Design and study of the action of the yarn-pulling mechanism of a carbon-fiber one-sided stitching device based on improved technology

Abstract

To realize a one-sided stitching action and stable stitch formation, a poor match between the lead and the hook yarn needles in the stitching process must be avoided as it can lead to hook dropping and hook errors, causing loop loss, thread breaking, and even thread relaxing. Based on an analysis of the principle of one-sided stitching and matching the hook and lead yarn needles, the original stitching technology is improved and a method of trajectory superposition is proposed. A yarn-pulling mechanism is designed for a one-sided stitching device for three-dimensional preformed carbon/carbon composites. By analyzing the principle of the yarn-pulling mechanism, a mathematical model of that mechanism is established, and a trajectory simulation analysis is carried out with MATLAB, which verifies the rationality of the yarn-pulling principle. Results for the two crank angles of the yarn-pulling mechanism and the crank angle of the hook yarn needle at two particular moments reflect the matching relationship of the three, which provides a theoretical reference for the stitching device to adjust to and work well, forming the desired stitch. Finally, stitching tests are carried out, and the test results show the designed yarn-pulling mechanism can cooperate with the hook and the lead yarn needles to complete the stitch lock. This realizes a stable stitching action and avoids hook dropping and hook errors, thereby increasing stitching efficiency.

Keywords

one-sided stitching yarn-pulling mechanism trajectory superposition method trajectory simulation

As material science has developed, the advantages of carbon/carbon (C/C) composites in high-technology fields such as the aerospace, automobile, and military industries have become increasingly important. C/C composites are commonly used in aircraft wings, solid rocket motor nozzle throats, nozzle divergent sections, and automotive brake discs for their high strength and light weight. The preforms of these components are usually processed and manufactured by a suture method. Longitudinal fibers can be added between the composite layer fibers during the suture process to enhance the structural properties of the materials, thus improving the damage tolerance of the composite¹ and enhancing the interlaminar shear strength of the composite laminate. Therefore, preformed stitching technology for composite materials has become a key factor affecting the structural properties of such materials.² A traditional double-sided stitching technique not only requires setting stitching mechanisms on both sides of the material but also imposes extremely strict requirements on that material, with the technique only applicable to two-dimensional planar materials.^3,4 Instead, using one-sided stitching (OSS) technology to stitch composite materials would not only avoid constraining the shape of the stitching object but also enable composite materials to have superior interlayer properties and be strongly tolerant of impact damage.^5–9

Europe and America are committed to manufacturing complex structural parts with OSS technology for aircraft,^10–12 promoting the development and improvement of stitching equipment. The German company ALTIN Naehtechnik has carried out a series of studies on OSS equipment and technology in which a special stitching head controlled by a mechanical arm is used to produce composite prefabricated parts.¹³ The company KSL uses industrial robots combined with OSS technology to manufacture furniture, automobile airbags, and aircraft parts made of carbon-fiber composite materials.¹⁴

In China, Yao and colleagues at Tianjin Polytechnic University are at the forefront of research into OSS technology. They studied a manipulator system and its stitching behavior regarding OSS of composite material, constructed OSS equipment, and conducted stitching experiments.¹⁵ Pan and colleagues at Nanjing University of Aeronautics and Astronautics studied equipment technology for one-sided and double-needle stitching of three-dimensional reinforced composite materials, and verified the stitching performance.^16–20 The extended section of a rocket-engine nozzle was stitched by one-sided stitching technology at the Xi’an Aerospace Composite Materials Research Institute.²¹ Nevertheless, research in China into OSS technology remains in the exploratory and experimental stage, and there remains some instability in stitching equipment and its action.

In the present study, the research content includes improving the stitching mechanism and adding the yarn-pulling mechanism. The purpose is to avoid hook dropping (when the hook yarn needle (HYN) dose not successfully hook the yarn loop) and wrong hooks (when the HYN incorrectly hooks the yarn loop formed in the previous cycle during the stitching process), improve stitching efficiency, enhance the material’s performance, and promote the development of OSS and its technology.

Improvement of one-sided stitching technology

One-sided double-needle suturing involves two stitching needles cooperating to complete a stitch, as shown in Figure 1.^18–20 The yarn is first drawn to the undersurface of the material by the lead yarn needle (LYN) and returns to form a loop under the action of friction. The HYN lags the LYN and descends to the lower surface of the sewing material to hook the yarn loop and bring the yarn back to the upper surface of the sewing material for locking with the ring formed in the previous cycle. The cycle is repeated to form an OSS stitch^21–25 as shown in Figure 2.

Figure 1.

One-sided stitching (OSS) technology. (1-6) shows the formation process of the stitches during the one-sided stitching process.

Figure 2.

One-sided stitching (OSS) trace.

In this technology, the needle hook of HYN is placed forward (i.e. in the forward direction of the stitching path), and there is no yarn-pulling mechanism. In suturing, when the yarn loop on the LYN reaches the ideal state, the HYN reaches its lower limit and hooks the yarn loop. In this process, it is easy for the HYN to fail to hook the yarn loop, resulting in hook dropping (a jump stitch); if the HYN successfully picks up the loop, the HYN brings the yarn back to the upper surface of the sewing material and passes through the loop formed in the previous cycle. Throughout this process, because the hook is placed forward (in the direction of the suture path), the HYN is easily hooked to the loop formed in the previous cycle when it moves out of the upper surface of the seam, causing a wrong hook phenomenon. The suturing action cannot be continued, as shown in Figure 3.

Figure 3.

(a) Dropped hook and (b) wrong hook.

In the improved stitching technology, the needle hook of HYN is placed backward (in the opposite direction to the stitching path) and the yarn-pulling mechanism added. During sewing, when the yarn loop is initially formed the HYN is inserted into the ring and tightens the yarn. The yarn slides into the hook along the needle rod as the needle moves up after reaching its lower limit. When the HYN brings the yarn back to the upper surface of the sewing material, the yarn-pulling mechanism completes the locking action, as shown in Figure 4.

Figure 4.

Process of stitch forming based on improved technology.

In matching the yarn-pulling hook (YPH) with the HYN, the YPH needs to move the yarn loop from the outer side of the path to the inner side and from the back of the HYN to the front, which requires the YPH to (a) make a swinging motion in the direction from the back and outside of the HYN to the front and inside as the YPH moves, and (b) return around the front and outside of the HYN when the yarn loop is pulled to the appropriate position. Therefore, the motion trajectory of the YPH is selected as an ellipse and placed at an angle to the forward direction of the stitching path, as shown in Figure 5. This type of hook yarn method can avoid dropped and wrong hooks and increase the chance that the HYN hooks the yarn loop successfully and improves stitching efficiency.

Figure 5.

Trajectory of the yarn-pulling hook (YPH).

Establishment and analysis of the mathematical model

Method of trajectory superposition

According to the requirements of improved OSS technology, the terminal trajectory of the yarn-pulling mechanism is roughly elliptical when thread pulling. A regular ellipse can be formed by elongating one axis of a regular circle. In forming the trajectory dynamically, the circular and swinging motions are superimposed and the phase between the two motions is adjusted to form the elliptical trajectory required by the yarn-pulling action. Based on the above method of trajectory superposition,^26,27 the yarn-pulling mechanism is designed schematically and the associated mechanism diagram is shown in Figure 6.

Figure 6.

Schematic of the yarn-pulling mechanism.

The working principle is as follows: the universal joints cooperate with the crank in the global coordinate system to drive the YPH to make a circular motion, and the rocker in the crank rocker mechanism transmits the swing motion to the YPH by the universal joints. Then the circular and swing motions act together on the YPH and make it elliptical.

After selecting the coordinate origin and establishing a coordinate system (Figure 5), the yarn-pulling mechanism of the three-dimensional space can be represented in the two-dimensional space using the equivalent model, as shown in Figure 6. The equivalent simplified model of the yarn-pulling mechanism is shown in Figure 7. According to the requirements of the stitching technology and the cooperative relationship between the YPH and HYN, the long and short axes of the elliptical trajectory parameters can be set preliminarily to d₁ and d₂. The position and angle of the elliptical trajectory in the coordinates system determined by the coordinates (X, Y) of its center point and the angle $ϕ_{O'}$ between its long axis and the x-axis, as shown in Figure 8.

Figure 7.

Seven-bar yarn-pulling mechanism.

Figure 8.

Coordinates of elliptical trajectory.

Modeling and analysis of yarn-pulling mechanism

To achieve the superposition of trajectories, the dynamic coordinate system $x' oy'$ and the static coordinate system $xoy$ are established as shown in Figure 7. The crank and rocker mechanism $O' ABC$ is located in the local coordinates $x' oy'$ , and the double crank mechanism is located in the global coordinates $xoy$ . The following model of the yarn-pulling mechanism is established and its kinematics are analyzed:

{\begin{matrix} L_{A C}^{2} = L_{1}^{2} + L_{4}^{2} - 2 L_{1} L_{4} cos θ_{1}, \\ ϕ_{1} = \arcsin (\frac{L_{1} sin θ_{1}}{L_{AC}}), \\ ϕ_{2} = \arccos (\frac{L_{AC}^{2} + L_{3}^{2} - L_{2}^{2}}{2 L_{AC} L_{3}}), \\ θ_{3} = π - ϕ_{1} - ϕ_{2}, \\ θ_{2} = \arcsin (\frac{L_{3} sin θ_{3} - L_{1} sin θ_{1}}{L_{2}}) \end{matrix}

(1)

where

ϕ_{1}

is the angle between AC and the connecting rod

O' C

ϕ_{2}

is the angle between AC and the connecting rod BC, and

ϕ_{3}

is the angle through which the rocker BC has moved. Therefore, the coordinates of point F in xoy are obtained as²⁸

\begin{matrix} {\begin{matrix} x_{F} = L_{5} cos θ_{4} + L_{4} + L_{FC} cos θ_{3}, \\ y_{F} = L_{5} sin θ_{4} + L_{F C} sin θ_{3} \end{matrix} \end{matrix}

(2)

In Eq. (1), suppose that $θ_{1} = ω_{1} t$ and the phase difference between the two cranks is φ, that is, we have $θ_{4} = - ω_{1} t - φ_{1}$ in Eq. (2). Then we have

\begin{matrix} {\begin{matrix} x_{F} = L_{4} + L_{5} cos (- ω_{1} t - φ_{1}) + L_{FC} cos θ_{3}, \\ y_{F} = L_{5} sin (- ω_{1} t - φ_{1}) + L_{F C} sin θ_{3} \end{matrix} \end{matrix}

(3)

where

\begin{matrix} θ_{3} = π - \arcsin (\frac{L_{1} \cdot sin (ω_{1} t)}{\sqrt{L_{1}^{2} + L_{4}^{2} - 2 L_{1} L_{4} sin (ω_{1} t)}}) \\ - \arccos (\frac{L_{1}^{2} + L_{4}^{2} - 2 L_{1} L_{4} sin (ω_{1} t) + L_{3}^{2} - L_{2}^{2}}{2 L_{3} \sqrt{L_{1}^{2} + L_{4}^{2} - 2 L_{1} L_{4} sin (ω_{1} t)}}) . \end{matrix}

Suppose that

cos θ_{3} = M \sqrt{1 - N^{2}} - N \sqrt{1 - M^{2}}

(4)

where

\begin{matrix} M = \frac{L_{1} \cdot sin (ω_{1} t)}{\sqrt{L_{1}^{2} + L_{4}^{2} - 2 L_{1} L_{4} sin (ω_{1} t)}}, \\ N = \frac{L_{1}^{2} + L_{4}^{2} - 2 L_{1} L_{4} sin (ω_{1} t) + L_{3}^{2} - L_{2}^{2}}{2 L_{3} \sqrt{L_{1}^{2} + L_{4}^{2} - 2 L_{1} L_{4} sin (ω_{1} t)}} . \end{matrix}

Then the velocity components of the moving point F along the two axes are

\begin{matrix} {\begin{matrix} v_{F_{x}} = {\overset{\cdot}{x}}_{F} = - L_{5} ω_{1} sin (ω_{1} t + φ_{1}) + L_{FC} sin θ_{3} \cdot {\overset{\cdot}{θ}}_{3}, \\ v_{F_{y}} = {\overset{\cdot}{y}}_{F} = - L_{5} ω_{1} cos (ω_{1} t + φ_{1}) + L_{FC} cos θ_{3} \cdot {\overset{\cdot}{θ}}_{3} \end{matrix} \end{matrix}

(5)

Therefore, the speed of point F is

v_{F} = \sqrt{v_{F_{x}}^{2} + v_{F_{y}}^{2}}

(6)

and the acceleration components of point F along the two axes are

\begin{matrix} {\begin{matrix} a_{F_{x}} = {\overset{··}{x}}_{F} = - L_{5} ω_{1}^{2} cos (ω_{1} t + φ_{1}) + L_{FC} cos θ_{3} \cdot {\overset{\cdot}{θ}}_{3}^{2} \\ + L_{FC} sin θ_{3} \cdot {\overset{··}{θ}}_{3}, \\ a_{F_{y}} = {\overset{··}{y}}_{F} = L_{5} ω_{1}^{2} sin (ω_{1} t + φ_{1}) - L_{FC} sin θ_{3} \cdot {\overset{\cdot}{θ}}_{3}^{2} \\ + L_{FC} cos θ_{3} \cdot {\overset{··}{θ}}_{3} \end{matrix} \end{matrix}

(7)

Therefore, the magnitude of the acceleration of point F is

a_{F} = \sqrt{a_{F_{x}}^{2} + a_{F_{y}}^{2}}

(8)

Analysis of matching motion of yarn pulling and HYN

Movement analysis of HYN

In the sewing process, the HYN makes a linear reciprocating movement in a vertical direction. The thread loop is hooked from the lower surface of the sewing material to the upper surface, then works with the YPH to complete the thread stitch lock. Therefore, the HYN is driven by a sliding-rod crank mechanism as shown in Figure 9.

Figure 9.

Sliding-rod crank mechanism of the hook yarn needle (HYN).

The displacement of point B during the movement of the crank and slide bar mechanism is⁴

y_{B} = - l_{1} sin γ_{1} - \sqrt{l_{2}^{2} - l_{1}^{2} cos 2 γ_{1}}

(9)

the velocity of point B is

v_{B} = {\overset{\cdot}{y}}_{B} = - l_{1} ω (cos γ_{1} + \frac{l_{1} cos γ_{1} sin γ_{1}}{\sqrt{l_{2}^{2} - l_{1}^{2} cos γ_{1}}})

(10)

and the acceleration of point B is

\begin{matrix} a_{B} = {\overset{··}{y}}_{B} = l_{1} ω^{2} sin γ_{1} + \frac{l_{1}^{2} ω^{2} (sin 2 γ_{1} - cos 2 γ_{1})}{\sqrt{l_{2}^{2} - l_{1}^{2} cos 2 γ_{1}}} \\ + \frac{l_{1}^{4} ω^{2} cos 2 γ_{1} sin 2 γ_{1}}{(\sqrt{l_{2}^{2} - l_{1}^{2} cos 2 γ_{1}})^{3}} \end{matrix}

(11)

Analysis of the yarn-pulling mechanism

In the process of stitching, the tip of the YPH moves elliptically on the horizontal plane whereas the HYN performs a straight reciprocating motion in a vertical direction. During this motion, the YPH should first press then pull the yarn loop from the back and outside of the HYN to the front and inside. When the yarn loop reaches the ideal position, the YPH should return around the front and outside of the HYN to avoid yarn slack caused by the yarn-pulling route being too long. A hooking yarn diagram of HYN is shown in Figure 10. The distance between the bottom of the hook and the tip of the needle is labeled A and the yarn pressing should be completed when the distance, l, between the bottom of the hook and the plane of the YPH is approximately a/2. At this time, the distance between the tip of the YPH and the axis of the HYN is set as x, and yarn pulling should be completed when the point of the hook needle is higher than the elliptical plane. Therefore, the optimal timing for cooperation between the two needles should be found.

Figure 10.

The yarn-pulling hook (YPH) is matched with hook yarn needle (HYN). In the figure, the four planes are: 1) the plane of the bottom of the needle hook when the HYN reaches its upper limit position, 2) the plane of the needle tip when the HYN is at its upper limit position, 3) the upper part of the YPH section, and 4) the plane of the axis of the YPH, and the position of the HYN indicated by the broken line is its upper limit position.

According to the experimental analysis, for the matching position the difference between the height of the pulling hook in the plane and the height of the hook needle tip when it reaches the upper limit should be greater than the radius of the cutting interface of the pulling hook, namely $h > d / 2,$ $l = a / 2,$ $b > 0$ . For the matching time, it must satisfy $t_{G 1} \geq t_{Z 1}$ . The YPH will loosen the yarn loop around the needle after it passes the return point and the yarn loop will need to entangle the needle bar of HYN. Consequently, the tip of the HYN should be lower than plane 4 of the YPH at this time and must satisfy $t_{G 2} \geq 2 t_{Z 2}$ for the matching time ( $t_{G 1}$ is the time the YPH takes from pressing the yarn loop to being at the needle axis of the HYN, directly below the tip of the needle; $t_{Z 1}$ is the time the HYN takes from the position of the YPH pressing the yarn loop to the HYN tip reaching plane 4; $t_{G 2}$ is the time the tip of the yarn-pulling needle takes from the HYN axis to its return point around the HYN; $t_{Z 2}$ is the time the HYN tip takes from plane 4 to plane 2). Only when the above conditions are met can the YPH successfully complete the yarn-pulling action. If the maximum stroke of the HYN is H and the working period is T, then $t_{Z 1} = (a / 2 H) T$ , $t_{Z 2} = (h / H) T$ . The angular velocity is approximately equal to the angular velocity ( $ω_{4}$ ) of crank $OO'$ during the formation of the ellipse trajectory, and the working angle α of YPH is composed of $α_{1}$ and $α_{2}$ , as shown in Figure 11. Therein, A is the point where the YPH starts to press the yarn loop, B is the point where the YPH returns around the HYN, and C is the position of the HYN axis. We have that $α_{1} = ω_{4} \cdot t_{G 1}$ and $α_{2} = ω_{4} \cdot t_{G 2}$ , namely that $α_{1} \geq ω_{4} \cdot t_{Z 1}$ and $α_{2} \geq 2 ω_{4} \cdot t_{Z 2}$ . Furthermore, we have that $α \geq ω_{4} (t_{Z 1} + 2 t_{Z 2})$ , therefore the working angle of the YPH is

α \geq ω_{4} (\frac{a}{2 H} + \frac{2 h}{H}) T

(12)

Figure 11.

Angle of the yarn-pulling hook (YPH).

In conclusion, point A can be regarded as the starting point for matching the YPH and HYN when the yarn-pulling mechanism pulls the yarn. At this time, the distance of the HYN from its upper limiting position is $h + a / 2$ .

Example analysis and trajectory simulation

Parameter calculation and trajectory simulation of the yarn-pulling mechanism

According to the requirements of the improved stitching technology, when the long axis of the elliptical trajectory is d₁ = 15 mm and the short axis is d₂ = 8 mm, it can meet the requirements of the yarn-pulling motion trajectory. The short-axis trajectory is completed by the double crank mechanism, so the double crank length is 8 mm, namely L₅ = L₆ = 8 mm. The crank angle between the extreme of the crank and the rocker mechanism is β as shown in Figure 12.

Figure 12.

Extreme angular position of crank and rocker mechanism.

The length of rod l $O' C$ and rod l_CB in the mechanism is determined by the design dimensions of the frame, namely l $O' C$ = 88 mm and l_CB = 26 mm. The swing angle of the rocker, as β = 4°, is calculated and determined according to the size of the long axis and the ratio of rod length $l_{CF}$ to rod length $l_{CB}$ . As given in Figure 11, $A_{1} B_{1}$ and $A_{2} B_{2}$ are the two limiting positions of the connecting rod AB, so we have

cos (∠ O' {CB}_{1}) = \frac{O' C^{2} + {CB}_{1}^{2} - O' B_{1}^{2}}{2 O' C \cdot {CB}_{1}}

(13)

cos (∠ O' {CB}_{2}) = \frac{O' C^{2} + {CB}_{2}^{2} - O' B_{2}^{2}}{2 O' C \cdot {CB}_{2}}

(14)

O' B_{1} = O' A + AB

(15)

O' B_{2} = - O' A + AB

(16)

Solving Eqs. (13)–(16) gives O′A = 1 mm and AB = 91.5 mm. Because of the requirements of the yarn-pulling technology, the yarn-pulling action is stable and reliable, and the yarn-pulling mechanism needs the same time to hook and exit the yarn loop in yarn pulling. Therefore, the crank and rocker mechanism is required to have no obvious quick-return characteristics. The angle $∠ B_{1} O' C$ in $Δ O' B_{1} C$ is denoted by $β_{1}$ , the angle $∠ B_{2} O' C$ in $Δ O' B_{2} C$ is denoted by $β_{2}$ , and the crank angle between extremes is denoted by β, thus we have

\begin{matrix} {\begin{matrix} β_{1} = arccos (\frac{(O' A + AB) 2 + O' C^{2} - {CB}^{2}}{2 (O' A + AB) \cdot O' C}), \\ β_{2} = arccos (\frac{(- O' A + AB) 2 + O' C^{2} - {CB}^{2}}{2 (- O' A + AB) \cdot O' C}) \end{matrix} \end{matrix}

(17)

Solving Eq. (17) gives β = 0.357° and K = 1.004, where K is the coefficient of travel speed variation and is approximately the same. There is no obvious quick-return characteristic that meets the technology requirements.

Equation (2) gives the coordinates of the elliptical trajectory point of the dialing yarn, and all the parameters of the yarn-pulling mechanism have been determined. The speed and acceleration of the elliptical track can be found from Eqs. (6) and (8), and the parameters are determined and substituted into MATLAB for simulation, as shown in Figure 13. It can be seen from the variation curve that the trend in the elliptical trajectory velocity and acceleration is continuous without abrupt changes.

Figure 13.

Change curves of velocity and acceleration of yarn-pulling trajectory with the crank angle.

To ensure the YPH can take the yarn loop successfully, the center coordinate of the elliptical track in the static coordinate system $xoy$ formed by the yarn-pulling mechanism, which can be calculated according to the positional relationship between YPH and HYN and the requirements of improved stitching technology, should be located near point (74, 99). The angle $ϕ_{O'}$ between the long axis of the elliptical track and the x-axis should range from 15° to 25°, namely $ϕ_{O'} = 15^{\circ} : 25^{\circ}$ . MATLAB software is used to simulate the motion of the yarn-pulling track. It has been suggested that the phase difference ( $φ_{1}$ ) between the two original crank angles ( $θ_{1}$ and $θ_{4}$ ) in the course of simulation and the best value of $φ_{1}$ make a yarn-pulling trajectory that satisfies the above requirements. The values of $φ_{1}$ are limited to between zero and π, and the corresponding elliptical parameters are calculated by taking points on the trajectory for different values of $φ_{1}$ . The results are given in Table 1, where it can be seen that the obtained trajectory meets the requirements of the yarn-pulling trajectory when $φ_{1} = 0.3 π$ , as shown in Figure 14.

Figure 14.

Elliptical trajectories of terminal of yarn-pulling mechanism for different values of $φ_{1}$ .

Table 1.

Parameters of ellipse for different values of $φ_{1}$

$φ_{1} / rad$	Long axis d₁/mm	Short axis d₂/mm	$ϕ_{O'} /^{\circ}$
$0.1 π$	16.12	9.26	7.15
$0.3 π$	15.00	7.60	23.40
$0.5 π$	12.78	5.33	38.23
$0.7 π$	10.72	3.22	59.77

So, taking points on the trajectory when $φ_{1} = 0.3 π$ rad and fitting the curve using these points and the least-square method, we can calculate the exact values of these parameters, including the long and short axes lengths (d₁ and d₂) of the elliptical trajectory, the center point coordinates $(X, Y)$ of the elliptical trajectory, and the angle $ϕ_{O'}$ between the long axis of the elliptical trajectory and the x-axis. The results are: d₁ = 2A=15.6 mm, d₂ = 2B = 7.58 mm, $(X, Y) = (73.88, 98.44)$ and $ϕ_{O'} = - 0.38 (21 . 77^{\circ})$ rad. Therefore, an oblique elliptic equation can be obtained by the rotation and translation transformation of the standard equation:

\begin{matrix} \frac{[(x - a) cos (ϕ_{O'}) + (y - b) sin (ϕ_{O'})] 2}{A^{2}} \\ + \frac{[(y - b) cos (ϕ_{O'}) - (x - a) sin (ϕ_{O'})] 2}{B^{2}} = 1 \end{matrix}

(18)

Example analysis of matching of the yarn-pulling mechanism and HYN

According to the original design of the mechanism, the values of the various dimensions in the motion of the hook yarn are a = 3 mm, d = 2 mm, h = 2 mm, and H = 60 mm, from which we have α = 33°. According to Eq. (18) for the ellipse and the working angle α of the YPH, the coordinates of starting point A, where the YPH and HYN are matched, are obtained as (69.8, 96.36).

The displacement, velocity, and acceleration of the HYN can be found from Eqs. (9)–(11). According to the design requirements, the lengths of the rods in the hook yarn mechanism are l₁ = 30 mm and l₂ = 80 mm, and the crank speed is $ω = 2 π rad / s$ , giving $γ_{1} = 0$ in the initial state. Using MATLAB for the simulation calculations, the velocity and acceleration change curves of the hook yarn terminal, namely point B, are obtained as shown in Figure 15. According to these curves, the trend of the velocity and acceleration of the mechanism is continuous without abrupt changes.

Figure 15.

Change curves of velocity and acceleration of the hook yarn needle (HYN).

The matching height of the HYN is determined by its crank angle $γ_{1}$ , and the phase difference between that angle and the crank angle of the yarn-pulling mechanism is adjusted to make the HYN cooperate with the YPH when the distance from the upper limit is $h + a / 2 = 3.5$ mm. For Eq. (13), MATLAB is used to calculate the values of $θ_{1}$ and $φ_{2}$ , which are $θ_{1} = 1.74$ rad and $φ_{2} = 5.48$ rad. The displacement change curves of the HYN and YPH are shown in Figure 16.

Figure 16.

Displacement of hook yarn needle (HYN) in z direction and displacement of yarn-pulling trajectory in x and y directions.

As can be seen from the displacement relationships in Figure 15, the HYN can be matched precisely with the YPH at point A when $φ_{2} = 5.48$ rad, which shows this is the best matching condition and verifies the rationality of the theory.

Stitching test

In the stitching technology used before improvement, the yarn is broken if the HYN drops or makes a wrong hook and stitching cannot be continued; the defect shown in Figure 17 will appear.

Figure 17.

The breakage of yarn caused by a dropped or wrong hook.

In this paper, to verify the accuracy of the theoretical analysis and ensure a stable stitching action can be carried out, an OSS device based on improved technology was designed and constructed according to the above analysis. The device was adjusted according to the calculation results and used to carry out stitching tests in which carbon-fiber yarn was selected to stitch a 25 mm-thick laminated carbon cloth. The yarn-pulling process of the YPH in the test is shown in Figure 18.

Figure 18.

Process of the yarn-pulling mechanism: (a) pushing the yarn; (b) pulling the yarn; (c) return around the hook yarn needle (HYN).

Figure 18(a) shows the process by which the YPH presses the outer yarn loop, (b) shows the YPH pulls the loop from the outside of the HYN to the inner side when the HYN descends, and (c) shows the YPH makes a return movement around the HYN, then the HYN passes through the loop and pierces the seam for the next cycle of stitching.

To verify the yarn-pulling mechanism can cooperate successfully with the HYN to pull the yarn loop without hook dropping or errors and complete the stitching action smoothly, five stitching tests were conducted on laminated carbon cloth using the OSS device (with 20 needles per stitching). The stitching patterns of the stitched yarn are shown in Figure 19. During the stitching process, the working stability of the yarn-pulling mechanism is evaluated by observing the successful rate of the YPH pulling the yarn loop; test data are shown in Table 2.

Figure 19.

Stitching patterns: (a) upper surface of seam; (b) underside of seam.

Table 2.

Successful yarn-pulling rate of the yarn-pulling mechanism in stitching tests

Test number	Yarn pulling (n)	Successes (n)	Success rate
1	20	20	100%
2	20	20	100%
3	20	20	100%
4	20	20	100%
5	20	20	100%

The data in Table 2 show the yarn loop was pulled successfully in the five stitching tests, comprising 100 occasions of yarn loop pulling. The tests show the yarn-pulling mechanism is based on correct principles, operates stably, and successfully avoids hook dropping and errors, thus improving the stitching efficiency and achieving the stated goal.

Conclusion

Aimed at solving the problems of yarn slack and yarn breaking caused by dropping and wrong hooks with a traditional stitching mechanism in the stitching process, in this paper the original stitching technology was analyzed and improved, the principle of forming a stitching trace was analyzed according to the improved stitching technology, and the motion trajectory of the yarn-pulling mechanism was established. The idea of trajectory superposition was then proposed according to the principle of forming the motion trajectory, and a yarn-pulling mechanism suitable for carbon-fiber yarn stitching was designed. In the stitching process, the yarn-pulling mechanism should work with the LYN and HYN, and the best matched position and time between the yarn-pulling mechanism and the HYN were derived via the analyzed and calculated coordinate motion of the three (the LYN, HYN, and yarn-pulling mechanism). The phase difference ( $φ_{1}$ ) between the angles of the two original moving cranks ( $θ_{1}$ and $θ_{4}$ ) of the yarn-pulling mechanism and the angle of the original moving crank under the best matching state were given, and the phase difference ( $φ_{2}$ ) between the angles of the hook yarn mechanism ( $γ_{1}$ ) and the original moving crank ( $θ_{4}$ ) was given. Finally,case analysis and stitching tests were carried out to verify the accuracy of the theory. Figure 17 shows yarn breakage caused by the wrong HYN hook before the improvement of the stitching technology. Figure 19 shows the stitching pattern after the stitching technology is improved. The comparison between the two patterns shows the stitching effect is better after the improvement, and dropped and wrong HYN hooks are avoided. The yarn can better form the loop and lock successfully. This proves the applicability of the yarn-pulling mechanism and the accuracy of theoretical calculations.

Footnotes

Acknowledgements

The authors gratefully acknowledge the support from Tianjin Science and Technology Committee towards this study.

Declaration of conflicting interests

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

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work is supported by the key technologies R&D program of Tianjin (Grant No. 15ZCZDGX00840).

ORCID iD

Lingchao Ji

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