Modeling and analysis of yarn tension in track-change interlocking braiding processes

Abstract

In order to study the fluctuation of yarn tension in the process of track-change interlocking braiding, the track-change interlocking mechanism and carrier motion process are taken as examples. The structure of carrier and yarn release process are analyzed to establish the equation of motion of yarn in the process of track-change braiding, and the theoretical value of yarn tension is obtained. Then the yarn tension in the track-change process is simulated in MATLAB simulation software. In order to verify the accuracy of the mathematical model, the yarn tension experiment is carried out. The box plot method is used to process the measured experimental data to deal with the outliers and optimize the yarn tension. After optimization, the maximum value of yarn tension was reduced by 8.42% and the minimum value of yarn tension was reduced by 4.67%. Reducing yarn tension during the braiding process can improve the uniformity of fiber distribution on the mandrel, avoid yarn pile-ups and gaps caused by sudden changes in yarn tension, and improve the mechanical properties after molding.

Keywords

yarn tension braiding carrier interlocking braiding kinematics model outliers

Introduction

Yarn tension is a crucial parameter in the braiding process, which directly affects fabric uniformity, productivity, and finished product quality.¹ If the tension is too low, the yarn is prone to sagging, resulting in loose or holes on the fabric surface, and even yarn breakage and downtime due to yarn entanglement; on the contrary, if the tension is too high, the overstretching of the yarn will reduce the elasticity, resulting in deformation of the fabric, stiffness of the fabric feel, and may accelerate the wear and tear of the yarn or breakage, thus affecting the production efficiency.^2–4 In the weaving process, yarns need to form interwoven structures through the synergistic action of carriers, dials, and traction devices. Different fiber materials (cotton, glass fiber, carbon fiber) have different sensitivities to tension due to differences in modulus of elasticity, which need to be analyzed or adjusted in a targeted manner. Accurate yarn tension analysis and control is the core technology to realize clear texture and mechanical properties of fabrics up to standard, directly related to the market competitiveness of the product and the economic benefits of enterprises, so it is necessary to analyze the yarn tension. The carrier is directly involved in the release and recovery of yarn, which has a direct impact on the yarn tension.

Some scholars have studied the yarn tension of braiding process. Ma⁵ proposed a mathematical model of yarn tension system of three-dimensional braiding machine, and analyzed the dynamic change of yarn tension and how to improve the stability of braiding through precise control. Hu⁶ analyzed the relationship between carrier release fiber length, lever rotation angle, and yarn tension, and studied the yarn tension’s fluctuation range, but its research object is lever carrier, and does not give the measurement method of yarn tension. Zhang⁷ improved a carrier structure, and used the kinetic equation to establish the mathematical model of carrier stretch coefficient, and numerical analysis and simulation, and the results show that the carrier structure is improved and the fluctuation of the yarn tension is reduced. Maidl⁸ installed Hall sensors through the weaving machine body, obtained carrier position information according to the magnetic field changes, and then indirectly measured the yarn tension, but due to the high cost of Hall sensors, there are monitoring blind spots along the distribution of the braiding machine track, the system responsiveness is slow, the detected tension accuracy is not high, and it is difficult to detect in real time. Samaniego et al.⁹ propose the deep energy method, which unifies modeling, simulation, experiments, and optimization naturally accounting for uncertainties.

These studies have solved the problem of yarn tension detection to a certain extent, but cannot be fully applied to the track-change interlocking braiding machine braiding process of yarn tension detection; the reason is that track-change interlocking braiding machine’s unique mechanism leads to complex carrier trajectory and yarn tension fluctuations, which undoubtedly increases the difficulty of detection of yarn tension. Since the carrier yarn release process and the mandrel braiding process are the stages that have a greater impact on yarn tension, analyzing the yarn release process and establishing a yarn tension model for the braiding process can effectively analyze the yarn tension.

Track-change interlocking in three-dimensional braiding machine

Braiding machine and carrier track-change

The track-change interlocking mechanism is an important part in braiding machine, which is used to realize the carrier entering into the non-adjacent track and the exchange of carriers. The electric gripper extending or retracting and electric rotary table rotating is driven by track-change interlocking mechanism, so as to achieve the purpose of track-change interlocking.¹⁰ The braiding machine and the carrier track-change are shown in Figure 1.

As shown in Figure 1(a), this machine is designed by our team, and the machine employs 12 track-change interlocking mechanisms and is capable of braiding composite preforms. As shown in Figure 1(b) to Figure 1(e), in the track-change process, Figure 1(b) illustrates carrier track-change to 45°, Figure 1(c) illustrates carrier track-change to 90°, Figure 1(d) illustrates carrier track-change to 135°, and Figure 1(e) illustrates carrier track-change to 180°, and thus the track-change is complete.

In the process of track-change, the carrier change movement will have a certain effect on the yarn tension, and in the analysis of the yarn tension, the carrier structure is analyzed first.

Analysis of carrier structure

In the braiding process, each yarn is controlled by a carrier moving along a predetermined path, and the yarns are interlaced to form a braided structure.¹¹ In order to analyze the movement of the yarn, the carrier structure is first analyzed to sort out the principle of releasing the yarn from the bobbin. The carrier consists of two types: lever-balanced carrier and slider-balanced carrier. The advantages of slider-balanced carrier are: less space required for slider-balanced carrier compared to lever-balanced carrier, lower loading of connecting parts, and more space to accommodate larger yarn tubes. The disadvantages of slider-balanced carriers are: higher friction forces during sliding for very fine yarns and delicate materials, compared to lever-balanced carriers. These forces may reach the yarn breaking force, which leads to plastic deformation of the yarn. This paper analyzes the slider-balanced carrier as an example, and the structure of the slider-balanced carrier is shown in Figure 2.

As shown in Figure 2(a), slider-balanced carrier consists of bobbin fixation clamp, bobbin, slider, bobbin adapter, pawl, sliding axes, down eyelet, middle eyelet, and upper eyelet. Among them, the bobbin fixation clamp is used to fix the bobbin; the bobbin is wound with yarn, the yarn from the bobbin winding through the middle eyelet, the down eyelet, and the upper eyelet out of the yarn.

The slider-balanced carrier utilizes spring-generated force to drive the slider assembly. Through direct mechanical coupling, this spring transfers energy to the yarn while enabling a compact configuration that accommodates larger bobbins, thereby improving braiding efficiency. Guided by precision sliding axes, the slider maintains stable motion throughout its trajectory. As the carrier-braiding point distance reduces, diminishing yarn tension triggers downward slider displacement via spring actuation until dynamic equilibrium between tension and spring forces is achieved. Upon depletion of the compensation zone’s yarn reserve, the slider ascends to its upper limit, activating the bobbin adapter for yarn replenishment.

According to the structural characteristics and working principle of the slider-balanced carrier, the release of yarn from the carrier can be divided into four stages as follows:

Stage 1: The ratchet wheel is locked, and at this time the slider does not move, no yarn release, as shown in Figure 2(c).

Stage 2: The slider moves upward, compressed spring 1, but the ratchet is still locked, as shown in Figure 2(d).

Stage 3: The pawl reaches the edge of the engaged ratchet wheel, begins to contact spring 2, and spring 2 begins to compress, as shown in Figure 2(e).

Stage 4: The ratchet wheel begins to rotate, spring 2 is fully compressed, the yarn cylinder and the ratchet wheel rotate, and the yarn continues to release, as shown in Figure 2(f).

After the entire yarn reserve is used, the yarn tension increases, and the inner weight moves up and shifts the bobbin fixation lever up. This releases the bobbin, so that it can rotate and release some more yarn.

Analysis of the process of yarn release from the carrier

According to the four stages of carrier yarn release, the tension required for carrier yarn release is analyzed, and the tension in the three cases of low (0.01 m/s), medium (0.05 m/s), and high velocity (0.1 m/s) is measured, and the results obtained are shown in Figure 3.

As shown in Figure 3, the yarn tension is different when the yarn exit velocity is different. As shown in Figure 3(a), at low velocity, the yarn tension is small, the minimum value is less than 1.56 N, and the maximum value is 8.62 N. As shown in Figure 3(b), at medium velocity, the minimum yarn tension is 2.05 N, and the maximum yarn tension is 10.42 N. As shown in Figure 3(c), at high velocity, the minimum yarn tension is 2.07 N, and the maximum yarn tension is 11.12 N. The tension is different at different velocity.

Yarn tension of track-change interlocking braiding process

The analysis of braiding process

The track-change interlocking braiding machine is more difficult than conventional three-dimensional because it involves a track-change interlocking mechanism, which drives the carrier to periodically change tracks during the braiding process. In the process of track-change, the parameter changes of the yarn are more complicated than those of the ordinary three-dimensional machine. In order to study the braiding process more effectively, the assumptions are made as follows.

(1) The yarn is non-elastic and non-stretchable.

(2) The yarns are continuous during the braiding process and there is no interaction between the yarns.

(3) The position of the yarn falling on the mandrel remains constant.

(4) The yarn weight is ignored, and gravity and inertial effects are not considered.

If the braiding machine speed is $n_{0}$ , the transmission ratio is $i_{n}$ , the number of yarn in clockwise or counter-clockwise is n, and the angle between yarn and the horizontal direction is θ(t), so we can get

θ (t) = \frac{4 π n_{0} t}{n \cdot i_{n}}

(1)

The braiding machine chassis radius is R, and the radius of mandrel is r_m; take the guiding ring center as the origin of coordinate system, the horizontal right as the x-axis, and the vertical upward as the y-axis.

In the chassis position of braiding machine, the clockwise yarn is led out from the carrier at position I; the coordinates of point I are

I : {\begin{cases} x^{2} + y^{2} = R^{2} \\ y = x \tan θ \end{cases}; (x < 0, y < 0)

(2)

Similarly, the counter-clockwise is led out from the carrier at point J; the coordinates of point J are

J : {\begin{cases} x^{2} + y^{2} = R^{2} \\ y = x \tan θ \end{cases}; (x > 0, y < 0)

(3)

The angle between OI/OJ and the clockwise/counter-clockwise yarn is φ₀; then

\sin φ_{0} = \frac{r_{m}}{R}

(4)

The clockwise yarn equation through point I is

L_{I}^{k} : Y = \tan (θ - φ_{0}) (X + \frac{R}{\sqrt{1 + \tan^{2} θ}}) - \frac{\tan θ R}{\sqrt{1 + \tan^{2} θ}}

(5)

After simplification, the clockwise yarn equation is

L_{I}^{k} : Y = \tan (θ_{t} - φ_{0} + \frac{2 π k}{n}) [X + R \cos (θ_{t} + \frac{2 π k}{n})] - R \sin (θ_{t} + \frac{2 π k}{n})

(6)

Similarly, the counter-clockwise yarn equation is

L_{J}^{k} : Y = \tan (- θ_{t} - φ_{0} + \frac{2 π k}{n}) [X - R \cos (θ_{t} + \frac{2 π k}{n})] - R \sin (θ_{t} + \frac{2 π k}{n})

(7)

In the braiding process, the clockwise and counter-clockwise yarns are distributed uniformly, and their numbers are n, respectively, and the spatial position of interlace point P_k is expressed as

{\begin{cases} Y = \tan (θ_{t} - φ_{0} + \frac{2 π k_{1}}{n}) [X + R \cos (θ_{t} + \frac{2 π k_{1}}{n})] - R \sin (θ_{t} + \frac{2 π k_{1}}{n}) \\ Y = \tan (- θ_{t} - φ_{0} + \frac{2 π k_{2}}{n}) [X - R \cos (θ_{t} + \frac{2 π k_{2}}{n})] - R \sin (θ_{t} + \frac{2 π k_{2}}{n}) \end{cases}

(8)

where

k_{1} = 0, 1, 2, \dots, n - 1

k_{2} = 0, 1, 2, \dots, n - 1

The analysis of yarn interlace

In order to analyze the yarn interlace, denote the machine coordinate system. For the interlaced points on a single braided yarn, without prejudice to the generality, fixed $k_{1} = 0$ , so that $k_{2}$ is able to iterate through all values, all the interlaced points on the specific braided yarn with respect to the parameters can be obtained. The x-axis coordinates points P_k can be obtained as

X_{P_{k}} = \frac{\tan (- θ_{t} - φ_{0} + \frac{2 π k_{2}}{n}) \cos (θ_{t} + \frac{2 π k_{2}}{n}) + \tan (θ_{t} - φ_{0}) \cos θ_{t} + \sin (θ_{t} + \frac{2 π k_{2}}{n}) - \sin θ_{t}}{\tan (- θ_{t} - φ_{0} + \frac{2 π k_{2}}{n}) - \tan (θ_{t} - φ)} R

(9)

Taking x-axis coordinates into the clockwise yarn equation, the y-axis coordinates $Y_{P_{k}}$ of point P_k can be obtained. Obviously, in braiding process, the point P_k coordinate value needs to satisfy

r_{m}^{2} \leq X^{2} + Y^{2} \leq R^{2}

(10)

According to equation (10), the distance from the braiding point to the braiding center is

r_{P_{k}} = \sqrt{X_{P_{k}}^{2} + Y_{P_{k}}^{2}}

(11)

The farthest braiding point from the center of braiding machine chassis is P₀, and the distance from the braiding point to the braiding center is

r_{\max} = \max (r_{P_{k}}) = r_{P_{0}}

(12)

According to the track-change interlocking process theory, it is necessary to change the track once every certain time in braiding process, so that the left and right sides of the braided net are interlace together to form a three-dimensional braided net. The time of track-change interlocking braiding is t₀, so the interlace point in two adjacent is

K = \frac{n_{0} t_{0} n}{3600 i_{n}}

(13)

The braided nets on both sides have been braided to form a three-dimensional braided net at the braiding point, with the current yarn changing its track, causing the braided net on the left and right sides to split at the braiding point P_k. The diagram of side view of braided net bifurcation is shown in Figure 4.

Analysis of minimum yarn tension based on track-change interlocking braiding

The yarn distribution in braiding process

The three-dimensional braiding machine with track-change interlocking mechanism has a guiding ring on each side of braiding center, called guiding ring 1 and guiding ring 2, respectively. If the guiding ring deviates from the symmetrical center distance e of the left and right braided net, then the “two-in-one” three-dimensional braided net will deviate from the left and right braided symmetry centers under the action of yarn, and pull the interlace point P_k away from the symmetry center line.

Taking the center of braiding machine chassis as the initial point, the horizontal right direction is the x-axis, and the vertical upward direction is the y-axis, the rectangular coordinate system is established. It can be seen that the equivalent force at the one-sided braided net F is variable, it fluctuates with the change of braided yarn, and the extreme value is taken when the braided yarn is uniformly distributed and overlapped.

When the braiding yarn is evenly distributed in the circumferential direction in braiding process, the length of arc segment clamped by the angle between the two adjacent braiding yarns is approximately equal to horn gear radius r_h. Make a straight line along the angle bisector between two adjacent yarns, then the angle is the half of β, and the circumferential uniform distribution is

{\begin{cases} \sin (\frac{β_{1}}{2}) = \frac{r_{h}}{2 l_{1}} \\ \tan (\frac{β_{1}}{2}) = \frac{r_{m}}{\sqrt{R^{2} - {r_{m}}^{2}} - l_{1}} \end{cases}

(14)

In the equation, l₁ is the length from the intersection point of two adjacent braided yarns to the yarn outlet, and β₁ is the angle between the two adjacent braiding yarns.

When the braiding yarn overlaps and is evenly distributed, the length of arc segment clamped by the angle between the two adjacent braiding yarns is approximately equal to two doubles of horn gear. The overlapping uniform distribution is

{\begin{cases} \sin (\frac{β_{2}}{2}) = \frac{r_{h}}{l_{2}} \\ \tan (\frac{β_{2}}{2}) = \frac{r_{m}}{\sqrt{R^{2} - {r_{m}}^{2}} - l_{2}} \end{cases}

(15)

In the equation, l₂ is the length from the intersection point of two adjacent braided yarns to the yarn outlet, and β₂ is the angle between the adjacent two braiding yarns.

As the total number of independent yarns in the braiding machine increases, the central angle between adjacent yarns decreases inversely. The angles of β₁ and β₂ between yarns can be concluded that:

{\begin{cases} β_{1} = \frac{2 (2 r_{m} + r_{h})}{\sqrt{R^{2} - {r_{m}}^{2}}} \\ β_{2} = \frac{4 (r_{m} + r_{h})}{\sqrt{R^{2} - {r_{m}}^{2}}} \end{cases}

(16)

The minimum yarn tension

In order to determine the spatial position of braided net on the left and right sides after the deviation, the angles between the braided net on the left and right sides, the three-dimensional braided net, and the symmetrical center line are taken as γ₁, γ₂, and γ₃, and the tension of each yarn is T.

Accordingly, during the movement of braiding yarns, an equivalent resultant force F is formed on one side of braided net, and the equivalent magnitude of resultant force fluctuates with the braiding process.

2 n T \cos [\frac{4 (r_{m} + r_{h})}{\sqrt{R^{2} - {r_{m}}^{2}}}] \leq F \leq 2 n T \cos [\frac{2 (2 r_{m} + r_{h})}{\sqrt{4 R^{2} - {r_{m}}^{2}}}]

(17)

Assuming that the space position $(e_{P_{K}}, r_{P_{K}})$ of interlace point P_k is in last track-change, according to the balance of left side braided net, right side braided net, and three-dimensional braided net at the bifurcation point, the balance equation can be listed as follows:

{\begin{cases} \tan γ_{1} = \frac{2 r_{h} + r_{t} + e_{P_{k}}}{R - r_{P_{k}}} \\ \tan γ_{2} = \frac{2 r_{h} + r_{t} - e_{P_{k}}}{R - r_{P_{k}}} \\ \tan γ_{3} = \frac{e - {e_{P}}_{k}}{r_{P_{k}} - r_{m}} \\ F \sin γ_{1} = F \sin γ_{2} + 2 F \sin γ_{3} \end{cases}

(18)

In the equation, r_t is the radius of track-change interlocking mechanism.

According to equation (18), the spatial position $(e_{P_{K}}, r_{P_{K}})$ fluctuation range of interlace point P_K can be formulated.

Assuming that the number of carriers on the left and right sides in the circumferential track-change is n_c, then with the continued braiding progress, the yarn carried by the left carrier in track-change interlocking mechanism will pull the left braided net to the right side, while the yarn carried by the right carrier in track-change interlocking mechanism will pull the right braided net to the left side until it is braiding to the interlace point P_k. The left and right sides of braided net form a three-dimensional braided net. In order to complete the above process, the component force of resultant force of yarn tension carried by the carrier in track-change interlocking mechanism on the left and right sides in the horizontal direction needs to be greater than the component force of resultant force of braided net in the horizontal direction. The equation is as follows:

n_{c} T \geq F_{\max (\sin γ_{1}, \sin γ_{2})}

(19)

Without loss of generality, taking the right guiding ring as an example, the fluctuation range of equivalent resultant force F in the unilateral braiding net is introduced. It can be seen that the minimum tension of each yarn is

n_{c} \cdot T_{\min} = F \sin γ_{1}

(20)

The minimum yarn tension is

T_{\min} = \frac{2 n_{c} T (2 r_{h} + r_{t} + e_{P_{k}}) \cos [2 (r_{h} + r_{m}) / \sqrt{R^{2} - {r_{m}}^{2}}]}{n_{c} \sqrt{{(2 r_{h} + r_{t} + e_{P_{k}})}^{2} + {(r_{P_{0}} - r_{P_{k}})}^{2}}}

(21)

In the braiding process, yarn slip over guide ring can extend yarn tension, so in the calculation process the minimum yarn tension should take into account the f_s and F_r, where f_s is the force of yarn slip and F_r is the friction between guide ring and yarn; the yarn and guide ring interaction model is shown as Figure 5.

The slip force f_s can be expressed as

f_{s} = μ T

(22)

So the minimum yarn tension is

T_{\min} = \frac{2 n_{c} T (2 r_{h} + r_{t} + e_{P_{k}}) \cos [2 (r_{h} + r_{m}) / \sqrt{R^{2} - {r_{m}}^{2}}]}{n_{c} \sqrt{{(2 r_{h} + r_{t} + e_{P_{k}})}^{2} + {(r_{P_{0}} - r_{P_{k}})}^{2}}} + μ T

(23)

The coordinate system is established with the center of track-change interlocking mechanism as the initial position, the central axis of braiding machine chassis as the x-axis, and the symmetrical center line of left and right braided layers as the y-axis.

During the track-change interlocking braiding process, as shown in Figure 6, the yarn is divided into two ends, one end of the yarn carrier by the carrier in the track-change interlocking mechanism fell on the mandrel, and the other end of the yarn is at the yarn outlet.

The height variation of carrier is ignored, and the spatial attitude variation of the carrier rotates around the horn gear is not considered, the braided net in left through bus point $(r_{t} - 2 r_{h}, 0, 0)$ and $(e_{P_{k}}, R - r_{P_{k}}, 0)$ , so the bus equations $Γ_{1}$ and $Γ_{2}$ can be express as follows:

{\begin{cases} \frac{x + 2 r_{h} + r_{t}}{2 r_{h} + r_{t} + e_{P_{k}}} = \frac{y}{R - r_{P_{k}}} \\ z = 0 \end{cases}

(24)

The braided net in left through bus point $(r_{t} + 2 r_{h}, 0, 0)$ and $(e_{P_{k}}, R - r_{P_{k}}, 0)$ , and the bus equation $Γ_{2}$ can be express as

{\begin{cases} \frac{x - 2 r_{h} - r_{t}}{2 r_{h} + r_{t} - e_{P_{k}}} = - \frac{y}{R - r_{P_{k}}} \\ z = 0 \end{cases}

(25)

The coordinates of interlace points $P_{0}$ and $P_{0}^{'}$ of yarn carried by the left and right track-change carriers passing through the bus bar $Γ_{1}$ and the bus bar $Γ_{2}$ side are:

At the other end of yarn carried by the left and right sides of track-change interlocking mechanism carrier, the spatial path equation $Γ_{t}$ of carrier in track-change interlocking mechanism is as follows:

{\begin{cases} x^{2} + z^{2} = {r_{t}}^{2} \\ y = 0 \end{cases}

(26)

Therefore, the endpoint on the other end of yarn through the spatial coordinates is $(r_{t} \cos φ_{r}, 0, r_{t} \sin φ_{r})$ , where $φ_{r}$ is the rotation angle of track-change interlocking mechanism.

In summary, the length of yarn S₁ carried by the left sides in track-change interlocking braiding process is

S_{1} = \sqrt{{[\frac{R - r_{P_{0}}}{R - r_{P_{k}}} (r_{t} + 2 r_{h} + e_{P_{k}}) - 2 r_{h} - r_{t} - r_{t} \cos φ_{r}]}^{2} + {r_{t}}^{2} \sin^{2} φ_{r} + {(R - r_{P_{0}})}^{2}}

(27)

Likewise, the length of yarn S₂ carried by the right sides in track-change interlocking braiding process is

S_{2} = \sqrt{{[\frac{R - r_{P_{0}}}{R - r_{P_{k}}} (e_{P_{k}} - 2 r_{h} - r_{t}) + 2 r_{h} + r_{t} - r_{t} \cos φ_{r}]}^{2} + {r_{t}}^{2} \sin^{2} φ_{r} - {(R - r_{P_{0}})}^{2}}

(28)

In the above equation, $r_{P_{0}}$ , $r_{P_{k}}$ , $e_{P_{k}}$ , and $φ_{r}$ are functions of time, which can cause the magnitude change of S₁ and S₂, and the amount of $Δ S$ change can be expressed as

Δ S = \max [\max (S_{i}) - \min (S_{i})]

(29)

where i is the non-negative integer, i = 1, 2.

The length of S₁ and S₂ is shown as Figure 7.

As can be seen from Figure 7, the length of yarn S₁ carried by the left side and the length of yarn S₂ carried by the right side show periodic changes, in which at the same moment, the length of yarn S₁ is greater than the length of S₂, and the yarn can be retracted and released freely during the braiding process. When designing the braiding carrier, the length of the yarn in the process of track-change interlocking braiding should also have a length difference; otherwise, after the release of the yarn in the process of track-change interlocking braiding, the yarn can’t be completely retracted, which leads to the relaxation of the tension of the yarn.

Yarn tension verification

Simulation analysis

In order to further analyze the yarn tension in the process of track-change interlocking braiding, MATLAB was used for simulation analysis and a 576 carrier three-dimensional braiding machine with track-change interlocking was selected as the simulation object. The main working parameters are shown in Table 1.

Table 1.

Working parameters of 576 carrier three-dimensional braiding machine.

$n_{0} (r / s)$	$r_{m} (m m)$	$t_{0} (s)$	n	$r_{h}$	$r_{t} (m m)$
300	400	2	144	49.9	68.47
$i_{n}$	$e (m m)$	$R (m m)$	$n_{c}$	$T (N)$	$n_{c a r r i e r}$
10	46	1843.5	12	5	576

The variation of yarn tension was simulated using MATLAB software, and the minimum yarn tension versus time curve for each yarn was obtained as follows:

As shown in Figure 8, the yarn tension shows periodic changes, with sharp fluctuations as time increases, the minimum yarn tension is 10 N, and the yarn tension ranges from 3.5 N to 10 N.

Yarn tension detection mechanism design

In order to verify the accuracy of the mathematical analysis and MATLAB simulation of the yarn tension during the braiding process, actual measurements were used to obtain the yarn tension.

During the working process of the braiding machine, the detected yarn tension signal is transmitted by means of wireless signal transmission, comparing the three different wireless signal transmission methods and their transmission characteristics as shown in Table 2.

Table 2.

Comparison of characteristics of three signal transmissions.

Transmission method	Bluetooth	Zigbee	Wi-Fi
Operating frequency	2.4 GHz	2.4 GHz	2.4 GHz
Transmission distance	10∼100 m	10∼75 m	20∼200 m
Power consumption	Low	Low	High
Transmission speed	1 mbps	250 kbps	11∼54 mbps
Anti-interference capability	Strong	Strong	General
Security comparison	High	Medium	Low

Since the braiding machine workplace is noisy, the signal transmission method needs to have strong anti-interference ability. At the same time, the yarn tension fluctuates greatly, and the signal response speed is also required to be high. After comprehensive consideration, Bluetooth transmission is selected to transmit the detected yarn tension signal.

The process of data acquisition is often accompanied by outliers, which significantly deviate from the detection data and need to be identified and processed.^12–14 Grubbs’ test or Z-score require numerical thresholds and lack immediate visual context. Grubbs’ test and Z-score assume normality; but the yarn tension is not normality, and violations can lead to false positives/negatives. Box plots are a method of describing data using the maximum, minimum, median, upper quartile, and lower quartile of the data, and can reflect the data distribution of outliers.^15–17 After identifying the outliers, Lagrange interpolation is applied to replace the outliers. The structure of the box plot is shown in Figure 9.

One of the functions of box plots is to identify outliers, which are determined when the data is greater than the maximum value or less than the minimum value.¹⁸ The difference between the upper quartile and the lower quartile is called the interquartile range (IQR), which is used to indicate the dispersion of the data. k is the outlier factor, usually 1.5 or 3. The larger the k value, the farther the outlier cutoff point is from the box, and the more the detected point deviates from the main distribution area of the data. When k is 1.5, the outlier cutoff point is called the inner limit, and when k is 3, the outlier cutoff point is called the outer limit. The outliers between the inner and outer limits are called mild outliers, and the outliers outside the outer limit are called extreme outliers.

Lagrange interpolation approximates the relationship between input and output through a polynomial function. For n+1 collected sample points (x₀,y₀),…,(x_i,y_i),…,(x_n,y_n), given any x in [a,b], the corresponding estimate at x can be computed as follows:

L_{n} (x) = \sum_{i = 0}^{n} y_{i} l_{i} (x)

(30)

l_{i} (x) = \prod_{j = 0, j \neq i}^{n} (x - x_{i}) / (x_{i} - x_{j})

(31)

where Ln(x) is the Lagrange interpolation polynomial, i is the number of n+1, y_i is the value of the function at x_i, x_i and x_j are the reciprocal nodes, and l_i(x) is the basis function.

Improved box plot outlier processing steps: step 1, solve for the upper quartile Q_U, lower quartile Q_L, and median of the data; step 2, set max = Q_U+1.5(Q_U−Q_L), min = Q_L−1.5(Q_U−Q_L); step 3, determine the outliers if data>max or data<min are satisfied; step 4, delete the outliers, and use the Lagrange interpolation method to fill in the resulting vacant values; and step 5, repeat steps 1 to 4 to test the handling of outliers.

Experiments

In order to verify the yarn tension model on the real-time detection, yarn tension in 576 carrier three-dimensional braiding machine with track-change interlocking, tension detection experiments are carried out, and the experimental equipment is shown in Figure 10. The experimental equipment includes 576 carrier three-dimensional braiding machine with track-change interlocking, TOF laser distance sensor, tension detection lower unit, Bluetooth communication device, upper unit, lithium battery, computer, and so on. During the braiding process, the carrier moves along the track under the drive horn gear, and the yarn is intermittently released from the carrier upper eyelet under the action of the traction device, the TOF laser ranging sensor transmits the detected slider displacement data to the host computer through the Bluetooth communication device, and the host computer completes outlier processing, and converts it into yarn tension through the displacement-tension model. The detected yarn tension is displayed in a visual form on the host computer.

Since the movement process of carrier and track-change interlocking mechanism are the main conditions that affect the yarn tension, the different yarn has a smaller effect on the tension. Therefore, we only chose glass fibers as an example for the validation of the kinematic model of yarn tension. The fiber used in the experiment is glass fiber, purchased from China Jushi Group, and the model of glass fiber is E8, which has a high modulus, compared with the traditional E glass fiber; the modulus of E8 is increased by 7%∼17%, which improves the deformation-resistant ability of the material. When making composite materials, the molding process is simple and the mechanical properties are good (Table 3).

Table 3.

The parameters of glass fiber.

Model	Elongation at break	Density	Modulus of elasticity
E8	≥4.8%	2.4∼2.76 g/cm³	>95 Gpa

When the braiding machine is in operation, the yarn is released from the carrier outward under the action of the traction mechanism, and the displacement of the slider changes, the detected data is transferred to the upper computer, which calculates the yarn tension, filters the signal and processes the outliers, and finally outputs the yarn tension fluctuation graph.

The analysis of the frequency-domain curve of the tension of the yarn shows that there is random noise in the process of signal acquisition by the sensor.¹⁹ Random noise is generated due to sensor electronic noise, interference in the environment, etc. Random noise is characterized by a uniform distribution and small amplitude in terms of magnitude and no clear pattern in terms of frequency. In the detection process, in addition to random noise, there is also impulse noise, which is caused by mechanical vibration impact, electrical interference causes, characterized by short duration and high amplitude. Not only is there noise but there are also outliers in the detection, which need to be processed.

According to the original data of yarn tension in the braiding with track-change interlocking process obtained from the experiment, the sliding correlation filtering algorithm proposed by me is used to filter the original data, and then the outlier processing is carried out. The following figure shows the yarn tension curve after filtering and the yarn tension before filtering.

As shown in Figure 11(a), the amplitude is larger at the frequency of 0, with a maximum of 0.3, and the amplitude decreases with the increase of the frequency, and after 2 Hz, the amplitude is less than 0.18. As shown in Figure 11(b), the yarn tension is a minimum of 2.26 N, and a maximum of 6.67 N, and the yarn tension shows a large fluctuation. This may be related to the different stages of the carrier releasing the yarn during the braiding process. In Figure 2(f), when the yarn is released, the compression of spring 2 by the slider decreases, and the yarn shows fluctuation in tension. Also, carrier vibration during the braiding process and friction between the yarns can cause tension fluctuations.

There are outliers in the yarn tension detection, and the yarn tension graph obtained before and after removing the outliers using the box plot method is shown below.

As shown in Figure 12(a), the amplitude of yarn tension decreases after removing the outliers, and the amplitude is less than 0.18 after the frequency is greater than 0.6 Hz. As shown in Figure 12(b), the minimum value of yarn tension is 4.25 N, and the maximum value of yarn tension is 6.52 N, and the fluctuation of yarn tension decreases after the removal of the outliers.

Since the track-change interlocking process is an important stage that affects the braiding effect, the degree of yarn tension regulation in this stage directly affects the braiding quality of the preform, so the yarn tension in this stage is optimized, and the yarn tension before and after the optimization is shown in Figure 13.

As shown in Figure 13(b), after optimization, the fluctuation amplitude of yarn tension at the stage of track-change is reduced, the maximum value of yarn tension at the stage of track-change before optimization is 7.08 N, and the maximum value after optimization is 6.53 N, which is reduced by 8.42%; the minimum tension of yarn at the stage of track-change before optimization is 1.57 N, and the minimum tension after optimization is 1.50 N, which is reduced by 4.67%.

The carrier yarn release stage and the track-change stage are important stages for the influence of yarn tension, and the fluctuation of yarn tension is related to the uniformity of yarn covering on the surface of the mandrel. In actual production, the mandrel traction velocity can be reduced during the track-change interlocking of the track-change mechanism, in order to reduce the fluctuation of yarn tension.

After obtaining the data results, the model should be tested to determine the correctness of the results.²⁰ Six time points were selected, three data at each time point, and the mean and mean squared deviation were obtained, and the error bar graph was plotted as shown in Figure 14.

As shown in Figure 14(a), the yarn tension is minimum when the time is 1s, the yarn tension error is maximum when the time is 3s, and the mean square error is 0.79, and the yarn tension error is minimum when the time is 2s, and the mean square error is 0.17; from Figure 14(b), the yarn tension error is reduced after optimization, and the yarn tension error is minimum when the time is 1s, and the mean square error is 0.15, and when the time is 3s, the yarn tension error is the largest and the mean square deviation is 0.31.

Conclusion

This paper models and analyzes the yarn tension in the track-change interlocking braiding process, and establishes the yarn kinematics model by analyzing the process characteristics of carrier release yarn, analyzing the motion characteristics of single yarn and multiple yarns in the process of track-change interlocking braiding, and combining with the characteristics of the track-change braiding machine. The theoretical model of minimum yarn tension is established and the yarn tension equation is deduced through the operation mechanism of the track-change interlocking mechanism. The conclusions are as follows.

(1) According to the four stages of carrier releasing yarn, the variation of yarn tension under three different yarn release velocity of low, medium, and high velocity is found, and the maximum yarn tension is 11.12 N and the minimum yarn tension is 1.56 N.

(2) Analyze the yarn movement in the process of track-change interlocking braiding, establish the yarn tension model, get the theoretical yarn tension, and simulate with MATLAB to get the yarn tension. The yarn tension shows periodic changes, with sharp fluctuations as time increases, and the yarn tension ranges from 3.5 N to 10 N.

(3) The braiding experiment is carried out, and the box plot method and Lagrange difference method are used to deal with the outliers in the experiment and optimize the yarn tension in the track-change process. After optimization, the maximum value of yarn tension was reduced by 8.42% and the minimum value of yarn tension was reduced by 4.67%.

Footnotes

Acknowledgments

The authors acknowledge Innovation Fund of National Commercial Aircraft Manufacturing Engineering Technology Research Center (COMAC-SFGS-2023-2207) and Open Subject Fund of Collaborative Innovation Center of Donghua University for Civil Aviation Composites (24S28102/016) for their financial support.

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) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work is supported by Innovation Fund of National Commercial Aircraft Manufacturing Engineering Technology Research Center (COMAC-SFGS-2023-2207); and Open Subject Fund of Collaborative Innovation Center of Donghua University for Civil Aviation Composites (24S28102/016).

ORCID iD

Gaowei Cai

Data Availability Statement

Data will be made available on request.*

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