KR101835150B1 - Winding apparatus and winding control method - Google Patents

Abstract

연산된 온도 분포에 근거하고, 상기 권취 롤의 내부 응력을 아래와 같은 식에 근거하여 연산하고, 그 후 최적화 방법에 따라 최적화한다.
[수식 2]

The temperature distribution after the lapse of the designated time in the take-up roll is calculated on the basis of the following expression based on the change of the environmental temperature and the designated time which affect the take-up roll.
[Equation 1]

Based on the calculated temperature distribution, the internal stress of the winding roll is calculated on the basis of the following equation and then optimized according to the optimization method.
[Equation 2]

Description

BACKGROUND OF THE INVENTION 1. Field of the Invention [0001] The present invention relates to a winding apparatus and a winding control method,

The present invention relates to a winding device and a winding control method.

BACKGROUND ART [0002] The winding process of webs (collectively, films, sheets, etc.) including metal or resin films is widely used in many industrial products such as liquid crystal displays, cellular phones, and printed sheets.

The basic theory of web winding began to be developed by Kodak in the 1960s, and the trend continues to this day. According to the related basic theory, an analytical model including a predetermined nonlinear two-phase differential equation can be used to quantitatively grasp the internal stress state of the winding roll on which the web is wound. Further, when it becomes possible to quantitatively model the internal stress state of the wind-up roll, it becomes possible to optimize various conditions when winding the web. The inventor of the present invention has developed and proposed a technique of calculating the radial stress and the circumferential stress of the winding roll based on the internal stress analysis model proposed earlier and calculating the optimal winding condition based on the calculation result One).

[Prior Art Literature]

[Non-Patent Document]

[Non-Patent Document 1] Hashimoto et al., &Quot; Optimum Winding Tension and Nip-load into Wound Webs for Protecting Wrinkles and Slippage ", published by Japan Institute of Mechanical Engineers, Journal of Advanced Mechanical Design, Systems, and Manufacturing, Vol. 4 (2010) no. 1pp. 238-248

In the above-described prior art, it has become possible to precisely calculate the winding conditions such as the winding tension, which have been set qualitatively based on the feeling and experience of the manufacturer, based on a qualitative internal stress analysis model. However, the actual winding rolls are affected by heat, such as changes in the environmental temperature during storage and transportation and heat treatment. It has been found that the heat received by the take-up roll affects the internal stress of the take-up roll, causing a failure in winding, which is not visible immediately after the take-up.

SUMMARY OF THE INVENTION The present invention has been made in view of the above problems, and it is an object of the present invention to provide a winding device and a winding control method capable of optimizing winding conditions in consideration of the heat effect to which the winding roll is subjected.

In order to solve the above problems, the present invention provides a winding device having a winding tension adjusting device for adjusting a winding tension of a wound web on winding rolls wound around a winding core, The winding tension adjusting device includes temperature distribution calculating means for calculating a temperature distribution after the specified time in the winding roll on the basis of a change in environmental temperature affecting the winding roll and a predetermined designation time, And an optimum value calculating means for calculating an optimum value of the winding tension based on the internal stress calculated by the stress calculating means . In the above-described aspect, the temperature distribution calculating means calculates the temperature distribution of the winding roll after the specified time has elapsed, according to the change of the environmental temperature to which the winding roll is subjected and the designated time. Then, the stress calculating means calculates the internal stress in consideration of the temperature distribution of the wound roll. The optimum value calculating means calculates the optimum value of the winding tension based on the calculated internal stress in consideration of the temperature distribution of the winding roll. Therefore, when the winding roll is affected by the heat after processing, the internal stress of the winding roll changes based on the predicted characteristic of the temperature distribution calculating means. As a result, due to the internal stress changed on the basis of the thermal effect, it is possible to prevent the post-warp winding failure expected to occur as much as possible, such as blocking, buckling or stretch wrinkling, do.

With respect to the preferred form, the temperature distribution calculating means has a function of calculating a temperature distribution of the winding roll based on a thermal conduction analysis model including an unsteady thermal conduction differential equation. In this configuration, the temperature distribution acting on the winding roll can be calculated in consideration of the heat conduction characteristic in the winding roll and the heat transfer characteristic from the environment, and therefore, It is possible to ensure the necessary interlaminar friction force and circumferential stress even when there is a gap in the temperature distribution of the winding roll. Therefore, it becomes possible to more accurately grasp the radial stress and the circumferential stress which each part of the winding roll receives by the temperature distribution. As a result, the optimum value calculation means can optimize the calculated value to a more suitable winding tension.

With respect to a preferred form, the temperature distribution calculating means has a function of evaluating the layer of the web constituting the winding roll and the layer of air interposed between the layers of the web as an equivalent layer and calculating the temperature distribution of the winding roll It is equipped. In this embodiment, it is possible to calculate a precise temperature distribution in consideration of the air layer formed in the winding roll. The thermal conductivity of air is significantly lower than that of the web, and the thermal resistance of the winding roll decreases with the increase of the contact pressure Considering this, the temperature distribution near the air is not linear. On the other hand, since roughness exists on the surface of the web, a part of the contact surface between the web layers is in contact with the other part, and the other part becomes a noncontact dispersive contact. Air is interposed in the non-contact part. When the air layer is thickened, the web is separated and becomes noncontact on the entire surface. In the above-described form, if the air layer exists in the wind-up roll, the thermal conductivity of the wind-up roll face changes. In this embodiment, the abnormal thermal conduction differential equation can be solved using the thermal conductivity of the equivalent layer in consideration of the thermal resistance depending on the presence of the air layer, and the accurate temperature distribution can be calculated.

In a preferred form, the stress calculating means has a function of evaluating the layer of the web constituting the take-up roll and the layer of air interposed between the layers of the web as an equivalent layer to calculate the internal stress of the take- have. In this embodiment, since the internal stress is calculated using the thermal conductivity of the equivalent layer in consideration of the heat resistance depending on the presence of the air layer, accurate internal stress can be calculated.

In a preferred form, the stress calculating means includes a function of calculating, as a stress analysis model, a differential equation including a linear expansion coefficient of the web as a parameter. In this embodiment, even if the difference in temperature distribution between the winding side of the winding roll and the outermost layer is large, it becomes possible to maintain the interlaminar friction force and the circumferential stress at a required value according to the temperature distribution of the winding roll.

In a preferred form, the stress analysis model is given the boundary condition of the innermost layer by a differential equation using the coefficient of linear expansion of the core as a parameter. In this embodiment, the internal stress of the winding roll can be accurately calculated in consideration of the linear expansion coefficient of the winding core.

In a preferred form, the optimum value calculating means stores a tension function for calculating a tension, an objective function for solving the tension function, design variables included in the objective function, and calculates a minimum value of the objective function as a winding diameter And has a function of performing calculation at every predetermined predetermined step. In this embodiment, the minimum tension in consideration of the change in the environmental temperature to which the winding roll is to be applied is calculated at every predetermined winding diameter, so that the tension can be optimized to a value that is optimal every time the step increases.

In a preferred form, the objective function of the optimum value calculation means includes either a circumferential stress acting on the winding roll, a frictional force between the webs, and a parameter made up of a critical frictional force at which the web starts to slip have. In this configuration, it is possible to reliably eliminate the factor of the winding failure of the winding roll.

Another aspect of the present invention is a winding control method for controlling a winding device that adjusts a winding tension of a wound web to a winding diameter when the web is wound around a winding core to form a winding roll, A temperature distribution calculating step of calculating a temperature distribution after the lapse of the designated time in the take-up roll based on a change in the environmental temperature affecting the take-up roll and a predetermined designated time, A calculating step of calculating an internal stress and an optimization step of calculating an optimum value of the winding tension based on the calculated internal stress. In the above-described aspect, the temperature distribution calculating step calculates the temperature distribution of the winding roll after the specified time has elapsed, depending on the setting of the change in the environmental temperature and the designated time to which the winding roll is to be subjected. Then, in the stress calculation step, an internal stress in consideration of the temperature distribution of the wound roll is calculated. In the optimum value calculation step, the optimum value of the winding tension is calculated based on the internal stress calculated in consideration of the temperature distribution of the winding roll. Therefore, when the wind-up roll is affected by the heat after the machining, the internal stress of the wind-up roll is changed based on the predicted characteristic of the temperature distribution calculation step. As a result, according to the internal stress changed on the basis of the heat effect, it is possible to prevent the post-warp winding failure such as blocking, buckling or tension wrinkling in which the films adhere to each other as much as possible.

In a preferred form, the temperature distribution calculating step includes a step of calculating a temperature distribution of the winding roll based on a thermal conduction analysis model including an unsteady thermal conduction differential equation. In this aspect, since the temperature distribution acting on the winding roll can be calculated in consideration of the heat conduction characteristics in the winding roll and the heat transfer characteristics from the environment, a difference arises in the temperature distribution of the winding roll accompanying the change in the environmental temperature It is possible to ensure the necessary interlaminar friction force and circumferential stress. Therefore, it is possible to grasp the radial stress and the circumferential stress received by each part of the winding roll more precisely by the temperature distribution. As a result, the optimum value calculation means can optimize the calculated value to a more suitable winding tension.

In a preferred form, the temperature distribution calculating step includes the steps of evaluating a layer of the web constituting the take-up roll and an air layer interposed between the layers of the web as an equivalent layer and calculating a temperature distribution of the take- . In this embodiment, it is possible to calculate a precise temperature distribution in consideration of the air layer formed in the winding roll, and it becomes possible to calculate a precise temperature distribution.

In a preferred form, the stress calculating step includes a step of evaluating, as an equivalent layer, a layer of a web constituting the winding roll and a layer of air interposed between the layers of the web, and calculating an internal stress of the winding roll have. In this embodiment, since the internal stress is calculated using the thermal conductivity of the equivalent layer in consideration of the thermal resistance due to the presence of the air layer, accurate internal stress can be calculated.

In a preferred form, the stress computing step computes the stress analysis model based on boundary conditions of an innermost layer given by a differential equation using a linear expansion coefficient as a parameter. In this embodiment, the internal stress of the winding roll can be accurately calculated in consideration of the linear expansion coefficient of the winding core.

In a preferred form, the stress calculating step includes a step of calculating, as a stress analysis model, a differential equation including a linear expansion coefficient of the web as a parameter. In this embodiment, even if the difference in temperature distribution between the winding side of the winding roll and the outermost layer is large, it becomes possible to maintain the interlaminar friction force and the circumferential stress at a required value according to the temperature distribution of the winding roll.

In a preferred form, the optimum value calculating step stores a tension function for calculating a tension, an objective function for solving the tension function, design variables included in the objective function, and calculating a minimum value of the objective function, And a step of performing calculation for every predetermined predetermined step. In this embodiment, the minimum tension in consideration of the change in the environmental temperature to which the winding roll is to be applied is calculated every predetermined step of the winding diameter, and the tension can be optimized to an optimal value every time the step increases.

In a preferred form, the objective function of the optimum value calculation step includes either of circumferential stress acting on the winding roll, frictional force between the web and a parameter consisting of critical frictional force at which the web starts to slip have. In this embodiment, it is possible to reliably remove the factor of the winding failure of the winding roll.

Another preferred embodiment of the present invention is a winding control method for controlling a winding device that adjusts a winding tension of a wound web to a winding diameter when the web is wound around a winding core to form a winding roll, The winding tension between the inner peripheral side of the winding intermediate layer and the inner peripheral side of the winding intermediate layer is set to be smaller than the circumferential direction of the winding roll, Is set to a high value. In this embodiment, when the environmental temperature is expected to rise after winding, the winding tension can be given in consideration of the change of the internal stress caused by the temperature change.

Another preferred embodiment of the present invention is a winding control method for controlling a winding device that adjusts a winding tension of a wound web to a winding diameter when the web is wound around a winding core to form a winding roll, The winding tension is set to be high in advance over the whole winding path of the winding to such an extent that the interlaminar friction force of the winding roll is not lower than the predetermined limit frictional force in the case where it is expected that the environmental temperature affecting the wind- The winding control method comprising: In the above embodiment, when a decrease in environmental temperature is expected after winding, a winding tension can be given in consideration of a change in internal stress caused by a simple temperature change.

As described above, according to the present invention, since the internal stress in consideration of thermal stress can be optimized by calculating the temperature distribution of the winding roll in accordance with the change of the environmental temperature to which the winding roll is subjected and the designated time, It is possible to obtain a remarkable effect that as much as possible the prevention of post-warp failure such as blocking, buckling wrinkles, or stretch wrinkles adhering to each other due to internal stress can be prevented.

Fig. 1A is a schematic view of a theoretical prediction model according to the present invention, showing a winding roll when the nip roller is wound without using a nip roller. Fig.
Fig. 1B is a schematic view of a theoretical prediction model according to the present invention, and is a schematic view showing a winding roll when the nip roller is used for winding.
2 is a view showing the internal stress and the nip line load of the winding roll.
Figs. 3A to 3D are explanatory views of an air layer formed between the layers of the winding roll. Fig.
4 is a schematic configuration diagram of a winding device according to an embodiment of the present invention.
5 is a graph showing the optimization (evolution) of the winding tension.
FIG. 6 is an Entity Relationship (ER) diagram showing a part of the database structure according to the embodiment of FIG.
Fig. 7 is a diagram showing an example of a screen for executing the optimization program according to the embodiment of Fig. 4;
8 is a diagram showing an example of a screen for executing a web and machine condition setting program according to the embodiment of Fig.
Fig. 9 is a diagram showing an example of a screen for executing the temperature condition setting program according to the embodiment of Fig. 4; Fig.
10 is a flow chart showing an example of optimization control processing according to the embodiment of FIG.
11A is an explanatory diagram according to an embodiment of the present invention, and is a graph showing the setting of a temperature condition.
Fig. 11B is an explanatory diagram according to the embodiment of the present invention, and is a graph showing the temperature distribution of the winding roll calculated by the condition of Fig. 11A. Fig.
Fig. 12 is a graph showing the optimum winding tension calculated under the conditions of Figs. 11A and 11A. Fig.
Figure 13a is a diagram showing the operation characteristic on the basis of the winding tension of Figure 12, a graph illustrating the frictional force of the non-dimensional radius location for each roll r / r _c.
Figure 13b is a diagram showing the operation characteristic on the basis of the winding tension of Figure 12, a graph showing a radial stress at each radial position dimensionless roll r / r _c.
Fig. 13C is a graph showing characteristics calculated on the basis of the winding tension in Fig. 12, and is a graph showing the circumferential stress for each dimensionless roll radius position r / r _c .
14A is an explanatory diagram according to another embodiment of the present invention, and is a graph showing the setting of a temperature condition.
Fig. 14B is an explanatory diagram according to another embodiment of the present invention, and is a graph showing the temperature distribution of the winding roll calculated by the conditions of Fig. 14A. Fig.
Fig. 15 is a graph showing the optimum winding tension calculated under the conditions of Figs. 14A and 14B. Fig.
Figure 16a is a diagram showing the operation characteristic on the basis of the winding tension of Figure 15, a graph illustrating the frictional force of the non-dimensional radius location for each roll r / r _c.
Figure 16b is a diagram showing the operation characteristic on the basis of the winding tension of Figure 15, a graph showing a radial stress at each radial position dimensionless roll r / r _c.
Figure 16c is a diagram showing the operation characteristic on the basis of the winding tension of Figure 15, a graph showing a circumferential stress of the non-dimensional radius of each roll location r / r _c.
17 is a graph showing the optimum winding tension calculated under the conditions in another embodiment of the present invention.
Fig. 18A is an explanatory diagram of the setting condition according to the embodiment of Fig. 17, and is a graph showing the setting of the temperature condition at the time of heating.
Fig. 18B is an explanatory diagram of the setting condition according to the embodiment of Fig. 17, and is a graph showing the temperature distribution of the winding roll calculated by the condition of Fig. 18A. Fig.
Figure 19a is a diagram showing a characteristic operation based on the setting conditions of the take-up tension of Figure 17 Figure 18a and Figure 18b, it is a graph showing a dimensionless roll radial position r / r _c of each friction.
Figure 19b is a view and a graph which shows the radial stress of the non-dimensional radius location for each roll r / r _c represents the operational characteristics based on the setting condition of the take-up tension, and Figure 18a and 18b of Fig.
Figure 19c is a graph showing a circumferential stress of the drawing, and the non-dimensional radius location for each roll r / r _c represents the operational characteristics based on the setting conditions of the take-up tension of Figure 17 Figure 18a and 18b.
Fig. 20A is an explanatory diagram of the setting condition according to the embodiment of Fig. 17, and is a graph showing the setting of the temperature condition at the time of cooling.
Fig. 20B is an explanatory diagram of the setting condition according to the embodiment of Fig. 17, and is a graph showing the temperature distribution of the winding roll calculated by the condition of Fig. 20A. Fig.
Figure 21a is a diagram showing a characteristic operation based on the setting conditions of the take-up tension of 17 Figure 20a and Figure 20b, it is a graph showing a dimensionless roll radial position r / r _c of each friction.
Figure 21b is a view and a graph which shows the radial stress of the non-dimensional radius location for each roll r / r _c represents the operational characteristics based on the setting condition of the take-up tension in FIG 20a and FIG 20b in Fig.
Figure 21c is a graph showing a circumferential stress of the drawing, and the non-dimensional radius location for each roll r / r _c represents the operational characteristics based on the setting conditions of the take-up tension of 17 Figure 20a and Figure 20b.
22A is an explanatory diagram according to another embodiment of the present invention, and is a graph showing the setting of a temperature condition.
Fig. 22B is an explanatory diagram according to another embodiment of the present invention, and is a graph showing the temperature distribution of the winding roll calculated by the condition of Fig. 22A. Fig.
Fig. 23 is a graph showing the optimum winding tension calculated under the conditions according to Figs. 22A and 22B. Fig.
Figure 24a is a diagram showing the operation characteristic on the basis of the winding tension of Figure 23, a graph illustrating the frictional force of the non-dimensional radius location for each roll r / r _c.
Figure 24b is a diagram showing the operation characteristic on the basis of the winding tension in FIG. 23 is a graph showing a radial stress at each radial position dimensionless roll r / r _c.
Fig. 24C is a graph showing characteristics calculated on the basis of the winding tension in Fig. 23, and is a graph showing the circumferential stress for each dimensionless roll radius position r / r _c .
25A is an explanatory diagram according to another embodiment of the present invention, and is a graph showing the setting of a temperature condition.
Fig. 25B is an explanatory diagram according to another embodiment of the present invention, and is a graph showing the temperature distribution of the winding roll calculated by the condition of Fig. 25A. Fig.
Fig. 26 is a graph of optimal winding tension calculated under the conditions according to Figs. 25A and 25B. Fig.
Figure 27a is a diagram showing the operation characteristic on the basis of the winding tension of Figure 26, a graph illustrating the frictional force of the non-dimensional radius location for each roll r / r _c.
Figure 27b is a diagram showing the operation characteristic on the basis of the winding tension of Figure 26, a graph showing a radial stress at each radial position dimensionless roll r / r _c.
Figure 27c is a diagram showing the operation characteristic on the basis of the winding tension of Figure 26, a graph showing a circumferential stress of the non-dimensional radius of each roll location r / r _c.
Fig. 28 is an explanatory diagram for explaining the influence of the linear expansion coefficient, and Figs. A and B show transitions in the case of??>? R, and transitions in the case of?>? R, respectively.

BEST MODE FOR CARRYING OUT THE INVENTION Hereinafter, the best mode for carrying out the present invention will be described with reference to the accompanying drawings.

First, a theoretical prediction model according to the present embodiment will be described. Table 1 and Table 2 show the main nomenclature used in the following description.

Referring to Figs. 1A and 1B, the present embodiment is directed to a winding device for winding the web 10 by the central drive type. The center driving type is a system in which the core 5a for winding the web 10 is rotated by a drive shaft (not shown). As shown in Fig. 1A, the center drive winding system is provided with a nip roller 4 for pressing the web 10 wound around the core 5a, as shown in Fig. 1A, It is classified into one format.

In either case, the circumferential stress?? _{Acting in} the circumferential direction and the radial stress? R acting in the radial direction act on the web 10 wound on the core 5a. As shown in Fig. 2, the interlayer pressure (radial compressive stress)? R always acts on the web 10 at the position of an arbitrary winding radius r of the winding roll 5, And is pressed by each layer of the web 10 at this outer diameter. On the other hand, in the circumferential direction, the circumferential stress?? _Acts , but depending on the radial position of the winding roll 5, it can be pulled or compressed. The width direction stress of the take-up roll 5 is normally calculated as one shape.

sign Justice unit A Truth contact area m ² A _a Apparent contact area m ² Cc Special heat of recommendation J / (kg · K) Cf The specific heat of the web J / (kg · K) Ca Specific heat of air J / (kg · K) Ceq The specific heat of the equivalent layer of the winding roll J / (kg · K) C0 ~ C2 (13) Coefficient of equation Eeq The equivalent elongation modulus of the take-up roll and the nip roller Pa Ec Elongation modulus Pa Er The radial elongation modulus of the web Pa E? The circumferential elongation modulus of the web Pa En Elongation modulus of nip roller Pa Eral The radial elongation modulus Pa Ereq The radial elongation modulus of the equivalent layer of the winding roll Pa E? eq Circumferential stretch elasticity of the equivalent layer of the winding roll Pa f (X) Objective function Fcr Critical frictional force with slip N Fi Web interlaminar friction force of winding roll N

Average value of web interlaminar friction force of winding roll N gi (X) (i = 1 to 2n + 4) Constraint function hal Air layer thickness in wound roll m Δ hal Increase in thickness of air layer in winding roll m hal0 Initial air layer thickness m hf Thickness of web m Ka Thermal Conductivity of Air W / (m · k) Stay Thermal conductivity of the air layer W / (m · k) Kc Thermal Conductivity W / (m · k) Keq Thermal Conductivity of the Equivalent Layer W / (m · k) Kf Thermal Conductivity of Web W / (m · k) L Nip Line Load N / m N Nip load N pa Atmospheric pressure Pa pg Gauge pressure of outermost air layer Pa qa Heat flux through the non-contact part W / m ² qal Heat flux through the air layer W / m ² qf Heat flux through the web W / m ² qfc Heat flux through contact W / m ² r Any radius of the winding roll m rc Radius of coverage m rn Radius of nip roller m rout The outermost layer radius of the winding roll m Δr Equivalent layer thickness m Req The equivalent radius of the take-up roll and the nip roller m

sign Justice unit tc Thickness m Tw Winding tension N / m Tw (r) Coiling tension function N / m Tw0 (r) Initial winding tension N / m Δ Twi (i = 1 to n) the amount of change from the initial set tension at the i-th node N / m Tc Kwon Shim Do h Tr Roll temperature h T∞ Environmental temperature ℃ T0 Initial temperature ℃ ΔT Increment of winding roll temperature K ΔTc Increment of the thickness K Tj Time h Tk Designated time (elapsed time after environmental temperature change) h V Web winding speed m / s W Width of web m αc Coefficient of linear expansion 1 / K αr The coefficient of linear thermal expansion of the film 1 / K αh Heat transfer rate W / (m ² K) αθ The circumferential coefficient of linear expansion of the web 1 / K 竜 r Radial transformation of the web ε ral Radial deformation of air layer εθ Circumferential deformation of the web η Viscosity of air Pa · s λ Non-dimensional parameters of web width X Design variable vector μ eff Effective friction coefficient between web layers μs Static friction coefficient between web layers vc Poe Songbi vn The pearl ratio of the nip roller ? r? The circumferential speed ratio of the web to the radial direction νθr The radial velocity of the web relative to the circumferential direction ρa Density of air kg / m ³ ρc Density of cordship kg / m ³ ρ eq Density of equivalent layer kg / m ³ ρf Density of the Web kg / m ³ σ ff Composite surface roughness between web layers m σr Radial stress in the wound roll Pa Δσr Increment of radial stress Pa σθ Circumferential stress inside the winding roll Pa Δσθ Increment of circumferential stress Pa φ Taper ratio of winding tension

Further, when the nip roller 4 is used, a nip load N [N] is generated in the nip 45 generated between the nip roller 4 and the winding roll 5. The nip load N has a great influence on the internal stress of the wind-up roll 5, as will be described later in detail.

Next, with respect to the winding process, the web 10 is wound in the air. At this time, the surrounding air is entrained into the winding roll 5, and an air layer is formed between the layers of the web 10. When the air layer is present, the roll stiffness of the outer tube is remarkably lowered, and the stress in the rolls is lowered, so that the rolls are liable to be displaced or the form to be displaced. Particularly, in the case where the nip roller 4 is not provided as shown in Fig. 1A, the influence of the lowering of the rigidity in a condition where the air is easily inserted, such as a case where the winding speed is high, becomes large. In order to overcome such drawbacks, it is preferable that the nip roller 4 be used for winding. When the nip roller 4 is used, the amount of air introduced by the nip load N can be limited.

For the predicted theoretical model according to the present embodiment, Hakiel's theoretical model is applied to a basic part of stress analysis, and (1) stress analysis taking into consideration the entrained air and thermal stress, (2) internal stress immediately after winding, Thermal stress analysis to predict stress variation due to temperature change, and (3) unsteady thermal conduction analysis considering the air layer and heat resistance.

(1) Stress analysis considering enclosed air

The web 10 is wound on the core 5a in a state in which the pressing load (nip load N) is given in the manner of the winding stress and the nip roller. As the winding progresses, the stress in the winding portion already changes in order. At the time of modeling, the following assumptions are made.

(I) The winding roll 5 is a complete cylinder, and the thickness h _f and width W of the web 10 are uniform.

(Ii) The effect of winding the web 10 in a spiral shape can be ignored, and the winding roll 5 can be handled as a thin cylindrical overlapping.

(Ⅲ) for the internal stress state of the take-up roll 5, and the radial stress σ _r and circumferential stress σ _θ is dominant, the axial stress is does not need to be considered.

Under this assumption, the radial stress σr _i in the jth layer of the winding roll 5 is obtained by adding all of the stress increments Δσr _i in each layer from the (j + 1) -th layer to the k-th layer And can be expressed by equation (1). However, the j-th layer indicates the j-th layer when the layer in the core 5a is the first layer and is counted in order toward the outer layer.

[Number 1]

(1)

(One)

However, Δσ _rij represents the stress increment in the jth layer when it is wound up to the ith layer.

The stress equilibrium equation, the fit condition equation for strain, and the constitutive equation in the cylindrical coordinate system are given as follows, respectively.

[Number 2]

(2)

(2)

(3)

(3)

(4)

(4)

(5)

(5)

Here, it is assumed that a mark cell (maxell) expression shown below is established.

[Number 3]

(6)

(6)

(1) and (6) are applied to the radial stress σ _r using Eqs. (2) to (5) and the basic equations for the radial stress increment, Δσ _r , You can get it together.

[Number 4]

(7)

(7)

In order to solve the equation (7), boundary conditions between the innermost layer and the outermost layer are required. In the innermost layer, from the first layer of the web 10 and the fit of the displacement in the core, the following expression is obtained.

[Number 5]

(8)

(8)

When the equation (5) is applied to the equation (8) and the equation (1) and the equation (6) are taken into consideration, the innermost boundary condition can be obtained as follows.

[Number 6]

(9)

(9)

Assuming that the radial stress increment? Sr in the outermost layer is equal to the gage pressure Pg of the air layer wound on the inside of the new layer during winding, the outermost layer boundary condition for the case with and without nip roller 4 Are given as follows, respectively.

[Numeral 7]

(10)

(10)

L: Nip line load (nip load ÷ web width)

Next, the basic equation (7) and the innermost layer boundary condition equation (9) are modified so that the lowering of the rigidity of the winding roll 5 by the entrained air can be taken into consideration.

In the case of the presence of the air layer in the winding roll 5, in the numerical analysis, the web 10 can be handled as an equivalent layer of a composite air layer, and the elongation elastic modulus E _req , E _{θ eq in} the radial direction and the circumferential direction of the equivalent layer Are given as follows, respectively.

[Numeral 8]

(11)

(11)

(12)

(12)

Here, the thickness h _al and radial elongation modulus E _ral of the air layer, and shows a value in the respective winding. It is widely known that the tensile elastic modulus in the radial direction of the web 10 exhibits nonlinearity with respect to the radial stress? _R. In this embodiment, the radial elongation modulus E _req is approximated by the following equation.

[Number 9]

(13)

(13)

However, the coefficient C ₀ -C ₂ in the equation (13) is an experimentally obtained constant.

When the web 10 is wound in a roll shape, an air layer is formed between the outermost layer and the already wound portion by the entrained air. The initial air layer thickness _hal0 in the absence of the nip roller 4 can be obtained from the following equation, depending on how the wound web and already wound portion are regarded as a foil bearing model.

[Number 10]

(14)

(14)

Here,? Is a dimensionless parameter related to the web width W, and is defined as follows.

[Number 11]

(15)

(15)

On the other hand, in the case where the nip roller 4 is provided, it is possible to evaluate the application of the elastic fluid lubrication theory between the winding roll 5 and the nip roller 4. In the following examples, the results of Chang ("Elastohydrodynamic Lubrication of Air Lubricated Rollers", ASME Journal of Tribology, Vol.118, (1996), pp.623-628) are used.

[Number 12]

(16)

(16)

Here, the equivalent radius R _eq and the equivalent Young's modulus E _eq of the winding roll 5 and the nip roll are respectively given by the following equations.

[Num. 13]

(17)

(17)

(18)

(18)

Next, the radial extension elongation modulus of the air layer is examined. Assuming that the air entrained in the winding roll 5 does not flow out from the roll end, the air layer is compressed by winding a new layer. An air inlet when a layer is to be wound around the outermost layer, decreases as the winding roll (5), radial stresses _al h (= h _al0 -Δh _al) from the compressed air _al0 thickness h is by σ _r in. Applying the Boyle's law based on the state when it is wound on the outermost layer, the following relationship can be obtained.

[Number 14]

(19)

(19)

Using the above equation, the thickness h _al of the air layer is expressed as follows.

[Number 15]

(20)

(20)

Here, when the equation (19) is applied to the definition of the deformation, the radial strain ε _ral of the air layer can be obtained as follows.

[Num. 16]

(21)

(21)

From the equation (21), the relationship between the radial stress σr and the deformation ε _ral is obtained.

[Number 17]

(22)

(22)

Accordingly, the radial elongation modulus Eral of the air layer can be obtained as follows.

[Number 18]

(23)

(23)

By using all the above equations (14) - (23), the elongation modulus of the equivalent layer can be obtained considering the entrained air. Thus, by interpolating E _r and E _θ in Eqs. (7) and (9) with E _req and E _{θ eq} , the analysis of the internal stress can be advanced. In addition, the circumferential stress can be obtained from Equation (2) of the stress as follows.

[Number 19]

(24)

(24)

(2) Thermal stress analysis

When the temperature inside the roll changes due to the environmental temperature change, the internal stress fluctuates due to the linear expansion coefficient of the web 10 or the core 5a. In such a case, equilibrium equations for the cylindrical coordinate system and the conditional expressions of fitness for deformation are the same as in equations (2) and (3), respectively, while the structural equations are given as follows.

[Number 20]

(25)

(25)

(26)

(26)

Here,? T is a change amount with respect to the initial roll temperature T _r0 immediately after winding, and is defined by the following equation.

[Num. 21]

(27)

(27)

In the same order as in Eq. (7), the basic equation for the radial increment Δσr due to thermal stress is given by

[Number 22]

(28)

(28)

Next, the boundary condition for solving equation (28) will be described. (1), (6) and (27) are applied to the equation (8) obtained from the compatibility between the first layer of the web 10 and the core 5a in the innermost layer, The boundary condition is obtained as follows.

[Number 23]

(29)

(29)

However, the temperature increment? T _c of the core 5a is given as follows.

[Number 24]

(30)

(30)

On the other hand, since no new layer is added to the outermost layer after completion of winding, the outermost layer boundary condition is given as follows.

[Number 25]

(31)

(31)

Here, in order to consider the effect of air introduced in the thermal stress analysis, E _r and E _θ shown in Eqs. (28) and (29) are replaced by E _req and E _{θ eq} , respectively. The elongation modulus E _r and E _θ of the web 10 and the coefficient of linear expansion σ _r and α _θ and the elongation modulus E _c of the core 5 a and the radial elongation modulus E _ral of the air layer are constant .

The details are as described below form, the linear expansion coefficient σ _r, α _θ is the take-up roll 5 when the received heat, affect the temperature distribution variation of the take-up roll 5 due to the temperature change on the abnormal condition of the internal stress is And the degree is due to the coefficient of linear expansion of the web 10 and the core 5a. Therefore, in the equation (28), having a coefficient of linear expansion deulyeojigo σ _{r, θ} α accept the web 10, according to clarify the relationship between the change in the internal stress of the temperature distribution, and has a great significance.

(3) Unsteady heat conduction analysis considering air layer and heat resistance

In the cylindrical coordinate system, assuming that (i) the heat movement occurs only in the radial direction and can be ignored in the circumferential direction and the axial direction, (ii) there is no heat generation inside the wind-up roll 5, It is expressed by the following differential equation.

[26]

(32)

(32)

The flow of heat energy at the interface between the air and the wind-up roll 5 is dominated by the convection heat being dominant and the heat flux at the winding roll 5 side or the core 5a side and the air side is the same The boundary condition equations for the outermost circumferential surface of the winding roll 5 and the innermost circumferential surface of the core 5a are given by the following equations, respectively.

[Number 27]

(33)

(33)

(34)

(34)

Further, assuming that the heat fluxes are equally the same at the interface between the core 5a and the web 10, the boundary condition at the interface is expressed as follows.

[Number 28]

(35)

(35)

Here, as the initial temperature condition, the roll temperature T _r and the winding core temperature T _c are given as follows at time T _j0 immediately after winding.

[Number 29]

(36)

(36)

On the other hand, the surface of the web 10 has roughness. Therefore, as shown in Fig. 3A and Fig. 3B, the contact surfaces are partially in contact (contact portion 10a), and other portions are in noncontact distributed contact. Air is interposed in the non-contact part. Further, when the layer of air becomes thick, the web 10 is separated and, as shown in Fig. In this case, considering that the heat transfer rate Ka of the air is remarkably low as compared with the web 10, and the thermal resistance decreases with the increase of the contact pressure, the temperature distribution near the air layer is not linearly formed. Here, in this embodiment, as shown in Figs. 3C and 3D, the contact portion of the web 10 is modeled to evaluate the thermal resistance.

The presence of the air layer changes the thermal conductivity of the outer surface of the wind-up roll 5. Assuming that the heat fluxes q _ff and q _fal flowing through the web 10 and the air layer are the same in the equivalent layer and the convection effect in the air layer is negligible, the heat conductivity K _eq of the equivalent layer can be obtained as have.

[Number 30]

(37)

(37)

Here, it is assumed that in the air layer, the heat flow rates q _a and q _fc flowing through the contact portion and the non-contact portion pass in parallel as shown in Figs. 3C and 3D, and the ratio of the contact area to the true contact area to the apparent contact area When given as (a / Aa), K _al thermal conductivity of the air layer is given by the following equation.

[Number 31]

(38)

(38)

However, the ratio A / Aa of the true contact area to the apparent contact area is given by the following equation as a function of the radial stress. Further, the contact surface of the web 10 is regarded as non-contact in the range of the air layer thickness h _a > 3 _ff .

[Num. 32]

(39)

(39)

The density ρ _eq and the specific heat C _eq of the equivalent layer are respectively defined as follows.

[Num. 33]

(40)

(40)

(41)

(41)

From the above, the thermal conductivity K, k _f , density C, C _f , and specific heat rho and rho _f of the web 10 shown in the basic equation 32 of the unsteady thermal conduction and the boundary conditionulas 33 to 35, With changes in k _eq , C _eq , and ρ _eq and taking into account the initial temperature condition (36), it is possible to obtain a change over time of the roll temperature considering the air layer and thermal resistance.

For example, the first-order and second-order differentials included in the basic equation and the boundary condition equation described above can be discretized by a differential approximation (differential approximation), and can be obtained numerically. It should be noted that a center difference approximation with respect to the roll radius r _out and a forward difference approximation with respect to time are applied, and each is shown below.

[Number 34]

(Center difference approximation)

(42)

(42)

(43)

(43)

(Forward difference approximation)

(44)

(44)

Here, Δr is the thickness of the equivalent layer (h _f + h _al ), the width of the core thickness t _c , f is the radial stress increment Δσ _r to be approximated by the difference, the roll temperature T _r , and " _c " In addition, in the expressions (42) to (44), j is a roll radius position, and i is a subscript with respect to time.

Next, an embodiment to which the above-described predictive theory model is applied will be described.

4, the winding device 100 shown in the figure is provided with a plurality of guide rollers 2, a pair of pinch rollers 1, And the nip roller 4 to the outer periphery of the winding core 5a of the winding roll 5. In this case, Although not shown, a path from the roll 1 to the winding roll 5 is provided with an edge position control device for preventing a difference in position of the web 10, a load cell for detecting the winding tension of the web 10, Respectively.

The nip roller (4) is provided with a nip load adjusting device (6) for adjusting the pressing force against the winding roll (5). The nip load adjusting device 6 is embodied as a power transmitting mechanism for transmitting the power of an air cylinder or an air cylinder to adjust the nip load N of the nip 45 formed between the nip roller 4 and the take- And has an adjustable configuration.

The winding core 5a is a cylindrical member constituting the winding roll 5 integrally with the web 10. [ Since the material of the core 5a affects the heat transfer rate on the inner circumferential side of the winding roll 5, when the winding roll 5 is expected to move to a region where the change in the temperature environment is large, .

A motor 7 is connected to the winding core 5a of the winding roll 5 so that the winding core 5a itself rotates to wind the web 10. [ A temperature sensor 8 for detecting the temperature at the time of winding is provided near the outermost periphery of the winding roll 5. The value detected by the temperature sensor 8 at the time of completion of winding up the winding roll 5 is the initial roll temperature T _r0 at the initial time T _j0 (the parameter of the equation (39)), (217).

The web 10 may be a flexible sheet or printed matter used in a liquid crystal panel, a display monitor, a cellular phone, a solar cell system, and various other products.

For the control of the nip load adjusting device 6 and the motor 7, the winding device 100 is provided with a control unit 20. The control unit 20 has a storage unit 21, an operation unit 22, a motor control unit 23, and a nip load adjustment unit 24 as a logical module. The display unit 25 and the input / output unit 26 are connected to the control unit 20 so that the operator can perform necessary data processing on the input / output unit 26 while viewing the display on the display unit 25. [

The storage unit 21 is a module that is embodied as a ROM, a RAM, an auxiliary memory, or the like and has an area for storing control programs and parameters for controlling the entire winding device 100. The storage unit 21 is provided with a database for storing parameters for computing the above-described predictive model.

The arithmetic unit 22 has a microprocessor, a storage device, and an input / output interface, reads a control program and data stored in the storage device, executes the control program, The motor control unit 23, the nip load adjustment unit 24, the display unit 25, and the input / output unit 26).

The motor control unit 23 is a module for controlling the rotation speed of the motor 7 on the basis of the calculation result of the calculation unit 22. [ The motor control unit 23 also serves as a tension adjusting means for adjusting the winding tension Tw of the web 10 through the rotation speed control of the motor 7 in the present embodiment.

The nip load adjusting section 24 is a module for adjusting the pressing force by the nip load adjusting device 6 based on the calculation result of the calculating section 22. [

The display unit 25 is a unit embodied as a liquid crystal display or other display device.

The input / output unit 26 is a unit embodied as a pointing device such as a keyboard or a mouse, or an input / output device such as a card reader.

It is also preferable that the control unit 20 be provided with a communication function so that the control program and data are communicated with the host computer, depending on the mode in which the winding device 100 is implemented.

Next, the storage unit 21 shown in Fig. 4 has a region for storing a function. In addition to the above-described equations (1) to (44), the tension function Tw (r), the objective function f The constraint function g _i (X) is stored.

First, as an object of optimization, in the present embodiment, the tension function Tw (r) is defined as follows and stored in the storage unit 21. [ In consideration of the flexibility of the function and ease of handling, the tension force Tw (r) related to the present embodiment is expressed by a cubic spline function relating to the winding radius r of the winding roll 5, as shown below And stores it in the storage unit 21. [

[Number 35]

(45)

(45)

 However, < RTI ID = 0.0 > Δr < / RTI >

M _i is a shape parameter determined from a condition that the first derivative at each node position of the curve indicated for each section is continuous.

Tension function Tw (r) is for calculating a winding tension Tw with respect to the take-up radius r. In order to evolve (opt) for the tension function Tw (r), in the present embodiment, the purpose of the circumferential direction average value of the stress σ _θ function And the conditions for solving the star defects, the plastic deformation, and the telescope are suitably provided, and the tension is optimized.

As can be clearly seen from the tension function Tw (r) in the equation (45), in the present embodiment, from the winding start point to the outermost circumference of the winding roll is divided into n back sections, And the winding tension Tw or L is interpolated. The winding tension Tw is expressed as a function for smoothly connecting each section according to the setting of M _i in the equation (45) as a condition. The tension function Tw (r) of the equation (45) is optimized (evolved) depending on the setting of the objective function and the constraint function. That is, the tension function Tw (r) of the equation (45) is evolved so that the minimum value of the circumferential stress in the winding roll 5 is non-negative and the average value of the circumferential stress becomes infinitely zero, It is possible to obtain Tw.

5, as a method of evolving the tension function Tw (r) of the equation (45), a shear layer (k step shown by the solid line) to the evolution process ((k + 1) with respect to the tension function, secure the r coordinate g of each point P ^(k) (r _i, T _wi), and by changing only ΔT _wi the Tw coordinate in the direction of positive (正) direction or negative (負) of the new The contact point P (k ^{+ 1} ) (r _i , T _wi + T _wi ) is obtained. The functional form is updated by the equation (45) using the new coordinate values thus obtained, and the functions are sequentially evolved until the value of the objective function f (X) becomes optimal.

Next, variables of the objective function f (X) will be described.

In the present embodiment, the design variable vector of the objective function f (X) is defined as follows and stored in the storage unit 21. [

[Number 36]

(46)

(46)

However, the executable area from the winding position to the outermost diameter of the winding roll is divided in the r direction.

ΔT _i represents the difference between the initial tension T _wo at any radial position r _i and the tension during the evolution (k stages).

In the present embodiment, in the process of evolving the tension function T _w (r) of the equation (45) according to adding the nip line load L to the design parameter vector of the equation (46) Lt; / RTI >

The objective function f (X) stored in the storage unit 21 is defined as follows.

[Number 37]

(47)

(47)

는 임의시간ｊ에서의 층간마찰력、only,

Is the interlaminar friction force at an arbitrary time j,

F _cr is the critical friction at which slip begins,

는、임의시간ｊ에서의 원주방향응력、

The circumferential stress at an arbitrary time j,

는、원주방향응력의 참조값이다.

Is a reference value of the circumferential stress.

In the present embodiment, the critical frictional force Fcr of the equation (47) is determined by experiment and is, for example, 5 kN. Further, the frictional force F _i and the true measures σ _θ and r _ef are respectively defined as follows.

[Number 38]

(48)

(48)

i를 부과하는 제약 조건은, 아래와 같이 정의되어 기억부(21)에 기억된다.On the other hand, the design maximum and minimum values of the variables _wi and ΔT nipseon load L, the minimum value of the circumferential stress σ _θmin, and the mean frictional force of the web layers

The constraint condition for imposing i is defined in the following manner and stored in the storage unit 21.

[Number 39]

(49)

(49)

For the expression (49), the constraint function g _i (X) (i = 1 to 2n + 2j) is defined as follows and stored in the storage section 21.

[Number 40]

In summary, the optimization of the winding tension Tw is expressed as follows.

[Number 41]

Find X to minimize  f (X)

（５１） subject to gi (X) 0

(51)

Next, in order to realize the above-described optimization processing, the storage unit 21 stores tables 211 to 220 relating to information for calculating the above-described predictive model. Here, the table refers to a set of data expressed in a two-dimensional matrix (rows and columns) in a database system.

Hereinafter, a table according to the present embodiment will be described with reference to FIG. In the following description, an item of a table is referred to as a "column", and an actual value of a table (an actual value assignable to a column) is referred to as a "row". In Fig. 6, (PK) denotes a primary key and (FK) denotes a foreign key. A primary key is a column that uniquely identifies a row in a table. The foreign key is to refer to the data of the table having the corresponding primary key, depending on what has the same value as the primary key. When a plurality of columns are represented as a set, they are displayed in {}. The arrows in the drawing indicate relationships between tables (relations), and the external keys in the table on the end point side of the arrows refer to the primary keys in the table on the origin side of the arrows. Between the two tables, the correspondence relationship between the primary key and the foreign key is represented by a cardinality (the number of rows), and arrows indicate that the starting point is 0 or 1 and the cardinality is large Respectively. In addition, the tables shown are logically present and physically the same data group may be represented by a plurality of tables, or a plurality of data groups may be represented by the same table. In addition, the columns set in the respective tables are merely for describing the present embodiment for the purpose of describing the present embodiment, and may have columns other than those shown in the table.

6, a web table 211, a core table 212, an air table 213, and a nip roller table 214 are stored as a master table in the auxiliary storage device of the storage unit 21. [

The web table 211 is a table for registering the specifications of the web 10. The web table 211 has a thickness h _f , a width W, a critical frictional force Fcr, a radial elongation modulus E _r , a circumferential elongation modulus E _θ , RMS composite roughness σ _ff, a static friction coefficient ㎲, radially peuah's ratio υ _θr, circumferential peuah's ratio υ _θr, the thermal conductivity K _f, specific heat Cf, density ρ _f, the radial linear expansion coefficient α _r, the circumferential direction thermal expansion coefficient α _θ Can be registered. In particular a tool, in the present embodiment, the linear expansion coefficient α _r, the linear expansion coefficient α _θ is adopted as a parameter of the basic equation (28), and, since that operation, the radial direction and due to the heat receiving the take-up roll 5 circumferentially It becomes possible to calculate the considered internal stress.

The core table 212 registers the specifications of the core and determines the tensile modulus E _c , the core thickness t _c , the punch ratio v _c , the core v _c , the radius r _c , the thermal conductivity K _c , the specific heat C _c , the density ρ _f , and the coefficient of linear expansion α _c .

The air table 213 registers the specification of the air and includes, as _a column, an air code as a main key (atmospheric pressure, thermal conductivity K _a , specific heat C _a , density ρ _a , gauge pressure Pg, viscosity η). The air table 213 is provided in the storage unit 21 and the internal stress and thermal distribution in the equivalent layer of the air layer and the web can be precisely calculated at the place where the specification of the air is registered.

The nip roller table 214 registers the specifications of the nip roller 4 and calculates the radius r _n of the nip roller 4, the elongation modulus E _n , the initial taper tension, It is possible to register parameters including υ _n .

In the present embodiment, as a transaction table for operating the winding device 100, a winding plan table 215, a winding plan specification table 216, a web product management table 217, a temperature change map 218, and a winding control table 220 are provided.

The winding plan table 215 stores a specification for managing the plan of the winding process, and is capable of registering an item including the date of manufacture and the order code for each winding plan code (main key).

The winding plan specification table 216 registers the specifications of the winding roll 5 produced by the winding plan and the general specifications of the fabrication for each winding plan code and specifies the specifications of the nip rollers 4 used for each specification code for each winding plan The product number of the core 5a, the part number of the web 10, the winding length, the number of turns n, the outermost layer roll radius r _out , and the number of the winding rolls 5 can be registered. Further, in order to control the winding control taking into consideration the temperature change after the winding, an air code is provided as an external key, and information on the air from the air table 213 can be specified for each specification of the production plan. In addition, the specifications of the take-up plan specification table 216, winding core table 212 winding core radius (core diameter) r _c, etc., winding core (5a) from the date in the transient is the relation easily set, from the winding core table 212 It is in a form that can be referred to.

The web product management table 217 is for managing the production conditions of individual concrete products (winding rolls 5) produced for each specification determined by the winding plan specification table 216, and includes a winding plan specification table 216 The manufacturing date, the initial temperature T ₀ (see equation (36)), and the designation time T _k can be registered as the primary key, using the composite key composed of the external key (production plan code, specification code) . In addition, the time step and the heat transfer rate? _H can be registered in the web product management table 217 in order to register the temperature change prediction for each product. The time step is a time interval of temperature change, and is a column (item) for registering a numerical value arbitrarily selectable by the user in the optimization control described later. Further, the heat transfer rate? _H is a parameter for solving Expressions (33) and (34), and it is possible to register a value that is calculated based on an experimentally determined value or a measured value in an environment in which the winding roll 5 is placed . In addition, in order to register the temperature change, the web product management table 217 includes an external key of the temperature change map table 218. [

Temperature change map 218, the winding roll (5) is designed to register the specification of which is placed in the environment (map data), and a temperature change map for each code, taking up the ambient temperature T _∞ for each time T _j plan specification table Can be set in the range of the designated time T _k set in the step 216.

The winding control table 220 is used to set the specifications necessary for the optimum winding control and the composite key of the main key {winding plan code, specification code} and winding control code of the winding plan specification table 217 is used as the main key take-up plan winding tension for each specification Tw, the take-up speed (motor rotation speed) V, nipseon load L, the non-dimensional radius of the roll location r / r _c And so on.

According to the use of the tables 211 to 220 as described above, various screens or view tables can be created so that the operator can realize the optimization operation.

Referring to Fig. 7, in this embodiment, a screen 300 for executing an optimization program is provided. This screen has been switched from the main menu not shown.

The screen 300 displays a command button 303 for setting a method of optimization calculation based on conditions set by a command button 301 for setting web and machine conditions and a command button 302 for setting a temperature condition ) Are prepared. In the text box 304, the winding control code of the winding control table 220 is displayed as a result of the optimization calculation setting, and the operation speed of the winding device 100 (the number of revolutions of the motor 7) Are displayed in the text boxes 305 and 306, respectively. When the numerical values displayed in these text boxes are checked, the operator judges whether correction is necessary. If it is determined that correction is not necessary, the command button 307 for transmission is operated and the control unit 20 is instructed of the setting result . The control unit 20 winds the web 10 on the winding roll 5 based on the set result and registers the transaction results in the tables 215 to 217 shown in Fig. 6 . In addition, a command button 308 is prepared on the screen 300 so that the user can switch to the main menu if necessary.

When the command button 301 shown in Fig. 7 is operated, the screen switches to the screen 310 for setting web and machine conditions.

8, a screen 310 includes a combo box 311 for selecting a part number of the web 10 and a list window 321 for displaying specifications of the web 10 selected by the combo box 311. [ 312 are provided. In the combo box 311, the web number registered in the web table 211 of Fig. 6 is listed up, and each specification about the selected part number is displayed in the list window 312. [ When it is necessary to register a new part number, the main menu is returned to and registered from a registration screen not shown.

The screen 310 has a combo box 313 for selecting the part number of the core 5a and a list window 314 for displaying the specification of the core 5a selected by the combo box 313. [ In the combo box 313, the core part numbers registered in the core table 212 in FIG. 6 are listed up, and the specifications concerning the selected part numbers are displayed in the list window 314. When it is necessary to register a new part number, the user returns to the main menu and registers from a registration screen not shown.

A combo box 315 for selecting the part number of the nip roller 4 and a list window 316 for displaying the specifications of the nip roller 4 selected by the combo box 315 are provided on the screen 310 . In the combo box 315, the nip roller part numbers registered in the nip roller table 214 of Fig. 6 are listed up, and the respective specification about the selected part number is displayed in the list window 316. Fig. When it is necessary to register a new part number, the user returns to the main menu and registers from the registration screen not shown.

The operator checks the specifications displayed in the list windows 312, 314, and 316, and switches to the next screen by operating the command button 317 for execution if there is no change in the displayed contents. When the command button 317 is operated, the screen is switched to the screen 320 for temperature condition setting in Fig.

9, a screen 320 includes a text box 321 for inputting a time step, a text box 322 for inputting a heat transfer rate, a combo box 323 for selecting a temperature change code, A text box 325 for displaying the initial temperature T ₀ , a graphic window 326 for displaying the setting result, and a command button 327 for executing the setting result It is equipped.

The time step is for setting the time step j being employed in the equations (47) to (50), and is an arbitrary value that the operator believes is appropriate.

The heat transfer coefficient is a value used in the equations (33) and (34) set as the boundary condition of the basic equation (32). The heat transfer rate can be obtained by actually measuring and calculating the environmental temperature. Therefore, it is preferable that the heat transfer rate is patterned according to the temperature setting conditions and can be separately registered by an operator (user) so as to be selectable and selected in a combo box or the like.

The temperature change map code is for calling the data registered in the temperature change map table 218 in Fig. 6 and selects the temperature change map code registered in the temperature change map table 218 from the combo box 323. [ It is possible to arbitrarily set the environmental temperature T _∞ for each time T _j depending on the work. When it is necessary to register a new temperature change map code, the CPU returns to the main menu and registers from the registration screen not shown.

The designation time is for reading the value corresponding to the temperature change map code from the temperature change map table 218 of FIG. 6 and displaying it.

The initial temperature T ₀ is a value of the environmental temperature read by the sensor 8 (FIG. 4). In the present embodiment, this value is displayed in the text box as the value of the equation (36). Alternatively, as an alternative method, it is also possible to set the initial environmental temperature on this screen 320 and register it in the web product management table 217 of Fig. 6 so that the environmental temperature at the time of winding the web 10 is controlled by the air conditioner desirable.

The graphic window 326 is for displaying a graph of temperature and time based on the value of the set temperature change map table 218. [ In the illustrated example, the winding process is performed at an initial environmental temperature T _{∞ 0} of 25 ° C, and the winding roll 5 after the process is heated at a high temperature of 20K for 2 hours.

The operator confirms the specification set in the screen 320 and, if there is no change in the displayed contents, switches to the next screen by operating the command button 327 for execution. When the command button 327 is operated, the screen switches to the screen 320 of FIG. The operator judges whether or not correction is necessary. When it is determined that correction is not necessary, the operator operates the command button 307 for transmission and instructs the control unit 20 of the setting result. By this instruction, the control unit 20 calculates the optimum winding condition considering the temperature change in the following order.

Next, the operation of the control unit 20 after the setting is transmitted with reference to Fig. 10 will be described.

The control unit 20 reads necessary data in each table of Fig. 6 based on the transmitted setting conditions (step S101). Next, the control unit 20 calculates a temperature distribution to occur in the winding roll 5 in the future based on the read data, the basic equation 26, and the price related to the basic equation 26 S102). Next, the control unit 20 initializes the counter variable k to 0 (step S103), calculates the tension function Tw (r) by applying initial taper tension, and calculates the winding tension Tw in the sections r0 to rs to (Step S104). In this first step (k = 0), the winding tension Tw is set at a linear taper ratio shown by the imaginary line in Fig.

Then, the control unit 20 searches for the minimum value of the k-th objective function f (X) ^(k) under the constraint of the constraint function gi (X) (step S105). Then, the control unit 20 evolves the tension function Tw (r) based on the winding tension Tw (? Tw1,? Tw2,? Tw3, ...? Tww) among the design parameter vectors obtained at this stage. Specifically, a new contact point P ^(k) is obtained by fixing the r-coordinate of each contact point P ^(k) and changing the Tw coordinate by only? Twi in the positive or negative direction. For example, when the initial winding tension T _wo shown by the imaginary line evolves, the tension function Tw (r) evolves to the winding tension T _wk shown by the solid line.

Next, the control unit 20 verifies whether or not the found objective function f (X) is the minimum value (step S107), and if not the minimum value, increments the step k (step S108) If the minimum value is reached, the control process is started.

Specifically, the motor 7 is controlled by the winding tension Tw and the nip line load function L based on the tension function Tw (r) of the evolving equation (45) until the objective function f (X) reaches a minimum value (Step S109). As a result, even immediately after winding, it is possible to obtain the winding roll 5 in which star defects, plastic deformation, and a telescope do not occur even after a temperature change occurs.

As described above, according to the present embodiment, when the web 10 is processed into the winding roll 5 wound around the core 5a, the winding tension of the winding web 10 is adjusted according to the winding diameter The control unit 20 controls the motor control unit 23 as the winding tension adjusting device and the change in the environmental temperature _T∞ affecting the winding roll 5 and the predetermined control A temperature distribution calculation means for calculating a temperature distribution after a specified time Tk in the take-up roll 5 based on the time Tk and an internal stress calculating means for calculating internal stresses _? hayeoseo based on the stress calculating means, and the internal stress σr, σ _θ a stress calculation means for calculating the operation, and has the optimum value calculating means for calculating the optimum value of the winding tension logically. For this reason, in the present embodiment, the change in the environmental temperature T _∞ to be received by the winding roll 5 and the designated time Tk are set in the web product management table 217 and the temperature change map table 218 of the storage unit 21 Depending on the work, the temperature distribution calculation means calculates the temperature distribution of the winding roll 5 after the specified time Tk has elapsed (temperature distribution calculation step). Then, the stress calculating means calculates the consideration of the temperature distribution of the calculated wound roll (5), the internal stress σr, σ _θ (internal stress calculation step). And optimal value calculating means is based on the internal stress σr, σ _θ calculated in consideration of the temperature distribution in the take-up roll 5, and calculating the optimum value of the winding tension (optimum value calculation step). Thus, the internal stress σr, σ _θ of when the take-up roll 5 are received the heat affected after processing, the take-up roll (5) is changed on the basis of the predicted characteristics of the temperature distribution calculating means. As a result, it is possible to prevent a winding failure which is expected to eleven internal stress change on the basis of the impact σr, blocking, by σ _θ, sticking between films or the like buckling wrinkles, or the occurrence of tensile wrinkles, after as much as possible.

In the present embodiment, the temperature distribution calculating means has a function or a step of calculating the temperature distribution of the winding roll 5 based on the thermal conduction analysis model including the unsteady thermal conduction differential equation (32). For this reason, in the present embodiment, the take-up roll (5) heat conductivity in the, and considering the heat transfer characteristics from the environment, it is possible to calculate the temperature distribution that acts on the take-up roll 5, the change in the ambient temperature T _∞ even when there is a gap generated in the temperature distribution of the winding roll (5) accompanying, it is possible to secure the inter-friction force F _i and the circumferential stress σ _θ required. Therefore, by the temperature distribution is possible to more precisely determine the take-up roll 5 radially it stresses σr and circumferential stress σ _θ receiving the different parts of the. As a result, the optimum value calculation means can optimize the calculated value to a more suitable winding tension.

In the present embodiment, the temperature distribution calculation means evaluates the layer of the web 10 constituting the winding roll 5 and the layer of air interposed between the layers of the web 10 as an equivalent layer, 5) in the case where the temperature of the exhaust gas is low. For this reason, in the present embodiment, it is possible to calculate a precise temperature distribution in consideration of the air layer formed in the winding roll 5. Considering that the thermal conductivity K _eq of the air is significantly lower than that of the web 10 and the thermal resistance of the winding roll 5 decreases with the increase of the contact pressure, the temperature distribution near the air is not linear. On the other hand, since there is roughness on the surface of the web 10, a part of the contact surface between the layers of the web 10 is in contact with the dispersed contact where the other parts are not in contact with each other. Air is interposed in the non-contact part. Further, when the air layer becomes thick, the web 10 is separated and is not in contact with the front surface. In such a form, if the air layer exists in the winding roll 5, the thermal conductivity K _eq of the outer surface of the winding roll 5 changes. In this embodiment, since the unsteady thermal conduction differential equation (32) is solved using the thermal conductivity K _eq of the equivalent layer in consideration of the thermal resistance depending on the presence of the air layer, accurate temperature distribution can be calculated.

In the present embodiment, the stress calculation means evaluates the layer of the web 10 constituting the wind-up roll 5 and the layer of air interposed between the layers of the web 10 as an equivalent layer, the internal stress is equipped with a function for computing a σr, σ _θ. For this reason, it becomes possible to in the present embodiment, since the internal stress σr, σ _θ is calculated using the thermal conductivity K _eq equivalent layer considering the heat resistance in accordance with one of the air layer is present, the calculation precision internal stress σr, σ _θ do.

In this embodiment, the stress calculating means includes a function for calculating the differential equations, including the linear expansion coefficient αr, σ _θ of the web 10 as the parameter as stress calculating means. For this reason, in the present embodiment, the take-up roll (5) of the winding core (5a) side and the difference in temperature distribution grow, between the outermost layer, interlayer friction and circumferential stresses with temperature distribution of the take-up roll 5 σ _θ Can be maintained at a required value.

In the present embodiment, in the stress analysis model, the boundary condition of the innermost layer is given by the differential equation (29) using the coefficient of linear expansion? _C of the core 5a as a parameter. Therefore, in the present embodiment, the internal stress of the winding roll 5 can be precisely calculated in consideration of the linear expansion coefficient? _C of the core 5a.

In the present embodiment, the optimum value calculation means calculates the optimum value of the tension function of the equation (45) for calculating the tension, the objective function of the equation (47) for solving the tension function of the equation (45) And has a function of storing the design variables of the included equation (46) and calculating the minimum value of the equation (47) for every predetermined step related to the winding diameter. For this reason, in the present embodiment, the minimum tension considering the change in the environmental temperature T _∞ to be subjected to the winding roll 5 at every predetermined winding step diameter is calculated, and the tension is optimized to the optimum value every time the step increases .

In the present embodiment, the objective function of the equation (47) of the optimum value calculation means is a function of the friction between the circumferential stress?? _Acting on the winding roll 5 and the web 10 and the slip of the web 10 And the critical frictional force Fcr. For this reason, in the present embodiment, it is possible to reliably remove the factor of the winding failure of the winding roll 5.

As described above, according to the present embodiment, the temperature distribution of the wind-up roll 5 is calculated according to the change of the environmental temperature T _∞ and the designated time Tk to which the wind-up roll 5 is to be applied, and the internal stress σr, it is possible to optimize the σ _θ, the take-up failure is expected to open inside a change on the basis of the impact stress σr, blocking, by σ _θ, sticking between films or buckling wrinkles, or the like occurs in the tensile wrinkles, after as much as possible And can produce a remarkable effect.

In the above-described embodiment, the nip line load L is set as an integer in the design parameter to be a parameter of the constraint function, but the nip line load L may not be used as the control parameter. In the following embodiments, the nip line load L is omitted.

[Example]

Next, Examples of the present invention will be described in comparison with Comparative Examples. The inventor of the present invention has set a plurality of analysis conditions and confirmed the effect of the above-described predictive theory model and the embodiment for each analysis condition. For any interpretation condition, the designated time Tk is 12 hours.

[Interpretation Condition A]

In the analysis condition A, the web 10 and the core 5a shown in the following table were used.

Item sign unit Specifications Web thickness t _w [m] 50 × 10 ^-6 width W [m] 0.28 Circumferential elongation modulus E _? [Pa] 5.18 × 10 ⁹ Radial elongation modulus E _r [Pa]

Static friction coefficient (Web-Web) μ _w 0.3 RMS Composite Roughness (Web - Web) σ _ww [m] 0.0923 × 10 ^-6 Radial direction υ _r 0 Thermal conductivity λ _w 0.115 specific heat c _pw 936 density ρ _w 1400 Radial coefficient of linear expansion α _r 15.5 x 10 ^-5 Circumferential coefficient of linear expansion α _θ 2.08 × 10 ^-5 Reverence Outer diameter r _c [m] 0.451 Inner diameter r _gin [m] 0.0381 Elongation modulus E _c [Pa] 17.0 × 10 ⁹ Pawasinui v _c 0.3 Coefficient of linear expansion α _c [1 / K] 1.4 x 10 ^-5

The winding conditions under the analysis condition A, the nip roller, and the heat transfer coefficient around the winding roll are shown in the following table.

Item sign unit Specifications Winding conditions




Number of floors n 1080 Winding tension T _w [N / m] 100 Taper ratio of winding tension φ 0 Winding speed U _w [m / s] 1.0 Nip load N [N / m] 235 Taper ratio of nip load φ _N 0 Nip roller

Elongation modulus E _n [Pa] 4.12 × 10 ⁶ Radius R _n [m] 0.0738 Pawasinui v _n 0.5 Heat transfer coefficient
(Environment of winding roll)
Upon heating h _h [W / m ² K] 33.1 Upon cooling h _c [W / m ² K] 33.1

For the analysis condition A, design variables, objective functions, and constraints are expressed as follows.

[Number 42]

(52)

(52)

(53)

는、미끄럼이 생기는 마찰력의 참조치only,

Is a measure of the frictional force that causes slippage

(54)

(54)

The objective function in the above example, the take-up roll (5) minimize the expression (53) of the objective function on the friction force F _i, the circumferential stress σ _θ after the designated time to receive the temperature T _k (= 12 hours) has elapsed . The equation (54) of the constraint condition is that the temperature around the roll wound around the elapsed time T _k = 0 to 12 hours changes by +20 K or -20 K from the initial roll temperature T _r0 at the time of winding, The conditions in which wrinkles and slippage do not occur are restricted in the course of the change.

The design conditions for the analysis condition A are as follows.

Item Design condition ΔT _Wimin -100 ΔT _Wimax 100 F _ref 3.0 kN σ _θref T _WS / t _W r ₁ 1.00 r ₂ 1.12 r ₃ 1.24 r ₄ 1.48 r ₅ 1.72 r ₆ 1.96 r ₇ 2.08 r ₈ 2.14 r ₉ 2.20

(Example 1: Results of Verification in Heat Treatment in Analysis Condition A)

In Example 1, the winding roll wound under the analysis condition A was heated. As shown in Fig. 11A, the temperature change condition at the time of heating was such that the roll temperature was 25 DEG C, the temperature difference upon heating was 20K, and the heating time was 12 hours. As shown in Fig. 11A, the calculation result based on the fundamental equation (23) of thermal stress shows that the temperature of the winding roll 5 heated in the aging chamber rises from the outer peripheral side as the heating time elapses, After that, the temperature distribution over the entire layer became almost the same as the room. The reason why the temperature rises from the outer layer side is considered to be that the heat transfer rate is higher on the outer peripheral side than on the inner peripheral side. In addition, the winding tension Tw calculated in consideration of the temperature change as shown in Fig. 11A is slightly higher and gradually decreased from the inner circumferential side in comparison with the example in which the temperature change is not taken into consideration.

When the optimization of the winding tension Tw is calculated based on the calculation result, the winding tension characteristics shown in Fig. 12 can be obtained. 12, the solid line X is a characteristic of the winding tension Tw according to the present embodiment, and the broken line Y indicates the characteristic of the comparison when a general winding equation is used without using the equations (28) and (32) It is a characteristic of courtesy.

As for the friction force F _i, the radial stress σr is, as shown in Figs. 13a and 13b, in the present embodiment, characteristic X (X1 ~ X3, hereinafter the same), over the entire temperature distribution changing, good frictional force F, the radial stress lt; / RTI >

Further, also with respect to the circumferential stress σ _θ, as shown in Figure 13c, all over the temperature distribution changes, to obtain all of the non-dimensional radius location roll sagging does not occur characteristics for the r / _c r.

On the other hand, in the characteristics Y (Y1 to Y3, the same applies hereinafter) of the comparative example without considering the temperature change, the circumferential stress? R on the inner circumferential side decreases as the inner temperature rises Respectively.

(Example 2: Results of Verification in Cooling Treatment in Analysis Condition A)

The winding roll of the analysis condition A was cooled. As a temperature change condition at the time of cooling, as shown in Fig. 14A, the roll temperature was set at 25 캜, the temperature difference at the time of cooling was set at 20 K, and the cooling time was set at 12 hours. As shown in Fig. 14A, the result of the calculation based on the fundamental equation (23) of thermal stress is that the cooled winding roll 5 is cooled on the outermost layer side, and after 12 hours, .

When the optimization of the winding tension Tw is calculated based on the calculation result, the results shown in Fig. 15 are obtained. The characteristic X of the present embodiment rose slightly from the inner circumferential side to the same extent until the vicinity of the outermost circumference and increased again after the outermost circumference. On the contrary, the characteristic Y of the comparative example was a result that the winding tension was lowered on the inner circumferential side and was estimated as a low level up to the vicinity of the outermost circumference, and then increased to a predetermined level from the vicinity of the outermost circumference.

Regarding the frictional force, as shown in Fig. 16A, in the characteristic X of the embodiment, the necessary frictional force F _i can be maintained regardless of the temperature change. On the contrary, in the characteristic Y of the comparative example, the coefficient of friction decreases as the temperature change increases (as the cooling time becomes longer), and slippage tends to occur at a wide roll radius position.

Regarding the radial stress? R, as shown in Fig. 16B, the characteristic X of the present embodiment can maintain the required radial stress? R regardless of the temperature change. On the contrary, in the characteristic Y of the comparative example, at the time of cooling, stress was lowered at a wide roll radius position.

In addition, for the circumferential stress, as shown in Figure 16c, an embodiment characteristic X, for every roll radial position, all of the temperature distribution, was able to maintain the necessary circumferential stress σ _θ. On the contrary, in the characteristic Y of the comparative example, the circumferential stress was negative at the outermost circumferential side.

[Analysis condition B]

Next, in the analysis condition B, it was verified that the temperature condition was set so that even if a temperature change occurred at ± 20 K after winding (that is, at -20 K even at a temperature difference of -20 K), no winding failure occurred. In order to verify the requirements, the objective function and the constraint condition in the analysis condition A were changed as follows.

[Number 43]

(56)

(56)

は、미끄러짐이 발생하는 마찰력의 참조값only,

Is a reference value of the friction force at which slippage occurs

(57)

(57)

The equation (55) of the objective function in the analysis condition B is calculated in such a manner that the frictional force immediately after the winding and the circumferential stress are minimized. As a result, the same results as in Fig. 17 were obtained even in the heating condition and the cooling condition. In the characteristic X of the embodiment, it is estimated that the winding tension Tw rises in the range of the dimensionless roll radius position r / r _c from the initial winding period to about 1.0, then gradually decreases to the outer layer side after returning to the initial value, The dimension roll radius position r / r _c showed a sudden rise again after passing 2.0. On the contrary, in the characteristic Y of the comparative example, it is estimated that the winding tension Tw falls in the range of the dimensionless roll radius position r / r _c of about 1.0 from the beginning of winding, and is assumed to be gentle toward the outer layer side. / r _c showed a behavior that rises again after 2.0.

Next, the results after the heat treatment are as follows.

(Example 3: Verification result in heat treatment in analysis condition B)

As shown in Fig. 18A, as the heat treatment, the initial roll temperature T _r0 at the time of winding was heated for 12 hours with the temperature difference set at 10K. The calculation result based on the fundamental equation (23) of the thermal stress becomes as shown in Fig. 18B.

Referring to Fig. 18B, the temperature distribution of the winding roll 5 after heating rises from the outer peripheral side as the heating time passes, and after 12 hours, the temperature distribution over the entire layer becomes almost the same as the room.

With respect to the frictional force and the radial stress? R, as shown in Figs. 19A and 19B, good frictional force F _i and radial stress? R were shown over all temperature distribution changes.

Further, also with respect to the circumferential stress σ _θ, as shown in Figure 19c, all over the temperature distribution changes, to obtain all of the non-dimensional radius location roll sagging does not occur properties against r / r _c.

(Example 4: Results of Verification in Cooling Treatment in Analysis Condition B)

As shown in Fig. 20A, as the cooling treatment, the initial roll temperature T _r0 at the time of winding was set to a temperature difference of -10 K, followed by cooling for 12 hours. The calculation results based on the fundamental equation (23) of the thermal stress were as shown in Fig. 20B.

20B, the temperature distribution of the winding roll 5 after cooling was lowered from the outer peripheral side as the cooling time elapsed, and after 12 hours, the temperature distribution over the entire layer became almost the same as the room temperature .

Regarding the frictional force, as shown in Fig. 21A, in the characteristic X of the embodiment, the necessary frictional force F _i can be maintained for all the roll radius positions and all the temperature distributions. On the other hand, in the characteristic Y of the comparative example, the coefficient of friction was lowered as the temperature change became larger (as the cooling time became longer), and the slip was likely to occur at a wide roll radius position.

Regarding the radial stress? R, as shown in Fig. 21B, in the characteristic X of the embodiment, the required radial stress? R could be maintained regardless of the temperature change. On the other hand, in the characteristic Y of the comparative example, at the time of cooling, the roller was located at a wide roll radius position and showed a decrease in stress.

In addition, for circumferential stress, in the, embodiments characteristic X as shown in Figure 21c, with respect to all the rolls radial position, all of the temperature distribution, was able to maintain the circumferential stress σ _θ required. On the contrary, in the characteristic Y of the comparative example, when the elapsed time was 12 hours, the circumferential stress became negative on the outermost circumferential side.

[Interpretation Condition C]

Next, in order to investigate the influence of the internal stress on the difference in heat transfer coefficient, an example in which the heat transfer coefficient among the analysis conditions A is changed as shown in the following Table 6 was examined.

Item sign unit Specifications Heat transfer coefficient
(Environment of winding roll) (t = 0-2 [h]) h _h [W / m ² K] 33.1 (t = 2-12 [h]) h _c [W / m ² K] 6.3

The remaining conditions were the same as the analysis condition A.

(Example 5: Results of Verification in Heat Treatment in Analysis Condition C)

In Example 5, the winding roll wound under the analysis condition C was heated. The conditions of the temperature change at the time of heating were as follows. As shown in Fig. 22A, the roll temperature was set at 25 캜, the temperature difference at the time of heating was set at 20 K, and the heating time was set at 2 hours. After the elapse of the heating time, the environmental temperature of the winding roll 5 was returned to the same temperature as the roll temperature. As shown in Fig. 22B, in the calculation result based on the fundamental equation (23) of thermal stress, in the winding roll 5 heated in the aging chamber, the temperature rises from the outer circumferential side with the elapse of the heating time, After the elapsed time, the temperature tended to decrease from the outer layer side. After 7 hours, the temperature at the end of heating was maintained relatively at the winding side, while the temperature was lower at the side of the outer side than the winding side. This phenomenon is also considered to be due to the fact that the heat transfer rate is higher on the outer peripheral side than on the inner peripheral side. Based on the calculation result, optimization of the winding tension Tw was calculated to obtain the results shown in FIG.

Referring to FIG. 23, the characteristic X of the winding tension Tw calculated in consideration of the temperature change as shown in FIG. 22A is set to be slightly higher on the inner circumferential side than the characteristic Y of the comparative example without considering the temperature change.

As shown in FIG. 24a and FIG. 24b, shown in this embodiment features in the X, in addition to over the entire temperature distribution changes, showing a good frictional force F _i, the radial stress σr,, Figure 24c about the circumferential stress σ _θ As a result, it was possible to obtain a property that no sagging occurs with respect to all the dimensionless roll radius positions r / r _c over all temperature distribution changes. On the contrary, in the comparative example attribute Y, the volume If the difference of temperature distribution in the simcheuk and the outer side is large, the stress σ in the circumferential direction _θ is decreased, there was a tendency that negative.

(Example 6: Verification result in heat treatment in analysis condition C)

And the winding roll of the analysis condition C was cooled. 25A, the roll temperature was set at 25 DEG C, the temperature difference at the time of cooling was set to 20K, and the cooling time was set to 2 hours, as shown in Fig. 25A as an upper condition of the temperature distribution on the winding side and the outer layer side at the time of cooling. After the lapse of the cooling time, the environmental temperature of the winding roll 5 was returned to the same temperature as the roll temperature. As shown in Fig. 25B, the result of the calculation based on the fundamental equation (23) of the thermal stress shows that the cooled winding roll 5 is cooled at the outermost layer side and the temperature tends to descend from the outer layer side. After 7 hours, the temperature at the end of heating was maintained relatively at the winding side, while the temperature was higher at the side of the outer side than the winding side. On the basis of this calculation result, the optimization of the winding tension Tw was calculated to obtain the results shown in Fig.

Referring to Figure 26, the dimensionless roll radial position r / r _c is increased as the rising manner, and a predetermined dimensionless roll radial position in the winding tension Tw the first predetermined gradient in respect to the characteristic X according to the present embodiment, r / r _c (approx. 1.0), and after the vicinity of the outer circumference (approx. 2.0) showed a suddenly rising behavior. On the other hand, in the comparative example Y, the winding tension Tw is lowered until the non-dimensional roll radius position r / r _c (about 1.0) elapses, and then it is stopped and rises after around the outer periphery I showed behavior.

As to the frictional force, as shown in Fig. 27A, in the characteristic X of the embodiment, it was possible to maintain the necessary frictional force F _i irrespective of the difference in temperature distribution on the winding side and the outer side. On the other hand, in the characteristic Y of the comparative example, when the difference in the temperature distribution between the winding side and the outer layer side is large, the friction coefficient is decreased and slippage tends to occur at a wide roll radius position.

27A, in the characteristic X of the present embodiment, the required radial stress? R can be maintained regardless of the difference in temperature distribution on the winding side and the outer layer side. On the contrary, in the characteristic Y of the comparative example, stress was lowered at a large roll radius position during cooling.

In addition, it embodiments characteristic X as shown in Fig. 16c for circumferential stress, for every roll radial position, all of the temperature distribution, was able to maintain the necessary circumferential stress σ _θ. On the contrary, in the characteristic Y of the comparative example, when the difference in temperature distribution between the winding side and the outer layer side becomes larger, the circumferential stress becomes negative on the outermost side.

Since the heat transfer rate has a large influence on the roll temperature in the abnormal state in a form apparent from the above-described embodiment, calculation of the temperature distribution of the winding roll 5 using the unsteady thermal conduction analysis model including the basic equation (28) It was confirmed to be extremely effective.

Referring to Figs. 28 (a) and 28 (b), when the web 10 of the winding roll 5 has an anisotropic coefficient of linear expansion that tends to extend in the circumferential direction, Stress is applied. As a result, when a temperature rise occurs, a clearance is easily formed in each layer on the outer layer side, and the radial stress is lowered. As a result, slip easily occurs in a place where the change of the temperature distribution is large. Further, on the core side, the web is not elongated, compression occurs, and corrugation blocking tends to occur. On the other hand, when the temperature is lowered, the radial stress increases because it shrinks in the radial direction. However, the circumferential stress is not in the negative direction because the core 5a is stretched without being contracted.

28 (c) and (d), when the web 10 of the winding roll 5 has an anisotropic coefficient of linear expansion that tends to extend in the radial direction, the web 10 is heated in the radial direction The stress to enlarge acts to open the outside of each layer. As a result, when the temperature rises, the thickness of each layer increases and the radial stress increases, and wrinkles and blocking easily occur. On the other hand, when the temperature is lowered, the web 10 is subjected to a stress reducing in the radial direction, and the outside of each layer is reduced in diameter. As a result, when the temperature is lowered, the radial stress at the inner circumferential side is decreased and the circumferential stress is converted to positive.

Therefore, the reason why the coefficient of linear expansion is included as a parameter in the basic equations and the like of the equation (28) is that the difference in the temperature distribution of the web, particularly in the case where the coefficient of linear expansion of the web has anisotropy, It was confirmed to be valid.

Further, even when the linear expansion coefficient in the circumferential direction and radial direction of the wound web has anisotropy, it is also possible to intermittently control based on the knowledge as described above. That is, in the case where the rise of the environmental temperature is expected after the winding, in the case where the circumferential direction linear expansion coefficient or the radial direction linear expansion coefficient is high, the circumferential stress is not added to the diameter of the middle or less of the core diameter and the winding diameter It is also preferable to give the tension in advance. On the other hand, in the case where the environmental temperature is expected to decrease after winding, even if the circumferential linear expansion coefficient and the radial direction linear expansion coefficient are high, the interlaminar friction force does not fall below the limit frictional force, . In the case of adopting such a configuration, when the environmental temperature is expected to rise after winding or when the environmental temperature is expected to decrease after winding, the winding tension Tw in consideration of the change in the internal stress accompanying the temperature change intermittently . Further, in the above embodiment, the internal stress is calculated in a general state equation as shown in equation (7), and after the optimization of the winding tension function based on the calculation result or the like, a temperature rise is expected, It is possible to obtain a very suitable winding tension corresponding to the temperature change only by correcting the respective calculation results, so that the calculation can be greatly simplified and the winding roll can be completed with a very suitable winding roll.

It is needless to say that the present invention is not limited to the above-described embodiment, and that various changes can be made without departing from the gist of the present invention.

For example, although the stress analysis model and the heat conduction analysis model are mainly used in consideration of the air layer, the air layer between the web layers does not need to be considered when the influence of the air layer is very small .

In the above-described embodiment, the radial elongation modulus of elasticity E _ral of the air layer is treated as being constant regardless of the temperature. However, it is also preferable that the modulus of elasticity modulus E _ral of the air layer is taken into consideration.

1: roll 2: guide roller
3: Pinch roller 4: Nip roller
5: Winding roll 5a: Core
6: Nip load adjusting device 7: Motor
8: Temperature sensor 10: Web
21: storage unit 22:
23: motor control unit 24: nip load adjusting unit
25: display unit 26: input /
45: nip 100: retractor
101:

Claims (18)

A winding device having a winding tension adjusting device for adjusting a winding tension of a wound web by a winding diameter when winding the web around a winding core and processing the winding web,
Wherein the winding tension adjusting device comprises:
A temperature distribution calculating means for calculating a temperature distribution after the specified time in the winding roll, based on a change in the environmental temperature affecting the winding roll and a predetermined designation time;
A stress calculation means for calculating an internal stress of the winding roll based on the calculated temperature distribution,
And optimum value calculation means for calculating an optimum value of the winding tension based on the internal stress calculated by the stress calculation means. The method according to claim 1,
Wherein the temperature distribution calculating means has a function of calculating a temperature distribution of the winding roll based on a thermal conduction analysis model including an unsteady thermal conduction differential equation. The method of claim 2,
Wherein the temperature distribution calculating means is provided with a function of evaluating the layer of the web constituting the winding roll and the layer of air interposed between the layers of the web as an equivalent layer to calculate the temperature distribution of the winding roll Winding device. The method of claim 3,
Wherein the stress calculating means is provided with a function of evaluating the layer of the web constituting the take-up roll and the layer of air interposed between the layers of the web as an equivalent layer to calculate the internal stress of the take- Device. The method according to claim 1,
Wherein the stress calculating means includes a function of calculating a differential equation including a web's linear expansion coefficient as a parameter as a stress analysis model. The method of claim 5,
Wherein the stress analysis model is given a boundary condition of an innermost layer by a differential equation using a linear expansion coefficient as a parameter. 7. The method according to any one of claims 1 to 6,
Wherein the optimum value calculation means stores a tension function for calculating a tension, an objective function for solving the tension function, and design variables included in the objective function, and calculating a minimum value of the objective function by a predetermined And a function of calculating each step is provided. The method of claim 7,
Wherein the objective function of the optimum value calculation means includes either a circumferential stress acting on the winding roll, a frictional force between the web and a parameter consisting of a critical frictional force at which the web starts to slip Device. A winding control method for controlling a winding device that adjusts a winding tension of a wound web in accordance with a winding diameter when winding the web around a winding core and processing the winding web,
A temperature distribution calculating step of calculating a temperature distribution after the lapse of the specified time in the take-up roll, based on a change in environmental temperature affecting the take-up roll and a predetermined designated time;
A stress calculating step of calculating an internal stress of the winding roll based on the calculated temperature distribution,
And an optimization step of calculating an optimum value of the winding tension based on the calculated internal stress. The method of claim 9,
Wherein said temperature distribution calculating step has a step of calculating a temperature distribution of said winding roll based on a thermal conduction analysis model including an unsteady thermal conduction differential equation. The method of claim 10,
The temperature distribution calculating step includes a step of evaluating a layer of the web constituting the winding roll and a layer of air interposed between the layers of the web as an equivalent layer and calculating a temperature distribution of the winding roll . The method of claim 11,
The stress calculating step includes a step of evaluating the layer of the web constituting the take-up roll and the layer of air interposed between the layers of the web as equivalent layers and calculating the internal stress of the take-up roll Winding control method. The method of claim 9,
Wherein the stress calculating step includes a step of calculating a differential equation including a linear expansion coefficient of the web as a parameter as a stress analysis model. 14. The method of claim 13,
Wherein said stress computing step computes said stress analysis model based on boundary conditions of an innermost layer given by a differential equation using a linear expansion coefficient as a parameter. The method according to any one of claims 9 to 14,
Wherein the optimum value calculating step stores a tension function for calculating a tension, an objective function for solving the tension function, and design variables included in the objective function, and calculating a minimum value of the objective function by a predetermined And a step of calculating each step. 16. The method of claim 15,
Wherein the objective function of the optimum value calculation step includes either a circumferential stress acting on the winding roll, a frictional force between the web and a parameter consisting of a critical frictional force at which the web starts to slip Control method. A winding control method for controlling a winding device that adjusts a winding tension of a wound web in accordance with a winding diameter when winding the web around a winding core and processing the winding web,
When the change in the environmental temperature affecting the winding roll is expected to become higher than the environmental temperature at the time of winding, the difference in the circumferential stress between the inner peripheral side and the winding middle layer And the winding tension is set high in advance. A winding control method for controlling a winding device that adjusts a winding tension of a wound web in accordance with a winding diameter when winding the web around a winding core and processing the winding web,
When the change in the environmental temperature affecting the winding roll is expected to be lower than the environmental temperature at the time of winding, the interlaminar friction force of the winding roll is set to be lower than the predetermined limit frictional force The winding tension is set to be high in advance.

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