Slide Number 15Slide Number 16Slide Number 17Equation for capacity factor CF in three roll equal-length trough idlers belt designationCapacity factor CF Data given compared to computed valuesRelationship of the cross-sectional area S and the belt width W Slide Number 21Integrated model for the calculation of the conveyor belt capacity Q (m3/h) Remarks-suggestions referred to the modelSlide Number 24RESULTSCONCLUSIONSSlide Number 27

Μathematical Modeling of the Conveyor Belt Capacity

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