Simulation and analysis of the twist propagation process of polyester staple yarn on the fiber scale

Abstract

The twisting process of the sliver is an important part of the yarn spinning process, but this process has not been fully characterized on the fiber scale. Herein, based on the assumption that fibers are randomly distributed in the sliver, we analyzed the simulation twisting process of the sliver model on the fiber scale. The mathematical model of the twisting process of the sliver is set up and the non-free-end twisting process is simulated using the finite element software ABAQUS®. The simulation process clearly shows the configuration changes of the sliver caused with the increase of the twist. We also divided the twisting process into 11 stages and obtained a three-dimensional model of staple yarn. Then, the relationship curve between the ring-spun yarn fineness and the number of fibers in the cross-section of the ring-spun yarn was established by spinning the yarns of different counts of 20, 25, 30, 35, 40, 45, 50, 55, 60 and 65 Ne, and the fineness of the simulated yarn was calculated. The accuracy of the simulated yarn was verified by comparing the weight of the simulated yarn and the ring-spun yarn. The model established can be used to predict yarn properties for different purposes and can also be further utilized to study other phenomena in ring-spinning technology.

Keywords

polyester fiber twist propagation staple yarn simulated twisting yarn fineness

In the spinning process, the twisting process gives the yarn a specific appearance and physical properties, especially staple yarn. In the spinning process of staple yarn, many discrete fibers are directly twisted by the twisting force or as a result of the effect from other fibers. The phenomenon is known as twist propagation. This leads to the complexity of the fiber configuration, and many different fibers form the main part and the hairiness part of the staple yarn. Therefore, twist propagation and fiber configuration attract numerous researchers in the field of spinning technology.

Based on the sliver and yarn scale, Grosberg et al.^1,2 and Tang et al.³ employed a mathematical model to analyze the twist change in the dynamic yarn forming process, and the mechanism of twist propagation and distribution of staple yarn were explained in detail. The twisting dynamic model of the filament was extensively explored by Yamamoto and Matsuoka.^4,5 These works explain the configurational changes in the twisting process through experiments and theories. The spiral structure in the twisting process of the sliver is also the focus of research. The yarn path and the yarn torsion equation established by the researchers^6–8 in the ring-spinning process have made an in-depth elaboration of the twisting process of the sliver.

Numerous studies have focused on fiber migration, two-dimensional modeling and fiber motion during yarn spinning.^9–11 Morton⁹ studied fiber migration and alignment in the yarn using the tracer fiber technique and the effects of two-stage self-twisting in staple yarns. His results showed that buckling of the fibers near the core was noticed with additional twist force. Smith and Roberts¹⁰ established a two-dimensional nonlinear motion model of fiber motion in ducts by considering varying stiffness, duct length and angles of convergence. Although their study neglected turbulence, wall effects and fiber–fiber interaction, the results showed that computationally fibers can be effectively straightened in an accelerating flow under appropriate operating conditions. Other scholars, such as Skjetne et al.¹¹ and Das et al.,¹² have also made a significant contribution toward numerical simulation and modeling of yarn formation. They assumed the fiber as a “beam-pole” model to study the force and configurational change of the fiber during the process of twisting. Twist propagation and three-dimensional modeling of the yarn formation process have not been explored due to the complex nature of the phenomena. At present, with the advancements in computational modeling, it has become more workable to tackle the change of fiber configuration using the computer-aided method and numerical simulations. Vahidkhah and Abdollahi¹³ and Maâtouk et al.¹⁴ and studied the mechanical properties and configurational changes of fiber during the twisting process based on the method of numerical simulation, which revealed significant results that matched the experimental data. Fu et al.¹⁵ proposed a dynamic model to evaluate the additional twist of the fiber strands and simulated the individual fiber trajectory in the suction slot in compact spinning; meanwhile, a related spinning experiment was carried out to verify the rationality of the simulation. Subsequently, Akankwasa et al.^16,17 also used the finite element method to simulate the configurational change of the fiber under the airflow field during the rotor spinning process. In their work, they designed and optimized a new dual-feed rotor spinning unit by utilizing numerical data and experimental analytics. This methodology can show the configurational change of fiber intuitively, but so far it is only for a single fiber or several fibers. Also, Xu et al.¹⁸ regard the cotton fiber assembly as three-dimensional open-cell foam material modeling to study the compression process, and a model of fiber aggregation is provided, but the configurational changes of the fibers are not obtained. Wang et al.¹⁹ assumed the fiber assembly as a braided model, and studied the stress distribution of the fibers, and the changes of fiber configuration and the interaction between fibers were analyzed in detail. Han et al.²⁰ studied the fiber configurational change in the vortex spinning, where the fiber was regarded as the flexible fiber finite element model. The finite element simulation and theoretical mechanical analysis were used to study the motion of the fiber during twisting, but only the changes of individual fibers were characterized.

At the same time, some scholars used image processing technology²¹ and the polygon modeling method²² to realize the direct establishment of a three-dimensional staple yarn model based on the yarn scale. The previous research regarding twist and sliver analysis was mainly aimed at the mathematical and theoretical model of the twisting process of the sliver and the configurational change of the individual fiber during the twisting process. Haleem et al.²³ used micro computerized tomography to obtain the microstructure of the staple fiber, and detailed information on the internal structure of the yarn is provided. Still, the size of the structure available is limited, and the dynamic yarn forming process cannot be captured. Besides, there is the relevant research²⁴ that was focused on the establishment of the sliver model. The paper²⁴ introduces the establishment of a fiber-scale sliver model at the fiber scale based on the assumption of random fiber distribution. Meanwhile, the simulation twisting of the sliver was carried out and the staple yarn model was obtained. However, the problems of twist propagation and yarn model fineness have not been solved, and the validation of the model is not perfect.

In this study, we simulated all the stages of twist propagation of staple yarn on the fiber scale and the rationality of the simulated staple yarn structure was verified by ring-spinning experiments. This method is based on the mechanical analysis of the twisting process of the sliver and the simulation of the twisting process of the sliver model on the fiber scale. A mathematical model of sliver twisting was established and the non-free-end twisting simulation method using the explicit module of the software ABAQUS® on the fiber scale was proposed to show the force and configurational change of fibrous assemblies during the twist propagation process of the sliver. Then, through the spinning experiment, the mathematical curve of polyester staple yarn fineness and the number of fibers in the cross-section of the yarn was established, and the fineness of the three-dimensional model of staple yarn was calculated.

Model theory analysis

Twisting process of an individual fiber

The staple yarn is formed by twisting the sliver, so the final configuration of each fiber is undoubtedly closely related to its initial position distribution in the sliver. In this paper, an ideal assumption was made that the center of gravity of the fiber is randomly distributed in the sliver, and the distribution is as shown in Figure 1.

Figure 1.

Distribution of fiber L_fiber in the sliver: (a) longitudinal view of the sliver; (b) cross-section view of the sliver. (Color online only.)

In the Z-axis direction of the sliver, we took the micro-segment dz, and the torque direction is as shown in Figure 1. So, the following equation can be obtained

\int d ϕ = \int M \cdot \frac{d z}{G \cdot I}

(1)

where

d ϕ

is the torsion angle of the micro-segment, M is the torque applied by an external force, z is the coordinate value of the Z-axis and G · I is the torsional rigidity of the sliver section. Here, M only depends on the actual twisting process and is independent of sliver performance. However, G · I is closely related to the distribution of fibers, and the longer the fiber length inside the sliver, the greater the torsional rigidity. So, we can use a new concept, the torsional rigidity coefficient, to characterize the impact parameter of the torsional rigidity of the sliver, and it is shown in the following equation

η_{GI} = \frac{\sum_{i = 0}^{n} L_{in} (F_{i})}{n \cdot L_{f}}

(2)

where

η_{GI}

is the torsional rigidity coefficient, L_in is the length of fiber inside the sliver, F_i is the fiber, n is the number of fibers and L_f is the length of the fiber. Based on the above analysis, only L_in is an unknown parameter related to the torsional rigidity of the sliver.

The fiber length inside the sliver

Figure 1(a) shows the position of one fiber, and the red line is one fiber named the L_fiber. The cylindrical area is the area where the centers of gravity of all fibers are distributed. Figure 1(b) is the view of the section of the sliver. (Since the diameter of the fiber is too small compared to the sliver, the analysis here considers the fiber as a straight line.)

Wherein, the length of the fiber is L_f, the point P(a, b, c) is the center of gravity of the fiber L_fiber, the point Q is the intersection of the fiber L_fiber and the X-axis and the point M is the intersection of the fiber L_fiber and the sliver boundary. The angle between the fiber L_fiber and the coordinate axes X, Y, Z is α_x, α_y, α_z, and the boundary equation of the sliver is shown in the following equation

x^{2} + y^{2} = R^{2}

(3)

where x, y are the values of the X-axis and Y-axis, respectively, R is the radius of the boundary of the sliver and the coordinates of the point Q can be obtained through the following equations

(a + \frac{- b \cdot cos α_{x}}{cos α_{y}}, 0)

(4)

Then

L_{PQ} = \frac{- b \cdot \sqrt{cos^{2} α_{x} + cos^{2} α_{y}}}{cos α_{y}}

(5)

where L_PQ is the length of the line segment PQ.

The coordinates of the point P and the point Q are known. In this two-dimensional coordinate system, the equation of the line segment PQ can be obtained as

y = \frac{cos α_{y}}{cos α_{x}} \cdot x + (b - \frac{a \cdot cos α_{y}}{cos α_{x}})

(6)

It can be linked to the boundary equation of the sliver to get the following equation

L_{QM} = [\frac{{ak}^{2} - bk + \sqrt{Δ}}{1 + k^{2}} - (a - \frac{b}{k})] \cdot \frac{\sqrt{cos^{2} α_{x} + cos^{2} α_{y}}}{cos α_{x}}

(7)

where

k = \frac{cos α_{y}}{cos α_{x}}

Δ = 4 (bk - {ak}^{2})^{2} - 4 (1 + k^{2}) \cdot ((b - ak)^{2} - R^{2})

and L_QM is the length of the line segment QM.

The length of the fiber inside the sliver can be calculated by the following equation

L_{in} = \frac{L_{f}}{2} + \frac{(L_{PQ} + L_{QM})}{cos α_{x}}

(8)

Then

L_{in} \sim (α_{x}, α_{y}, a, b)

(9)

It can be seen from Equation (9) that the fiber length L_in existing inside the sliver is related to the parameters α_x, α_y, a, b.

Through the above analysis, we obtained the equations of the twisting process of the sliver, which can effectively analyze the configurational change of the individual fiber, but the twisting process of the sliver also involves a large number of fiber collision and friction, which cannot be solved by these equations. The finite element analysis (FEA) can simulate the contact and collision of multiple objects and is a good supplement to the mechanical analysis method.

Simulation process

Material parameters

The polyester fiber was used for simulation and the spinning experiment. There are six main performance parameters of the fiber used in the simulation twisting process, which are the fiber length, Young’s modulus, the coefficient of friction, density, fineness and Poisson's ratio. The parameters of the polyester fiber are given in Table 1.

Table 1.

Parameters of the fiber

Fiber type	Fiber length/(mm)	Fiber density/(g/cm³)	Young’s modulus/(MPa)	Friction coefficient	Fiber fineness/(dtex)	Poisson’s ratio
Polyester	33	1.37	900	0.2	1.8	0.3

Process of sliver twisting simulation

Based on the assumption of fiber random distribution, we can create the sliver model and define the simulation twisting method through the above theoretical analysis. The sliver model used to simulate is the type of fibrous assembly that is drafted but untwisted in the ring-spinning frame. The sliver model is closely related to the distribution of the fiber center of gravity and the position of an individual fiber. The distribution of the fiber centers of gravity is random and the position of an individual fiber can be defined by Equation (9). The twisting type is directly twisting, which is one type of non-free-end twisting, and is as shown in Figure 2 (for the sake of clarity, the sliver is radially magnified five times).

Figure 2.

The twisting type of the sliver.

Firstly, a fibrous assembly model contained 240 fibers is established, where the length of the sliver is 10 cm and the distribution radius of the gravity center of the fibers in the sliver is 2 mm. Each fiber is independent and the overlapping fibers are removed.

Then, two pairs of units are established, which are fixing units and twisting units. During the start of the simulated twisting process, each unit of the fixing units and the twisting units is approaching and holding the sliver. Then, the fixing units remain fixed, and the twisting units hold the bead twisted around the axis of the sliver to give the yarn a certain twist. The simulated twisting process is shown in Figure 3.

Figure 3.

The simulated twisting process of the sliver. SEM: scanning electron microscopy.

FEA using ABAQUS

The simulation process was calculated by the Explicit module in ABAQUS® software, and the parameters of the settings are as shown in Table 2.

Table 2.

Parameters of the simulation settings

Element shape	Element type	Number of elements	Number of nodes	Number of elements of one fiber	Number of nodes of one fiber	Contact type
Hex	C3D8R	222,240	496,272	1200	2807	General contact

The distance between each pair of units is 8 mm, and the time of the holding process and twisting process are both 0.1 s. When the fixing units and twisting units contact with each other, it is considered that they have enough holding effect on the sliver. Considering that the fiber will not be overstretched and reduce the calculation time in the simulation of the twisting process, the fiber was regarded as a linear elastic model.

The sliver was twisted by three twists (considering the calculation time and process details, the number of twists is set as three), and the twisting unit rotates around the axis line of the sliver while holding the sliver, which gives the sliver a twist. The fibers near the twisting units have been agglomerated to form a staple yarn, which is similar to ring-spun yarn; a scanning electron microscopy (SEM) image of one real ring-spun yarn segment with the same twist is shown in Figure 3.

Results and discussion

The analysis of the twist propagation

For the sake of clearly analyzing the process of twisting, the sliver segment M near the twisting units (Figure 2) was selected to be the object. The twist propagation process is shown in Figure 4.

Figure 4.

The different stages of the twist propagation.

The twisting process is very complicated and will be divided into 11 stages; the configurational structure of the sliver in each stage is shown in Figures 4(a)–(k).

The twisting units contact the fibers of the sliver.

The twisting units hold to control the sliver. The gripped fibers are called control zone fibers in this paper. The twisting units have a strong or weak control effect on different regions of the sliver. The closer the fiber is to the twisting units, the greater the control force on the fiber. At this time, the configuration of the sliver that directly contacts the twisting units changes obviously due to the strong force.

The twisting units begin to twist. During this process, the first circle-twisting zone is formed (as shown in area A of Figure 4), and the fibers near the twisting units are more deformed and more stressed.

Circle-twisting zone transfer. In this stage, the first circle-twisting zone gradually transfers to the left-hand end, and it moves away from the twisting units during the propagation process. Therefore, the control constraints of the first circle-twisting zone gradually weaken and, at the same time, the first circle-twisting zone collides with more fibers in the weak control zone.

Formation of the second circle-twisting zone. With the propagation of the first circle-twisting zone, the second circle-twisting zone is formed near the twisting units (as shown in area B of Figure 4).

Propagation of the second circle-twisting zone. The second circle-twisting zone is still obvious with the twisting process, while the first circle-twisting zone presents a diffusion trend due to the interaction with many fibers in the weak control zone; accordingly, the configurations of the fibers changed due to being affected by external forces.

Formation of the third circle-twisting zone. At this stage, the first circle-twisting zone has almost disappeared, showing many wavy fibers with a similar configuration (as shown in area A₂ of Figure 4). This kind of fiber has shown the trend of twisting around the axis line of the sliver. At the same time, the third circle-twisting zone is formed (as shown in area C of Figure 4).

Loop fibers are abundantly formed. With the gradual disappearance of the first circle-twisting zone, many loop fibers appeared between the second circle-twisting zone and the third circle-twisting zone (as shown in area D of Figure 4). Because the second circle-twisting zone is interacting with many fibers in the weakly controlled zone, its propagation speed is slowed down, while the third circle-twisting zone is still subject to the strong twisting effect of the twisting unit, so the propagation speed is fast. This speed difference will have a greater extrusion effect on the left-hand end of the fibers, and promote the fibers to present a loop shape.

The circle-twisting zone almost disappeared. With the continuous twisting of the twisting units, the twisting zone interacts with many fibers to form relatively high-density fibers region, while the fibers that do not enter the high-density fibers zone float independently in the edge region.

Formation of the virtual-twisting zone. The slivers near the twisting unit have basically formed a yarn (as shown in area E of Figure 4), and the yarn in this section will not change greatly. At the same time, there is a virtual-twisting zone, located at the left-hand end of the yarn (as shown in area F of Figure 4). The torque of the twisting units is transferred to the virtual-twisting zone through the yarn. At this time, the virtual-twisting zone will continue to twist the fibers in the weakly controlled zone.

The yarn shrinks gradually. In this stage, the yarn length between the twisting units and virtual-twisting zone gradually increases (as shown in area E₁ of Figure 4), in which the fibers are shrinking and gathering, and the density of the yarn is also gradually increasing.

Ring-spinning experiment

We re-establish three sliver models, A–C. The number of fibers in the slivers A–C are 240, 320 and 400, respectively, and the remaining parameters are the same as previously. According to the above method, the slivers were twisted to obtain three staple yarns, a–c, with a length of about 15 mm. They are shown in Figure 5. We can obtain the number of fibers in any cross-section of the yarn through the three-dimensional staple yarn.

Figure 5.

Simulated staple yarns of different fineness.

Fineness determination of the simulated staple yarns

Ten yarns with different counts of 20, 25, 30, 35, 40, 45, 50, 55, 60 and 65 Ne were spun from polyester fiber, and they are shown in Figure 6. Then we used the Kazakhstan slicer to get 20 cross-sections of each yarn. During sample preparation, the yarn was wrapped with wool and placed in the Kazakhstan slicer. After being compressed, the samples were cut and observed under an optical microscope. The average value of the number of fibers in each yarn cross-section was counted, and the fitting curve is as shown in Figure 7.

Figure 6.

The ring-spun yarns and the cross-section of one yarn (45 Ne).

Figure 7.

Relationship between yarn fineness and the number of fibers in the cross-section of the staple yarns.

The quadratic equation fitted is as follows and the correlation coefficient is 0.997

y = 0.0697 x^{2} - 10.09 x + 390.6

(10)

where y is the number of fibers in the cross-section of the yarn and x is the fineness of the yarn.

In Figure 7, there are three simulated staple yarns, Yarn_a, Yarn_b and Yarn_c, and the number of fibers of each yarn cross-section were counted as 68, 83 and 102, respectively. According to Equation (10), the fineness of the three simulated yarns is 48, 44 and 39 Ne, respectively.

Weight verification of staple yarns

The ring-spun yarns with the fineness of 39, 44 and 48 Ne were respectively spun and the twist of the yarn was processed to the same extent as the simulated staple yarn (3 twists/15 mm). We took a long enough ring-spun yarn (greater than 1000 m) to calculate the weight of each 15 mm yarn. Then, the weight of the three simulated staple yarns can be calculated after outputting the volume of the simulated three-dimensional model. A comparison between the two is shown in Figure 8.

Figure 8.

Weight comparison of staple yarns.

It can be seen from Figure 8 that the weight of the real yarn and the simulated yarn are almost the same, and the error is within 4%, which largely explains the correctness of the established spun yarn model and indirectly explains the rationality of the simulated twisting method.

Conclusion

Through the above analysis, the following conclusions can be drawn.

The theoretical model of sliver twisting was established and we also established the twist propagation process of the sliver model and the three-dimensional model of the staple yarn by simulating non-free-end twisting of the sliver.

The twist propagation process was subdivided into 11 stages, which mainly include the formation of different circle-twisting zones, the formation of the loop fibers and the configuration of the virtual twist zone. It clearly showed the configurational changes of the fibers during the twisting.

During the validation of the model, 10 yarns with different counts of 20, 25, 30, 35, 40, 45, 50, 55, 60 and 65 Ne were spun by ring spinning. The mathematical relationship between the yarn fineness and the number of fibers in the cross-section of ring-spun yarn was established. According to the fitted equation, the fineness of the three simulated staple yarns was calculated as 48, 44 and 39 Ne, respectively. Comparing the weight of the same fineness of the simulated yarn and the real yarn, the error is less than 4%, which also determines the structural rationality of the simulated staple yarn; meanwhile, it indirectly proves the correctness of the sliver simulation twisting process.

Footnotes

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article

Funding

The authors disclosed receipt of the following financial support for the research, authorship and/or publication of this article: This work was supported by the Fundamental Research Funds for the Central Universities (Grant No. 2019061105), the Fundamental Research Funds for the Central Universities and Graduate Student Innovation Fund of Donghua University (Grant No. CUSF-DH-D-2020022) and the National Natural Science Foundation of China (Grant No. 61379011, 11802161).

ORCID iDs

Nicholus Tayari Akankwasa https://orcid.org/0000-0001-8571-4261 Jun Wang https://orcid.org/0000-0002-5655-6070 Huiting Lin

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