Numerical simulation of the fiber trajectories in vortex spinning under different process parameters based on the finite element model

Abstract

This paper studied the fiber movement in vortex spinning based on the flexible fiber finite element model, according to the theoretical mechanical analysis of the vortex spun yarn forming process. The finite element simulation and analysis of the different trajectories of free-end fiber in vortex spinning under different process parameters were carried out. The influence of the fiber count, fiber bending stiffness and nozzle pressure on the fiber transfer and distribution was analyzed and verified by experiments of tracer fiber and yarn slicing. The numerical simulation and the experiments’ results show a consistent correlation of different process parameters and fiber movement, such as the fiber diameter increasing, the fiber bending stiffness increasing, the nozzle pressure decreasing, and the fiber tending to get a smaller twist angle and becoming more easily distributed in the center of the yarn. This paper provides a theoretical basis for the structure design of vortex spun yarn and the production practice of vortex spinning.

Keywords

processing fabrication spinning materials structure properties

In 1995, the Murata Company in Japan first proposed vortex spinning technology, which set MVS (Murata Vortex Spinning) as the representative. The spinning principle of vortex spinning^1–2 is that the trail end of the fiber rotates close to the surface of the hollow spindle under the action of a high-speed rotating flow, wrapping core fibers into yarn. In 1999, Rozelle³ and Gray⁴ described the spinning process and the yarn mechanism of vortex spinning system in detail. Among the new spinning technology, the vortex spinning is one of the fastest. Li⁵ studied the effect of the nozzle hole pressure and the distance from the guide pin to the hollow spindle top on polyester yarn tensile performance by experiments. Pei et al.^6–8 came up with the correlation of the hollow spindle cone angle and the yarn performance. Zou et al.^9–10 recognized the relationship between the nozzle structural parameters, the velocity of the air flow at nozzle hole exit and the airflow characteristics by numerical calculation. Oxenham¹¹ used an untwisting way to verify the structure of vortex spun yarn. His studies have shown that the space distribution and morphological conformation of the fiber in the yarn is consistent with the movement law of the free-end fiber in the spinning process. Kyaw et al.¹² proposed the relationship between the proportion of core fiber, wrapped fiber and floating fiber in vortex spun yarn and the yarn performance, by comparing the structure of ring yarn, rotor spinning yarn and MVS yarn. Different process parameters such as fiber count, fiber bending stiffness and nozzle pressure will impact directly on the fiber trajectory under the vortex airflow of high velocity in the twisting chamber, then impact on the yarn structure and performance. However, there are fewer researchers studying the fiber trajectory during the vortex spun yarn forming process. Han et al.^13–14 established the fiber finite element model based on the spatial elastic thin-rod unit, and deduced the static equilibrium equation of that, which presented an effective and feasible theoretical model and method for the study of fiber movement. In this paper, the trajectories of free-end fiber in vortex spinning under different fiber count, fiber bending stiffness and nozzle pressures are simulated based on the elastic thin-rod finite element model of flexible fiber. The nonlinear geometric large deformation of the free-end fiber is studied by the method of step-by-step loading and successive approximation. According to experiments of tracer fiber and yarn slicing, the influence of different fiber count, fiber bending stiffness and nozzle pressures on the fiber transfer and distribution is analyzed and verified. This paper will present the correlation of different process parameters and fiber movement, which is helpful to guide the structure design of vortex spun yarn and the production practice of vortex spinning.

Theoretical mechanical analysis of vortex spun yarn forming process

Data of airflow velocity extraction

During the vortex spinning process, the compressed air through the nozzle holes goes tangentially into the twisting chamber of the main nozzle, along the inner wall of the nozzle and flows along the chamber formed by the outer wall of the hollow spindle and the inner wall of the nozzle chamber. The vortex formed flows downwards spirally. The compressed air generates the negative pressure at the entrance of the hollow spindle. The fiber bundle is sucked into the hollow spindle along the spiral curved surface and the guide pin after drafting. The front part of the fiber is formed of the yarn core. The fiber becomes the fiber of free end after passing into the hollow spindle. Under the high-speed rotating airflow, the free end of fibers lay flat on the wall of the still hollow spindle, presenting an umbrella shape. The free end of fibers slide on the wall of the still hollow spindle and wrap the core fiber. Finally the yarn is formed.

In the twisting chamber, the velocity of vortex airflow could be resolved into three components along the axial, tangential and radial direction. The data extracted of the vortex airflow velocity in the twisting chamber by computational fluid dynamics technology are shown in Figure 1. The nozzle pressure in the simulating model was 0.55 MPa.¹⁵ According to Boltzmann (Boltzmann model) and ExpDec1 (index simulation), the tangential velocity V_Ta, radial velocity V_Ra and axial velocity V_Aa in Figure 1 were derived according to equations (1), (2) and (3) using Origin 8.5 software. The tangential velocity V_Ta, radial velocity V_Ra and axial velocity V_Aa under different nozzle pressures could be derived by the same method.

\begin{matrix} v_{Ta} = {\begin{matrix} 223.93 - \frac{180.24}{1 + exp (2.18 \cdot H - 2.97)} H < 5.25 mm \\ - 1.65 + 1023.89 \cdot exp (- \frac{H}{3.34}) H \geq 5.25 mm \end{matrix} \end{matrix}

(1)

\begin{matrix} v_{Ra} = {\begin{matrix} 0 H < 5.25 mm \\ 3.44 + \frac{45.56}{1 + exp (1.70 \cdot H - 12.17)} H \geq 5.25 mm \end{matrix} \end{matrix}

(2)

\begin{matrix} v_{Aa} = {\begin{matrix} 257.32 - \frac{6121.98}{1.81 \cdot π (H - 1.81)^{2} + 7.25 π} H < 5.25 mm \\ - 12.41 + 1071.19 \cdot exp (- \frac{H}{2.51}) H \geq 5.25 mm \end{matrix} \end{matrix}

(3)

Figure 1.

Velocity of airflow in the position of fiber axis.

Theoretical mechanical analysis of airflow force

Based on the vortex spun yarn forming process, the high-speed rotating airflow in the twisting chamber has a series of complex forces on the fiber. In order to analyze the fiber transfer and distribution during the vortex spun yarn twist forming process concisely, this research assumes that the forces are acting in the yarn uniformly. The tangential velocity V_Ta, radial velocity V_Ra and axial velocity V_Aa generate the tangential, radial and axial forces F_T, F_R and F_A, as shown in Figure 2. Based on the interaction of the fiber and airflow in the twisting chamber, the fiber infinitesimal segment is defined as a rigid round rod rotating around the hollow spindle.¹⁵

Figure 2.

Forces analysis of the free-end fiber.

According to the formula of flow around the cylinder,^16–17 the tangential force F_T applied on the fiber along the lateral wall could be derived as

\begin{matrix} F_{T} = \int_{0}^{H_{0}} {K_{T} \cdot ρ \cdot r_{f} [V_{Ta} - ω_{f} (H \cdot tan δ + r_{0})]}^{2} \frac{dH}{cos δ} \end{matrix}

(4)

\begin{matrix} H_{0} = cos δ \cdot l_{0} \end{matrix}

(5)

\begin{matrix} l_{0} = L_{0} - r_{0} \end{matrix}

(6)

where K_T is the resistance coefficient of tangential air flow;^18–19 ρ_a is the density of air flow; r_f is the fiber radius; V_Ta is the tangential flow velocity; L₀ is the length of the free-end fiber; ω_f is the constant rotational angular velocity of the free-end fiber; H is the distance between the infinitesimal segment and the top plane of the hollow spindle; l₀ is the length of fiber from its tail end to the top plane of the hollow spindle; H₀ is the projected length of l₀ on the hollow spindle axis; r₀ is the periphery radius of the top plane of the hollow spindle; δ is the angle between the free-end fiber axis and the hollow spindle axis.

Because the airflow rotates downward around the wall of the hollow spindle, the force F_A applied on the fibers along the hollow spindle axis is

F_{A} = \int_{0}^{H_{0}} K_{A} \cdot r_{f} \cdot ρ_{a} (V_{A a} + cos σ \cdot cos δ \cdot V_{J})^{2} \frac{dH}{cos δ \cdot cos σ}

(7)

where K_A is the resistance coefficient of axial air flow;^18–19 V_Aa is the axial flow velocity; V_J is the speed of fibers wound on the yarn; σ is the angle of nozzle hole axis with the horizontal.

The radial airflow allows fibers to be attached to the wall of the hollow spindle. According to the formula of flow around the cylinder, the radial force F_R on fibers is

F_{R} = \int_{0}^{H_{0}} K_{R} \cdot ρ_{a} \cdot r_{f} (V_{R a} + cos σ \cdot sin δ \cdot V_{J})^{2} \frac{dH}{cos δ \cdot cos σ}

(8)

where K_R is the resistance coefficient of radial air flow;^18–19 V_Ra is the radial flow velocity.

When the free-end fiber rotates on the surface of the hollow spindle, the centripetal force F_L on fibers can be obtained

d F_{L} = a_{f} \cdot d m_{f}

(9)

d F_{L} = π \cdot r_{f}^{2} \cdot ρ_{f} \cdot ω_{f}^{2} (H \cdot tan δ + r_{0}) \frac{d H}{cos δ}

(10)

F_{L} = \int_{0}^{H_{0}} π \cdot r_{f}^{2} \cdot ρ_{f} \cdot ω_{f}^{2} (H \cdot tan δ + r_{0}) \frac{d H}{cos δ}

(11)

where ρ_f is the fiber density; m_f is the mass of the fiber infinitesimal segment; dF_L is the centrifugal force of the fiber infinitesimal segment during the rotation around the hollow spindle; a_f is the centripetal acceleration of fiber infinitesimal segment during the rotation around the hollow spindle.

The free-end fibers lodge on the hollow spindle outer surface. During the fibers’ rotating process, the fibers are in contact with each other. Between the fibers, there occurs a relative movement and a friction resistance F_fm. The calculation formula of the friction F_fm is

F_{fm} = μ N + ks

(12)

N = sin σ \cdot F_{A}

(13)

S = 2 π r_{f} \frac{dH}{cos σ \cdot cos δ}

(14)

where μ is the friction coefficient between the fibers; N is the positive pressure on the fiber; k is the constant; S is the friction contact area.

Dynamic finite element model of flexible fiber

Establishment

The fiber is a kind of elongated body with large aspect ratio, elasticity and flexibility. The actual movement law of the free-end fiber in the high-speed twisting airflow field is very complicated, involving translation, rotation, bending, stretching and so on. Han et al.^13–14 established the fiber finite element model, and deduced the static equilibrium equation of the spatial elastic thin-rod unit, which presented an effective and feasible theoretical method. In this research, the whole single fiber is equally divided into n + 1 independent elastic thin-rod units, and a node is set at the center of the midpoint cross-section of each elastic thin-rod unit.

Dynamics analysis

In order to achieve the feasibility and rationality of the calculation about the nonlinear large deformation problem of the free-end fiber, the fiber finite element model based on the spatial elastic thin-rod unit is established such as shown in Figure 3.^13–14 $O - xyz$ is the overall coordinate system. $O' - uvw$ is the local coordinate system. The u-axis is the axis direction of the rod element and the $uO' v$ and $uO' w$ planes are the two main plane orientations in the process of the rod element bending. Each spatial elastic rod unit has two nodes, such as i and j as shown in Figure 3.^13–14

Figure 3.

Space diagram of fiber rigid microsegment.

The freedom degree of the external force on the node is converted into the freedom degree of the fixed total coordinate system, and then expressing the kinetic motion differential equation

[m^{b}]_{_{6 (n + 1) \times 6 (n + 1)}}^{^{i}} {a}_{6 (n + 1) \times 1} + {R^{b}}_{_{6 (n + 1) \times 1}}^{^{i}} = {F^{b}}_{_{6 (n + 1) \times 1}}^{^{i}}

(15)

where

{R^{b}}_{_{6 (n + 1) \times 1}}^{^{i}}

is the vacancy element;

{a}_{6 (n + 1) \times 1}

is the acceleration of all the nodes;

{F^{b}}_{_{6 (n + 1) \times 1}}^{^{i}}

is the external force required for each node.

The freedom degree of the external force on the rod is converted into the freedom degree of the fixed total coordinate system, and then expressing the external force equation

\begin{matrix} {F}_{\times 1}^{e} = {k}_{6 (n + 1) \times 6 (n + 1)}^{e} {\underline{δ}}_{6 (n + 1) \times 1}^{e} \end{matrix}

(16)

where

{F}_{\times 1}^{e}

is the external force required for each elastic thin-rod;

[k]^{e}

is the element stiffness matrix of the elastic thin-rod relative to the fixed total coordinate system

o - xyz

The total finite element analysis is carried out by combining the infinitesimal rigid segment nodes and the elastic thin-rod elements together

\begin{matrix} {Q} = \sum_{i + 1}^{n + 1} {F^{b}}^{i} + \sum_{e = 1}^{n} {F}^{e} \end{matrix}

(17)

where

{Q}

is the external force on the fiber, which has 6 (n + 1) components.

Numerical simulation and analysis

Initial parameters

The process of fiber transfer in the vortex spun yarn formation could be simplified to the model shown in Figure 4. The initial parameters of the fiber model in ANSYS software is shown in Table 1.²⁰ The figure is a partial cross-section, in which the large cylinder is a fixed twisting chamber. The inner center cylinder CD is the central fiber strand, which is regarded as a fixed rigid body relative to the small cylinder AB. The internal eccentric small cylinder AB is the fiber, which is wrapping around the central fiber strand during its transfer process. The fiber is seen as a flexible rod, with its A-side fixed, and B-side free. The airflow in the twisting chamber rotates at a high speed around the x-axis and moves at a low speed along the x-axis. The fiber will wind on the central strand under high-speed airflow. The finite element method is used to simulate the transfer process of the fiber under the airflow during the vortex spun yarn formation. The initial position of the fiber AB is Z = 0.5 mm; the length of the fiber AB is 19 mm; the shear elastic modulus G of the fiber AB is 10.4 cN/tex; the initial velocity of the fiber AB is 0. The radius of the fiber strand CD is 0.3 mm; the length of the fiber strand CD is 19 mm. The radius of the twisting chamber is 3 mm; the length of the twisting chamber is 25 mm. The density of the air inside the twisting chamber is 1.25 kg/m³; the velocity of the airflow inside the twisting chamber is extracted and derived by computational fluid dynamics technology and converted into the forces acting on the fiber finite element model according to equations (1), (4), (5), (16) and (17).

Figure 4.

Space diagram of vortex spun yarn forming process model.

Table 1.

Initial parameters

Parameters	Fiber count (dtex)	Fiber bending stiffness (cN/tex)	Nozzle pressure (MPa)
A	1.33	500	0.50
B	1.33	500	0.55
C	1.56	500	0.55
D	1.33	1000	0.55

Boundary constraints

The working process of the numerical calculations is an adiabatic condition, and the fluid is high-speed unsteady ideal gas which is compressible. During the actual fiber wrapped process, we considered the fiber movement resistance from the stand, the other fibers and the airflow. The size and direction of the resistance will change with the fiber movement position changing, which could not be specifically determined in the model. We directly calculated the resistance effect to the airflow velocity reduction, so the airflow velocity in the simulation is the final result of the actual airflow velocity minus the resistance reduction value. To be on the safe side, we chose the minimum value within the normal range of resistance as −5%. The size of the fiber AB division unit is 0.5 mm the number of the fiber AB division units is 200, which is shown in Figure 5.

Figure 5.

Fiber finite element model.

The A-side of the fiber AB is a fixed constraint. The contact constraint between the fiber, the strand and the twisting chamber inner wall is treated by the penalty function method in this paper. For each node, we first construct a repulsive force between the fiber, the strand and the twisting chamber inner wall, which increases rapidly when the distance between them is closer, and quickly decays to zero when the distance between them is more than a certain distance. The penalty function method prevents the fiber and the strand embedding in each other. The repulsive force can be seen as a positive pressure between the fiber, the strand and the twisting chamber inner wall, according to the following formula

F_{Ri} = \frac{c}{S^{2}}

(18)

where s is the distance between the fiber and the strand, or the distance between the fiber and the chamber inner wall; c is a small coefficient: when the fiber is in contact with the strand, c = 10^–¹⁵, and when the fiber is in contact with the chamber inner wall, c = 10^–¹⁴.

Solving methods

In order to ensure that the position of the elastic thin-rod unit in the local coordinate system is close to the exact position of the elastic thin-rod unit after the large displacement, this paper adopts the load incremental step loading method. The load is divided into N loading steps from zero, which ensures that the load increment for each step is a small amount. For the first load step at which the load is zero, the position of the entire non-loaded state of the elastic rod unit is taken as the initial position. The second load step at the initial position is taken after establishing a local coordinate system. The displacement of each elastic rod unit under the load is solved by the element stiffness equation established under the small displacement condition, and the new position of the whole fiber after the first deformation will be obtained. For any N loading step calculation, the position of the elastic rod unit in step N–1 is taken as the initial position. As long as the load increment for each loading step is a sufficiently small amount, the displacement of each elastic rod unit obtained relative to the local coordinates must also be a small amount, thus ensuring that the element stiffness equation is accurate. In this paper, the simulation of the fiber motion under the airflow during the air-assisted twisting process is subjected to the laws of conservation of mass, conservation of momentum and conservation of energy. When {Q} = 0, the ${\bar{Δ}}^{θ}$ of the fiber under the force equilibrium will be obtained.^21–22

Simulation results and analysis

When t = 3 ms, the simulated fiber-wrapped side views of A, B, C and D during the vortex spun yarn forming process are shown in Figure 6, and the simulated top views of A, B, C and D during the vortex spun yarn forming process are shown in Figure 7. When the nozzle pressure increases, the velocity of the airflow in the twisting chamber will increase and the force generated by the airflow will increase. When the count and bending stiffness increase, it is more difficult for the flexible fiber to bend. During the vortex spun yarn forming process, the twist angle of the free-end fiber wrapped on the strand is the angle between the yarn axis and the fiber axis; as the bending deformation of the free-end fiber increases, the twist angle of the free-end fiber will increase. Comparing the simulation results of A and B, when the nozzle pressure increases, the twist angle of the free-end fiber increases. This is because when the flexible fiber has the same count and bending stiffness, the force on the free-end fiber is larger and the bending deformation of the free-end fiber is larger. Comparing the simulation results of B and C, when the fiber count increases, the twist angle of the free-end fiber decreases. This is because when the flexible fiber has the same bending stiffness and is under the same force, the free-end fiber is more difficult to bend with the larger count. Comparing the simulation results of B and D, when the fiber bending stiffness increases, the twist angle of the free-end fiber decreases. This is because when the flexible fiber has the same count and is under the same force, the free-end fiber is more difficult to bend with the larger bending stiffness.

Figure 6.

Side view of fiber-wrapped form. (a) Fiber-wrapped side view of A at t = 3 ms. (b) Fiber-wrapped side view of B at t = 3 ms. (c) Fiber-wrapped side view of C at t = 3 ms. (d) Fiber-wrapped side view of D at t = 3 ms.

Figure 7.

Top view of fiber-wrapped form. (a) Top view of A at t = 3 ms. (b) Top view of B at t = 3 ms. (c) Top view of C at t = 3 ms. (d) Top view of D at t = 3 ms.

Experimental verification

Because of the narrow, closed and invisible twisting chamber, the actual movement of the fiber cannot be observed by the imaging device. The movement law of the free-end fiber is consistent with the space distribution and morphological conformation of the flexible fiber in the yarn. Therefore, the research on the motion characteristics of the free-end fiber in the twisting chamber could be transformed into the research on the space distribution and morphological conformation of the flexible fiber in the yarn structure.

Experimental parameters

The spinning process parameters are shown in Table 2. The raw materials are viscose fiber k, viscose fiber n and cotton fiber. The length of viscose fiber k is 38 mm. The viscose fiber k is ordinary viscose fiber. The relative bending stiffness of viscose fiber k is 2.03 × 10^–4 (cN·cm²)/tex². The count of viscose fiber k is 1.56 dtex. The bending stiffness of viscose fiber k is 515.5 cN/tex. The length of viscose fiber n is 38 mm. The viscose fiber n is strong viscose fiber. The relative bending stiffness of viscose fiber n is 3.12 × 10^–4 (cN·cm²)/tex². The count of viscose fiber n is 1.33 dtex. The bending stiffness of viscose fiber n is 515.5 cN/tex.²⁰ The length of cotton fiber is 38 mm. The count of cotton fiber is 1.33 dtex. The bending stiffness of cotton fiber is 877.1 cN/tex. The fiber material is produced by Leading Fiber Innovation. The production equipment is MVS870. The quantity of the sliver is 0.42 g/m; the unevenness of the rough brands is ≤2%; the moisture regain of the rough brands is 11%. The distance between the front roller and the hollow spindle is 20 mm. The roller center distance is 43 mm × 45 mm. The hollow spindle diameter is 1.1 mm. The spinning speed is 360 m/min. The yarn count is 19.6 tex. The environment of the workshop is under standard atmospheric conditions; the relative humidity is 65 ± 3%; the temperature is 20 ± 2℃.

Table 2.

Spinning process parameters

Process parameters	Raw material	Nozzle pressure (MPa)	Total draft multiple	Main draft multiple	Feeding ratio	Winding ratio
a	100% viscose fiber n	0.50	214	35	0.98	1.02
b	100% viscose fiber n	0.55	214	35	0.98	1.02
c	100% viscose fiber k	0.55	214	35	0.98	1.02
d	50% viscose fiber n, 50% cotton fiber	0.55	214	35	0.98	1.02

Yarn appearance structure

The specimen was tested using a Digital Microscope KH-7700, according to GB/T398-2008.²³ Select a certain length of the sample yarn and fix its two ends on the observing glass, keeping the original shape without being changed by the external forces. Place the sample yarn under the hi-scope microscope. The magnification of the yarns is 160 times. The main appearance morphological characteristics of yarns a, b, and c are shown in Figure 8. The twist angle θ is the angle between the yarn axis and the fiber axis on the yarn surface.

Figure 8.

Yarn appearance structure. (a) Appearance structure of a yarn. (b) Appearance structure of b yarn. (c) Appearance structure of c yarn.

Comparing the yarn appearance structure of a and b, the twist angle θ of b yarn is larger than that of a yarn, which is better for the yarn tensile properties. The yarns a and b use the same raw material of viscose fiber n which has the same count and bending stiffness. The yarn b under the nozzle pressure of 0.55 MPa received a larger airflow force on the free-end fiber, which generates a larger fiber bending deformation. Comparing the yarn appearance structure of b and c, the twist angle θ of b yarn is larger than that of c yarn. The yarn b uses the raw material of viscose fiber n which has the same bending stiffness, but larger count than the viscose fiber k. Under the same nozzle pressure of 0.55 MPa which generates the same airflow force on the free-end fiber, the yarn b will get a larger fiber bending deformation.

Yarn cross-section structure

The specimen was tested using a Digital Microscope KH-7700, according to GB/T5324-2009.²⁴ Hardy’s thin cross-sections were used to analyze the cross-section characteristic parameters of yarn d. Take a bundle of wool fibers and straighten them by hand. Wrap a piece of yarn d in the wool and place it in the groove of the Hardy’s slicer. Use a sharp single-sided blade to cut the fibers exposed on the front and back of the Hardy’s slicer. Turn the screw back in place. Rotate the precision screw half or one grid so that the fiber bundle slightly protrudes from the surface of the metal plate and is then exposed. The fibers are coated with a thin layer of collodion. After the collodion is dry, it is sliced at an angle of about 10° along the metal plate surface with a sharp single-sided blade. Place the sample under the hi-scope microscope. The magnification is 800 times. The main cross-section appearance morphological characteristics of the yarn d are shown in Figure 9. According to the microscope image of the cross-section of the yarn, the yarn center is selected and the circular outline of the yarn is drawn. Then, the radius of the yarn circular outline is divided into five equal parts and four concentric circles are drawn. In order to make the test result more accurate, each yarn sample is cut into 20 slices.

Figure 9.

Cross-section structure of d yarn.

The number of fiber components in each concentric circle is counted, and the average value is taken as the frequency distribution of the fibers in each layer. When counting the number of fiber components in each layer of the concentric circle, take the one-half of the fiber cross-section as the boundary. If the fiber cross-section is greater than one-half, it is counted as 1. If the fiber cross-section is smaller than one-half, it is counted as 0. If each adjacent concentric circle contains one-half of the fiber cross-section, then the number of fibers per layer is plus 1. Comparing the Hamilton Transfer Index of viscose fiber n and cotton fiber in the cross-section structure of d yarn, the cotton fiber cross-section is waist round in Figure 9. The numberof fibre components for viscose fiber n in cross-section is evaluated as 55. The number for cotton fiber in cross-section is evaluated as 63. The cross-section of viscose fiber n is different from the cotton fiber, so the packing density of fibers in yarn cross-section is the ratio of fibers cross-sectional area to yarn cross-sectional area. The packing density of viscose fiber n in cross-section is 46%. The packing density of cotton fiber in cross-section is 54%. The Hamilton index of viscose fiber n in cross-section is 1.8%. The Hamilton index of cotton fiber in cross-section is −1.1%. The cotton fibers were distributed in the center of d yarn more and viscose fibers n were distributed around the cotton fibers. The number of cotton fibers is a little larger than the number of viscose fibers n. The cotton fiber has the same count with the viscose fiber n and the cotton fiber has a larger bending stiffness than the viscose fiber n. During the vortex spun yarn forming process, under the same nozzle pressure of 0.55 MPa which generates the same airflow force on the free-end fiber, the viscose fiber n will receive a larger fiber bending deformation and twist angle. Then the viscose fiber n tends to be distributed in the surface of d yarn and pulled out of d yarn. The cotton fiber tends to distribute in the center of d yarn.

Conclusions

This paper studied the fiber movement in vortex spinning based on the flexible fiber finite element model, according to the theoretical mechanical analysis of the vortex spun yarn forming process. The finite element simulation and analysis of the different trajectories of free-end fiber in vortex spinning under different process parameters were carried out. The influence of the fiber count, fiber bending stiffness and nozzle pressure on the fiber transfer and distribution was analyzed and verified by experiments of tracer fiber and yarn slicing. The numerical simulation and the experiments’ results show a consistent correlation of different process parameters and fiber movement, such as the fiber count increasing, the fiber bending stiffness increasing, or the nozzle pressure decreasing, and the fiber tending to get a smaller twist angle and becoming more easily distributed in the center of the yarn. So, this paper provides a theoretical basis for the study of free-end fiber trajectory in vortex spinning under different process parameters. It provides a guide to the structure design of vortex spun yarn and the production practice of vortex spinning.

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 National Key R&D Program of China (2017YFB0309200), Fundamental Research Funds for the Central Universities (JUSRP11801), Top-notch Academic Programs Project of Jiangsu Higher Education Institutions (PPZY2015B147) and Priority Academic Program Development of Jiangsu Higher Education Institutions (37[2014] issued by General Office of the People’s Government of Jiangsu Provence).

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Study on the stress relaxation mechanism of air jet vortex spinning yarns with naturally colored cotton. J Text Res 2008; 29(8): 27–34.

23.

GB/T398-2008. Cotton grey yarns.

24.

GB/T5324-2009. Combed polyester/cotton blended grey yarn.