Yarn modeling and winding process simulation based on 3D beam elements

Abstract

In order to study the tension variation of cotton yarn in the winding process, a finite element model of yarn based on three-dimensional beam elements is proposed. As the size of yarn in the length direction is much larger than the cross-sectional size, this paper assumes that the yarn cross-section is circular and ignores the change of the cross-sectional area in the winding process. The winding process of yarn is simulated using Abaqus dynamic explicit, and the influence of the yarn fineness on the yarn tension during winding is analyzed. The results show that the average relative error between the simulation results and the experimental data is 14.09%, and the maximum relative error is 17.06%; therefore the model is reasonable. Compared with the solid element model of yarn, the yarn simulated by this model can save a lot of computing resources while taking into account the yarn stacking effect. The winding length that can be simulated in the same time is tens of times that of the solid element model, thus the winding simulation of nine-layer yarn on the bobbin is realized. The conclusion is that the inner yarn loop presents weak tension while the outer yarn loop has large tension.

Keywords

Winding process yarn tension finite element model 3D beam element

Bobbin yarn is produced by a winding process in the spinning factory, and its quality directly affects the production of the warping and weaving process, as well as the quality of the final product textiles. During the winding process, the yarn is laid on the outer side of the bobbin through the winding mechanism and the yarn guide mechanism, as is shown in Figure 1.

Figure 1.

Schematic diagram of the winding process.

The tension of the yarn is not constant from the contact with the bobbin until it is covered by the subsequent yarn loops. Appropriate yarn tension can ensure the relatively stable force inside the bobbin yarn.¹ Yarn tension is highly important in the winding process, which can be reflected in two aspects. First of all, uneven yarn tension will lead to abnormal yarn winding shape, resulting in uneven yarn winding density, uneven dyeing in the weaving process, and yarn loop slippage in high-speed unwinding. Second, too much yarn tension significantly affects the elasticity of the yarn, destroys the original stable structure of the yarn, and leads to yarn breaking and frequent stops, which seriously reduces the production efficiency.² So it is necessary to monitor and evaluate the yarn tension in the winding process.

Finite element analysis of yarn is often used in tensile simulation. Sriprateep and Bohez proposed a method to simulate the tensile properties of braided filament yarns, taking into account the geometry and nonlinear mechanical properties of the yarns.³ Nemov et al.⁴ tied the shell model to the beam model in finite element software to model the fiber aggregate. By setting the beam model as the master surface, and the cylindrical shell model as the slave surface, the main mechanical performance is reflected by the beam element, while the simulation of fiber contact is carried out on the shell element. Compared with solid element modeling, although some precision is lost, computing resources are saved, and the results can be obtained faster.⁴ Sriprateep and Bohez proposed a method to simulate the stretching behavior of multifiber braided yarns, taking into account the nonlinear and geometric nonlinear characteristics of fiber structural materials, and the simulation results are consistent with the experimental data.³ Daelemans et al. proposed a modeling method based on the truss element, which simulated the yarn with a bundle of virtual fibers, constructed the fabric model for dynamic simulation, and obtained the stress results of the fabric model under tensile and shear actions.⁵

The three-dimensional (3D) beam element can be used as a metal wire model to simulate the winding process in the automotive electronics field. Bnig et al. used the 3D beam element to conduct the linear winding process of the metal loop in an automobile motor, and verified the stress of simulated results through experiments.⁶ Weigelt et al. simplified the finite element model of the linear winding process of the metal loop in an automobile motor.⁷ After verifying the rationality of the linear winding simulation of loop winding modeled by the 3D beam element through experiments. The simulation model was used to find out the process variables with great influence and optimize the process parameters.⁷ The beam element is chosen to model the yarn winding process in this paper. Compared with the existing model built with solid elements,⁸ the beam element model is about 16 times faster to process in the solver and the result is reasonable. The simulation is executed using Abaqus dynamic explicit.

Yarn model establishment and winding process parameter calculation

Analysis of yarn structure

Yarns are made of fiber through the yarn-forming process. According to different fiber varieties and forming processes, yarns have great differences in structure. Taking cotton yarn as an example, cotton fiber has a natural twist structure. After being twisted to produce tension, cotton fibers will move around in the yarn and entangle with each other. Due to the large number of entangled fibers in cotton yarn, it is necessary to simplify the modeling and simulation of the geometric shape of cotton yarn in order to make efficient use of computing resources.

The cross-section of cotton yarn is approximately circular, the length direction dimension of yarn is much larger than the cross-section dimension in practical application, and the yarn tension of the same layer of the yarn loop is close in the winding process. So, in order to improve the calculation efficiency, the following assumptions are made in the modeling of yarn:

The yarn has a uniform circular cross-section along the length direction, and the change of the yarn cross-sectional area during winding is ignored.

The yarn material is regarded as isotropic, without considering the influence of fiber clearance.

A section of the bobbin is intercepted to simulate the winding process, and the taper-shaped bobbin is converted into a cylindrical bobbin with equivalent diameter.

3D modeling of yarn

The research objects of this paper are cotton yarns with a fineness of 32.8 tex, 65.6 tex and 131.2 tex, respectively. The yarn diameter calculation formula is as follows:⁹ tex is the unit of yarns fineness. It is defined as g/L × 1000, where g is the weight of yarn under conventional moisture regain in grams, and L is the length of yarn in meters.

D = 0.0356 \sqrt{\frac{T_{t}}{ρ}}

(1)

where

T_{t}

is the fineness of yarn in tex and

ρ

is the density of yarn in g/cm³. Cotton yarn density

ρ

= 0.8 g/cm³ was substituted to obtain the yarn diameter as shown in Table 1.⁹

Table 1.

Calculation results of yarn diameter

Parameter items	Set 1	Set 2	Set 3
The fineness of yarn (tex)	32.8	65.6	131.2
The yarn diameter (mm)	0.229	0.324	0.458

The 3D beam element is suitable for simulating structures in which the scale in one direction is significantly larger than that in the other two directions, and the stress along the length direction is the most important. Several features of the 3D beam element meet the geometric characteristics of the slender yarn. According to the obtained yarn diameter, Abaqus is used to set the circular section radius parameter of the 3D beam element.

Calculation of winding process parameters

The yarn winding process includes the winding motion along the radial direction of the bobbin and the guiding motion along the axial direction of the bobbin. In this paper, the cross-winding motion of the cylindrical bobbin is studied. A point is taken from any yarn segment to the surface of the cylindrical bobbin, as shown in Figure 2. Let the instantaneous speed of the yarn at this point be V, the speed component perpendicular to the rotational axis of the bobbin at this point be V₁, and the speed component parallel to the rotational axis of the bobbin be V₂, in mm/s. The winding angle α is the acute angle between the vectors V and V₁. In cross-winding, the value is generally 11° to 14°. According to the stability conditions of the cross-winding of the cylindrical bobbin, the winding angle is 12°. h is the intercept of adjacent yarn circles, and D is the overall diameter of the bobbin and yarn layers, both in mm. ω is the angular velocity of the bobbin rotation, in rad/s. t is the time taken for a yarn guide cycle, in seconds. The yarn guiding movement within a yarn guiding cycle is denoted as 2S, in millimeters. The relationship between the above physical quantities is expressed by equations (2), (3), (4), (5) and (6).

V = \sqrt{V_{1}^{2} + V_{2}^{2}}

(2)

V_{2} = V_{1} \tan α

(3)

h = π D \tan α

(4)

ω = \frac{2 V_{1}}{D}

(5)

t = \frac{2 S}{\tan α} \cdot \frac{\sqrt{1 + \tan^{2} α}}{V}

(6)

Figure 2.

Motion diagram of the yarn winding process.

In practical production, the groove drum is often used to drive the bobbin by friction. In order to reduce the solution time we simplify the winding mechanism, the rotating speed of the original moving part of the groove drum is converted into the radial linear speed on the surface of the bobbin, equation (7) is the conversion formula. The rotating speed of the groove drum n₂ is transformed to the bobbin resultant speed V in Table 2 by equations (2), (5) and (7).

V_{1} = \frac{π d n_{2} η}{60}

(7)

where d is the cylinder diameter in mm;

n_{2}

is the cylinder speed in r/min; η is the slip rate between the groove drum and the bobbin, which is generally 0.95.¹⁰

Table 2.

Bobbin resultant speed

Parameter items	Set 1	Set 2	Set 3
$n_{2}$ (r/min)	500	800	1000
V (mm/s)	2059.5	3295.3	4119.1

For the bobbin driven by the grooved drum, the radial linear speed and yarn guide travel are constant, and the decimal part of the bobbin rotation number leads to the displacement between the starting points of adjacent yarn loops. The included angle between the starting point of adjacent loops and the axis of the bobbin is called the yarn loop displacement angle φ, as shown in Figure 3. The relationship between the yarn displacement angle and the bobbin rotation number in a yarn guide cycle is shown in equation (8):¹¹

φ = 2 π (i - i_{2})

(8)

where i is the number of the bobbin rotation number in a yarn guiding cycle; i₂ is the integer bobbin rotation number in a yarn guiding cycle.

Figure 3.

Loop displacement angle.

The parameter S can be determined by the bobbin rotation number i and the pitch of adjacent yarn loops h, as shown in equation (9):

S = \frac{i h}{2}

(9)

In this paper, bobbin modeling is simplified based on the assumptions, which shortens the length of the bobbin and directly affects the bobbin rotation number. In order to lay the yarn evenly on the surface of the bobbin, the winding motion of the simulation model needs to be designed. We divide the outer circumference of the end face of the bobbin into 20 equal parts, and mark numbers 1 ∼ 21 as the position of the starting points of each yarn loop, as shown in Figure 4. At this time, the loop displacement angle is 198°, and $i - i_{2} = 0.55$ can be obtained according to equation (7). In the simulation of the first 20 yarn loops, the overall diameter D is set as the bobbin diameter plus the radius of the most roving yarn, which is 55.229 mm, so as to leave the margin of the stacking thickness between the yarns. According to equation (3), the intercept of adjacent yarn circles is 36.88 mm. Combined with equation (8), the yarn guide travel S = 18.44 (0.55 + $i_{2}$ ), in mm. The bobbin length is shortened to 100 mm, and the maximum integer $i_{2}$ is set as 4. Therefore, the yarn guide travel S of the first 20 yarn circles is 83.902 mm. Then we calculate the angular velocity ω of the bobbin at three different speeds and the time t for one yarn guide cycle using equations (5), (6) and (7), and the results are shown in Table 3.

Figure 4.

Distribution of starting points of the yarn loops.

Table 3.

The angular velocity of the bobbin and the time spent in one yarn guide cycle

Parameter items	Set 1	Set 2	Set 3
$n_{2}$ (r/min)	500	800	1000
ω (rad/s)	73.262	117.213	146.524
T (s)	0.39188	0.24492	0.19594

Set simulation parameters of the winding process

In order to obtain the dynamic tension of yarn during winding and verify the rationality of yarn modeled by the 3D beam element, this paper uses Abaqus explicit dynamic to solve the finite element model of the winding process.

Geometric dimensions and material parameters of the model

In the actual production, there are many mechanisms involved in the winding process of yarn winding, such as the groove drum, yarn cleaner, yarn guide hook, etc., which need to be simplified to save computing resources. The simplified model retains only the core winding parts: bobbin, yarn guide and yarn, as shown in Figure 5. The geometry size of the model is shown in Table 4, and the corresponding material parameters are shown in Table 5.

Figure 5.

Winding mechanism model diagram; 1: yarn; 2: yarn guide; 3: bobbin.

Table 4.

Model geometry size

Geometric parameters	Size (mm)
Bobbin diameter	55
Length of the bobbin	100
Inner diameter of yarn guide	0.47
Length of yarn guide	4
Length of the yarn	9000

Table 5.

Material parameter table

Geometry	Modulus of elasticity (MPa)	Poisson’s ratio	Density (tonne/mm³)
Bobbin	2200	0.394	1.05 × 10⁻⁹
Yarn guide	20,000	0.3	7.85 × 10⁻⁹
Yarn 32.8 tex	1438	0.2	8 × 10⁻⁹
Yarn 65.6 tex	1290	0.2	8 × 10⁻⁹
Yarn 131.2 tex	1118	0.2	8 × 10⁻⁹

Cotton fiber is a kind of classic viscoelastic material. The effect that viscoelasticity has on the elastic modulus of yarn is considered in this paper. You¹² described the viscoelastic mechanical properties of cotton fiber with a four-parameter Burgers model and transformed it into a Prony series form of viscoelasticity expressed in Ansys, namely equation (10). The corresponding material parameters were τ₁ = 3.53, τ₂ = 3.53, a₁ =0.123, a₂ = 924.09.¹² In Abaqus, the time-domain viscoelasticity is expressed as equation (11). The four-parameter model used in this paper has two sets of coefficients, so n is 2 and equation (12) can be obtained after sorting equation (11). By comparing equation (10), the viscoelastic parameters in Abaqus can be determined. Due to the regulation of Abaqus that $G (\infty) = G_{0} (1 - \sum_{i = 1}^{n} g_{i})$ is not zero, τ₁ = 3.53, g₁ = 0.123, τ₂ = 924.09, g₂ = 0.8769.

G (t) = G (\infty) + G_{0} (a_{1} e^{\frac{- t}{τ_{1}}} + a_{2} e^{\frac{- t}{τ_{2}}})

(10)

where G(t) is the shear modulus at time t; G₀ is the initial shear modulus; a_i is the relaxation modulus; τ_i is the relaxation time.

G (t) = G_{0} (1 - \sum_{i = 1}^{n} g_{i} (1 - e^{\frac{- t}{τ_{i}}}))

(11)

where G(t) is the shear modulus at time t; G₀ is the initial shear modulus; g_i is the relaxation modulus; τ_i is the relaxation time.

G (t) = G_{0} (1 - g_{1} - g_{2}) + G_{0} (g_{1} e^{\frac{- t}{τ_{1}}} + g_{2} e^{\frac{- t}{τ_{2}}})

(12)

Set contact, boundary conditions and loads

Contact, boundary conditions and loads in Abaqus mainly involve interaction and load modules. First, contact should be set for the yarn, bobbin and yarn guide. In the first pair of contacts, the outer cylindrical surface of the bobbin is set as the master surface, the yarn is set as the slave surface, and the contact type is rough to avoid slipping between the beam element and the shell element. In the second pair of contacts, the cylindrical surface in the yarn guide is set as the master surface, the yarn is the slave surface, and the contact form is frictionless to simulate the smooth surface of the yarn guide parts in actual production. In the third pair of contacts, the static friction factor of yarn self-contact is set as 0.3, and the dynamic friction factor is set as 0.25.¹³ As edge-to-edge contact of beam elements exists, the above contact conditions are applied using the general contact method.

The deformation of the yarn guide and bobbin is small and is not the focus of the research. The calculation of their stress or deformation will increase the time required for the solution, so the yarn guide and bobbin are set as a rigid body. The other five degrees of freedom of the bobbin except the z-axis are constrained, and the rotation angle linearly increased with time is applied to simulate uniform rotation motion. The five degrees of freedom except the z-axis movement of the yarn guide are constrained, and the displacement condition of transverse reciprocating motion is applied to simulate the yarn guide motion. A coupling constraint is used to connect the yarn head with the rotating center of the bobbin to realize the yarn winding movement.

The initial tension force was applied to the yarn end in the negative direction of the x-axis, and the initial tension force of 30 cN, 50 cN and 50 cN was selected according to the technological parameters of the winding process in the textile calculation manual, which were 32.8 tex, 65.6 tex and 131.2 tex, respectively.⁹

Meshing and solving settings

After the above model and boundary conditions are determined, the finite element method is used for winding simulation. When meshing the model, it should be noted that the axial element size of the beam element needs to be larger than the cross-section size, otherwise the algorithm will automatically reduce the cross-section size to meet the calculation requirements. The bobbin and yarn guide in contact with the yarn are simulated by the shell element, and the grid needs to be appropriately roughened to adapt to the axial grid size of the beam element. If the grid division of the bobbin and yarn guide is too fine, the master surface will penetrate the slave surface, and the yarn will penetrate other objects. In this paper, the edge of the beam element and shell element is set as 2 mm. In the simulation work, it is observed that the calculation steps of long-distance yarn winding simulation often exceed 30,000 steps. If the single precision solution is used, the rounding error will increase the uncertainty of the result. Therefore, double precision needs to be set in the packaging and solution process in Abaqus. Before solving, it is necessary to turn on the large deformation switch to adapt to the dynamic winding process of yarn. In total, 8848 elements are involved, the time period is set as 1.5 s and the output interval is set as 0.001 s.

Analysis of simulation results of winding process

Comparison between simulation results and experimental data on yarn tension

In this paper, the winding process of the cotton yarn with fineness of 32.8 tex, 65.6 tex and 131.2 tex are simulated at a groove drum speed of 500 r/min, 800 r/min and 1000 r/min, respectively. The stress cloud diagram at 1.5 s of winding is shown in Figure 6.

Figure 6.

Yarn stress diagram. (a) 32.8 tex 500 r/min; (b) 32.8 tex 800 r/min; (c) 32.8 tex 1000 r/min (d) 65.6 tex 500 r/min; (e) 65.6 tex 800 r/min (f) 65.6 tex 1000 r/min; (g) 131.2 tex 500 r/min (h) 131.2 tex 800 r/min and (i) 131.2 tex 1000 r/min.

In the experiments, the yarn tension was recorded 100 times per second before the yarn moved to the bobbin using the resistance tension sensor, so we compared the yarn tension before the yarn reached the bobbin with the experimental data. The data points were taken from the yarn segment between the yarn guide and the bobbin, and the extreme stress points caused by the yarn guide collision were removed. According to the continuum mechanics theory and the assumptions mentioned above, the yarn stress in simulation was converted into yarn tension for comparison with the experimental data. The tension and relative error were calculated according to equations (13) and (14). In this paper, 30 tension data are evenly taken at the time interval of 0.05 s for each group of simulation, and the relative error is calculated according to the corresponding experimental data of each group.

T = σ \cdot A

(13)

where A is the circular cross-sectional area of yarn, in mm²; and σ is the yarn stress, in MPa.

δ = \frac{| T - T^{*} |}{T^{*}} \cdot 100 %

(14)

where T is the simulation result of yarn tension, and T* is the experimental data of yarn tension, both in N.

The obtained yarn tension is compared with the experimental data, as shown in Figure 7. The relative errors of every simulation result in each group are calculated according to equation (14), then averaged to obtain the average relative error of each group, as listed in Table 6.

Figure 7.

Comparison between simulation results and experimental data of tarn tension. (a) 32.8 tex 500 r/min; (b) 32.8 tex 800 r/min; (c) 32.8 tex 1000 r/min (d) 65.6 tex 500 r/min; e) 65.6 tex 800 r/min; (f) 65.6 tex 1000 r/min; (g) 131.2 tex 500 r/min (h) 131.2 tex 800 r/min and (i) 131.2 tex 1000 r/min.

Table 6.

Average relative errors of each group

Group	Simulation results (N)	Experimental data (N)	Average relative error (%)
32.8 tex 500 r/min	0.14–0.33	0.16–0.28	14.78
32.8 tex 800 r/min	0.17–0.45	0.2–0.42	9.39
32.8 tex 1000 r/min	0.18–0.53	0.22–0.46	17.06
65.6 tex 500 r/min	0.12–0.52	0.16–0.46	16.23
65.6 tex 800 r/min	0.28–0.65	0.3–0.64	14.17
65.6 tex 1000 r/min	0.49–0.99	0.49–0.85	13.72
131.2 tex 500 r/min	0.71–1.29	0.7–1.03	13.08
131.2 tex 800 r/min	0.67–1.54	0.57–1.23	16.15
131.2 tex 1000 r/min	0.87–1.86	0.77–1.61	12.25

As can be seen from Figure 7, the experimental data of yarn tension within 1.5 s showed an upward trend, while the simulation results of yarn tension fluctuated, and the overall trend was close to the experimental data. The average relative error of each group varies from 9.39% to 17.06%. The average relative error of all nine simulations is 14.09%, and yarn tension in the winding process is well simulated from a low level to the normal value, so the model is reasonable. The error between the experiments and predictions could result from the simplified modeling of the winding mechanism. First, the simulation data fluctuates many times due to the frequently changing yarn guiding direction caused by the shortened cone model. Moreover, only rear mechanisms are considered, as a result the balloon effect caused by the front mechanisms is not shown in this simulation. Therefore, a detailed modeling of the winding process may produce a better result curve.

Influence of yarn fineness on yarn tension

Yarn fineness is customized according to the specific requirements of the next process, users and products, so the winder needs to perform winding tasks of yarns of different fineness. The change of yarn fineness differentiates the mass of yarn per unit length, which has a certain effect on yarn tension in the dynamic winding process. In order to study the effect of yarn fineness on yarn tension more intuitively, the tension of yarns with different fineness at the groove drum speed of 1000 r/min is selected for analysis in this paper.

It can be seen from Figure 6(c), (f) and (i) that the maximum stress of yarns of different fineness varies. As yarn fineness increases, the maximum stress value of the yarn decreases. This is because the yarn of high fineness has a larger cross-sectional area. When applied with similar tension, the yarn of low fineness will produce greater stress. Also, yarn of lower fineness has a higher elasticity modulus, thus producing greater stress under similar strain. The information obtained from the stress diagram is limited and can only be used to judge the general trend. The simulation result of yarn tension in the first 1.5 s at 1000 r/min calculated by equation (13) is analyzed separately. The curve of yarn tension changing with time is shown in Figure 8. It can be seen from Figure 8 that the yarn tension value with larger yarn fineness will be higher at the same winding speed.

Figure 8.

Tension curve of yarn of different fineness at 1000 r/min drum speed.

Influence of stack of yarn loops on the tension of package yarn

Yarns modeled by the 3D beam element can reduce the calculation resources consumed in solving the section force, retain the force details in the length direction, and the axial size of the beam element is larger, which shortens the time required for stable solution, thus it is capable of simulating large-scale winding motion in a short time. During the simulation, we found that with the same processor, memory and hard disk configuration, it took 45 h to simulate 9000 mm yarn of 131.2 tex fineness at a groove drum speed of 1000 r/min by using the 3D beam element model, while it took hundreds of hours to simulate by using the solid element model in the same conditions.

The results of the 3D beam element yarn model are reasonable and fast to solve, so it can be used to simulate the force of yarn inside the bobbin when multiple yarn loops overlap. The reciprocating movement of the yarn guide makes one layer of yarn loops. The simulation results of the 131.2 tex winding model at the speed of 1000 r/min were studied by taking the first, third, fifth, seventh and ninth layers of yarn loops, respectively, as shown in Figure 9.

Figure 9.

Diagram of the first nine layers of yarn loops. (a) First loop; (b) third loop; (c) fifth loop (d) seventh loop and (e) ninth loop.

The first layer of yarn loops on the stress nephogram is mostly green, meaning the yarn loop has large inner stress. When the third layer of yarn loops are up, the first layer of the yarn is covered with only light green at the contact point. The remaining parts are blue and in weak tension state. This is because the binding effect of the other yarns increases the normal pressure between the first layer of yarn loops and the bobbin, increasing the friction force and balancing the yarn tension. In the stress diagram of the 5th, 7th and 9th yarn loop, the inner yarns close to the bobbin are blue with weak tension, and only the parts whose surface are not covered by other yarns show larger tension.

Conclusions

To summarize the work of this paper, the following contents are presented:

The 3D beam element is used to model yarn, and to simulate the yarn winding process using finite element software. The average relative error between the simulation results and experimental data varies from 9.39% to 17.06%, and the overall average relative error is 14.09%, which is consistent with the description of the trend of yarn tension. In most simulations, the yarn tension fluctuates greatly, and occasionally an error of over 30% occurs. Therefore, the model is reasonable to some extent, but needs to be improved.

The effect of yarn fineness on yarn tension at the same winding speed is compared. The simulation results show that yarns of larger fineness have higher yarn tension at the same winding speed, which is consistent with the tension variation trend observed in actual production.

Under the same conditions, the 3D beam element yarn model can save a lot of computing resources compared with yarn modeled in the solid element. The simulation results show that the inner yarn loop has weak tension while the outer yarn loop has large tension.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iDs

Xiaochuan Chen

Jun Wang

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