AUTEX Research Journal, Vol. 8, No4, December 2008 Š 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: azizsharrouf@yahoo.com
2
Textile Division, National Research Centre, Egypt e-mail: monamsalem@yahoo.com
El Sherouk for Synthetic Fibres Co, Ropes Dept. Cairo Egypt, e-mail: azizsharrouf@hotmail.com
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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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 http://www.autexrj.org/No4-2008/ 0228.pdf
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 Š 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 http://www.autexrj.org/No4-2008/ 0228.pdf
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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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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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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
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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 http://www.autexrj.org/No4-2008/ 0228.pdf
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
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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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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
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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.
M Kamel, “ History of ancient Egyptians arts”, Madbuly Publisher Co, Cairo, 1991.
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Z Escandar, “Industrial material used by ancient Egyptians” Madbuly Publisher Co, Cairo, 1991. M Gad, “Improvement of the functional performance of polyethylene ropes” Ph.D, Faculty of applied arts, 1999. 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 Japan, 5-7 Sep,1985. Hwai Chung Wu, JTI, 1993,84,No.2 p199-213 JWS Hearle, “Structural mechanics of fibres, yarns, and fabrics”, Wiley Interscience, New York, 1969. WJ Person, “Modern plastic encyclopedia”, 1988.
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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. http://www.autexrj.org/No4-2008/ 0228.pdf
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Reviewed: 5.01.2009
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