AUTEX Research Journal, Vol. 8, No4, December 2008 © AUTEX
STUDY OF SOME FACTORS AFFECTING BENDING RESISTANCE
OF POLYETHELENE ROPES
Abdel Aziz M Sharrouf1, Mona M Salem2, Mohamed Gad3
3
1
Textile Division, National Research Centre, Egypt
e-mail: [email protected]
2
Textile Division, National Research Centre, Egypt
e-mail: [email protected]
El Sherouk for Synthetic Fibres Co, Ropes Dept. Cairo Egypt,
e-mail: [email protected]
Abstract:
The ease of accomplishing a tight knot in a rope depends mainly on the bending resistance of that rope, hence
the bending behaviour of ropes becomes a matter of considerable importance. Reducing the bending resistance of ropes, while retaining their other physical and mechanical properties unchanged is a demand of rope
consumers. Unfortunately there is no standardised method to measure the bending resistance of ropes. The
bending resistance as a mechanical property depends on many factors, such as the type of material used, the
processing methods, and the technical specification of the rope. In the present work, four factors were subjected to study, these being: filament denier twist in the primary strand, twist in the final strand, and percentage
distribution of filament between core and sheath. A simple method, similar in principle to that used in the Shirley
Fabric Stiffness Tester, was used to measure the bending length of polyethylene ropes. A simple model was
derived to calculate the bending resistance of ropes. Multiple regression analysis was used to determine
multiple correlation factors, degree of contribution of each factor to the measured properties, and its significant
levels. Surface plots are used to demonstrate the shape of the effect of the factors that have significant effects.
Keywords:
ropes, bending length, bending resistance, polyethylene ropes, filament denier, primary strand, final strand
1. Introduction
The use of ropes in Egypt dates back to the 5th Dynasty of the
ancient Egyptians. Those ropes were manufactured from palm
leaves, flax or papyrus [1, 2]. Polyethylene ropes have been
manufactured in Egypt since 1981. Since that time and to
date, many trials have been conducted to improve the quality
and performance of those ropes. It has been found from field
study [3] that the majority of rope produced in Egypt at the
present time is polyethylene. This is due to its satisfactory
properties and its economics. However, these ropes in general
suffer from a lack of easiness to be bent during usage, and
thus there is a great demand for improvement in performance
in general of these ropes and in their bending resistance in
particular. The polyethylene filaments, in general, are divided
according to density into 3 main categories:
1-Low density polyethylene, (0.91 – 0.925 g/cm3),
2-Medium density polyethylene, (0.936 -0.940 g/cm 3)
3-High density polyethylene, (0.941 -0.959 g/cm 3)
The importance of this classification is due to the influence of
density on filament properties. Increasing the density leads
to increasing stiffness, tensile strength, shrinkage, and stress
cracking, while it reduces elasticity, clarity, heat resistance
and dye-ability; moreover, there is an inverse proportional
relationship between density and MFI (melt flow index) [4].
In reviewing the standard specifications that determine the
required properties of ropes [5, 6, 7, 8, and 9]; it was found
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that most of those standards do not pay attention to a very
important property of ropes, which is their bending resistance.
Several published papers discuss rope performance [10, 11],
and it Ha been found that bending resistance depends on
the type of raw material more than on the manufacturing
parameters, and that increasing the twist results in a reduction
in the bending length. Hearle [12] determined that the bending
stiffness of yarns depends on the manner of fibre binding in
the yarn by the twisting or other fibres. He also cleared that
the bending stiffness of yarns depends on the bending
stiffness of fibres and the applied twist factor. There is a strong
relation between stiffness of yarns and the bending stiffness
of woven and knitted fabrics. From another point of view,
Martino and others [4] stated that adding plasticisers
increases in general the ability of polymer chains to bend,
and also increases breaking elongation. Person [13] stated
that adding plasticisers leads to a reduction in fibre strength.
There are no available published papers dealing with
measuring the bending resistance of ropes, or the effect of
the manner of construction a rope, i.e. choosing filament
denier, twist in primary strand, twist in final strand, or
distribution of filament between core and sheath of the rope;
moreover, there is no standardised test method for measuring
the bending resistance of ropes and its acceptable range of
values. In a prior work [3] a simple apparatus similar to the
Shirley Fabric Stiffness Tester [14] was constructed and
evaluated. Polyethylene ropes of 12 mm diameter mm were
subjected to study, because they comprise the majority of
distribution of ropes in Egypt [3].
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AUTEX Research Journal, Vol. 8, No4, December 2008 © AUTEX
2. Experimental work
2.1. Measuring the bending resistance of ropes
The bending resistance of ropes was estimated from their
bending length. The definition of bending length as defined
by Booth [15] is ‘the length of fabric that will bend under its
own weight to a definite extent. The fabric was simulated by a
cantilever and the following equation was derived:
C=l [(cos 0.5 Q /8 tanQ )]0.5
where:
C - bending length,
L - measured length,
Q - binding angle,
Q was assumed to be 41.5o in order to simplify the calculation
procedure. Due to the difference in nature between ropes
and fabrics, the definition for bending length for ropes in the
present article, is suggested to be ‘the length of rope at which
it just begins to bend’. The testing equipment for measuring
this bending length is similar in principle to that of the Shirley
Fabric Stiffness Tester [14] with modification to suit the ropes
[3]. In this case the following simple derivation could be made,
referring to Figure 1.
commercial name ‘Mobil A600 (production of SABIC, KSA)’.
The added dying material was 1% for all experiments. No
other additives were used throughout the experiments.
Monofilaments at different deniers were extruded according
to availability on the production line and the experimental plan
shown in Table (1); two monofilaments are twisted to produce
a primary strand, and 23 strands are twisted to produce the
final strand. Distributions of these strands were made so as
to obtain different core/sheath percentages as shown in the
experimental plan. These percentages were achieved by
varying the number of filaments in a core in the stranding
machine. Three final strands are twisted to construct the rope.
The chosen parameters are filament denier, twist in primary
strand, twist in final strand, and percentage core to sheath in
Table 1. Experimental plan for mechanical parameters.
L
W
Figure 1. Basic principle of calculating the bending
resistance of rope, as it just begins to bend.
M = WL/2
(1)
where:
M - bending moment at which rope starts to bend (bending
resistance),
L - bending length at which rope starts to bend,
W - weight of the piece of rope at which the rope starts to
bend.
Figure (1) shows a schematic diagram for this equipment.
From the definition of rope count in
denier:
D = 9000 W/L
Primary
strand twist
TPM
Final
strand
twist TPM
% core to
sheath
1
3100
44
31
17.4
2
3100
44
26
17.4
3
3100
44
24
17.4
4
3100
44
20
17.4
5
3100
44
20
17.4
6
3100
44
20
43.5
7
3100
44
20
69.6
8
3100
44
20
95.7
9
3000
44
20
69.6
10
3100
64
20
69.6
11
3100
108
20
69.6
12
3100
174
20
69.6
13
2400
64
20
69.6
14
3100
64
20
69.6
15
3800
64
20
69.6
16
4500
64
20
69.6
0.121
0.142
0.164
0.185
0.206
0.227
0.248
0.269
0.291
0.312
0.333
0.354
0.375
0.396
0.418
0.439
(3)
Substituting from 3 in 1 we then get:
M = D L2 / 1800
Filament
denier
(2)
where:
W in gm and L in metres (mt.)
then:
W = DL/9000
Run
(4)
The bending moment M will be used
to express the bending resistance
of ropes in the present investigation.
2.2. Experimental plan
The raw material used was high
density polyethylene (0.955gm/cm3)
with MFI = 0.3, having the
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Figure 2. Effect of filament denier and twist in final strand on rope bending resistance.
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AUTEX Research Journal, Vol. 8, No4, December 2008 © AUTEX
Table 2. Regression analysis for bending length of the rope.
R= .94439654 R²= .89188483 Adjusted R²= .85257022
F(4,11)=22.686 p<.00003 Std.Error of estimate: .03720
St. Err.
BETA
St. Err.
of BETA
B
of B
t(11)
p-level
-.378069
.122711
-3.08096
.010453
.100098
.000132
.000022
5.89187
.000104
Intercpt
DINER
.589763
TPM PRIMS
-.121143
.105998
-.000343
.000300
-1.14288
.277351
TPM FINLS
.475130
.124404
.014783
.003871
3.81923
.002847
CORE%
-.374292
.129560
-.001346
.000466
-2.88894
.014734
The
measured
properties of ropes are:
the bending length, then
calculating the bending
resistance from equation
(4) in this article,
breaking strength and
elongation.
3.
Results
discussion
and
Multiple
regression
analysis was carried out,
coefficients of multiple regressions
were estimated, and surface plots
0.161 were shown to illustrate the relation
0.179 between each two factors that have
significant effect on the measured
0.198
properties.
0.217
0.235
0.254
0.273
0.292
0.310
0.329
0.348
0.366
0.385
0.404
0.423
0.441
Figure 3. Effect of Filament denier and core/sheath ratio on rope bending resistance.
0.143
0.161
0.179
0.197
0.216
0.234
0.252
0.270
0.289
0.307
0.325
0.343
0.362
0.380
0.398
0.416
3.1. Effects on rope bending
resistance
Table 2 shows the regression
analysis of filament denier, primary
strand twist TPM, final strand twist
TPM, and core/sheath% on the
bending resistance of the rope.
It is clear from Table 2 that the
multiple correlation factor is 0.94 at
a very high significant level
(99.99%), which is a very good
correlation. Filament denier, twist in
final strand and core% has strong
significant effect on rope bending
resistance (significance level is
99.9%, 99.7%, and 98.5%
respectively). Twist in primary
strand seems to have no significant
influence on rope bending
resistance. From the Beta values it
is clear that the sequence of the
factors of higher contribution on
bending resistance is: core
percentage, twist in final strand, and
filament denier. Figure 2 shows the
effect of filament denier and twist in
final strand on the bending
resistance of ropes.
It is clear that increasing filament
denier leads to an increase in the
bending resistance at all levels of
twist in final strand, i.e. it increases
the difficulty of bending the rope,
and therefore it is better to reduce
filament denier. It is will known that
reduction of filament denier may
Figure 4. Effect of final strand twist and core/sheath% on rope bending resistance.
lead to an increase in production
cost, so a compromise solution
final strand. The final rope twist was kept constant at 30 TPM
should be taken into consideration so as to select the finest
[turns/m]. Table 1 shows the experimental plan.
filament denier which gives satisfactory bending resistance
at acceptable cost. It is also clear that increasing the twist in
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AUTEX Research Journal, Vol. 8, No4, December 2008 © AUTEX
the final strand leads to an increase in rope bending
resistance up to a certain limit, and then starts to decrease
again at all levels of filament denier, so it is better to apply
less twist in the final strand; which will be more economic,
but its effect on other physical and mechanical properties
should be taken into consideration. The minimum bending
resistance was achieved at lower
filament denier and lower twist in
the final strand. Figure 3 shows the
effect of filament denier and core/
407.059 sheath% on the bending resistance
of ropes.
414.118
421.176
428.235
435.294
442.353
449.412
456.471
463.529
470.588
477.647
484.706
491.765
498.824
505.882
512.941
Figure 5. Effect of filament denier and primary strand twist on rope strength.
406.915
413.829
420.744
427.659
434.573
441.488
448.402
455.317
462.232
469.146
476.061
482.976
489.890
496.805
503.719
510.634
It is clear that increasing core
percentage leads to a decrease in
rope bending resistance to
approximately core/sheath 50/50%,
and then starts to increase again at
levels of filament denier of
approximately 4200. The rate of the
effect of core/sheath on bending
resistance depends on the levels
of filament denier. The minimum
bending resistance was found to be
in the region of 50/50% core/sheath
and low levels of filament denier.
Figure (3) shows the effect of both
twist in the final strand in TPM and
percentage core/sheath on rope
bending resistance. It is clear that
increasing twist levels in the final
strand leads to increasing rope
bending resistance at all levels of
core/sheath%. Increasing core/
sheath% has a slight decreasing
effect on rope bending resistance,
depending on the levels of final
strand twist. The minimum values
were achieved at lower final strand
twist and in the region of 50/
50%core/sheath. In general, from
Figures 2, 3 and 4 it is clear that
better (less) rope bending
resistance could be achieved at low
filament denier, low final strand
twist, and in the region of core/
sheath 50/50%.
3.2. Effects on rope strength
B
of B
t(11)
453.4353
22.1867
20.43717
.0260
.00405
6.42529
.090831
-.4145
.05421
-7.64492
-.202440
.106604
-1.3290
.69983
-1.89898
Table 3 shows the regression
analysis for rope strength. It is clear
from Table 3 that the multiple
correlation factor is about 0.96 at a
very high significant level
(99.999%), which is a very good
correlation. Filament denier, twist in
primary strand and core/
sheath% has strong
significant effect on rope
bending
resistance
(significance level is
99.99%, 99.99%, and
99% respectively). Twist
in final strand has a ‘p’
p-level
value of 0.084, which
.000000
means a significant level
.000049
of 92%; which is not
.000010
statistically significant,
but in the authors’
.084095
-.340805
.111022
-.2586
.08425
-3.06970
.010666
Figure 6. Effect of filament denier and final strand twist on rope strength.
Table 3. Regression analysis for rope strength.
R= .95948441 R²= .92061034 Adjusted R²= .89174137
F(4,11)=31.889 p<.00001 Std.Error of estimate: 6.7258
St. Err.
St. Err.
BETA
of BETA
DINER
.551131
.085775
TPM PRIMS
-.694398
TPM FINLS
CORE%
Intercpt
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114
AUTEX Research Journal, Vol. 8, No4, December 2008 © AUTEX
opinion it is an effect sufficient to be taken into consideration.
Figure 5 shows the effect of filament denier and twist in primary
strand on the bending resistance of ropes.
It is clear that increasing filament denier leads to an increase
in rope strength at all levels of primary strand twist. This effect
is not clear at fine denier, but begins
to become clear at denier levels
from 2600. Increasing primary
strand twist leads to an increase in
443.149 rope strength, but the rate of
increase depends on the levels of
447.952
filament denier. Also this effect is
452.755 clear when denier starts from 2600.
457.558 Maximum strength was achieved at
462.361 both higher deniers and primary
467.165 strand twist.
471.968
476.771
481.574
486.378
491.181
495.984
500.787
505.590
510.394
515.197
Figure 7. Effect of filament denier and core/sheath% on rope strength.
406.143
412.287
418.430
424.574
430.717
436.861
443.004
449.148
455.291
461.435
467.578
473.722
479.865
486.009
492.152
498.296
Figure 8. Effect of primary strand twist and final strand twist on rope strength.
Figure 6 shows the effect of both
filament denier and final strand twist
on rope strength.
It is clear that the relation presents
the ideal saddle shape. Increasing
filament denier, at lower final strand
twist results in increasing rope
strength. This effect is reversed at
higher final strand twist, i.e. there is
an interaction between filament
denier and final strand twist on rope
strength. Increasing final strand
twist at lower filament denier leads
to increasing rope strength. This
effect is reversed at higher filament
denier. Maximum strength is
obtained at higher filament denier
and lower final strand twist. This
result should be compared with that
obtained for bending resistance,
which is that both low filament
denier and final strand twist are
required, so a compromise solution
is necessary. Figure 7 shows the
effect of filament denier and core/
sheath% on rope strength.
Increasing filament denier results
in increasing rope strength at rates
dependent on levels of core/
sheath%. Maximum strength was
achieved at higher levels of filament
denier and at core/sheath% in the
region of 60-70%.
Increasing core/sheath% leads to
an increase in rope strength at lower
levels of filament denier. Figure 8
shows the effect of primary strand
twist and final strand twist on rope
strength.
Table 4. Regression analysis for rope elongation%.
R= .91276083 R²= .83313234 Adjusted R²= .77245319
F(4,11)=13.730 p<.00030 Std.Error of estimate: .78322
St. Err.
St. Err.
BETA
of BETA
DINER
-.463349
.124356
TPM PRIMS
.525107
.131686
Intercpt
B
of B
t(11)
p-level
22.97239
2.583658
8.89142
.000002
-.00176
.000471
-3.72599
.003347
.02517
.006313
3.98757
.002131
TPM FINLS
.351476
.154553
.18533
.081495
2.27414
.043987
CORE%
-.450740
.160958
-.02748
.009811
-2.80035
.017264
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115
Increasing
primary
strand twist leads to an
increase
in
rope
strength, depending on
the levels of final strand
twist. Maximum rope
strength is achieved at
higher levels of both final
and primary strand
twists. This result should
be
taken
into
AUTEX Research Journal, Vol. 8, No4, December 2008 © AUTEX
in terms of the obliquity effect, as in
the case of spun yarns [12].
3.3. Effects on rope elongation%
405.908
411.815
417.723
423.631
429.539
435.446
441.354
447.262
453.169
459.077
464.985
470.892
476.800
482.708
488.616
494.523
Figure 9. Effect of primary strand twist and core/sheath% on rope strength.
Table (4) shows the regression
analysis for rope elongation%.
It is clear from Table 4 that the
multiple correlation factor is
approximately 0.91at a very high
significant level (99.97), which is a
very good correlation. Filament
denier, primary strand twist, final
strand twist and core/sheath% has
strong significant effect on rope
elongation (significance level is
99.7%, 99.8%, 95.7% and 98.3%
respectively). From the Beta values
it is clear that primary strand twist
has the greatest effect on rope
elongation, followed by filament
denier, core/sheath%, and finally
twist in final strand.
Figure 11 shows the effect of
filament denier and twist in primary
strand on rope elongation%. It is
clear that increasing primary twist
leads to an increase in rope
elongation at higher filament denier;
however this effect is reversed at
lower filament denier and low
primary strand twist, and then
begins to increase again at higher
primary strand twist. This means
that there is an interaction between
primary strand twist and filament
denier on rope elongation%.
Maximum rope elongation% was
achieved at higher levels of filament
denier and higher levels of primary
strand twist.
406.013
411.303
416.593
421.883
427.172
432.462
437.752
443.042
448.332
453.621
458.911
464.201
469.491
474.781 It is clear that increasing filament
480.070 denier leads to an increase in rope
485.360 elongation% at a range of lower
levels of filament denier and lower
levels of final strand twist. At higher
levels of final strand twist,
increasing filament denier leads to a decrease in rope
elongation%. Increasing final strand twist in general leads to
an increase in rope elongation%. Higher values of rope
elongation% are achieved at higher levels of final strand twist
and lower levels of filament denier, and lower values of
elongation% can be achieved at higher filament denier at all
levels of final strand twist.
Figure 10. Effect of final strand twist and core/sheath% on rope strength.
consideration in comparing the effect on bending resistance,
which means that final strand twist is required, so a
compromise solution is required. Figure 9 shows the effect
of primary strand twist and core/sheath% on rope strength.
Increasing core/sheath% at higher primary strand twist leads
to an increase in rope strength at higher levels of primary
strand twist, however this trend is reversed at lower primary
strand twist, i.e. there is an interaction between primary strand
twist and core/sheath% on rope strength. Figure 10 shows
the effect of final strand twist and core/sheath% on rope
strength. Increasing final strand twist leads to decreasing
rope strength at all levels of core/sheath%. Increasing core/
sheath% at higher levels of final strand twist leads to a
decrease in rope strength, but at lower primary strand twist
the effect is reversed at core/sheath% above 60-70%. The
effect of final strand twist on rope strength may be explained
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Figure 13 shows the effect of filament denier and core/
sheath% on rope elongation.
Increasing the levels of filament denier leads to a decrease
in rope elongation% at all levels of core/sheath%. The rate of
decrease depends on the levels of core/sheath%. Increasing
core/sheath% leads to a decrease in rope elongation% at
rates that depend on the levels of filament denier. Higher
values of elongation% are obtained at lower levels of filament
116
AUTEX Research Journal, Vol. 8, No4, December 2008 © AUTEX
17.912
18.324
18.735
19.147
19.559
19.971
20.382
20.794
21.206
21.618
22.029
22.441
22.853
23.265
23.676
24.088
Figure 11. Effect of filament denier and primary strand twist on rope elongation.
17.912
18.324
18.735
19.147
19.559
19.971
20.382
20.794
21.206
21.618
22.029
22.441
22.853
23.265
23.676
24.088
strand twist leads to decreasing
rope elongation%. Increasing
primary strand twist leads to
increasing rope elongation% at
rates depending on final strand
twist. Higher values of rope
elongation% are obtained at higher
levels of primary strand twist and at
lower levels of final strand twist.
Lower rope elongation% can be
achieved at higher final strand twist
and at medium range of primary
strand twist.
Figure 15 shows the effect of
primary strand twist and core/
sheath% on rope elongation%.
Increasing the core/sheath% leads
to decreasing rope elongation at
low to medium ranges of primary
strand twists; this effect is reversed
at higher levels of primary strand
twists. Increasing primary strand
twist leads to an increase in rope
elongation% at higher levels of core/
sheath%, but at low levels of core/
sheath% it is seen that increasing
primary strand twist results in a
slight
decrease
in
rope
elongation% in the range of low
levels of core/sheath%; after that it
starts to increase again. This
produces a saddle shape within the
range of medium to higher levels of
core/sheath% and primary strand
twist. Higher values of elongation%
can be obtained at higher primary
strand twists and at higher levels of
core/sheath%.
Figure 16 shows the effect of final
strand twist and core/sheath% on
rope elongation%.
It is clear that increasing final strand
twist leads to increasing rope
elongation% at all levels of core/
Figure 12. The effect of filament denier and twist in final strand on rope elongation.
sheath%. The rate of increase
depends on the levels of core/
sheath%, and higher values of elongation% are obtained at
denier and at low levels of core/sheath%; and lower elongation
higher levels of both final strand twist and higher levels of
is obtained at higher filament denier at all levels of core/sheath
core/sheath%. Lower values of elongation% can be achieved
levels.
at lower levels of final strand twist and at both higher and
lower levels of core/sheath %.
Figure 14 shows the effect of primary strand twist and final
strand twist on rope elongation%.
4. Conclusion
Referring to Table (4), it is clear that final strand twist has a
greater effect on rope elongation% than primary strand twist.
The difference between the two Betas is less high, and the
effect of both twists is complicated to some extent. From Figure
14 it is clear that increasing the final strand twist up to medium
twist levels and at lower primary strand twist will lead to an
increase in rope elongation%; after that however, the trend is
reversed. At medium to higher levels of primary strand twist,
the effects are seen to be different, i.e. increasing the final
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117
1.
lower rope bending resistance can be obtained at
low levels of filament denier at both low and high
levels of final strand twist; at low levels of filament
denier at medium levels of core/sheath%; and at
low levels of final strand twist at medium levels of
core/sheath%.
2.
Higher rope strength can be obtained at different
treatment combinations, which are: higher levels
AUTEX Research Journal, Vol. 8, No4, December 2008 © AUTEX
17.818
18.136
18.454
18.772
19.090
19.407
19.725
20.043
20.361
20.679
20.997
21.315
21.633
21.951
22.269
22.587
Figure 13. Effect of filament denier and core/sheath% on rope elongation.
19.029
19.371
19.713
20.055
20.397
20.739
21.080
21.422
21.764
22.106
22.448
22.790
23.132
23.474
23.816
24.158
Figure 14. Effect of primary strand twist and final strand twist on rope elongation%.
of filament denier at higher levels of primary strand
twist; low levels of final strand twist, higher levels of
filament denier; and medium to higher levels of core/
sheath% (above 50%) at higher levels of filament
denier.
3.
2.
3.
4.
5.
6.
7.
8.
9.
10.
Higher rope elongation% can be obtained at higher
levels of filament denier at higher levels of primary
strand twist; and can also be obtained at higher levels
of final strand twist at low levels of filament denier,
as well as at higher levels of primary strand twists at
medium levels of final strand twist.
11.
12.
References:
1.
13.
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J Martino,”Modern plastic encyclopedia, 1984.
ISO 9554, Fibre ropes-General Specification, 1991.
ISO 1969, Ropes-Polyethylene-Specification, 1990.
ISO 1140, Ropes-Polyamide Specification, 1990.
ISO 1181, Ropes-Manila Specification, 1990.
ISO 1344, Ropes-Polypropylene Specification, 1990.
S Backer and Seo, 3rd Japan-Austria Symposium, Kyoto
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AUTEX Research Journal, Vol. 8, No4, December 2008 © AUTEX
18.998
19.342
19.686
20.029
20.373
20.717
21.061
21.405
21.749
22.093
22.437
22.781
23.124
23.468
23.812
24.156
Figure 15. Effect of primary strand twist and core/sheath% on rope elongation%.
18.468
18.841
19.214
19.587
19.960
20.333
20.706
21.079
21.451
21.824
22.197
22.570
22.943
23.316
23.689
24.062
Figure 16. Effect of final strand twist and core/sheath% on rope elongation%.
14. ASTM, D 1388-64, Standard test methods for stiffness of
fabrics, 1975.
15. JE Booth, “Principles of Textile Testing”, NewnesButterworths, London ,1969.
Acknowledgement
The authors would like to express their sincere appreciation
to the El Sherouk company for synthetic fibres, and Cairo
Egypt for their assistance and financial support for the work of
the present article.
Note:
This paper was accepted for publication in the Proceedings
of the 3rd International Conference of the Textile Research
Division, National Research Centre, which will be held on 24 April 2006 in Cairo, Egypt.
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Reviewed: 5.01.2009
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