Research on mechanical properties of the Siro-spinning triangle using the Finite Element Method

Abstract

Siro-spinning (two-strand yarn spinning) is a new kind of modified ring spinning method, which is achieved by feeding two rovings into the apron zone at a predetermined separation simultaneously. There are three spinning triangles, including two primary spinning triangles and one final spinning triangle, in Siro-spinning. Therefore, in this paper, the quantitative relationships between the mechanical performance of a Siro-spinning triangle and the spinning parameters are investigated by using the Finite Element Method. The finite element model of the Siro-spinning triangle is constructed under the assumption in which the constituent fibers are considered as three-dimensional elastic beam elements with tensile, compressive, torsion, and bending capabilities. Three different cases where the ends of all fibers, the initial strain of all fibers, and the angle between any two adjacent fibers gripped in the front roller nip distribute evenly are discussed. Meanwhile, in each case, three different cases where the initial strains of the shortest boundary fiber, the central fiber, and the virtual fiber on the direction of yarn spinning tension are set as zero are discussed respectively. Then, taking the spinning triangle in Ne40 (14.6 tex) cotton Sirospun yarn as an example, the fiber tension distribution and fiber torsion distribution in the corresponding Siro-spinning triangle with and without fiber buckling are numerical simulated. It is shown that the fiber tension distributions are influenced by the setting of the fiber initial strain, while the magnitudes of fiber tension are not affected. Finally, Ne40 cotton ring yarns were spun on an EJM128K ring spinning machine, and the properties of spun yarns were evaluated and analyzed according to the simulation results.

Keywords

Siro-spinning Finite Element Method fiber tension yarn torque

The spinning triangle is a critical region in staple yarn spinning. Its geometry influences the mechanical performances of fibers in the spinning triangle and determines the qualities of spun yarns directly, such as yarn strength, torque, and hairiness.^1–3 Taking appropriate measures to reduce the spinning triangle and improve the quality of yarn has attracted great interest in yarn spinning recently, using methods such as Siro-spinning.⁴ Siro-spinning is a new spinning method invented by the Division of Textile Industry laboratories of the Commonwealth Scientific and Industrial Research Organization (CSIRO) in Australia and International Wool Secretariat (IWS) together around 1975–1976, which is conducted on a conventional ring frame by feeding two rovings into the apron zone at a predetermined separation simultaneously.⁵ In the spinning process of Siro-spinning, firstly, two rovings are fed into the apron zone at a predetermined separation simultaneously, and two fiber strands come from the draft zone and enter the nip of the front roller. Then, a primary twist is imposed to those two fiber strands, where two smaller primary triangles are produced. Finally, two strands are twisted into a Sirospun yarn by a final twist, and the corresponding final triangle is produced.⁶ That is, Siro-spinning is a modified ring spinning method by dividing the original one-ring spinning triangle into three Siro-spinning triangles, including two primary spinning triangles and one final spinning triangle. Recently, studies on Siro-spinning have attracted greater attention, involving issues such as the convergence twisting point at the final spinning triangle.^7,8

Recently, research on the spinning triangle has attracted greater attention.^1–3,6 The energy method has been one of the most important methods during the investigations of the spinning triangle, since the full description of geometry is not required before hand.⁹ By using the energy method, one theoretical model of fiber tension distribution in a symmetric spinning triangle and corresponding numerical simulations under different yarn counts, twist angles, and spinning tensions have been conducted by Shaikhzadeh.¹⁰ Then, the model was extended to one kind of asymmetric spinning triangle with and without the consideration of fiber buckling by considering the migration of the central fiber at the front nip line.^1,2 Furthermore, taking into account the inclined angle of yarn spinning tension in some new modified ring spinning systems, the model was also extended to this kind of asymmetric spinning triangle.³ Meanwhile, a theoretical model of the fiber tension distributions in the general spinning triangle has been proposed by considering both the inclination angle of the spinning tension and the migration of the axis fiber at the front roller nip according to the principle of minimum potential energy.¹¹ The spinning triangle in a modified ring spinning system where a kind of airflow twisting device, which can produce the twist by high vortex airflow, is employed for improving the twist propagation process of ring spinning system has been studied by Liu and Su.¹² However, some important mechanical properties of the spinning triangle are not considered in these theoretical models, due to the mathematical complexities in formulating fiber bending and torsional strains, such as fiber torsion distribution, etc. Therefore, the quantitative relationships between the mechanical performance of a symmetric ring spinning triangle and the spinning parameters were investigated by using the Finite Element Method (FEM),⁹ and some important theoretical factors ignored previously, including the fiber torsional strain and the frictional contact of fibers with the bottom roller, have been considered. Furthermore, a new generalized FEM model of the spinning triangle was developed in order to analyze the fiber structural and mechanical performance in fabrication of slender yarn structures theoretically.¹³

Motivated by the research works above, this paper attempts to investigate the quantitative relationships between the mechanical performance of a Siro-spinning triangle and the spinning parameters by using the FEM. Three different cases where the initial strains of the shortest boundary fiber, the central fiber, and the virtual fiber on the direction of yarn load are set as zero are discussed. Then, taking the spinning triangle in Ne40 (14.6 tex) cotton Sirospun yarn as an example, the fiber tension distribution and fiber torsion distribution in the corresponding Siro-spinning triangle with and without fiber buckling are numerical simulated.

Siro-spinning triangle modeling

A symmetric geometric model of spinning triangles in Siro-spinning is shown in Figure 1. It is easy to see that there are three spinning triangles, including two primary spinning triangles and one final spinning triangle, in Siro-spinning. Corresponding geometric models of the left and right primary spinning triangles and one final spinning triangle are shown in Figures 2 –4, respectively. Here, w and h are the width and height of the primary triangle, β is the apex angle of the primary triangle, α/2 is the inclination angle of the yarn spinning tension, $θ_{i}$ is the angle between the ith fiber and the central fiber, and n is the fiber number in each fiber strand, that is, there are $2 n$ fibers in the Siro-spinning triangle. $O_{1}$ and $O_{2}$ are the middle point of the nip line of each primary triangle, $C_{1}$ and $C_{2}$ are the twisting point of each fiber strand, and $F_{1}$ and $F_{2}$ are the spinning tension of each fiber strand. The final spinning triangle is shown in Figure 4. Here, C is the twisting point of the final spun yarn, F is the yarn spinning tension, which can be measured using a tension tester directly, and α is the apex angle of the final triangle.

Figure 1.

A symmetric geometric model of spinning triangles in Siro-spinning.

Figure 2.

A geometric model of the left primary triangle.

Figure 3.

A geometric model of the right primary triangle.

Figure 4.

A geometric model of the final triangle.

According to force balance in Figure 4, we know

F_{1} \cos (\frac{α}{2}) + F_{2} \cos (\frac{α}{2}) = F

(1)

F_{1} \sin (\frac{α}{2}) = F_{2} \sin (\frac{α}{2})

(2)

Then, we have

F_{1} = F_{2} = F \frac{\sin (\frac{α}{2})}{\sin α}

(3)

In order to investigate the mechanical performance of a Siro-spinning triangle by using the FEM, the following assumptions are made.^1–3

Assumption 1.^1,3 The cross-section of all fibers is a circle with identical diameters. All fibers are gripped between the front roller nip and the twisting point. The velocity of fibers in the spinning triangle is constant, and the delivery velocities of fibers and yarn are the same. The stress–strain behavior of the fibers follows Hooke's law for small strain.

Assumption 2.² All the fibers are ideally packed in the yarn cross-section in concentric circular rings, where there are single core fibers at the center around which six fibers are arranged. Then, the number of fibers arranged in each layer is given by

{N_{j} = 1 j = 1 N_{j} = 6 (j - 1) j \geq 2

(4)

where

N_{j}

is the fiber number in the jth layer.

Assumption 3. It is assumed that half of the apex angle α is equal to the helical angle of the surface fibers of spun yarn.⁹ For an idealized yarn structure with a single-fiber core and closed packing of circular fibers, the surface helical angle can be calculated as follows:¹⁴

\tan (\frac{α}{2}) = 2 π r_{1} T_{1}

(5)

Here, $r_{1}$ is the radius of the final Sirospun yarn and $T_{1}$ is the twist of the final Sirospun yarn.

Assumption 4. The fibers in the primary spinning triangles are considered as three-dimensional (3D) elastic beam elements with tensile, compressive, torsional, and bending capabilities. The beam element, which exhibits a uniaxial line feature and has six structural degrees of freedom at each node, is chosen to represent the fiber. Meanwhile, all the degrees of freedom of the points of fibers on the front roller nip line are constrained.⁹

In the following, the spinning triangle of Ne40 Sirospun yarn will be analyzed. The material properties of cotton include the fiber elastic modulus

E = 5 N / tex

, fiber shear modulus

G = 1.351 N / tex

, fiber radius

r = 0.008 mm

, fiber strand radius

r_{2} = 0.0495 mm

, final Sirospun yarn radius

r_{1} = 0.0715 mm

, and number of fibers in the Siro-spinning triangle

2 n = 114

. The other simulation parameters are listed in Table 1.

Table 1.

Simulation parameters

Yarn twist (tpm)	α(°)	w(mm)	h(mm)	F(cN)	$F_{1} = F_{2}$ (cN)	M(cN.mm)
360	45.3	1.1	3.83	20	10.8	2.14
				40	21.6	4.28
				60	32.5	6.44

In Table 1, M is the initial torque applied on two fiber strands produced by the fiber strand load, which can be calculated by

M = 2 F_{1} r_{2} + 2 F_{2} r_{2}

(6)

Simulation results

In this section, the quantitative relationships between the fiber tension and torque in a Siro-spinning triangle and the spinning parameters will be investigated by using the FEM. The spinning triangle of Ne40 Sirospun yarn will be analyzed. Three different cases will be investigated.

The ends of all fibers gripped in the front roller nip distribute evenly

In this case, the ends of all fibers are supposed to be distributed evenly in the front roller nip. That is, $w_{1} = w / n$ , where $w_{1}$ is the distance between two adjacent fibers at each primary triangle. Three different cases will be discussed.

Case 1: the initial strain of the shortest fiber setting as zero

In this case, we suppose that the initial strain of the shortest fiber is zero. That is, the initial strain of the right boundary fiber in the left primary triangle (see Figure 5(a)) and the left boundary fiber in the right primary triangle (see Figure 5(b)) are set as zero.

Figure 5.

Primary triangles: (a) left primary triangle; (b) right primary triangle.

Case 2: the initial strain of the virtual vertical fiber setting as zero

In this case, we suppose that the initial strain of the virtual vertical fiber in the left primary triangle (see Figure 6(a)) and right primary triangle (see Figure 6(b)) are set as zero.

Figure 6.

Primary triangles: (a) left primary triangle; (b) right primary triangle.

Case 3: the initial strain of the middle fiber setting as zero

In this case, we suppose that the initial strain of the middle fiber in the left primary triangle (see Figure 7(a)) and right primary triangle (see Figure 7(b)) are set as zero.

Figure 7.

Primary triangles: (a) left primary triangle; (b) right primary triangle.

The initial strain of fibers with three different cases is shown in Figure 8. It is shown that the initial strain of fibers in Case 2 is the largest, the initial strain of fibers in Case 1 takes the second place, and the initial strain of fibers in Case 3 is the smallest. However, the magnitudes of fiber initial strain in the three different cases are similar.

Figure 8.

Initial strain.

The fiber tension distributions are given by using the FEM as shown in Figure 9 when the fiber buckling is not considered and Figure 10 when the fiber buckling is considered. Figure 9 shows the fiber tension at different spinning tensions of 20, 40, and 60 cN with three different cases. In Figure 9, it is shown that with an increase of spinning tension, the fiber tension at each position of the Siro-spinning triangle is constantly increased. Therefore, the maximum value of spinning tension in the actual spinning should be well controlled in order to avoid fiber breakage in the Siro-spinning triangle. Meanwhile, compared with the Case 1, for all three spinning tensions, fiber tensile forces in Case 2 are increased while fiber compressive loadings are decreased, that is, the magnitudes of fiber tensions are increased, and fiber tensile forces in Case 3 are decreased while fiber compressive loadings are increased, that is, the magnitudes of fiber tensions are decreased. The possible reason is that compared with the initial strain of fibers in Case 1, initial strain of fibers is larger in Case 2, and is smaller in Case 3.

Figure 9.

Fiber tensions under different spinning parameters without fiber buckling.

Figure 10.

Fiber tensions under different spinning parameters with fiber buckling.

Figure 10 shows the fiber tension at different spinning tensions of 20, 40, and 60cN with three different cases when the fiber buckling is considered. Compared with the case where fiber buckling is not considered (see Figure 9), fiber tensile forces are reduced greatly in the case with fiber buckling considered (see Figure 10). This is because when the fiber buckling is considered, most compressive loadings acting on the central compressive fibers are released, leading to the reduced tensile forces of other fibers.⁹ In Figure 10, it is also shown that with an increase of spinning tension, the fiber tensile force at each position of the Siro-spinning triangle is constantly increased. Meanwhile, compared with Case 1, for all three spinning tensions, the tensile forces of the outer fibers in Case 2 are increased while tensile forces of the outer fibers in Case 3 are decreased slightly. However, compared with the case where the fiber buckling is not considered, the effect of the fiber initial strain distribution on fiber tension distributions is less.

Furthermore, considering the case without fiber buckling, Figure 11 shows a comparison of the fiber tension distribution calculated by the proposed FEM model in this paper and the energy model by our earlier theoretical model⁶ in Case 3. It is shown that the FEM results are generally slightly smaller than the results with the energy method and both the trend of curves and the numerical values of fiber tension distribution are in a good agreement.

Figure 11.

Fiber tensions under different spinning tensions.

In the following, the effects of spinning parameters on fiber torque distributions will be investigated. By applying the initial torque on two fiber strands produced by the fiber strand load, the fiber torque distributions are given in Figure 12 by using the FEM when the fiber buckling is not considered and Figure 13 when the fiber buckling is considered correspondingly, and the total fiber torque (yarn torque) is given in Table 2. As shown in Figures 12 and 13, it is apparently noted that with the increase of spinning tension, fiber torque is obviously increased, and the effect of the fiber initial strain distribution on fiber torque distributions is tiny. That is, the fiber torque distributions in all three cases are almost same. As shown in Table 2, it is also easy to see that with the increase of spinning tension, yarn torque is increased, and the yarn torques in all three different cases are almost same.

Figure 12.

Fiber torques under different spinning parameters without fiber buckling.

Figure 13.

Fiber torques under different spinning parameters with fiber buckling.

Table 2.

Yarn torque (cN.mm)

		F = 20 cN	F = 40 cN	F = 60 cN
Case 1	Without fiber buckling	1.34	2.67	4.01
Case 1	With fiber buckling	0.892	1.91	3.13
Case 2	Without fiber buckling	1.34	2.67	4.01
Case 2	With fiber buckling	0.892	1.91	3.13
Case 3	Without fiber buckling	1.34	2.67	4.01
Case 3	With fiber buckling	0.892	1.99	3.25

The initial strain of all fibers gripped in the front roller nip distributes evenly

In this case, the initial strain of all fibers is supposed to be distributed evenly in the front roller nip. That is, $ɛ_{1} = ɛ / n$ , where $ɛ_{1}$ is the initial strain difference between two adjacent fibers at each primary triangle, ɛ is the initial strain of the left boundary fiber (right boundary fiber) in the left (right) primary spinning triangle, and can be calculated according to the geometric parameters of the spinning triangle. Three different cases will be discussed.

The initial strain of fibers with three different cases is shown in Figure 14. It is also shown that the initial strain of fibers in Case 2 is the largest, the initial strain of fibers in Case 1 takes second place, and the initial strain of fibers in Case 3 is the smallest. However, the magnitudes in the three different cases are similar.

Figure 14.

Initial strain.

By using the FEM, the fiber tension distributions with different spinning parameters are given in Figure 15 without fiber buckling and Figure 16 with fiber buckling. Figure 15 shows the fiber tension at different spinning tensions of 20, 40, and 60 cN with three different cases. In Figure 15, it is also shown that with an increase of spinning tension, the fiber tension at each position of the Siro-spinning triangle is constantly increased. Meanwhile, compared with the Case 1, for all three spinning tensions, the magnitudes of fiber tensions in Case 2 are increased, while the magnitudes of fiber tensions in Case 3 are decreased. Meanwhile, compared with the case in the section titled The ends of all fibers gripped in the front roller nip distribute evenly, the value of fiber tension at each position is decreased slightly in this case.

Figure 15.

Fiber tensions under different spinning parameters without fiber buckling.

Figure 16.

Fiber tensions under different spinning parameters with fiber buckling.

Figure 16 shows the fiber tension at different spinning tensions of 20, 40, and 60 cN with three different cases when the fiber buckling is considered. It is also shown that with an increase of spinning tension, the fiber tensile force at each position is constantly increased. Compared with the case where fiber buckling is not considered (see Figure 15), fiber tensile forces are also reduced greatly in the case with fiber buckling considered (see Figure 16). Meanwhile, compared with the Case 1, for all three spinning tensions, the tensile forces of the outer fibers in Case 2 are increased while tensile forces of the middle nonzero fibers are the same. Tensile forces of the outer fibers in Case 3 are the same and tensile forces of the middle nonzero fibers are decreased. However, compared with the case where the fiber buckling is not considered, the effect of the fiber initial strain distribution on fiber tension distributions is also less when the fiber buckling is considered.

The fiber torque distributions are given without fiber buckling in Figure 17 and with fiber buckling in Figure 18, and corresponding yarn torque is given in Table 3. As shown in Figures 17 and 18, it is also apparently shown that with the increase of spinning tension, fiber torque is increased greatly. Compared with the case in the section titled The ends of all fibers gripped in the front roller nip distribute evenly, the effect of the fiber initial strain distribution on fiber torque is more significant. As shown in Figure 17, compared with Case 1, for all three spinning tensions, fiber torque at each position in Case 2 is decreased slightly, while in Case 3 it is increased slightly, which causes the corresponding change of yarn torque (see Table 3). As shown in Figure 18, compared with the Case 1, for all three spinning tensions, fiber torque at each position in Case 2 is almost same, while fiber torque at each position in Case 3 is increased slightly, but the number of nonzero fibers is decreased, which makes the yarn torque almost unchanged (see Table 3). Meanwhile, compared with the yarn torque calculated in the section titled The ends of all fibers gripped in the front roller nip distribute evenly, yarn torque is decreased slightly when the fiber buckling is not considered, while it is the same when the fiber buckling is considered.

Figure 17.

Fiber torques under different spinning parameters without fiber buckling.

Figure 18.

Fiber torques under different spinning parameters with fiber buckling.

Table 3.

Yarn torque (cN.mm)

		F = 20 cN	F = 40 cN	F = 60 cN
Case 1	Without fiber buckling	1.31	2.63	3.94
Case 1	With fiber buckling	0.893	1.98	3.11
Case 2	Without fiber buckling	1.31	2.62	3.92
Case 2	With fiber buckling	0.889	1.9	3.1
Case 3	Without fiber buckling	1.33	2.66	3.99
Case 3	With fiber buckling	0.889	1.91	3.12

The angle between any two adjacent fibers gripped in the front roller nip distributes evenly

In this case, the angle between any two adjacent fibers is supposed to be distributed evenly in the front roller nip. That is, $θ_{1} = θ / n$ , where $θ_{1}$ is the angle between two adjacent fibers and θ is the angle between the left boundary fiber and the right boundary fiber in the left or right primary spinning triangle, which can be calculated according to the geometric parameters of the spinning triangle. Three different cases will be discussed.

The initial strain of fibers with three different cases is shown in Figure 19. It is also shown that the initial strain of fibers in Case 2 is the largest, the initial strain of fibers in Case 1 takes second place, and the initial strain of fibers in Case 3 is the smallest. However, the magnitudes in the three different cases are similar.

Figure 19.

Initial strain.

By using the FEM, the fiber tension distributions with different spinning parameters are given in Figure 20 without fiber buckling and Figure 21 with fiber buckling. Figure 20 shows the fiber tension at different spinning tensions of 20, 40, and 60 cN with three different cases. In Figure 20, it is also shown that with an increase of spinning tension, the fiber tension at each position of the Siro-spinning triangle is constantly increased. Meanwhile, compared with the Case 1, for all three spinning tensions, the magnitudes of fiber tensions in Case 2 are increased, while the magnitudes of fiber tensions in Case 3 are decreased. Meanwhile, compared with the case in the section titled The ends of all fibers gripped in the front roller nip distribute evenly, the value of fiber tension at each position is almost the same when the fiber buckling is not considered, while it is increased slightly when the fiber buckling is considered. Compared with the case in the section titled The initial strain of all fibers gripped in the front roller nip distributes evenly, the value of fiber tension at each position is increased slightly.

Figure 20.

Fiber tensions under different spinning parameters without fiber buckling.

Figure 21.

Fiber tensions under different spinning parameters with fiber buckling.

Figure 21 shows the fiber tension at different spinning tensions of 20, 40, and 60 cN with three different cases when the fiber buckling is considered. It is also shown that with an increase of spinning tension, the fiber tensile force at each position is constantly increased. Compared with the case where fiber buckling is not considered, fiber tensile forces are also reduced greatly in the case with fiber buckling considered. Meanwhile, compared with Case 1, for all three spinning tensions, the tensile forces of the outer fibers in Case 2 are increased and tensile forces of the middle nonzero fibers are the same, while tensile forces of all nonzero fibers in Case 3 are decreased. However, compared with the case where the fiber buckling is not considered, the effect of the fiber initial strain distribution on fiber tension distributions is also less.

The fiber torque distributions are given without fiber buckling in Figure 22 and with fiber buckling in Figure 23, and the corresponding yarn torque is given in Table 4. As shown in Figures 22 and 23, it is also apparently noted that with the increase of spinning tension, fiber torque is obviously increased. Meanwhile, the effect of the fiber initial strain distribution on fiber torque distributions is tiny, that is, the fiber torque distributions in all three cases are almost same, which is the same as in the section titled The ends of all fibers gripped in the front roller nip distribute evenly. As shown in Table 4, it is also easy to see that with the increase of spinning tension, yarn torque is increased, and the yarn torques in all three different cases are changed little. Meanwhile, compared with the yarn torque calculated in the sections titled The ends of all fibers gripped in the front roller nip distribute evenly and The initial strain of all fibers gripped in the front roller nip distributes evenly, yarn torque is increased slightly.

Figure 22.

Fiber torques under different spinning parameters without fiber buckling.

Figure 23.

Fiber torques under different spinning parameters with fiber buckling.

Table 4.

Yarn torque (cN.mm)

		F = 20 cN	F = 40 cN	F = 60 cN
Case 1	Without fiber buckling	1.36	2.71	4.07
Case 1	With fiber buckling	0.909	2.01	3.19
Case 2	Without fiber buckling	1.36	2.71	4.07
Case 2	With fiber buckling	0.867	2.01	3.28
Case 3	Without fiber buckling	1.36	2.71	4.07
Case 3	With fiber buckling	0.909	2.01	3.19

Spinning experiments

In this section, for evaluating the simulation results above, Ne40 cotton ring yarns were spun on an EJM128K ring spinning machine. The detailed spinning parameters are shown in Table 5. Combed roving of 360 tex (Ne1.62) was used as the raw material. The test instruments are as follows: single yarn tester YG068C, hairiness tester YG173A, and evenness tester Uster tester 5 S-800. All the samples were conditioned for at least 48 hours under standard conditions before testing (65 ± 2% relative humidity (RH) and 20 ± 2℃). The measured properties of Sirospun yarn are shown in Table 6.

Table 5.

Spinning parameters

Case	Spinning tension	Yarn twist (tpm)	Distance between two feeding bell mouths (mm)	Spindle speed (r/min)	Traveler
1	20	360	2	10,000	Bracker5/0
2	40			12,000
3	60			14,000

Table 6.

Measured properties of Sirospun yarn

Case	Breaking strength/cN	Evenness CV/%	Hairiness/H	Snarling /25 cm
1	294.5	11.03	4.41	78
2	298.1	10.99	4.67	84
3	289.5	11.22	4.73	89

Hairiness is one of the most important properties of the spun yarn. In the spinning triangle, there is difference of tensions between the central fibers and boundary fibers, which makes the migration between the internal fibers and external fibers and the head and tail of some fibers unable to roll into the yarn body easily and hairiness is formed. Therefore, the larger tension forces acting on the outer fibers in the spinning triangle would lead to the reduction of hairiness.¹⁵ According to the numerical simulation results above, although the tensions of outer fibers are increased slightly with increasing spinning tension, fiber compressive loading of inner fibers is also increased, which makes the fibers migrate in the yarn body more easily, and leads to possible increase of yarn hairiness (see Table 6).

One kind of self-made tester is made for measuring yarn residual torque. Firstly, the yarn sample is placed at the standard atmospheric condition over 24 hours. Then, a 50 cm yarn sample with two ends clamped and 0.02 cN/tex loads are applied at the middle of sample, and the two ends are joined with each other. Finally, the sample is placed in water for some time, and the number of snarlings is used to characterize the yarn residual torque.⁶ As shown in Table 6, the number of yarn snarls is constantly increased with an increase of spinning tension, indicating an increase of the residual torque of spun yarns, which is consistent with the calculated results using the FEM in the Simulation results section.

Conclusion

In this paper, by using the FEM, the quantitative relationships between the mechanical performance of a Siro-spinning triangle and the spinning parameters have been discussed. One potential parameter ignored previously, the fiber initial strain distribution, is taken into consideration. Three different cases where the ends of all fibers, the initial strain of all fibers, and the angle between any two adjacent fibers gripped in the front roller nip distribute evenly have been discussed. Meanwhile, in each case, three different cases where the initial strains of the shortest boundary fiber, the central fiber, and the virtual fiber on the direction of yarn load are set as zero have been discussed respectively. In addition, the obtained results of fiber tension in the Siro-spinning triangle using the FEM model are validated by comparing it with the theoretical results obtained in our earlier study.

Taking the spinning triangle in Ne40 cotton Sirospun yarn as an example, the numerical simulations of fiber tension distribution and fiber torsion distribution in the corresponding Siro-spinning triangle with and without fiber buckling have been given. The results show that the setting of the initial strain of fibers has important influences on the fiber tension distribution and yarn torque distribution. The fiber tension distributions are influenced by the setting of the fiber initial strain, while the magnitudes of fiber tension are not affected. Meanwhile, the results showed that comparing with the case that the fiber buckling is not considered, the setting of the fiber initial strain has a more obvious effect on fiber torque distributions and yarn torque when the fiber buckling is considered.

Footnotes

Funding

This work was supported by the National Natural Science Foundation of P. R. China under Grant 11102072, the Natural Science Foundation of Jiangsu Province under Grant BK2012254, Prospective industry-university-research project of Jiangsu Province BY2014023-13, the Fundamental Research Funds for the Central Universities (No. JUSRP51301A).

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