Vermelding onderdeel organisatie

14 - 18 January, 2013

1

Determination of rolling resistance of belt conveyors using rubber data: fact or fiction? Prof.dr.ir. Gabriel Lodewijks

Belt conveying of bulk solids

Johannesburg, Republic of South Africa

Mechanical Engineering and Marine Technology Transport Engineering and Logistics

23/07/2003 2

Contents

  Introduction   Recent South African Projects   Visco Elasticity   Rheological Testing   Indentation Rolling Resistance   Discussion & Conclusions

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Introduction

  Supplier selection   Total cost of ownership   Design standards (DIN 22101)   Belt conveyor lay-out

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Recent South Africa Projects

  Coal Resources Utilization Project (CRU-II) (1999/2000)   Optimum (2001/2002)   Savmore (2001/2002)

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CRU-II, Hendrina -  14.5 km overland system -  1200 mm, ST 2200, 6+6 -  1050 mm, ST 1100, 6+4

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Optimum, Hendrina -  21 km overland system -  1200 mm, ST 1400, 6+4 -  1050 mm, ST 900, 6+4

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Savmore, Piet Retief -  6.5 km overland system -  900 mm, ST 1000, 6+5

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Visco Elasticity

Time [s]

Am

plit

ude

Applied strain Elastic solid stress Viscous fluid stress Viscoelastic fluid stress

Tension

γ(t)

Visco-elasticity means losing energy

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σσ ΨΨγγd '

d '

'-

t'(t) = (t - t ) (t )

tdt∂

∂∞∫

ΨΨ ΨΨ(t) = + g( ) exp(- t ) d∞

∞

∫ ττ

τ0

ΨΨ ΨΨ(t) = + g exp(- t )jjj 1

N

∞=∑ τ

g1 g2 gN

η1

ηN

η2

Ψ∞

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E

E

1

2

ση

The trick is to pick the right parameters!

ΨΨ(t) E E exp(- t )1 2= +τ

From dynamic/mechanic tests we determine E1, E2, and η

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T [ C]

E' [MPa]

1000 Hz

100 Hz

1 Hz

0.1 Hz

0.01 Hz

0.001 Hz

10 Hz

T [ C]

tan( )

1000 Hz

100 Hz

10 Hz

1 Hz

0.1 Hz

0.01 Hz

0.001 Hz

δ

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Rheological Testing

Rheological test modes:

  Steady, dynamic, transient mode   Strain, frequency, temperature, time,

time/cure sweep

  Problem: number of tests or test range?

Tension

γ(t)

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The dynamic frequency of oscillation directly links the material time and laboratory time (Coxx-Merz relation). By employing the Boltzmann principle and time-temperature superposition, data can be obtained to predict material behavior outside the range of conventional rheometers.

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DMA testers – rheometric dynamic mechanic analyser III

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Three point bending Dual cantilever

Tension

Compression

Three point bending Dual cantilever

Tension

Compression

Relation between tests and reality

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Mechanic-Dynamic Analysis - Rubber XYZ

0.00E+00

2.50E+07

5.00E+07

7.50E+07

-30 -20 -10 0 10 20 30 40 50

Temperature [C]

E' a

nd E

" [P

a]

0.00

0.25

0.50

0.75

Tan

(del

ta)

[-]

E' E" Tan(delta)

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Indentation Rolling Resistance

x = -bx = a x = 0

x' = x' = 0 x' = a' -a'

Vy0

x

y

R

b

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Fz

h

Rigid base

Spring

( ) ( )⎭⎬⎫

⎩⎨⎧

⎥⎦

⎤⎢⎣

⎡⎟⎠

⎞⎜⎝

⎛ −−⎟⎠

⎞⎜⎝

⎛++⎟⎠

⎞⎜⎝

⎛ +⎟⎠

⎞⎜⎝

⎛ −=σ

axa)

ax-a

k1exp(--1k1

RhkE

axa

axa

2RhEa(x) 212

Today also for pipe and pouch belt conveyors

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∫−

σ=a

bz (x)dxF

f ffsih*

im*=

M (x)x dx-b

a

= ∫ σ

Fz

h

Rigid base

Spring

x = -bx = a x = 0

x' = x' = 0 x' = a' -a'

Vy0

x

y

R

b

z

ii FFf = f f fi s im=

RMFi =

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V [m/s]

f

f

f

f

im

ih

i

im

*

*

Hunter (solid line), May et al. (dashed line),

uncorrected (dashdot line) and corrected (dotted line).

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nz nh nD nV nk nT

Lachmann [1954] 1.50 - 0.5 - - -

van Leyen [1959] 1.40 - 0.8-1.0 - - -

Schwarz [1966] 1.14-1.34 - 0.81-1.02 - - -

Behrens [1967] 1.30 - - - - -

Quaas [1968] 1.24-1.40 - - - - -

Hettler [1976] 1.30 - - - - -

Kehlert [1977] 1.333-1.5 - 0.8 - - -

Gladysiewics [1983] 1.333 - 0.667 - - -

Kostrzewa [1985] 1.30 - 0.74 0.208 0.041 5.04

Jonkers, eq. (5.39) 1.333 0.333 0.667 f(ω) f(D0 ) f(E')

Spaans, eq. (5.36) 1.333 - 0.667 - f(D0 ) -

Spaans, eq. (5.38) 1.333 0.333 0.667 f(ω) f(D0 ) f(E')

equation (5.52) 1.333 0.333 0.667 f(ω) f(D0 ) f(E')

F C F h D V K Ti zn n -n n

N-n nz h D V k T=

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Discussion & Conclusions

  We know that rubber plays a major role in belt conveying

  We now understand visco-elasticity   We know how to measure the relevant parameters   We have a model that can predict the indentation

rolling resistance

  How about the repeatability?   How about the accuracy?

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0

1

2

3

4

5

6

7

-30 -20 -10 0 10 20 30

Temperature [C]

E' [

MP

a]

Extern laboratory rubber A TU Delft laboratory rubber AExtern laboratory rubber B TU Delft laboratory rubber B

Repeatability

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Accu

racy

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Determination of rolling resistance of belt conveyors using rubber data: fact or fiction? Facts are that:

  there are theoretical models to describe the visco-elastic behaviour of rubbers

  there are models that predict the power consumption of belt conveyors using rubber data

  there are scientifically accepted methods to measure the mechanic/dynamic properties of rubber (DMA)

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  the performance of two rubber compounds can be compared to each other.

  the power requirements of a belt conveyor can be estimated using computational design tools provided that they are tuned for the results of the mechanic/dynamic rubber compound tests performed on a specific test facility.

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Fiction is:

  the application of mechanic/dynamic properties of rubber measured at a specific rheometer can be used in any design model yielding the same accurate prediction of the power consumption of the system.

  the deviation between the power consumption of belt conveyors predicted by theoretical models and measured in practice can be less than 5%.

  the indentation rolling resistance is always the driving design parameter for long overland systems.

  the measurement of power consumption of a new belt conveyor should be done as soon as possible after installation to enable comparison between theory and practice.

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