Mechanic Modelling of the tenacity: Application for the Ring and Open End plied yarns.

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Author: F.ZAGHOUANI, M.BEN HASSEN, A.DOGUI and M.CHEIKHROUHOU.

Mechanic Modelling of the tenacity: Application for the Ring and Open End plied yarns.

F.ZAGHOUANI, M.BEN HASSEN, A.DOGUI and M.CHEIKHROUHOU.

Textile Research Unit of ISET Ksar Hellal, B.P 68 Ksar Hellal 5070, TUNISIA.

Abstract: This work presents an analysis of a mechanical model for cotton plied yarns tenacity. Results show that the tenacity of a plied yarn depends on the parameters of twisting and the linear density. For verification of the theory, we have also applied this model for the ring and Open End plied yarns. Comparison between experimental data and theoretical predictions showed that the predicted yarn tenacity is in reasonable agreement with experiment results.

Key words: cotton, tenacity, plied yarn, twisting, ring-spinning, rotor spinning, mechanical model.

Introduction Yarn folding is an operation of spinning mill which aims to join two or several yarns of the same or the different nature and to confer them a twisting in one or several operations to improve the strength, the regularity and the yarn aspect. Much research has been carried out on modelling the dependencies between the structure of fibre and the parameters of yarns. X.SHAO [1] analyzed a mechanics model which studies the deformation of the textile yarn during the breaking. He presented a model stress-extension which describes the behaviour of fibers in a yarn during the increase and the decrease of the stress. Treloar [2] determined the length of the single yarn in the structure of the plied yarn. This researcher was interested in the behaviour of the plied yarns according to the properties of fibers which compose them. W.B.FRASER [3] presented a mathematical model which describes the phenomenon of twisting. This model presents equations of tensile and moment of twisting of elastics plied yarns according to the parameter of twisting and of the density of the single yarn. He noticed that his model can be applied for a plied yarn of n single yarns. Neckar [4] modelled the fibre arrangement in the yarn cross-sec¬tion. Göktepe and Lawrence [5] analysed the deformations of yarn cross-sections in dependence on the fibre structure. Baykal and Babaarslan [6] predicted the tenacity and elongation at break of cotton/polyester rotor yarn blends on the basis of fibre parameters. Jiang and Chen [7] used geometrical and alge¬braic algorithms for modelling yarns dedicated to woven products. Das and Ishiaque [8] applied artificial neuron networks to predict the properties of ro¬tor yarns.

The aim of our work is to propose a theoretical model of the tenacity of a plied yarn from the tenacity of the single yarn, the linear density and the twisting parameters. In second time, we applied our study for the Ring and Open End plied yarns of cotton.

Theoretical Modelling of the tenacity: The initial geometry of two assembled yarns is chosen as being that of two right single yarns with a defined length. The twisting applied to the two assembled yarns changes the right profiles of the single yarns in helical profiles in a plied yarn. The approach undertaken in this study is shown in figure 1.

Figure 1: Geometry of the profile of the single yarn in the plied yarn.

M (θ, z) is the point of the helix of the single yarn, ( ) Being a cylindrical coordinate such as, we have during the break of plied yarns: (1) The vector (2) ds is the element of the plied yarn during the loading: ds= (3) The tangent vector of the plied yarn is defined by the following relation: ; (4) With, (5)

Figure 2: The forces acting on the plied yarns during the loading. According to the figure 2; we are the breaking force of plied yarn: Such as: and (6) : The breaking force of single yarn 1 and : The breaking force of single yarn 2. We suppose that for each type of the ring and the Open End plied yarns, the singles yarns have the same properties. And they have the same profile of the helix, so the parameters of two helixes 1 and 2 are identical. So, we have and F1=F2; with R1, P1, and θ1: the parameters of helix of single yarn 1; R2, P2, θ2: the parameters of helix of single yarn 2. R: The radius of helix, : The pitch of helix during the loading ; with ; αRNm : The coefficient of twisting ; ε(%) : The deformation of single yarns; Tf(tex) : The linear density of single yarn. And θ: The angle of helix. (7) (8) (9) Where from, (10) (11) The stress of the plied yarn is given by the following relation: (12) For the single ring and Open End yarn, we have the stress Where from, we have a mechanic model which expresses the stress of the plied yarns according to the stress of single yarn which forming this plied yarns. (13) Or the tenacity of single yarn is given by the following relation: Ten1 = ; we suppose that the yarn have a cylindrical shape with ρ: The density of single yarn, Ten1: The tenacity of single yarn and Tf : The linear density of single yarn. Where from, (14) And (15) Where from, the tenacity of plied yarn is given by the following relation: With, : The density of plied yarns; TR(tex)=2*Tf(tex): The linear density of plied yarns. So, we have: (16) As a result, (17) In this paper, we supplied an important estimate formula of the tenacity of plied yarns according to the geometry of the single yarn in a plied yarn during the loading.

Results and model verification: Materials and methods: Table I gives a summary of the cotton fibers characteristics used to produce the plied yarns and which were measured by the High Volum Instrument. Table I: Cotton properties. Micronaire Index(μg/inch) 4,25 Maturity 0,89 Mean length (mm) 28,32 Uniformity (%) 82 Tenacity (CN/Tex) 32,1 Yellow colour ( b ) in (%) 9,3 Réflectance (Rd) (%) 75,3 Short fiber count SFI(%) 9,5 Elongation (Elg)(%) 7,5 (trash count) (%) 11

In this research, Two types of plied yarns are discussed: the first, ring plied yarns (R) is composed of two ring spun yarns while the second, Open End plied yarns (OE) is composed of two Open End yarns. The twist direction of single yarn is Z and the twist direction of plied yarn is S. Ring spun yarns (R) were produced on spinning machine type ZINSER 321. Autocorner Schlafhorst -338 was used for the operation of winding. Rotor yarns (OE) were produced by using Autocoro Schlafhorst of type ACO 240U/288. Assembly and twisting operations were carried out respectively on "SSM" machine and the Two-for-one yarn folding machine Volkmann of the VTS-07 type with a constant speed. The mechanical properties of single and plied yarn were tested by the USTER TENSORAPID whereas: unevenness, hairiness were controlled by using the USTER TESTER 3. Table II gives a summary of the test results for ring and Open End singles yarns.

Table II: Single spun yarn properties. Type of single yarns Tf(tex) αSNm Radii R1(mm) Density (g/mm3) unevenness Cv(%) hairiness Elongation (%) Tenacity (cN/Tex) OE 40 125 0,128 0,77751 13,27 9,31 7,241 11,180 OE 40 135 0,124 0,82848 13,05 10,57 6,77 11,860 OE 40 145 0,119 0,89957 13,01 9,30 6,158 10,050 OE 50 125 0,127 0,98726 13,03 8,29 6,00 9,745 OE 50 135 0,123 1,05251 13,27 9,16 7,33 12,120 OE 50 145 0,158 0,63786 14,37 9,30 7,275 11,040 OE 60 125 0,127 1,18471 14,16 9,20 6,772 11,575 OE 60 135 0,168 0,67702 14,58 7,65 6,921 10,525 OE 60 145 0,165 0,7018 14,41 7,89 6,621 11,420 R 40 110 0,12 0,88464 14,21 7,94 5,596 13,371 R 40 120 0,118 0,91488 13,55 7,39 6,561 14,312 R 40 130 0,116 0,94670 13,73 7,12 5,924 13,852 R 50 110 0,129 0,95688 16,32 7,28 6,240 12,382 R 50 120 0,127 0,98726 16,27 6,96 7,130 14,441 R 50 130 0,178 0,50257 16,47 6,62 5,712 13,441 R 60 110 0,129 1,14826 16,47 6,55 5,520 13,121 R 60 120 0,182 0,576 16,71 6,36 5,324 13,450 R 60 130 0,157 0,775 18 6,31 5,917 14,70

Table III gives a summary of the tenacity results for ring and Open End plied yarns.

Tableau III: Experimental tenacity of plied yarns. Type of plied yarns Tf(tex) αSNm αRNm Tenacity (cN/tex) Ring plied yarns (R) 80 110 130 18,67 80 120 140 18,87 80 130 150 19,02 100 110 140 18,38 100 120 150 19,54 100 130 130 17,74 120 110 150 19,825 120 120 130 17,9333 120 130 140 18,591 Open End plied yarns OE 80 125 130 15,12375 80 135 140 16,2925 80 145 150 16,5875 100 125 140 15,54 100 135 150 15,87 100 145 130 15,16 120 125 150 15,5833 120 135 130 14,4666 120 145 140 15,0166

The theoretical model was used to predict the tenacity of plied yarns listed in table III. Figures 3 to 8 show the experimental and predicted tenacity of the ring and the Open End plied yarns.

*For the ring plied yarns:

Figure 3: Comparison between theoretical and experimental Ten Plied yarn of the ring plied yarns of linear density= 80 tex.

Figure 4: Comparison between theoretical and experimental Ten Plied yarn of the ring plied yarns of linear density= 100 tex.

Figure 5: Comparison between theoretical and experimental Ten Plied yarn of the ring plied yarns of linear density= 120 tex.

*For the Open End plied yarns :

Figure 6: Comparison between theoretical and experimental Ten Plied yarn of the Open End plied yarns of linear density = 80 tex.

Figure 7: Comparison between theoretical and experimental Ten Plied yarn of the Open End plied yarns of linear density = 100 tex.

Figure 8: Comparison between theoretical and experimental Ten Plied yarn of the Open End plied yarns of linear density = 120 tex.

According to these figures, the comparison between the experimental and theoretical results shows that the predictions of plied yarns tenacity are reasonable. We can notice that: - The tenacity of plied yarns is expressed according to the tenacity of a single yarn; indeed, for the thin yarn of cotton, we estimate that: . And for the middle yarn, we estimate: . - Mathematical formulation established of Ten Plied yarn help to foresee in theory the tenacity of the plied yarns and to compare the mechanics behaviour of various structures. In fact, the ring plied yarns are more resistant than Open End plied yarns. - The coefficient of twist and the linear density of the plied yarns have a very important influence on the tenacity of the ring and Open End plied yarns. - The increase of coefficient of twist gives an improvement of the tenacity of plied yarns. - The decrease of linear density of the yarns gives an increase of the tenacity of the plied yarns. These explanations are in complete coherence with industrial practices and realized research works concerning the twisting [1, 2 and 3].

Conclusions: The plied yarn tenacity varies with coefficient of twisting and linear density, within, according to the formula of the tenacity; we can notice that Ten Plied yarn depends: - Of the division between the density of the single and the plied yarns. - Of diameter of the yarn, indeed, more the linear density of plied yarns increases more tenacity decreases. - Of the coefficient of twisting αRNm, in fact, the increase of αRNm leads to an increase of plied yarns tenacity. Comparison between experimental data and theoretical predictions showed that the predicted yarn tenacity is in reasonable agreement with experiment results.

References: [1] : X.Shao, Y.Qiu and Y.Wang. "Theoretical modelling of the tensile behaviour of low-twist staple yarns: Part II- theoretical and experimental results", The Journal of Textile Institute, vol 96, N°2, (2005) pp 69-76, [2] :Treloar, L.R.G. "The stress-strain properties of multiply cords", Part 1. Theory, Journal of Textile Institute, 1965 b vol 56, T 477. [3] : W.B.Fraser."Air drag and friction in the two-for-one twister: Results from the theory", Journal Textile Institute, vol 84 1993 n°3 p 364-373. [4] : Neckar B., Soni M.K. and Das D. 'Modelling of Radial Fiber Migration in Yarns,' Textile Research Journal, vol. 76, 2006, No. 6, pp. 486-491. [5] : Göktepe E., Lawrance C.A. 'Deformation of Yarn Cross-Section in Relation to Yarn Structure.' Fibres & Textiles in Eastern Europe, 2001, vol. 9, No. 2. pp. 18-22. [6] : Baykal P. D., Babaarslan D., Erol R., 'Pre¬diction of Strength and Elongation Proper¬ties of Cotton-Polyester-Blended OE Ro¬tor Yarns'. Fibres and Textiles in Eastern Europe, vol. 14, 2006, No.1, p:18-21. [7] : Jiang Y.,Chen X. 'Geometric and algebra¬ic algorithms for modelling yarn in woven fabrics.' Textile Research Journal, vol. 96, 2005, No 4, pp. 237-245. [8] : Das D., Ishiaque S.M., Veit D., Gmes T. 'Application of artificial neural network to predict rotor spun yarn properties'. Mel¬liand International 2004, No. 3, p. 183.