# Design and Analysis of a Novel Tension Control Method for Winding Machine

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## Abstract

Filament winding has emerged as the main process for carbon fiber reinforced plastic (CFRP) fabrication, and tension control plays a key role in enhancing the quality of the winding products. With the continuous improvement of product quality and efficiency, the precision of the tension control system is constantly improving. In this paper, a novel tension control method is proposed, which can regulate the fiber tension and transport speed of the winding process by governing the outputs of three different driven rollers (the torque of the unwind roll, the torque of the magnetic powder brake roller, and the speed of the master speed roller) in three levels. The mechanical structures and dynamic models of the driven rollers and idle rollers are established by considering the time-varying features of the roller radius and inertia. Moreover, the influence of parameters and speed variation on fiber tension is investigated using the increment model. Subsequently, the control method is proposed by applying fiber tension in three levels according to the features of the three driven rollers. An adaptive fuzzy controller is designed for tuning the PID parameters online to control the speed of the master speed roller. Simulation is conducted for verifying the performance and stability of the proposed tension control method by comparing with those of the conventional PID control method. The result reveals that the proposed method outperforms the conventional method. Finally, an experimental platform is constructed, and the proposed system is applied to a winding machine. The performance and stability of the tension control system are demonstrated via a series of experiments using carbon fiber under different reference speeds and tensions. This paper proposes a novel tension control method to regulate the fiber tension and transport speed.

## Keywords

Tension control Control method Fuzzy logic Filament winding## 1 Introduction

High modulus carbon fiber is an excellent industrial material, which is widely used in several fields such as satellite supporting cylinder, shells of rocket engine, and solar array. The composite manufacturing process is the key to the application of carbon fiber. Filament winding has emerged as the main process for fabricating composite structures. It is widely used in building rotational parts. In the filament winding process, the carbon fiber is delivered from the unwind roll and passed through the resin bath to mix with resin under different temperatures and finally wrap around the surface of the mandrel in the designed pattern. The major specifications that should be satisfied during the winding process are the winding line type and the fiber tension, which are considered to be the key factors related to the tensile strength of the fiber products. The winding line type is determined using the numerical control system, so this paper focuses on the tension control problem during the winding process. Researchers have shown that unstable tension may lead to loss in strength of fiber winding products [1]. Therefore, fiber tension should be maintained at the reference value during the winding process for ensuring the product quality.

Several factors shape the tension control design to be challenging, which include significant parameter variations and disturbances. Small variations in the change of velocity of the transport rollers can cause significant variations in tension. On the other hand, we used different shapes of mandrels for maintaining the line speed in acceleration or deceleration states. Because of the coupling between the tension and the line speed, it is difficult to maintain the tension at a desired value. Researchers have investigated considerably for acquiring better control result. Lee et al. [2] used a magneto rheological brake to provide back tension to prevent frequent part changes and fatal malfunction for a tension control system, and a PID controller was designed, and test results showed the feasibility with satisfying the time constant and the allowable error. Nishida et al. [3] divided the transport system into several subsystems and a self-tuning PI controller with an estimator based on a novel adaptive particle swarm optimization method was constructed to solve the strong coupling between the velocity and tension of the web. A self-tuning PID controller to control the tension for tape winding of composites was designed and the constant extension ratio is guaranteed. To reduce the time required for the stabilization of the tension, a faststabilization method [4] for web tension is proposed. The model of dancer system and stabilization of web tension in drying process are established, and the variation of tension is used as a reference value for the tension stabilization. The integration of load cells and active dancer system for printed electronics applications was used to improve the accuracy of web tension, and self-adapting neural network control was proposed to reduce tension spikes due to the change in roll diameter of winder and unwinder rolls. Wu et al. [5] developed a tension detection and control mechanism and analyzed the main causes of wire tension variation, and then a PI algorithm was proposed to reduce tension variation. An accurate dynamic model for the unwind roll by considering the time variation of the roll inertia and radius was developed, and a decentralized controller for computing the equilibrium inputs for each driven roller was proposed [6]. A sliding mode control with guaranteed cost technique [7] was applied for reducing the system uncertainties. The simulation results showed that the proposed method had good robustness and quick response time. Compensation method [8] by calculating the torque of a driven loop lifter was developed to control the tension and thickness of hot-rolled strip. For the control strategy, several control methods have been proposed including disturbance rejection control [9, 10, 11, 12], neuro-fuzzy control [13, 14, 15, 16], and \( {\text{H}}\infty \) control [17, 18, 19]. Choi et al. [20] conducted a survey on various types of control algorithms by investigating their strengths and weaknesses, and demonstrated some areas of potential future development.

Most of the above studies considered the dynamics of driven rollers in the models but the behavior of idle rollers was ignored. Consequently, the models were under some limited conditions, which ignored detailed complex tension dynamics. On the other hand, most research focused on dynamic modeling and control strategy design, but the mechanical structure and the influence of parameter variation on fiber tension were ignored. In this paper, a novel tension control method is presented, which can regulate the tension and speed of the filament winding process. The mechanical structure and dynamic model of the system are established, and the influences of the parameter and the speed variation on fiber tension are examined. Subsequently, according to the features of driven rollers and the influence of variation, the control method is proposed by regulating the outputs of the torque of unwind roll, the torque of magnetic powder brake roller, and the speed of the master speed roller in three levels. Simulations are conducted for verifying the effect by comparing the results with those of the conventional PID controller. Finally, the performance of the proposed control system is verified through experimental studies using a filament winding machine.

The structure of the paper is organized as follows. Section 2 presents the mechanical structure of system. In addition, the dynamic models are constructed, and the influence of parameter and speed variation on the rollers is examined. In Section 3, the control strategy is proposed. Simulations are conducted for verifying the effect of the proposed controller by comparing with that of the conventional PID controller in Section 4. In Section 5, the proposed mechanical structure and control strategy are applied to a winding machine, and the experimental study is conducted for verifying the performance of the tension control system.

## 2 Mechanical Structure and Dynamic Modeling

### 2.1 Unwind Section

*v*

_{0}and tension

*T*

_{0}can be expressed as follows:

*J*

_{0}(

*t*) is the inertia of the unwind section,

*U*

_{0}is the input torque from the torque motor,

*n*

_{0}is the gearing ratio between the torque motor shaft and the unwind roll shaft,

*ω*

_{0}is the angular velocity of the unwind roll and

*b*is the coefficient of friction.

*t*,

*J*

_{0}(

*t*) consists of three parts:

*J*

_{ω}(

*t*) is the inertia of the carbon fiber on the core. As the radius of unwind roll decreases due to the carbon fiber continuously releases into the process, \( J_{\omega } \left( t \right) \) is time varying:

*W*is the width of the carbon fiber,

*R*

_{0}(

*t*) is the radius of the carbon fiber,

*r*

_{0}is the radius of the carbon fiber core. Therefore, Eq. (1) can be written as

*J*

_{0}(

*t*) is

*R*

_{0}(

*t*) is approximately expressed as follows:

In Figure 4(a), \( U_{0} \left( t \right) = R_{0} \left( t \right) * 3 0\,\, {\text{N}} \), \( v_{0} = 0 . 5 \,\,{\text{m/s}} \), *a* varies from 0.1 to 1 m/s^{2}, and the radius varies from 0.16 to 0.1 m. Larger acceleration causes greater tension deviation from the set value for the same radius. However, in the same acceleration, smaller radius causes smaller tension deviation. In Figure 4(b), \( U_{0} \left( t \right){ = 0} . 1 6T \), \( v_{0} = 0 . 5\, \,{\text{m/s}} \), \( a = 0.4 \,\,{\text{m}}/{\text{s}}^{2} \), and the radius varies from 0.16 to 0.1 m. Tension increases as the radius decreases because the torque is constant. Thus, larger torque causes greater tension deviation.

*δ*is constant.

*T*

_{0}and the tension

*F*on the unwind roll are related as follows:

*θ*is associated with the length of the unwind roll

*L*and the distance between the unwind roll and the guide roller

*s*. In general, the diameter of the guide roller is considerably smaller than the length and the distance, so the diameter of the guide roller is ignored. Assuming that \( l = 0 \),

*R*

_{0}is

*T*

_{0}is associated with angle

*θ*, which is associated with

*s*and

*L*. The tension variation under different relationships between

*s*and

*L*is studied, which is shown in Figure 6. In Figure 6, \( U_{0} = 1.6\,\,{\text{N}} \cdot {\text{m}} \), \( \delta { = 0} . 0 2\,\,{\text{m}} \),

*W*= 0.01 m, \( v_{0}\, { = 0} . 5\,{\text{m/s}} \), \( a{ = 0} . 4 {\text{m/}}s^{2} \),

*L*= 0.18 m, and

*s*varies from

*L*to 6

*L*. From Figure 6, we observe that the tension

*T*

_{0}deviates from the set value as the acceleration is not equal to zero. Moreover, as \( {\text{s }} \) increases, the tension fluctuation becomes smaller. When \( s \ge 4L \), the tension fluctuation is less than 0.5 N. Therefore, the mechanical structure should be well designed to increase the distance

*s*. So under the condition that

*s*is much larger than

*L*, Eq. (13) can be simplified as Eq. (7) for the control process.

### 2.2 Magnetic Brake Roller

### 2.3 Master Speed Roller

### 2.4 Idle Roller

Typically, the coefficient of friction *b* is small and can be ignored. Therefore, in the steady-state process, the idle rollers will not contribute to the dynamic of the system, which indicates that \( T_{{i{ + 1}}} = T_{i} . \)

## 3 Control Method Design

*x*(

*k*) includes error

*e*(

*k*) and error change Δ

*e*(

*k*), and they are inputs to the fuzzy logic control. \( K_{1} \) and \( K_{2} \) are the input scaling factors of

*e*(

*k*) and Δ

*e*(

*k*), respectively.

*t*(

*k*) is the tension input, and \( t_{r} \left( k \right) \) is the reference tension. The output

*u*(

*k*) is \( \Delta K_{p} (k) \) and \( \Delta K_{i} (k) \), which are the change in the scaling factor and the derivation time of the PID controller. The output

*u*(

*k*) can be achieved through three stages: fuzzification, decision-making fuzzy logic, and defuzzification.

### 3.1 Fuzzification

*e*(

*k*), \( \Delta K_{p} (k) \), and \( \Delta K_{i} (k) \) have been normalized to [− 6, 6], and the domain for the variable \( \Delta {\text{e}}(k) \) has been normalized to [− 3, 3]. Figure 11 shows the input and output membership functions of the controller.

### 3.2 Decision-making Fuzzy Logic

Rule base of \( \Delta K_{p} (k) \)

∆e\e | NB | NM | NS | Z0 | PS | PM | PB |
---|---|---|---|---|---|---|---|

NB | NB | NB | NB | NB | NM | NM | NS |

NM | NB | NB | NB | NM | NM | NS | NS |

NS | NB | NM | NM | NS | NS | NS | Z0 |

Z0 | NM | NM | NS | NS | Z0 | PS | PS |

PS | NS | NS | Z0 | PS | PS | PM | PM |

PM | PS | PS | PM | PM | PM | PB | PB |

PB | PM | PM | PM | PB | PB | PB | PB |

Rule base of \( \Delta K_{i} (k) \)

∆e\e | NB | NM | NS | Z0 | PS | PM | PB |
---|---|---|---|---|---|---|---|

NB | NB | NB | NB | NB | NB | NB | NM |

NM | NB | NB | NB | NB | NM | NM | NM |

NS | NB | NM | NS | NS | NS | Z0 | Z0 |

Z0 | NS | NS | Z0 | Z0 | PS | PS | PM |

PS | NS | NS | Z0 | PS | PM | PM | PM |

PM | PS | PS | PS | PM | PM | PM | PB |

PB | PM | PM | PB | PB | PB | PB | PB |

### 3.3 Defuzzification

## 4 Simulation

Parameters used in simulation

Parameter | Description | Value |
---|---|---|

\( {\text{AE}} \) | Modulus and area of carbon fiber | 8900 N |

\( J_{1} \) | Inertia of unwind roll | \( 0.09\, {\text{kg}}\cdot{\text{m}}^{2} \) |

\( R_{1} \) | Radius of unwind roll | \( 0.08\, {\text{m}} \) |

\( J_{3} \) | Inertia of magnetic powder brake roll | \( 0.002\, {\text{kg}}\cdot{\text{m}}^{2} \) |

\( R_{3} \) | Radius of magnetic powder brake roll | \( 0.06\, {\text{m}} \) |

\( J_{i} \) | Inertia of idle roller | \( 0.00005\, {\text{kg}}\cdot{\text{m}}^{2} \) |

\( R_{i} \) | Radius of idle roller | \( 0.025\, {\text{m}} \) |

\( L_{i} \) | Distance between span | \( 0.5\, {\text{m}} \) |

\( b \) | Coefficient of friction | \( 0.0015\) |

\( L \) | Length of unwind roll | \( 0.18 \,{\text{m}} \) |

\( \delta \) | Screw pitch of unwind roll | \( 0.02\, {\text{m}} \) |

\( s \) | Distance of the unwind span | \( 1.2 \,{\text{m}} \) |

The torque of the magnetic brake roller is

Simulations of the conventional method and the proposed method were conducted to verify the performance of the system.

*t*= 2 s. Simulation results for six cases (Table 4) are shown in Figures 17, 18 and 19.

Speed and tension parameters

Case no. | Reference tension (N) | Initial speed (m/s) | Final speed (m/s) |
---|---|---|---|

1 | 10 | 0.2 | 0.5 |

2 | 10 | 0.5 | 1 |

3 | 30 | 0.2 | 0.5 |

4 | 30 | 0.5 | 1 |

5 | 50 | 0.2 | 0.5 |

6 | 50 | 0.5 | 1 |

When the speed varies from 0.5 m/s to 1 m/s at reference tensions 10 N, 30 N, and 50 N for the steady-state error, the conventional PID controller becomes unstable. Moreover, the proposed controller demonstrated a steady performance. The proposed controller provided faster settling time and lower steady-state error, and the dynamic behavior and accuracy were better than those obtained using the conventional PID controller.

*t*= 2 s. Moreover, in Figure 21(b), the speed varies from 0.5 m/s to 1 m/s at

*t*= 2 s.

As shown in Figure 21, the number of idle rollers influences both the settling time and the overshooting value of the tension. In Figure 21(a), the overshooting value is 2.8 N when *N *= 21, which is greater than the values 2 N and 2.1 N when *N *= 14 and *N *= 17, respectively, and the settling time is slower. In the three cases, the errors *e*(*k*) are in the interval [− 2.8, −2] and the linguistic labels are NM and NS. Consequently, the outputs \( \Delta K_{p} (k) \) and \( \Delta K_{i} (k) \) of the fuzzy control are almost the same, and it requires more time to reach the equilibrium position in the case *N *= 21. In Figure 21(b), the overshooting value is 4.6 N when *N *= 21, which is greater than the value 3.0 N and 2.8 N when *N *= 14 and *N *= 17; however, the settling time is faster. The peak error *e*(*k*) is −4.6 N, and the linguistic labels are NB and NM in the case of *N *= 21. Compared to the error linguistic labels NM and NS, the outputs \( \Delta K_{p} (k) \) and \( \Delta K_{i} (k) \) of the fuzzy control are larger, and it requires less time to return to the equilibrium position.

## 5 Experiments

### 5.1 Experimental Platform

### 5.2 Experimental Results

Parameters used in experiment

Case 1 | Case 2 | Case 3 | Case 4 | |
---|---|---|---|---|

Mandrel | Round pipe | Rectangular pipe | Round pipe | Rectangular pipe |

Reference tension (N) | 10 | 11.5 | 12 | 12.5 |

Winding method | Hoop | Helical | Hoop | Helical |

Torque of unwind roll (N·m) | 0.24 | 0.3 | 0.32 | 0.34 |

Torque of magnetic powder brake roll (N·m) | 0.48 | 0.54 | 0.59 | 0.63 |

As shown in Figures 25 and 26, in the steady-state stage, the motor speed efficiently traces the reference speed, and the error of tension is regulated to near zero. In Figures 27 and 28, the reference speed changes rapidly, and the disturbance of the speed has significant influence on the tension, the proposed controller can reduce large speed variations to maintain the stability of the system. The proposed controller exhibits excellent performance in terms of tension regulation during the steady-state stage and the acceleration/deceleration stage.

## 6 Conclusions

- (1)
In the unwind roll process, the acceleration of the transport speed, the change of radius and the swing of carbon fiber along the core can cause tension deviation from the desired value. Larger acceleration and larger radius cause greater tension deviation. The length of unwind roll and the distance between unwind roll and guide roller can cause tension deviation from the set value periodically.

- (2)
In the magnetic powder brake roller, the tension increment is independent of the output torque of magnetic powder brake. A large tension can be applied to the carbon fiber without introducing considerable tension interference by increasing the radius and decreasing the inertia of the magnetic powder brake roller.

- (3)
In this paper, a tension control method is proposed by applying tension to the carbon fiber with three different driven rollers (the torque of unwind roll, the torque of magnetic powder brake roller, and the speed of master speed roller) in three levels and a fuzzy-PID controller is designed for the speed control of the master speed roller. Simulation and experimental study show that the proposed method provides faster setting time and lower steady-state error than conventional PID controller in the steady stage and the acceleration stage. The system can stay stable under different reference tensions and transport speeds.

## Notes

### Authors’ Contributions

X-MX and W-XZ wrote the manuscript; X-LD and W-XZ were in charge of the whole structure of the manuscript; MZ and S-HW assisted with experimental analysis. All authors read and approved the final manuscript.

### Authors’ Information

Xiao-Ming Xu, born in 1988, is currently a PhD candidate at *School of Mechanical Engineering and Automation, Beihang University, China.* His research interests include design and control of filament winding machine.

Wu-Xiang Zhang, born in 1978, is currently an associate professor at *School of Mechanical Engineering and Automation, Beihang University, China*. He received his PhD degree from Beihang *University, China*, in 2009. His research interests include the dynamics of compliant mechanical systems and robots, intelligent device and detection technology.

Xi-Lun Ding, born in 1967, is currently a professor and a PhD candidate supervisor at *School of Mechanical Engineering and Automation, Beihang University, China*. He received his PhD degree from *Harbin Institute of Technology, China*, in 1997. His research interests include the dynamics of compliant mechanical systems and robots, nonholonomic control of space robots, dynamics and control of aerial robots, and biomimetic robots.

### Competing Interests

The authors declare that they have no competing interests.

### Funding

Supported by National Natural Science Foundation of China (Grant No. 51575018).

### Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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