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Abstract

A low-quality unwinding process of the unwinding machine can lead to downtime of the knitting machine and loss of fabric quality. To address this issue, we studied the tension and vibration of carbon fiber yarns during unwinding. Based on the theory of axially moving strings, the dynamic model of carbon fiber yarn was established during the unwinding process, bringing the parameters into the simulation. According to the simulation results, the yarn tension in the unwinding process is closely related to the spring preload, which needs control within a certain range. When the unwinding speed increases, the fluctuation amplitude, lateral vibration amplitude, and axial vibration amplitude of the yarn tension gradually increase, causing friction and wear of the carbon fiber yarn. By controlling factors such as spring preload, unwinding speed, and the number of bobbins unwound simultaneously, one can effectively control the yarn’s vibration and improve the quality of the yarn.

Keywords

Axial moving string vibration yarn tension dynamic model carbon fiber unwinding machine

Introduction

The unwinding process is the preparatory process for the weaving machine. Before carbon fiber weaving, the carbon fiber needs to be wound onto the bobbin through the Unwinding machine; that is, the carbon fiber is unwound from the raw yarn bobbin to the bobbin of the spindle.

Filament winding products are significant in product weight reduction and can ensure the comprehensive performance of products such as high strength, corrosion resistance, and fatigue resistance while reducing product weight. In composite materials, filament winding is an important processing technology. Therefore, fiber composite winding technology has become popular in parts manufacturing such as aircraft, launch vehicles, artificial satellites, and space stations.¹

Zhao Zhan² studied the development of knitting machines and weaving technology; with the improvement of the performance requirements of woven fabrics, the requirements for knitting machines will also increase. In particular, the problems of low efficiency, bulky size, high cost, and poor product uniformity and repeatability of 3D weaving have seriously limited its development and popularization. Moreover, it also pointed out some future research hotspots for knitting machines, such as increasing the degree of automation, increasing the number of simultaneously braided yarn bundles, and precise control of the braiding process.

China’s high-performance fiber polymer field has made significant progress and technological breakthroughs, impacting the leading position of Japan, Europe, and the United States. The composite material has good stability and strong corrosion resistance. Furthermore, it has good thermal conductivity and sound insulation effect.^3,4 The material is also widely used in textile, aerospace, military and other industries. It can replace workpieces that have been difficult to meet in production requirements or design requirements that are difficult to meet with general materials after a textile machine forms the carbon fiber yarn according to a given weaving process.

The research on axial motion string vibration and vibration control has high theoretical and practical significance. Many researchers studied the axial motion strings from the earlier experiments and observations of Aiken⁵ and Skutsch⁶ in 1878 from different application scenarios, models, and experiments. Zhang Wei and Liqun Chen⁷ studied the longitudinal vibration control of an axially moving string-coupled system based on the transmission principle of traveling wave energy. In 2014, Liqun Chen⁸ studied active and adaptive control of linear and nonlinear vibration of axially moving strings and proposed some potential research topics. Pham and Hong⁹ summarized 33 partial differential equation models from various fields of dynamics of the axial motion system. The model guides choosing the appropriate model and analysis for the dynamic analysis of various composite materials. Liqun Chen^10–16 made a detailed review of the research progress of axially moving string transverse nonlinear vibration. Mote,¹⁷ Ulsoy,¹⁸ Wickert and Mote,¹⁹ Wang and Liu,²⁰ Abrate,²¹ and others who have made more comprehensive summaries at different times. The researchers also expounded on the research status of the vibration problem of axially moving strings in different periods.

The development of composite materials has brought a lot of interdisciplinary space. The application of carbon fiber in the textile field is a good example. It is extremely important to have bobbins with high unwinding quality for the weaving process and winding process of carbon fiber yarns. Taking advantage of the characteristics of carbon fiber, such as lightweight, high strength, and flexibility, the combination of weaving technology and robotics provides an opportunity to manufacture preforms useable in longitudinal and hollow parts.²² The three-axis circular weaving process and an improved mechanical structure of the carrier proposed by Yujing Zhang^23,24 can significantly reduce the friction problem in the weaving process of the multi-dimensional braiding machine providing a better space for the weaving process and weaving volume after weaving and molding. We can obtain the required workpiece by hardening, and this plays a massive role in aerospace, military industry,²⁵ automobile manufacturing,²⁶ and the new lithium batteries.

During the unwinding process before weaving, the tension change and vibration of carbon fiber yarn are still to be studied. When there is uneven tension in the carbon fiber multifilament and breaking of some monofilaments, it is very easy to cause problems such as downtime during the weaving process and reduced fabric quality. This problem will directly determine the quality of the bobbin after completing the unwinding process.

In this paper, we investigated the unwinding process of carbon fiber yarn to establish a dynamic model of the yarn unwinding process. Further, we analyzed the tension and vibration of the carbon fiber yarn and optimized the structural parameters of the guide wheel. Moreover, we reduced the yarn amplitude and the fluctuation of yarn tension, making the beating process stable and improving the quality. Thus we avoided stoppages and fabric defects caused by low unwinding quality during weaving.

Modeling of carbon-fiber yarn unwinding process

Unwinding machine and principle of carbon fiber bobbin

Before carbon fiber weaving, we need to wound the carbon fiber onto the bobbin through the unwinding machine; that is, to unwind the carbon fiber from the raw yarn bobbin to the bobbin of the spindle. The process mentioned above plays a crucial role in the subsequent unwinding process. In case of poor quality of yarn unwinding, the resulting uneven tension in the carbon fiber tow and filament breakage can significantly disrupt production and reduce fabric quality during weaving. Therefore, ensuring high-quality yarn unwinding is essential to prevent these issues from occurring. The quality of unwinding is related to the yarn tension and vibration set in the process of unwinding. It is imperative to investigate the dynamic behavior of yarn during spinning and develop a dynamic model of the unwinding process to minimize yarn vibration, reduce tension fluctuations, and stabilize the yarn spinning process.

Figure 1 shows the machine for unwinding the yarn from the bobbin to the bobbin during the spinning process.

Figure 1.

Unwinding machine.

On the mounting frame of the raw silk drum, the raw silk drum is clamped by two friction plates on the left and right and is installed on the rotating shaft together. By applying spring pressure to the friction plate’s end face on the mounting bracket’s right side, the spring pressure’s size directly affects the output yarn’s tension. On one side of the bobbin, the bobbin is mounted on a rotating shaft driven by a motor and rotates at a set speed. The main motor drives the polished rod through the transmission mechanism, which can control the lateral movement speed of the yarn during winding. The carbon fiber yarn is discharged from the raw yarn tube and wound onto the yarn tube through the guide wheel on the polished rod straightener.

The mechanical principle of the unwinding machine is shown in the corresponding mechanical schematic diagram in Figure 2. As shown in the figure, releasing the carbon fiber yarn with the rotation of the original bobbin and, at the same time, controlled by the yarn unwinder to wind onto the target bobbin. The yarn is under tension during the unwinding process. Friction plates $1$ and $2$ are clamped by the spring pressure to clamp the original yarn cylinder and are coaxially installed on the support frame.

Figure 2.

Schematic diagram of the unwinding machine.

We installed the yarn at the other end of the carbon fiber yarn, keeping its axis parallel to the axis of the original yarn spool.

The parameter assignment for the unwinding process is shown in Figure 3. $L$ is the length of the carbon fiber yarn, $s_{1}$ is the original bobbin length, $s_{2}$ is the length of the bobbin on the spindle, $ω_{1}$ is the angular velocity of the unwinding of the original bobbin, $ω_{2}$ is the angular velocity of the spinning bobbin on the spindle, $R_{1}$ is the actual radius when the original bobbin is unwound, $R_{0}$ is the full yarn radius of the original bobbin, $R_{i}$ is the yarn-free radius of the original bobbin, $r_{0}$ is the radius of the empty bobbin, $r_{2}$ is the actual radius when the bobbin is unwinding, $m_{0}$ is the quality of the empty bobbin, $θ_{1}$ is the yarn winding angle, $m_{f}$ is the mass of the friction plate, $J_{f}$ is the moment of inertia of the friction plate, $μ$ is the friction coefficient of the friction plate, $N_{2}$ is the spring pressure on the right side, $b$ is the pitch when the carbon fiber yarn is full row, $δ$ is the thickness of the single-layer carbon fiber yarn, $A$ is the cross-sectional area of a single carbon fiber yarn, $T$ is the internal tension of the yarn, $M_{1}$ and $M_{2}$ are the frictional forces on both ends of the original filament tube, $k$ is the stiffness of the spring.

Figure 3.

Tension system during unwinding.

This study is carried out in four parts, as shown in Figure 4. First, we established the force analysis of the yarn beating process and the kinetic model, then determined the boundary conditions and parameters and solved the kinetic equations. Finally, we analyzed the influence of process parameters on the yarn-beating process according to the simulation results.

Figure 4.

Work flow.

Modeling of the tension system during unwinding

Yarn tension partial differential equation system based on axial moving string

The process of unwinding the yarn from the original bobbin to the bobbin can be regarded as an axially moving string with a certain tension, generating transverse and axial vibrations during the movement. We establish the coordinates by taking the axial movement direction of the chord as the x-axis and the lateral direction as the y-axis. Suppose we assume the axial displacement of the chord, the axial velocity, and lateral displacement are $u (x, t)$ , $v (x, t)$ and $w (x, t)$ , from the Euler differential equations of motion of the continuum, we can establish the following dynamic equations (1∼2)

\begin{array}{l} \sum F_{x} = m \frac{d^{2} u}{d t^{2}} \\ ρ A (\frac{\partial u}{\partial t^{2}} + \frac{d v}{d t} (1 + \frac{\partial u}{\partial t}) + 2 v \frac{\partial u^{2}}{\partial x \partial t} + v^{2} \frac{\partial^{2} u}{\partial x^{2}}) = E A (\frac{\partial^{2} u}{\partial x^{2}} + \frac{\partial w}{\partial x} \frac{\partial^{2} w}{\partial x^{2}}) \end{array}

(1)

\begin{array}{l} \sum F_{y} = m \frac{d^{2} w}{d t^{2}} \\ \begin{array}{l} ρ A (\frac{\partial^{2} w}{\partial t^{2}} + \frac{d v}{d t} \frac{\partial w}{\partial x} + 2 v \frac{\partial^{2} w}{\partial x \partial t} + v^{2} \frac{\partial^{2} w}{\partial x^{2}}) + \tilde{E} I_{z} \frac{\partial^{4} w}{\partial x^{4}} + f_{g} (x, t) - T \frac{\partial^{2} w}{\partial x^{2}} = \\ E A (\frac{\partial u}{\partial x} \frac{\partial^{2} w}{\partial x^{2}} + \frac{\partial^{2} u}{\partial x^{2}} \frac{\partial w}{\partial x} + \frac{3}{2} {(\frac{\partial w}{\partial x})}^{2} \frac{\partial^{2} w}{\partial x^{2}}) \end{array} \end{array}

(2)

In the formula,

ρ A

is the linear density of carbon fiber,

ρ

is the density of carbon fiber, and

A

is the cross-sectional area of carbon fiber.

E A

is the flexural rigidity of carbon fiber and

E

is the elastic modulus of carbon fiber.

\tilde{E} I_{z}

is the flexural section coefficient of carbon fiber

f_{g}

, the transverse uniform load of carbon fiber under its gravity, and

T

the internal tension of the carbon fiber yarn.

They are establishing the constitutive equation (3) of carbon fiber strings.

ε = \frac{\partial u}{\partial x} + \frac{1}{2} {(\frac{\partial w}{\partial x})}^{2}

(3)

In the equation,

ε

is the internal strain of the carbon fiber string.

According to the geometric relationship during unwinding, the axial velocity of the carbon fiber string should satisfy

\tilde{e} (x, t) = ω_{2} r_{2} - ω_{1} R_{1}

(4)

In the equation,

ω_{2}

is the angular velocity of the bobbin end

r_{2}

the real-time radius when the bobbin is wound, and

ω_{1}

the angular velocity of the yarn bobbin end;

R_{1}

is the actual radius of the yarn bobbin unwinding.

Assuming that before unwinding, the initial radius of the original filament tube is $R_{0}$ , the original bobbin without yarn radius is $R_{i}$ . The radius when there is no yarn in the bobbin is $r_{0}$ . The relationship between the original bobbin’s radius and the new one should satisfy

(r_{2}^{2} - r_{0}^{2}) s_{2} = (R_{0}^{2} - R_{1}^{2}) s_{1}

(5)

Suppose the yarn completes the movement from one end to the other in every $n$ circle of the yarn discharger. In that case, the relationship between the angular velocity of the yarn spool and the radius of the spool is as shown in

\frac{ω_{2} t}{n} δ = r_{2} - r_{0}; n = \frac{s_{2}}{b}

(6)

The equation shows $δ$ is the thickness of the single-layer carbon fiber yarn, $s_{2}$ the bobbin length, and $b$ the yarn pitch.

When the carbon fiber yarn is unwound from the original bobbin, friction forces $M_{1}$ and $M_{2}$ affect the left and right ends; concurrently, the active pulling force is the tension of the carbon fiber yarn. If the yarn winding angle of the original filament cylinder at the time of winding preparation is $θ_{1}$ , then there is an angle between the tension of the carbon fiber and the x-axis at the time of rewinding, which is also the yarn winding angle $θ_{1}$ . After analyzing the force of the original bobbin, we can get the equations (7∼13)

J_{R} {\dot{ω}}_{1} = M_{1} + M_{2} + T (0, t) R_{1} \cos θ_{1}

(7)

J_{R} = ρ \frac{π {(R_{1}^{2} - R_{i}^{2})}^{2} s_{1}}{8} + 2 J_{f} + J_{0}

(8)

M_{1} = μ {({({(- 1)}^{[\frac{ω_{1}}{n}]} T (0, t) \sin θ_{1} + N_{2})}^{2} + {(\frac{1}{2} (2 m_{f} + m_{R} + m_{0}) g)}^{2})}^{\frac{1}{2}}

(9)

M_{2} = μ {(N_{2}^{2} + {(\frac{1}{2} m_{R} g)}^{2})}^{\frac{1}{2}}

(10)

m_{R} = \frac{π (R_{1}^{2} - R_{i}^{2}) s_{1}}{4}

(11)

v (x, t) = ω_{2} r_{2}

(12)

T (x, t) = {\begin{cases} \bar{p} + E A ε (x, t) = \bar{p} + E A (\frac{\partial u}{\partial x} + \frac{1}{2} {(\frac{\partial w}{\partial x})}^{2} + \tilde{e}), \frac{\partial u}{\partial x} \geq \frac{- \bar{p}}{E A} \\ 0, \frac{\partial u}{\partial x} \geq \frac{- \bar{p}}{E A} \end{cases}

(13)

Equations (7∼13) $J_{R}$ is the moment of inertia of the yarn drum, which changes with time. $J_{0}$ is the moment of inertia of the empty yarn of the original yarn package. $J_{f}$ is the moment of inertia of the friction plate. $μ$ is the friction coefficient of the friction plate. $s_{1}$ is the length of the original bobbin. $N_{2} = k λ$ is the pressure of the right spring, $k$ is the spring stiffness coefficient, $λ$ is the spring preload length and $\bar{p}$ is the initial tension inside the carbon fiber string.

Additional strain

\tilde{e} (t) = \frac{\int_{0}^{L} e_{x} d x = (ω_{2} r_{2} - ω_{1} R_{1})}{L}

(14)

Separating parameters to solve equations

Combining the above equations, we can obtain the dynamic equations of carbon fiber strings. For us to solve the above equations (7∼14), we separated the axial displacement $u (x, t)$ and the lateral displacement $w (x, t)$ by parameters

u (x, t) = \sum_{t = 1}^{N} ϕ_{r} (x) p_{r} (t); w (x, t) = \sum_{t = 1}^{M} ϕ_{r} (x) q_{r} (t)

(15)

Bringing equation (15) into equation (1) and equation (2), we can get

\begin{array}{l} ρ A (\sum_{j = 1}^{N} (ϕ_{j} {\ddot{p}}_{j}) + \frac{d v}{d t} (1 + \sum_{j = 1}^{N} ({\dot{ϕ}}_{j} p_{j})) + 2 v \sum_{j = 1}^{N} ({\dot{ϕ}}_{j} {\dot{p}}_{j}) + v^{2} \sum_{j = 1}^{N} ({\ddot{ϕ}}_{j} p_{j})) \\ = E A (\sum_{j = 1}^{N} ({\ddot{ϕ}}_{j} p_{j}) + \sum_{j = 1}^{N} \sum_{k = 1}^{M} ({\ddot{ϕ}}_{j} {\dot{ϕ}}_{k} q_{j} q_{k})) \end{array}

(16)

\begin{array}{l} ρ A (\sum_{j = 1}^{M} ϕ_{j} {\ddot{q}}_{j} + \frac{d v}{d t} \sum_{j = 1}^{M} {\dot{ϕ}}_{j} q_{j} + 2 v \sum_{j = 1}^{M} {\dot{ϕ}}_{j} {\dot{q}}_{j} + v^{2} \sum_{j = 1}^{M} {\ddot{ϕ}}_{j} q_{j}) \\ + \tilde{E} I_{z} \sum_{j = 1}^{M} {\overset{⃜}{ϕ}}_{j} q_{j} + f_{g} - \bar{p} \sum_{j = 1}^{M} {\ddot{ϕ}}_{j} q_{j} \\ = E A ((\sum_{j = 1}^{N} {\dot{ϕ}}_{j} p_{j} + \tilde{e}) \sum_{k = 1}^{M} {\ddot{ϕ}}_{k} q_{k} + \sum_{j = 1}^{N} \sum_{k = 1}^{M} {\dot{ϕ}}_{k} {\ddot{ϕ}}_{j} p_{j} q_{k} + \frac{3}{2} \sum_{j = 1}^{M} \sum_{k = 1}^{M} \sum_{l = 1}^{M} {\dot{ϕ}}_{j} {\dot{ϕ}}_{k} {\ddot{ϕ}}_{l} q_{l} q_{j} q_{k}) \end{array}

(17)

Multiplying equations (16) and (17) $ϕ_{i}$ respectively and integrating over $[0, L]$ can get

\begin{array}{l} ρ A (\begin{array}{l} \sum_{j = 1}^{N} (\int_{0}^{L} ϕ_{i} ϕ_{j} d x) {\ddot{p}}_{j} + \frac{d v}{d t} (1 + \sum_{j = 1}^{N} (\int_{0}^{L} ϕ_{i} {\dot{ϕ}}_{j} d x) p_{j}) + 2 v \sum_{j = 1}^{N} (\int_{0}^{L} ϕ_{i} {\dot{ϕ}}_{j} d x) {\dot{p}}_{j} \\ + v^{2} \sum_{j = 1}^{N} (\int_{0}^{L} ϕ_{i} {\ddot{ϕ}}_{j} d x) p_{j} \end{array}) \\ = E A (\sum_{j = 1}^{N} (\int_{0}^{L} ϕ_{i} {\ddot{ϕ}}_{j} d x) p_{j} + \sum_{j = 1}^{N} \sum_{k = 1}^{M} (\int_{0}^{L} ϕ_{i} {\dot{ϕ}}_{j} {\ddot{ϕ}}_{k} d x) q_{j} q_{k}) \end{array}

(18)

\begin{array}{l} ρ A (\begin{array}{l} \sum_{j = 1}^{M} (\int_{0}^{L} ϕ_{i} ϕ_{j} d x) {\ddot{q}}_{j} + \frac{d v}{d t} \sum_{j = 1}^{M} (\int_{0}^{L} ϕ_{i} {\dot{ϕ}}_{j} d x) q_{j} + \\ 2 v \sum_{j = 1}^{M} (\int_{0}^{L} ϕ_{i} {\dot{ϕ}}_{j} d x) {\dot{q}}_{j} + v^{2} \sum_{j = 1}^{M} (\int_{0}^{L} ϕ_{i} {\ddot{ϕ}}_{j} d x) q_{j} \end{array}) \\ \begin{array}{l} + \tilde{E} I_{z} \sum_{j = 1}^{M} (\int_{0}^{L} ü_{i} ϕ_{j} d x) q_{j} + f_{g} (\int_{0}^{L} ϕ_{i} d x) - \bar{p} \sum_{j = 1}^{M} (\int_{0}^{L} ϕ_{i} {\ddot{ϕ}}_{j} d x) q_{j} \end{array} \\ \begin{array}{l} = E A \sum_{j = 1}^{N} \sum_{k = 1}^{M} (\int_{0}^{L} ϕ_{i} {\dot{ϕ}}_{j} {\ddot{ϕ}}_{k} d x) q_{k} p_{j} + E A \tilde{e} \sum_{j = 1}^{M} (\int_{0}^{L} ϕ_{i} {\ddot{ϕ}}_{j} d x) q_{j} \end{array} \\ + E A \sum_{j = 1}^{N} \sum_{k = 1}^{M} (\int_{0}^{L} ϕ_{i} {\dot{ϕ}}_{k} {\ddot{ϕ}}_{j} d x) p_{j} q_{k} + \frac{3}{2} E A \sum_{j = 1}^{M} \sum_{k = 1}^{M} \sum_{l = 1}^{M} (\int_{0}^{L} ϕ_{i} {\dot{ϕ}}_{j} {\dot{ϕ}}_{k} {\ddot{ϕ}}_{l} d x) q_{j} q_{k} q_{l} \end{array}

(19)

Boundary conditions

According to the known boundary conditions (20) and (21)

{u |}_{x = 0} = {u |}_{x = L} = 0; {w |}_{x = 0} = {w |}_{x = L} = 0

(20)

{\frac{\partial^{2} w}{\partial x^{2}} |}_{x = 0} = {\frac{\partial^{2} w}{\partial x^{2}} |}_{x = L} = 0

(21)

Let $ϕ_{i} (x) = x^{i + 2} {(1 - x / L)}^{3}$ to satisfy the above boundary conditions (20) and (21). Therefore, the first six stages can be taken for axial $u (x, t)$ and lateral displacement $w (x, t)$ , respectively, and brought into (18) and (19). That is, the system of equations can be solved.

Solution and process parameter optimization

Bring in parameters: Using $12 K$ carbon fiber, the model is $T 700$ . The string length $L = 5 m$ . The length of the original yarn drum is $s_{1} = 300 m m$ , and the bobbin s is $s_{2} = 168 m m$ . The angular velocity of the bobbin end is $ω_{2} = 10 r / s$ and $ω_{1}$ is the angular velocity of the original bobbin end. $R_{1}$ is the actual radius $δ = 0.6 m m$ when the original bobbin is unwinding. The original spool full yarn radius is $R_{0} = 40 m m$ . The empty yarn spool radius is $r_{0} = 10 m m$ . The empty yarn mass is $m_{0} = 0.2 k g$ , and the yarn winding angle is $θ_{1} = π / 36 r a d$ . The mass of the friction plate is $m_{f} = 0.5 k g$ , and the moment of inertia is $J_{f} = 2.4 k g c m^{2}$ . The friction coefficient of the friction plate is $μ = 0.2$ . The right spring pressure is $N_{2} = 100 N$ . The pitch of the full row of $12 K$ carbon fiber yarns is $b = 7 m m$ , and the thickness of the single-layer carbon fiber yarn is $δ = 0.6 m m$ . The density of carbon fiber is $ρ = 1.9 \times 10^{3} k g / m^{3}$ . The cross-sectional area is $A = 4.2 m m^{2}$ . The axial elastic modulus is $E = 235 G P a$ , and the flexural section coefficient is $\tilde{E} I_{z} = 2.52 \times 10^{- 10} P a$ . The thickness of single-layer carbon fiber yarn is $δ = 0.6 m m$ while the transverse uniform load is $f_{g} = 40 \times 10^{- 3} N$ .

The carbon fiber string tension directly affects the yarn guiding process, directly related to the pressure generated by the side springs on the friction pads.

In addition, since the initial mass of the carbon fiber precursor is $3 k g$ , $10$ bobbins can wound if the capacity of each bobbin is $300 g$ . When each bobbin is wound, the diameter of the yarn bobbin is different, which will have different effects on the carbon fiber string tension. In summary, we can select different spring pressures and bobbins for analysis.

Since we do not pay attention to the dynamic process of the initial tension establishment when starting the machine, we can ignore the initial winding can if the additional stress $\tilde{e} = 0$ , only the unwinding yarn in the steady state, is considered and simulated.

Influence of friction plate spring preload on yarn tension and vibration

According to the above parameters, if the spring pressure is $50 N$ at the beginning of unwinding, the yarn tension $T (x, t)$ , axial displacement $u (x, t)$ , and lateral displacement $w (x, t)$ are on the string, respectively. Yarn tension fluctuates between $[17.52 22.72] N$ , and the maximum fluctuation amplitude of axial displacement is $2.61 \times 10^{- 3} m m$ . The lateral displacement fluctuates between $[- 2.8 0.3] m m$ , and the maximum fluctuation amplitude is $3.12 m m$ . Figure 5 shows the change curve of the position.

Figure 5.

In the picture: $N_{2} = 50 N {R_{1} |}_{t = 0} = 0.04$ .

With the change of spring preload, the changes of various parameters are shown in Table 1, taking the most initial unwinding position

{R_{1} |}_{t = 0} = 0.04

and the unwinding speed

ω_{2} = 15 r / s

. With the change of spring preload, the changes of various parameters are shown in Table 1. As the spring pressure increases, the internal tension of the carbon fiber string increases, but the tension fluctuation amplitude

T_{a}

decreases. The axial vibration amplitude

u_{a}

and the lateral vibration amplitude

w_{a}

both decrease.

Table 1.

Influence of spring preload $N_{2}$ on various parameters.

N₂ (N)	T_max (N)	T_min (N)	U_max (10⁻⁶m)	U_min (10⁻⁶m)	W_max (10⁻⁴m)	W_min (10⁻⁴m)	T_a (N)	U_a (10⁻⁶m)	W_a (10⁻⁴m)
5	4.97	0.95	3.00	−3.00	9.11	−31	5.92	3.00	40.11
10	6.97	1.09	2.98	−2.98	9.31	−32	5.88	2.98	41.31
20	10.96	5.18	2.92	−2.92	4.69	−29	5.78	2.91	33.69
30	14.93	9.30	2.82	−2.82	1.50	−28	5.63	2.82	29.50
40	18.93	13.39	2.75	−2.75	0.69	−28	5.54	2.75	28.69
50	22.72	17.52	2.61	−2.61	3.18	−28	5.20	2.61	31.18
60	26.85	21.59	2.56	−2.56	1.73	−27	5.27	2.56	28.73
70	30.80	25.70	2.49	−2.49	5.04	−27	5.09	2.49	32.04
80	34.75	29.94	2.40	−2.40	4.26	−26	4.81	2.40	30.26
90	38.74	33.93	2.31	−2.31	3.40	−25	4.81	2.31	28.40
100	42.77	38.00	2.25	−2.25	2.87	−24	4.77	2.25	26.87
110	46.77	42.06	2.21	−2.21	2.65	−24	4.71	2.20	26.65
120	50.78	46.19	2.12	−2.12	2.22	−23	4.59	2.12	25.22
130	54.58	50.19	2.07	−2.07	1.95	−22	4.39	2.07	23.95
140	58.56	54.38	1.98	−1.98	2.74	−22	4.18	1.97	24.74
150	62.72	58.36	1.94	−1.94	1.61	−22	4.35	1.94	23.61

However, during the unwinding process, due to the continuous rotation of the original wire drum, it is easy for the nut to unwind, causing the spring preload to decrease. If we reduce the preset spring pressure to a certain level, there are fluctuations in the yarn tension. Therefore, it is easy to make the instantaneous tension of carbon fiber strings disappear or rise suddenly, causing severe vibration and even loss of control in the unwinding process. As shown in Figure 6, although the axial and lateral vibrations are not large, this ignores the fact that the yarn tension cannot be compressed when it is less than zero. At this time, there are some moments where the minimum tension is $- 0.5031 N$ , and the oscillation mentioned above will inevitably occur, and the unwinding process is out of control.

Figure 6.

In the picture: $N_{2} = 3 N {R_{1} |}_{t = 0} = 0.02$ .

Influence of the side height of the yarn guide wheel on the yarn vibration

Here is a relationship between the side height of the yarn guide wheel and the yarn specification, as shown in Table 2. The transverse amplitude is large when the yarn tension is small; the carbon fiber yarn jumps relatively large. If the width of the carbon fiber is

b

and the yarn’s lateral vibration is

w

, the actual side height

h

of the yarn guide wheel should satisfy

h \geq w + b

. When the side height of the yarn guide wheel is lower than this value, the yarn will easily fall outside the yarn guide wheel, causing yarn wear and yarn breakage if it is required to keep the minimum tension

30 N

when the carbon fiber yarn is unwinding, according to the actual carbon fiber width of different specifications.

Table 2.

The relationship between the side height of the yarn guide wheel and the yarn specification.

Yarn specification	3K	12K	24K
h_min(mm)	4	7	10

Effects of different unwinding stages on yarn tension and vibration

Since the original carbon fiber spool can be wound with multiple spools in unwinding, each spool’s tension and vibration are different. With the increase in the number of unwinding bobbins, the tension of the carbon fiber string gradually increases, and the amplitude of the fluctuation does not change significantly. At the same time, the transverse and axial vibration amplitudes of the carbon fiber string gradually increase. Figure 7 shows the results of the simulation analysis carried out.

Figure 7.

Graph of carbon fiber yarn tension as a function of the number of bobbins that have completed unwinding.

In Figure 7: when the spring pressure $N_{2} = 100 N$ , the winding tension curve of the $i - t h$ bobbin. ( $T_{\max}$ is the maximum tension; $T_{\min}$ is the minimum tension)

Figure 8: shows the results of the simulation analysis carried out when the spring pressure $N_{2} = 100 N$ , and the variation curve of the transverse vibration amplitude and the axial vibration amplitude of the $i - t h$ bobbin winding.

Figure 8.

Variation curve of lateral vibration amplitude and axial vibration amplitude of the $i - t h$ bobbin winding.

Influence of unwinding speed on yarn tension and vibration

Table 3 shows the change of the unwinding speed

ω_{2}

to various parameters during the unwinding process. Take the initial unwinding position and the spring pre-pressure

N_{2} = 20 N

with the increase of rotational speed, the amplitude of tension fluctuation, transverse vibration amplitude, and axial vibration amplitude all increase gradually, which will cause friction and wear of carbon fiber yarn.

Table 3.

Influence of unwinding speed $ω_{2}$ on various parameters.

W₂ (r/s)	T_max (N)	T_min (N)	U_max (10⁻⁶m)	U_min (10⁻⁶m)	W_max (10⁻⁴m)	W_min (10⁻⁴m)	T_a (N)	U_a (10⁻⁶m)	W_a (10⁻⁴m)
10	10.94	5.18	2.90	−2.90	4.45	−29	5.76	2.87	33.45
15	10.96	5.18	2.92	−2.92	4.69	−29	5.78	2.91	33.69
50	10.92	5.17	2.93	−2.93	4.16	−29	5.75	2.90	33.16
100	10.94	5.18	2.90	−2.90	4.45	−29	5.76	2.87	33.45
200	10.92	5.12	3.04	−3.04	4.93	−28	5.80	2.84	32.93
500	14.51	2.48	6.85	−6.85	45.00	−51	12.04	5.43	96.00
1000	80.95	−53.26	73.52	−73.52	171.00	−192	134.21	60.41	363.00

Conclusion

Based on the theory of axially moving strings, this paper analyzes the problem of yarn vibration in the unwinding process. Then the mathematic model in the unwinding process of the bobbin is established. The model’s mechanical equilibrium equation and boundary conditions are deduced, and then the results are obtained by MATLAB.

The results show: When the preload of the spring gradually increases in a specific interval, the corresponding maximum value of the tension of the yarn also increases continuously. At the same time, the axial vibration amplitude $u_{a}$ and lateral vibration amplitude $w_{a}$ decreased by $35.33 %$ and $41.14 %$ , respectively. During the unwinding process, the actual height of the guide wheel must be greater than the sum of the yarn’s width and the yarn’s lateral vibration distance, avoiding situations where the yarn falls off the wheel. At different unwinding stages, the tension of the carbon fiber yarn increases gradually as the number of unwinding bobbins increases. At the same time, the transverse vibration amplitude and axial vibration amplitude of the carbon fiber string will also increase. When the unwinding speed gradually increases in the range of $[10 1000] r / s$ , the vibration range of the yarn tension will increase. And the tension fluctuation amplitude, transverse vibration amplitude, and axial vibration amplitude will also increase gradually. The growth intervals are $[5.76 134.21] N$ , $[33.45 363.00] 10^{- 4} m$ , and $[2.87 60.41] 10^{- 6} m$ .

In conclusion, we can solve the problems caused by the vibration of the yarn during the unwinding process. Actively control the preload of the spring, the unwinding speed of the carbon fiber yarn, and the number of bobbins produced at the same time. This can effectively reduce the vibration problem of the carbon fiber yarn, thereby improving the unwinding quality of the bobbin and reducing the problems caused by the bobbin. Therefore, the next research step can focus on judging whether the bobbin’s unwinding quality is qualified. Usually, after the yarn bobbin is unwound, it is due to the winding of multiple layers of carbon fiber yarn. Judging whether the unwinding quality is acceptable from the outside is difficult. Not only is this a waste of worker time, but it is also difficult to pick out bobbins with quality problems. Therefore, how to judge the quality of the yarn bobbin after the unwinding is completed and even detect the quality decline in time during the unwinding process is worth studying.

Footnotes

Acknowledgements

The National Natural Science Foundation of China, under a grant [51905008], supported this work.

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 was supported by the National Natural Science Foundation of China.

ORCID iDs

Yujing Zhang

Yang Zhiguo

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Yarn tension model and vibration analysis during unwinding of carbon fiber bobbins

Abstract

Keywords

Introduction

Modeling of carbon-fiber yarn unwinding process

Unwinding machine and principle of carbon fiber bobbin

Modeling of the tension system during unwinding

Yarn tension partial differential equation system based on axial moving string

Separating parameters to solve equations

Boundary conditions

Solution and process parameter optimization

Influence of friction plate spring preload on yarn tension and vibration

Influence of the side height of the yarn guide wheel on the yarn vibration

Effects of different unwinding stages on yarn tension and vibration

Influence of unwinding speed on yarn tension and vibration

Conclusion

Footnotes

Acknowledgements

Declaration of conflicting interests

Funding

ORCID iDs

References