_{1}

Flexible continuous plastic films are used to produce various products, including optical films and packaging materials, because plastic film is suited to use in mass production manufacturing processes. Generally, the web handling process is applied to convey the plastic film, which is ultimately rewound into a roll using a rewinder. In this case, wrinkles, slippage and other defects may occur if the rewinding conditions are inadequate. In this paper, the authors explain the development of a rewinder system that prevents wound roll defects—primarily starring and telescoping. The system is able to prevent such defects by optimizing the rewinding conditions of tension and nip-load. Based on the optimum design technique, the tension and nip-load are calculated using a 32-bit personal computer. Our experiments have also empirically shown that this rewinder system can prevent roll defects when applying optimized tension and nip-load. Additionally, inexperienced operators can control this system easily.

Thin, flexible plastic films (webs) are widely used in various fields as different materials, including functional and packaging materials. Common examples include the optical films used in liquid-crystal displays (LCD) and packaging films used for the storage and transport of foods. The reason for this is that webs are suited to use in mass production and can be given moisture proofing, light blocking, optical properties, and such in a continuous process. In general, during the final web handling process, the web is rewound into a roll using a rewinding system. Finally, the rewound web is cut to the appropriate size in making the final product and shipped. Therefore, it is extremely important to prevent defects during rewinding in order to maintain the quality of the web. When rewinding condition settings are inappropriate, however, defects such as slip, telescoping, and wrinkles will occur in the rewound roll. These types of defects are closely related to the internal stress condition of the roll. As such, we believe that by theoretically determining the internal stress, we can predict and prevent such defects ahead of time. In this light, Hashimoto et al. have proposed a rewinding tension optimization method designed to prevent slip and wrinkles inside the roll [

In this research, we investigate the optimal rewinding conditions, including tension and nip-load, and developed a rewinding system in which the software is integrated to minimize rewinding defects.

The web is fed from the unwinding unit and transported to the rewinding unit, where it is ultimately rewound into a roll. Moreover, processes located between the unwinding and rewinding units, such as printing and coating, are used to provide the web with various properties.

Such production processes are used widely for such applications as printing of webs for food packaging and coating and drying of functional materials on webs to produce LCDs and lithium-ion batteries.

In this research, we focused on the rewinding unit―in which defects are particularly likely to occur―and investigated the commonly used dual-shaft turret rewinder shown in

In this research, we predict the occurrence of defects by first theoretically determining the internal roll stress, from which we determine the optimal rewinding conditions. Therefore, to determine the internal roll stress, we assume the web that has been wound into a spiral to be a series of thin walled concentric cylinders, such as that shown in

When solving for Equation (1), we need to set the following two boundary conditions for radial stress σ_{r}. First, we can define the following equation for the boundary condition at the innermost layer, given that displacement at the first layer of the web and at the core are equal.

Meanwhile, we can define the following equation for the boundary condition at the outermost layer of the roll during rewinding.

Because there is no new web added to the outermost layer at the completion of rewinding, we can define the boundary condition at the outermost layer as follows:

By applying the boundary conditions shown in Equations (2) through (4) and solving for rewinding equation (1), we can determine the internal radial stress. At this point, we can determine radial stress σ_{ri} at the i-th layer of the roll by adding the stress increment from the (i+1) layer to the n-th layer (final roll layer) as in Equation (5).

Here, δσ_{rij} expresses the stress increment at the j-th layer when the web is wound to i layers. During specific calculations, we successively solve the rewinding equation for stress increment δσ_{r} obtained by substituting

Equation (5) into Equation (1) under boundary conditions (2) through (4) and repeating in compliance with Equation (5).

Moreover, under most manufacturing conditions, the region where the internal tangential stress becomes negative (compressive stress), in other words, the region in which wrinkles form, has a higher likelihood of occurring near the roll core. Because this phenomenon is often experienced in manufacturing plants, we must accurately estimate the internal stress near the roll core to prevent such wrinkles. In the actual machine, however, phenomena can occur that create disturbance near the rewinding core at the outset of web winding, so the approach does not necessarily satisfy the boundary conditions mentioned earlier. Some of these typical phenomena include tension variation in the web width direction caused by geometric steps in the rewinding core and adhesive tape, or by variation in adhesion and wrinkling in the web.

These phenomena cause variation in internal roll stress in the width direction, sometimes causing the web to be rewound on the roll core in a distorted geometry. When these types of phenomena occur near the roll core, the internal stress in the width direction will be uneven through the outermost layer because the web is successively layered. Wrinkles that occur at the outset of rewinding are different from wrinkles caused by internal roll compressive stress, and are thus difficult to improve using tension and nip-load.

Therefore, we investigated a method of avoiding these defect phenomena that conforms with the boundary conditions in order to apply the theoretical rewinding model mentioned earlier to the actual machine.

Web splicing during rewinding typically uses adhesive tape, as shown in

In actual manufacturing lines, the web width, thickness, and mechanical properties often differ depending on the item being produced. As such, it is desirable if the rewinding tension and nip-load can be set over a wide range. Conventionally, rewinding conditions are set based on experience, while a method for proportionally decreasing tension in the roll radial direction under a constant nip-load (taper tension), in particular, has come to be used widely. As will be mentioned later, however, a rewinding method that increases the final winding tension is more useful to realize rewinding conditions that maintain an optimal internal roll stress condition. Meanwhile, it is believed to be important to variably control the entrained air volume to maintain the optimal roll quality using nip-load, so a system that strictly fixes the running conditions is not flexible enough. Therefore, in this research, we selected a method that indicates the rewinding conditions using the calculation model mentioned earlier, as shown in

We used a standard computer in optimizing the rewinding conditions. The software is composed of two main parts―a user interface that displays the precondition settings necessary for optimization along with the calculation results, and a calculation unit that provides the computational analysis for optimization. Confirmation of the precondition settings and calculation results is best when the operational method relies on the experience of the operator as little as possible. As such, we used a method that visually displays these using graphs and such.

The rewinding tension obtained via optimization is converted to a torque command value and applied to an electric motor through the control unit. The nip-load obtained via optimization is converted to an equivalent pressure and applied by the control device as a command value. The rewinding tension and nip-load are expressed as the following design variable vector.

Here, ΔT_{i} _{j} _{w}_{max} and maximum nip-load N_{max}, and a lower limit of minimum tension T_{w}_{min} and minimum nip-load N_{min}. These values are determined ahead of time by the designer.

To prevent web wrinkles, it is necessary to prevent the circumferential stress from becoming compressive. As such, we impose a condition where the minimum circumferential stress is a non-negative. At the same time, to prevent slip, it is necessary to ensure that web interlayer friction remains greater than critical friction F_{cr} at which slip begins.

Considering the above factors, we express the constraint conditions as the following inequality.

Here, constraint function g_{i}(X) is defined by each of the following equations.

When designing the objective function, we set the circumferential stress to be a non-negative close to zero, and set the difference between interlayer friction and critical friction to be a positive close to that approaching zero over a wide range of radial positions in the roll. Moreover, we set the difference between stress at the start of rewinding and at the end of rewinding as close to zero as possible to ensure stability during web splicing. Therefore, the objective function that must be minimized is defined by the following equation.

Moreover, interlayer friction F(r) is determined by Equation (10). Circumferential stress σ_{θref} is a physical value introduced for purposes of scaling and is given by Equation (11).

Given the above, the optimized problem for rewinding tension and nip-load is formularized by the following equation.

We conducted rewinding tests to investigate the applicability of the rewinding condition optimization method proposed above and confirmed the performance. We calculated the optimal rewinding conditions using this optimization method and observed the appearance of a roll rewound under these rewinding conditions.

_{w}_{0} = 200 (N/m) (taper tension), the dash-dot line shows rewinding tension for an initial tension of T_{w}_{0} = 140 (N/m) (taper tension), and the solid line shows the optimized rewinding tension. On the other hand,

Normalized radius for web length of 4000 (m) | r/r_{c} | 1.0 - 3.7 |
---|---|---|

Reference value for friction force | F_{cr} (kN) | 50.0 |

Reference value for tangential stress | σ_{θref} (MPa) | 8.0 |

Maximum tension limit | T_{w}_{max} (N/m) | 200 |

Minimum tension limit | T_{w}_{min} (N/m) | 0 |

Maximum nip-load limit | N_{max} (N/m) | 200 |

Minimum nip-load limit | N_{min} (N/m) | 0 |

Web thickness | h_{w} (μm) | 25 |

Web width | W (m) | 1.0 |

Wound roll radial Young’s modulus | A = 123, n = 1.0 | |

Wound roll circumferential Young’s modulus | E_{θ} (Pa) | 5.18 × 109 |

Core young’s modulus | E_{c} (Pa) | 17.0 × 109 |

Core radius | r_{c} (m) | 0.038 |

Winding velocity | V (m/min) | 100 |

Coefficient of friction | Μ_{eff} | 0.3 |

friction. In

As can be seen from _{c} = 1.1 to 2.5), a region in which there is a high risk of wrinkle generation [

This is equivalent to a condition of so-called roll tightening. Meanwhile, when using the optimized tension and nip-load (solid line), we see that there is no compression stress in any of the regions.

_{r}, which acts as the web interlayer pressing force, increases so that the air layer formed between the web layers becomes thinner, increasing interlayer friction. At the same time, however, compressive stress is generated in circumferential stress σ_{θ}, which risks causing wrinkles. Meanwhile, using the optimization models in this research, we set the rewinding tension after estimating the tangential stress (compressive stress), used nip-load to constrain the entrained air volume near the outermost layers where the pressing force (radial stress) decreases, and set a high value for the interlayer friction. Moreover, another approach is to use a fixed value for the nip-load and increase the rewinding tension near the outermost layers, but a high tensile force risks causing the creep phenomenon to occur in the web. In addition, given limitations on the cost of the electric motors and installation space, it is not always possible to increase the rewinding tension. As such, it is desirable to use a variable nip-load in actual manufacturing locations.

Although we showed that we can calculate the optimized rewinding conditions using these types of optimization models, we also made an appearance comparison of rewound webs to confirm its applicability to real-world situations.

As such, it is important to theoretically ensure that the internal roll stress will be non-negative before rewinding.

Next, we conducted drop tests to compare the slip resistance force.

In this paper, we created a simple rewinding condition setting system that considers the standard properties that a rewinding machine must meet in applying the rewinding condition optimization method. The following summarizes our main conclusions.

1) We created a tapeless system to suitably operate the rewinding model and showed the results.

2) We integrated the optimizing function for rewinding tension and nip-load into an actual rewinder in creating a method for easy operation by the operator [

3) We showed that the optimization function was able to effectively prevent defects, such as telescoping and wrinkles.

HiromuHashimoto, (2016) Intelligent Winding Machine of Plastic Films for Preventing Both Wrinkles and Slippages. Modern Mechanical Engineering,06,20-31. doi: 10.4236/mme.2016.61003

E_{c}: rewinding core Young’s modulus (Pa)

E_{r}: wound roll radial Young’s modulus considering influence of entrained air (Pa)

E_{θ}: wound roll circumferential Young’s modulus (Pa)

f(X): objective function

F_{cr}: critical friction reference value (N)

F: interlayer web friction (N)

h_{w}: web thickness (m)

m: nip-load function radial partitions

N: nip line load (N/m)

n: tension function radial partitions

r: arbitrary radial position on roll layer (m)

r_{c}: core radius (m)

s: wound roll outer radius (m)

T_{w}_{0}: initial rewinding tension (N/m)

T_{w}: rewinding tension

W: web width, m

V: web rewinding velocity (m/min)

X: design variable vector

σ_{min}: minimum wound roll tangential stress (Pa)

σ_{r}: wound roll internal radial stress (Pa)

δσ_{r}: wound roll radial stress incremental (Pa)

σ_{θ}: internal roll circumferential stress (Pa)

σ_{θref}: circumferential stress reference value (Pa) (=T_{w}_{0}/h_{w})