KR20120103467A - Winding apparatus and winding control method - Google Patents

Abstract

PURPOSE: A winding apparatus and a winding control method are provided to optimize internal stress considering thermal stress by calculating the temperature profile of a winding roll according to a predetermined time and the variation of environmental temperatures that the winding roll receives. CONSTITUTION: A winding apparatus comprises a winding tension adjusting device having a temperature profile calculating unit, a stress calculating unit, and an optimal value calculating unit. The temperature profile calculating unit calculates the temperature profile of a winding roll after a predetermined time based on the variation of environmental temperature affected to the winding roll and the predetermined time. The stress calculating unit calculates the internal stress of the winding roll based on the calculated temperature profile. The optimal value calculating unit calculates the optimal value of winding tension based on the calculated internal stress. [Reference numerals] (308) Converting to a main menu; (321) Time step; (322) Thermal conductivity; (323) Selecting a map code of temperature variation; (324) Predetermined time; (325) Initial environmental temperature; (327) Start; (AA) Setting temperature conditions; (BB) Environmental condition; (CC) Elapsed time

Description

Winding apparatus and winding control method

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

BACKGROUND OF THE INVENTION The winding process of a web (a generic term such as a film or a sheet) including a film made of metal or resin is widely used in many industrial products such as a liquid crystal display, a mobile phone, and a printing sheet.

The basic theory of web winding began to be developed around Kodak in the 1960s and continues to this day. According to the related basic theory, it was possible to quantitatively grasp the internal stress state of the winding roll on which the web was wound using an analytical model including a predetermined nonlinear two-phase differential equation. Moreover, when it becomes possible to model the internal stress state of the winding roll quantitatively, it becomes possible to optimize various conditions when winding up a web. This inventor developed and proposed the technique which calculates the radial stress and the circumferential stress of a winding roll based on the internal stress analysis model proposed previously, and calculates the optimal winding conditions based on the calculation result (nonpatent literature). One).

[Prior Art Literature]

[Non-Patent Documents]

[Non-Patent Document 1] Hashimotoger et al., Optimating Winding Tension and Nip-load into Wound Webs for Protecting Wrinkles and Slippage, Published by the Japan Society 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 winding conditions such as winding tensions, which have been qualitatively set based on only the feelings and experiences of the producers, based on a qualitative internal stress analysis model. However, the actual winding rolls are affected by heat, such as a change in environmental temperature and heat treatment during storage and transportation. It turned out that the heat which the winding roll received affects the internal stress of the said winding roll, and causes the winding defect which was not seen immediately after winding.

SUMMARY OF THE INVENTION The present invention has been made in view of the above-described problems, and it is an object of the present invention to provide a winding apparatus and a winding control method capable of optimizing the winding conditions in consideration of the heat effects that the winding rolls will receive.

In order to solve the above problems, the present invention relates to a winding apparatus having a winding tension adjusting device that adjusts the winding tension of a wound web according to the winding diameter when the web is processed by a winding roll wound around the core. The winding tension adjusting device includes temperature distribution calculating means for calculating a temperature distribution after the designated time elapses in the winding roll, based on a change in the environmental temperature affecting the winding roll and a predetermined designated time; Stress calculation means for calculating the internal stress of the winding roll based on the temperature distribution, and optimum value calculating means for calculating the optimum value of the winding tension based on the internal stress calculated by the stress calculation means. It is a winding device. In the above aspect, the temperature distribution calculating means calculates the temperature distribution of the winding roll after the designated time elapses by the change in the environmental temperature and the designated time that the winding roll receives. Next, the stress calculating means calculates the internal stress in consideration of the calculated temperature distribution of the winding rolls. 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 rolls. Therefore, when the winding roll is subjected to the heat influence after processing, the internal stress of the winding roll changes based on the predicted characteristics of the temperature distribution calculating means. As a result, due to the internal stress changed based on the thermal effect, it is possible to prevent post-expected winding failures, such as blocking, buckling, or occurrence of tensile wrinkles, that the films adhere to each other. do.

In a preferred embodiment, the temperature distribution calculating means has a function of calculating the temperature distribution of the winding roll based on a thermal conductivity analysis model including an abnormal thermal conductivity differential equation. In this embodiment, the temperature distribution acting on the winding roll can be calculated in consideration of the heat conduction characteristics in the take-up roll and the heat transfer characteristics from the environment. Even when a gap occurs in the temperature distribution of the winding rolls, it becomes possible to ensure necessary interlayer frictional force and circumferential stress. Therefore, it becomes possible to grasp | ascertain more accurately the radial stress and the circumferential stress which each part of a winding roll receives by this temperature distribution. As a result, the optimum value calculating means can optimize the calculated value to a more suitable winding tension.

In a preferred embodiment, the temperature distribution calculating means evaluates 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 calculates the function of calculating the temperature distribution of the winding roll. Equipped. In this aspect, it is possible to calculate a precise temperature distribution in consideration of the air layer formed on the winding roll. The thermal conductivity of the air is significantly lower than that of the web, and the thermal resistance of the winding roll decreases with the increase in the contact pressure. In consideration, the temperature distribution near air does not become linear. On the other hand, since the roughness exists on the web surface, a part of the contact surface between the web layers is in contact, and the other part is a non-contact distributed contact. Air is interposed in the non-contact part. In addition, when the air layer becomes thick, the web is separated and non-contacted on the entire surface. In the above-described form, if an air layer exists in the winding roll, the thermal conductivity of the appearance of the winding roll changes. In this embodiment, the abnormal thermal conductivity differential equation can be solved by using the thermal conductivity of the equivalent layer in consideration of the thermal resistance according to the presence of the air layer, so that a precise temperature distribution can be calculated.

In a preferable aspect, the stress calculating means has a function of calculating the internal stress of the winding roll by 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. have. In the above aspect, since the internal stress is calculated using the thermal conductivity of the equivalent layer in consideration of the thermal resistance depending on the presence of the air layer, it is possible to calculate the precise internal stress.

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

In a preferred embodiment, the stress analysis model is provided with the boundary condition of the innermost layer by a differential equation using the linear expansion coefficient of the core as a parameter. In the above aspect, it is possible to precisely calculate the internal stress of the winding roll in consideration of the linear expansion coefficient of the winding core.

In a preferred embodiment, the optimum value calculating means stores a tension function for calculating the tension, an objective function for solving the tension function, and a design variable included in the objective function, so that the minimum diameter of the objective function is wound and It is equipped with a function to calculate for each predetermined step involved. In the above aspect, the minimum tension in consideration of the change in the environmental temperature to be received by the winding roll is calculated for each predetermined step of the winding diameter, so that the tension can be optimized to the optimum value every time the step is increased.

In a preferred aspect, the objective function of the optimum calculating means includes any one of a parameter consisting of a circumferential stress acting on the winding roll, a friction force between the web, and a critical friction force at which slip of the web begins. have. In this aspect, it becomes possible to reliably remove the cause of the winding failure of a winding roll.

According to another aspect of the present invention, in the winding control method for controlling a winding device for adjusting a winding tension of a wound web in response to a winding diameter when the web is wound around the core and processed into a winding roll, the winding roll The temperature distribution calculation step of calculating the temperature distribution after the predetermined time elapses in the winding roll based on the change of the environmental temperature affecting the temperature, and the calculated temperature distribution, A winding control method comprising a stress 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 aspect, in the temperature distribution calculation step, the temperature distribution of the winding roll after the lapse of the predetermined time is calculated in accordance with setting the change in the environmental temperature and the designated time to be received by the winding roll. Next, in the stress calculation step, the internal stress in consideration of the temperature distribution of the calculated winding roll is calculated. In the optimum value calculating 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 winding roll is subjected to the heat influence after processing, the internal stress of the winding roll is changed based on the predicted characteristics of the temperature distribution calculating step. As a result, according to the internal stress changed based on heat influence, the winding failure anticipated after death, such as blocking, buckling wrinkles, or tensile wrinkles which film sticks, can be prevented as much as possible.

In a preferable embodiment, the temperature distribution calculating step includes a step of calculating a temperature distribution of the winding roll based on a thermal conductivity analysis model including an abnormal thermal conductivity differential equation. In the above 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 characteristic from the environment, a gap occurs in the temperature distribution of the winding roll accompanying the change of the environmental temperature. Even if present, it is possible to ensure necessary interlayer frictional force and circumferential stress. Therefore, it becomes possible to grasp | ascertain more accurately the radial stress and the circumferential stress which each part of a winding roll receives by this temperature distribution. As a result, the optimum value calculating means can optimize the calculated value to a more suitable winding tension.

In a preferable embodiment, the temperature distribution calculating step includes 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. Equipped with. In the said form, it becomes possible to calculate the precise temperature distribution which considered the air layer formed in the winding roll, and it becomes possible to calculate the precise temperature distribution.

In a preferable embodiment, the stress calculation step includes 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 internal stress of the winding roll. have. In the above aspect, 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, it is possible to calculate the precise internal stress.

In a preferable embodiment, the stress calculation step is to calculate the stress analysis model based on boundary conditions of the innermost layer given by a differential equation whose linear expansion coefficient of the core is used as a parameter. In the above aspect, it is possible to precisely calculate the internal stress of the winding roll in consideration of the linear expansion coefficient of the winding core.

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

In a preferred embodiment, the optimum value calculating step includes a tension function for calculating tension, an objective function for solving the tension function, and a design variable included in the objective function, so that the minimum diameter of the objective function is wound and Computation is provided for each predetermined step involved. In the above aspect, the minimum tension in consideration of the change in the environmental temperature to be received by the winding roll is calculated for each predetermined step of the winding diameter, and the tension can be optimized to the optimum value every time the step is increased.

In a preferred form, the objective function of the optimum value calculating step includes one of a parameter consisting of a circumferential stress acting on the winding roll, a friction force between the webs, and a critical friction force at which the slip of the web starts. have. In the said aspect, it becomes possible to reliably remove the factor of the winding failure of a winding roll.

Another preferable aspect of the present invention is a winding control method for controlling a winding device for adjusting the winding tension of a wound web according to the winding diameter when winding the web around the core and processing the winding roll. In the case where the change in the environmental temperature affecting is expected to be higher than the environmental temperature at the time of winding, the winding tension between the winding intermediate layers is preliminarily from the inner circumference side to the extent that the circumferential stress of the winding roll is not added. It is a winding control method characterized by setting high. In the above aspect, when an increase in the environmental temperature is expected after the winding, the winding tension can be imparted in consideration of the change in the internal stress accompanying the temperature change.

Another preferable aspect of the present invention is a winding control method for controlling a winding device that adjusts the winding tension of a wound web according to the winding diameter when winding the web around the core and processing the winding roll, wherein the winding roll is used. If the change in the environmental temperature affecting the temperature is expected to be lower than the environmental temperature at the time of winding, the winding tension is set high in advance over the entire winding diameter such that the interlaminar frictional force of the winding roll does not fall below a predetermined limit frictional force. It is a winding control method characterized by the above-mentioned. In the said aspect, when the fall of environmental temperature is anticipated after winding, winding tension can be given in consideration of the change of the internal stress accompanying a temperature change easily.

As described above, according to the present invention, since the temperature distribution of the take-up roll can be calculated according to the change in the environmental temperature to be received by the take-up roll and the designated time, the internal stress in consideration of the thermal stress can be optimized, and thus the By internal stress, the remarkable effect which can prevent the winding failure anticipated after death, such as blocking, buckling wrinkles, or tension wrinkles which film adheres to each other, can be acquired.

Fig. 1A is an outline of a theoretical predictive model according to the present invention, and is a schematic view showing a winding roll when winding up without using a nip-roller.
Fig. 1B is an outline of a theoretical predictive model according to the present invention, and is a schematic diagram showing a winding roll when winding up using a nip roller.
2 is a diagram showing the internal stress and the nip line load of the take-up roll.
3A to 3D are explanatory views of the air layer formed between the layers of the winding rolls.
4 is a schematic configuration diagram of a winding apparatus according to an embodiment of the present invention.
5 is a graph showing optimization (evolution) of the winding tension.
FIG. 6 is an entity relationship (ER) diagram illustrating a portion of a database structure according to the embodiment of FIG. 4.
FIG. 7 is a diagram illustrating an example of a screen for executing an optimization program according to the embodiment of FIG. 4.
8 is a diagram illustrating an example of a screen for executing a web and machine condition setting program according to the embodiment of FIG. 4.
9 is a diagram illustrating an example of a screen for executing a program for setting a temperature condition according to the embodiment of FIG. 4.
FIG. 10 is a flowchart showing an example of optimization control processing according to the embodiment of FIG. 4.
11A is an explanatory diagram according to an embodiment of the present invention, and is a graph showing setting of temperature conditions.
It is explanatory drawing which concerns on the Example of this invention, and is a graph which shows the temperature distribution of the winding roll calculated by the conditions of FIG. 11A.
12 is a graph showing the optimum winding tension calculated under the conditions according to FIGS. 11A and 11A.
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.
Figure 13c is a diagram showing the operation characteristic on the basis of the winding tension of Figure 12, a graph showing a circumferential stress of the non-dimensional radius of each roll location r / r _c.
14A is an explanatory diagram according to another embodiment of the present invention, and is a graph showing setting of temperature conditions.
It is explanatory drawing which concerns on other Example of this invention, and is a graph which shows the temperature distribution of the winding roll calculated by the conditions of FIG. 14A.
15 is a graph showing the optimum winding tension calculated under the conditions according to FIGS. 14A and 14B.
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 still another embodiment of the present invention.
18A is an explanatory diagram of setting conditions according to the embodiment of FIG. 17, and is a graph showing setting of temperature conditions at the time of heating.
18B is an explanatory diagram of setting conditions according to the embodiment of FIG. 17, and is a graph showing a temperature distribution of the winding rolls calculated by the conditions of FIG. 18A.
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.
FIG. 19B is a diagram showing characteristics calculated based on the winding tension in FIG. 17 and the setting conditions in FIGS. 18A and 18B, and is a graph showing radial stresses for each of the dimensionless roll radius positions r / r _c .
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.
20A is an explanatory diagram of setting conditions according to the embodiment of FIG. 17, and is a graph illustrating setting of temperature conditions at the time of cooling.
20B is an explanatory diagram of setting conditions according to the embodiment of FIG. 17, and is a graph showing a temperature distribution of the winding rolls calculated by the conditions of FIG. 20A.
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 setting of temperature conditions.
It is explanatory drawing which concerns on other Example of this invention, and is a graph which shows the temperature distribution of the winding roll calculated by the condition of FIG. 22A.
FIG. 23 is a graph showing the optimum winding tension calculated under the conditions according to FIGS. 22A and 22B.
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.
Figure 24c is a diagram showing the operation characteristic on the basis of the winding tension in FIG. 23 is a graph showing a circumferential stress at each radial position dimensionless roll r / r _c.
25A is an explanatory diagram according to another embodiment of the present invention, and is a graph showing setting of temperature conditions.
It is explanatory drawing which concerns on other Example of this invention, and is a graph which shows the temperature distribution of the winding roll calculated by the conditions of FIG. 25A.
FIG. 26 is a graph of the optimum winding tension calculated under the conditions according to FIGS. 25A and 25B.
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, where (A) (B) shows a transition in the case of αθ> αr and (C) (D) shows a transition in the case of αθ> αr, respectively.

EMBODIMENT OF THE INVENTION Hereinafter, the best form for implementing this invention with reference to an accompanying drawing is demonstrated.

First, the theoretical prediction model which concerns on this embodiment is demonstrated. The main nomenclature used in the following description is shown in Table 1 and Table 2.

1A and 1B, in this embodiment, the winding apparatus which winds up the web 10 by the center drive type is made into object. The center drive type is a method of rotating the core 5a that winds up the web 10 with a drive shaft, not shown. As shown in FIG. 1A, the center drive winding method includes a form of a single body of the core 5a and a nip roller 4 for pressing the web 10 wound around the core 5a as shown in FIG. 1A. Are classified as one type.

For the case in which, in the web 10 is wound around the winding core (5a), and the circumferential stress σ _θ and the radial stress σr acting radially action acting in the circumferential direction. As shown in FIG. 2, the interlayer pressure (radial compressive stress) sigma always acts on the web 10 at the position of the arbitrary winding radius r of the winding roll 5, and the web 10 in this inside is applied. At the same time as pressing each layer of, the pressure from each layer of the web 10 in this outer diameter is applied. On the other hand, in the circumferential direction, the circumferential stress σ _θ acts, but depending on the radial position of the take-up roll 5, it may be pulled or compressed. The width direction stress of the winding roll 5 is normally regarded as one shape and calculated.

sign Justice unit A True contact area m ² A _a Apparent contact area m ² Cc Mean heat J / (kg? K) Cf The heat of the web J / (kg? K) Ca The specific heat of air J / (kg? K) Ceq Specific heat of equivalent layer of winding roll J / (kg? K) C0 ~ C2 (13) coefficient of formula Eeq Equivalent elongation at break of winding roll and nip roller Pa Ec Elongation Modulus of Core Pa Er Radial elongation of the web Pa Eθ Circumferential Elongation Modulus of the Web Pa En Elongation Modulus of Nip Roller Pa Eral Radial elongation modulus of air layer Pa Ereq Radial Elongation Modulus of the Equivalent Layer of the Winding Roll Pa Eθ eq Circumferential stretch elasticity of the equivalent layer of the winding roll Pa f (X) Objective function Fcr Critical friction force that causes slip N Fi Friction force between web layers of winding rolls N

Average value of friction between web layers of winding rolls N gi (X) (i = 1-2n + 4) Constraint function hal Air layer thickness in winding roll m Δ hal Increase of air layer thickness in winding roll m hal0 Initial air layer thickness m hf Thickness of web m Ka Thermal conductivity of air W / (m? K) Kal Thermal Conductivity of Air Layer W / (m? K) Kc Core Conductivity W / (m? K) Keq Thermal Conductivity of Equivalent Layer W / (m? K) Kf Thermal conductivity of the web W / (m? K) L Nip Load N / m N Nip load N pa Atmospheric pressure Pa pg Gauge pressure in outermost air layer Pa qa Heat flux through 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 the contact W / m ² r Arbitrary radius of winding roll m rc Radius m rn Radius of nip roller m rout Outermost layer radius of winding roll m Δr Equivalent layer thickness m Req Equivalent radius of take-up roll and nip roller m

sign Justice unit tc Thickness of core m Tw Winding tension N / m Tw (r) Winding tension function N / m Tw0 (r) Initial winding tension box 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 Core temperature h Tr Roll temperature h T∞ Environmental temperature ℃ T0 Initial temperature ℃ ΔT Increment of winding roll temperature K ΔTc Increment of Core Temperature K Tj Time h Tk Designated time (elapsed time after environmental temperature change) h V Winding speed of web m / s W Width of web m αc Coefficient of Linear Expansion 1 / K αr Coefficient of linear expansion of film 1 / K αh Heat transfer rate W / (m ² ? K) αθ Circumferential linear expansion coefficient of web 1 / K εr Radial deformation of the web ε ral Radial deformation of air layer εθ Circumferential deformation of the web η Viscosity of air Pa? S λ Dimensionless parameters of webwidth X Design variable vector μ eff Effective friction coefficient between web layers μs Static friction coefficient between web layers νc Psyson νn Poisson's ratio of nip roller νrθ Poisson's ratio in the circumferential direction of the web νθr Radial Poisson's ratio relative to the circumference of the web ρa Density of air kg / m ³ ρc Core density kg / m ³ ρ eq Equivalent layer density kg / m ³ ρf Density of web kg / m ³ σ ff Composite surface roughness between web layers m σr Radial stress inside the winding roll Pa Δσr Increment of radial stress Pa σθ Circumferential stress inside the winding roll Pa Δσθ Increment of circumferential stress Pa φ Taper rate of winding tension

In the case where the nip roller 4 is used, the nip load N [N] is generated in the nip 45 generated between the winding rolls 5. In detail, the nip load N also has a big influence on the internal stress of the winding roll 5 in the form mentioned later.

Next, about the winding process, the web 10 is wound up in air | atmosphere. At that time, the surrounding air is wound up into the take-up 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 appearance is remarkably lowered, the internal stress of the roll is lowered, and the winding is easily shifted or the shape is easily shifted. In particular, in the case where there is no nip roller 4 as shown in FIG. In order to improve such a fault, it is preferable to wind up using the nip roller 4. When the nip roller 4 is used, the amount of air charged up by the nip load N can be limited.

For the predictive theoretical model according to the present embodiment, the basic part of the stress analysis is applied to the theoretical model of Hakiel, (1) stress analysis considering the air and thermal stress entrained, (2) internal stress and roll immediately after winding Thermal stress analysis to predict stress fluctuations due to temperature changes, and (3) abnormal thermal conduction analysis considering air layer and thermal resistance.

(1) Stress Analysis Considering Enclosed Air

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

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

(Ii) The effect in which the web 10 is wound in a spiral shape can be ignored, and it is also possible to treat the winding roll 5 as a thin cylindrical stack.

(Iii) In the internal stress state of the winding roll 5, the radial stress σ _r and the circumferential stress σ _θ dominate, and the axial stress may not be considered.

This assumption under the radial stress at the j-th layer of the winding roll (5) σr _i is, the j + 1 layer from the k-th layer all of the stress increment Δσr _i of the respective layers to the (last layer of the winding) is added to obtain It can be represented by Formula (1). In addition, the jth layer makes the layer in the core 5a the 1st, and shows the jth layer when it counted in order toward the outer layer one by one.

[1]

(1)

(One)

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

In addition, the balance equation of stress in a cylindrical coordinate system, the suitable conditional expression for a deformation | transformation, and a structural equation are respectively given as follows.

[Number 2]

(2)

(2)

(3)

(3)

(4)

(4)

(5)

(5)

Here, it is assumed that the mark cell (maxell) equation shown next holds.

[Number 3]

(6)

(6)

Summarizing the radial stress σ _r using equations (2) to (5), and applying equations (1) and (6) here, the basic equation for the radial stress increment Δσ _r is You can get it together.

[4]

(7)

(7)

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

[Number 5]

(8)

(8)

Applying Equation (5) to Equation (8) and considering Equations (1) and (6), the innermost boundary condition can be obtained as follows.

[Number 6]

(9)

(9)

Assuming that the radial stress increment Δσr in the outermost layer is equal to the gauge pressure Pg of the air layer wound inside the new layer during winding, the outermost layer boundary condition with and without the nip roller 4 Are given by

[Numeral 7]

(10)

(10)

However, L: nip wire load (nip load ÷ web width)

Next, the basic equation (7) and the innermost layer boundary condition equation (9) are corrected so that the reduction in the rigidity of the take-up roll 5 due to the wound air can be considered.

When the air layer exists in the winding roll 5, on the numerical analysis, the web 10 can be treated as an equivalent layer which combined the 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 by

[Numeral 8]

(11)

(11)

(12)

(12)

Here, the thickness h _al of the air layer and the radial elongation modulus E _ral each represent values in winding. It is also widely known that the radial elongation modulus of the web 10 exhibits nonlinearity with respect to the radial stress σ _r . In this embodiment, the radial elongation modulus E _req is approximately applied in the following equation.

[Number 9]

(13)

(13)

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

When the web 10 is rolled up in roll shape, an air layer is formed between the outermost layer and the part already wound by the air wound up. The initial air layer thickness h _al0 in the absence of the nip roller 4 can be obtained from the following equation, depending on the wound web and the already wound part as a foil bearing model.

[Number 10]

(14)

(14)

Here, lambda is a dimensionless parameter relating to the web width W and is defined as follows.

[Jos 11]

(15)

(15)

On the other hand, in the case where the nip roller 4 is present, the elastic fluid lubrication theory can be evaluated between the take-up roll 5 and the nip roller 4. In the examples below, the results of Chang (“Elastohydrodynamic Lubrication of Air Lubricated Rollers”, ASME Journal of Tribology, Vol. 118, (1996), pp. 623-628) are used.

[Joe 12]

(16)

(16)

Here, the equivalent radius R _eq and the equivalent elongation modulus E _eq of the winding roll 5 and the nip roll are given by the following formulas, respectively.

[13]

(17)

(17)

(18)

(18)

Next, the radial elongation modulus of the air layer is examined. Assuming that the air enclosed in the winding roll 5 does not flow out from the roll end, the air layer is compressed by the winding of a new layer. The air introduced when one layer is wound on the outermost layer is compressed by the radial stress σ _r in the winding roll 5 to decrease the air thickness from h _al0 to h _al (= h _al0 -Δh _al ). Applying Boyle's law on the basis of the state when it is wound on the outermost layer, the following relationship can be obtained.

[Jos 14]

(19)

(19)

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

[Joe 15]

(20)

(20)

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

[Joe 16]

(21)

(21)

If the relationship between the radial stress σ r and the strain ε _ral is obtained from equation (21), the following equation can be obtained.

[17]

(22)

(22)

Accordingly, the radially stretched elastic modulus Eral of the air layer can be obtained as follows.

[Wed 18]

(23)

(23)

By using all the above formulas (14) to (23), the elongation modulus of the equivalent layer in consideration of the air taken up can be obtained. Accordingly, the analysis of the internal stress can be advanced by substituting E _r and E _θ shown in equations (7) and (9) with E _req and E _{θ eq} , respectively. In addition, circumferential stress can be calculated | required as follows from the balance formula (2) of a stress.

[Jos 19]

(24)

(2) thermal stress analysis

When the temperature in a roll changes by environmental temperature change, an internal stress arises and fluctuates due to the linear expansion coefficient of the web 10 and the core 5a. In such a case, the balance equation in the cylindrical coordinate system and the suitable conditional expression for deformation are the same as in the formulas (2) and (3), respectively, while the structural equations are given as follows.

[Jos 20]

(25)

(25)

(26)

(26)

Here, (DELTA) T is a change amount with respect to the initial roll temperature T _r0 immediately after winding, and is defined by following Formula.

[Jos 21]

(27)

(27)

Summarizing in the same order as in the case of equation (7), the basic equation for the radial increment Δσr due to thermal stress is given as follows.

[Jos 22]

(28)

(28)

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

[23]

(29)

(29)

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

[Wed 24]

(30)

(30)

On the other hand, since a new layer is not added to the outermost layer after completion of winding, the outermost boundary condition is given as follows.

[25]

(31)

(31)

Here, since the influence of the air wound up in the thermal stress analysis is taken into consideration, E _r and E _θ shown in equations (28) and (29) are replaced with E _req and E _{θ eq} , respectively. The elongation elastic modulus E _r , E _θ , and the linear expansion coefficient σ _r , α _θ of the web 10, the elongation elastic modulus E _c of the core 5a, and the radial elongation modulus E _ral of the air layer are not dependent on temperature but are constant. Are treated.

In detail, the linear expansion coefficients σ _r and α _θ are described below. When the winding roll 5 receives heat, the influence of the temperature distribution change of the winding roll 5 due to the temperature change on the abnormal state of the internal stress is In addition, the degree is due to the coefficient of linear expansion of the web 10 and the core 5a. Therefore, in the equation (28), the linear expansion coefficients σ _r and α _θ of the web 10 are accepted in order to clarify the relationship between the change in the temperature distribution and the internal stress.

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

In the cylindrical coordinate system, (i) the heat movement occurs only in the radial direction and can be ignored for the circumferential direction and the axial direction, and (ii) assuming that there is no heat generation inside the winding roll 5, the basic equation of abnormal heat conduction is It is represented by the following differential equation:

[Jos 26]

(32)

(32)

Convection heat is predominant in the inflow and outflow of thermal energy at the interface between air and the winding roll 5, and the heat flux at the winding roll 5 side or the core 5a side and the air side is the same at the interface. Assume that the boundary condition equations on the outermost circumferential surface of the winding roll 5 and the innermost circumferential surface of the winding core 5a are given as follows, respectively.

[Jos 27]

(33)

(33)

(34)

(34)

In addition, assuming that the heat flux is the same at the interface between the core 5a and the web 10, the boundary condition at the interface is expressed as follows.

[Jos 28]

(35)

(35)

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

[29]

(36)

(36)

On the other hand, roughness exists on the surface of the web 10. For this reason, as shown in FIG. 3A and FIG. 3B, a part of a contact surface contacts (contact part 10a) and the other part becomes a non-contact distributed contact. Air is interposed in the non-contact part. In addition, when the layer of air becomes thick, the web 10 is separated and, as shown in Fig. 3A, becomes non-contact in the whole surface. In this case, considering that the heat transfer rate Ka of the air is significantly lower than the web 10, and that the thermal resistance decreases with the increase in the contact pressure, the temperature distribution near the air layer is not linear. Here, in this embodiment, as shown to FIG. 3C and FIG. 3D, the thermal resistance is evaluated by modeling the contact part of the web 10. FIG.

The presence of the air layer changes the thermal conductivity of the appearance of the winding roll 5. Assuming that the heat fluxes _{ff ff} and _{fal 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 thermal conductivity K _eq of the equivalent layer can be obtained as follows. have.

[30]

(37)

(37)

Here, in the air layer, it is assumed that the heat fluxes ｑ _a , _{fc 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 is the ratio of the true contact area to the apparent contact area. When it is given as (A / Aa), the thermal conductivity K _al of the air layer is given by the following equation.

[Jos 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 radial stress. In addition, the contact surface of the web 10 is regarded as non-contact in the range of the air layer thickness h _a > 3σ _ff .

[32]

(39)

(39)

In addition, the density rho _eq and specific heat C _eq of an equivalent layer are defined as follows, respectively.

[Jos 33]

(40)

40

(41)

(41)

From the above, the thermal conductivity K, k _f , the density C, C _f , and the specific heat ρ, ρ _f for the web 10 shown in the basic equations (32) and the boundary condition equations (33) to (35) of the abnormal thermal conductivity, respectively, according to an unwinding replaced by k _eq, C _eq, and ρ _eq, and considering the initial temperature 36, it can obtain the time variation of the air layer and the roll temperature considering heat resistance.

For example, the differential of the first and second layers included in the above-described basic equations and boundary condition equations can be discretized by differential approximation and numerically obtained. However, the center difference approximation is applied with respect to the roll radius r _out , and the forward difference approximation is applied with respect to time, and each is shown next.

[Jos 34]

(Central difference approximation)

(42)

(42)

(43)

(43)

Forward difference approximation

(44)

(44)

Here, Δr is the division width of the equivalent layer thickness (h _f + h _al ) and the core thickness t _c , while f is the radial stress increment Δσ _r , the roll temperature T _r and the core temperature T, which are objects of differential approximation. _c is represented respectively. In addition, as for Formula (42)-(44), j is a roll radius position and i is the superscript regarding time.

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

With reference to FIG. 4, the winding apparatus 100 shown by the figure shows the several guide roller 2 and a pair of pinch roller from the roll 1 of the unwinding apparatus 101 which wound the web 10. FIG. (3) And it winds around the outer periphery of the core 5a of the winding roll 5 via the nip roller 4. In addition, although not shown, in the path from the roll 1 to the winding roll 5, the edge position control device which prevents the position difference of the web 10, and the load cell which detects the winding tension of the web 10 are shown. This is arranged.

The nip roller 4 is provided with the nip load adjustment device 6 which adjusts the pressing force with respect to the winding roll 5. The nip load adjusting device 6 is embodied as an air cylinder or a power transmission mechanism for transmitting the power of the air cylinder, and thus the nip load N of the nip 45 formed between the nip roller 4 and the winding roll 5. It is an adjustable configuration.

The core 5a is a cylindrical member constituting the winding roll 5 integrally with the web 10. Since the material of the winding 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 an area with a large change in temperature environment, the selection of the material is problematic. Becomes

Moreover, the motor 7 is connected to the winding core 5a of the winding roll 5, and the winding core 5a itself is comprised so that the web 10 may be wound up. Moreover, the temperature sensor 8 which detects the temperature at the time of winding is provided in the outermost periphery of the winding roll 5. The value detected by the temperature sensor 8 at the completion of the winding of the winding roll 5 is the web product management table of the storage unit 21 as the initial roll temperature T _r0 (parameter of equation (39)) at the initial time T _j0 . It is remembered at 217.

As the web 10, the flexible sheet used for a liquid crystal panel, a display monitor, a mobile telephone, a solar cell system, various other products, or printed matter can be targeted.

In order to control the nip load adjusting device 6 and the motor 7, the winding device 100 includes a control unit 20. The control unit 20 includes a storage unit 21, a calculation unit 22, a motor control unit 23, and a nip load adjustment unit 24 as logical modules. In addition, the display unit 25 and the input / output unit 26 are connected to the control unit 20 so that an operator can perform necessary data processing on the input / output unit 26 while watching the display of the display unit 25.

The storage unit 21 is a module, which is embodied as a ROM, a RAM, an auxiliary storage device, or the like, and has an area for storing control programs and parameters for controlling the entire winding device 100. The storage unit 21 has a database that stores parameters for calculating the above-described prediction theory model.

The computing unit 22 includes a microprocessor, a storage device, and an input / output interface, reads out a control program and data stored in the storage device, executes the control program, and constitutes the control unit 20 ( It is a module in charge of controlling the motor control unit 23, the nip load adjusting unit 24, the display unit 25, and the input / output unit 26.

The motor control unit 23 is a module that controls the rotational speed of the motor 7 based on the calculation result of the calculation unit 22. In addition, in this embodiment, this motor control part 23 also serves as tension adjustment means which adjusts the winding tension Tw of the web 10 through the rotation speed control of the motor 7. As shown in FIG.

The nip load adjustment part 24 is a module which adjusts the pressing force by the nip load adjustment device 6 based on the calculation result of the calculation part 22.

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

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

In addition, depending on the embodiment in which the winding device 100 is implemented, it is also preferable to give the control unit 20 a communication function so that the control program and data can be communicated with the host computer.

Next, the storage unit 21 shown in FIG. 4 has an area for storing a function. In addition to the above-described equations (1) to (44), the tension function Tw (r), the objective function f (X), 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. The tension function Tw (r) according to the present embodiment, in consideration of the flexibility of the function and the ease of handling, expresses the winding tension Tw as a cubic spline function with respect to the winding radius r of the winding roll 5 as shown below. This is stored in the storage unit 21.

[Jos 35]

(45)

(45)

 Where Δr is an equal proportion interval in radial coordinates,

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

The tension function Tw (r) calculates the winding tension Tw with respect to the winding radius r. In order to evolve (optimize) this tension function Tw (r), in this embodiment, the average value of the circumferential stress σ _θ is the objective function. The conditions for solving the star defects, plastic deformation, and the telescope are suitably solved, and the tension is optimized.

As can be clearly seen from the tension function Tw (r) of the formula (45), in the present embodiment, the winding start point of the winding roll is divided into n equal intervals and the spline method The winding tension Tw or L is interpolated. According to setting M _i of the formula (45) as a condition, the above-mentioned winding tension Tw is expressed as a function of smoothly connecting each section. The tension function Tw (r) of this expression (45) is optimized (evolved) by setting the objective function and the constraint function. That is, the minimum value of the circumferential stress in the take-up roll 5 is non-negative, and the tension function Tw (r) of the formula (45) is evolved so that the average value of the circumferential stress is infinitely zero. It is possible to obtain Tw.

Referring to FIG. 5, as a method of evolving the tension function Tw (r) of Equation (45), a shear layer (step k shown by a solid line) in the evolutionary process (step (k + 1)) shown by the broken line in FIG. The r coordinate of each contact P ^(k) (r _i , T _wi ) is fixed g with respect to the tension function of, and the Tw coordinate is changed by changing only ΔT _{wi in the} positive or negative direction. Contact P (k ^{+ 1} ) (r _i , T _wi + ΔT _wi ) is obtained. The functional type is updated by equation (45) using the new coordinate values thus obtained, and evolved in order until the value of the objective function f (X) becomes optimal.

Next, the variable of the objective function f (X) is demonstrated.

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.

[Jos 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 evolution (step k).

In the present embodiment, the nip line load L is optimized in the process of evolving the tension function T _w (r) of the formula (45) by adding the nip line L as an integer to the design variable vector of the formula (46). This becomes possible.

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

[Wed 37]

(47)

(47)

는 임의시간ｊ에서의 층간마찰력、only,

Interlayer friction at random time

F _cr is the critical frictional force at which slip starts,

는、임의시간ｊ에서의 원주방향응력、

Circumferential stress at any time

는、원주방향응력의 참조값이다.

Is the reference value of the circumferential stress.

In this embodiment, the critical frictional force Fcr of Formula (47) is determined by experiment, for example, 5 kN. In addition, the frictional force F _i , the reference values σ _θ and r _ef are defined as follows, respectively.

[Jos 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 imposing i is defined as follows and stored in the storage unit 21.

[Wed 39]

(49)

(49)

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

[Jos 40]

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

[Jos 41]

Find X to minimize  f (X)

（５１） subject to gi (X) 0

(51)

Next, in order to realize the above-described optimization process, tables 211 to 220 relating to information for calculating the above-described prediction theory model are stored in the storage unit 21. Here, a table means a set of data represented by a two-dimensional matrix (rows and columns) in a database system.

Hereinafter, with reference to FIG. 6, the table which concerns on this embodiment is demonstrated. In addition, in the following description, the item of a table is called "column", and the actual value (actual value which can be assigned to a column) of a table is called "row". In Fig. 6, (PK) denotes a primary key and (FK) denotes a foreign key, respectively. A primary key is a column that uniquely identifies a row in a table. A foreign key is for referencing data of a table having a corresponding primary key, depending on the same value as a primary key. When a plurality of columns are represented as a set, they are displayed by grouping them in ｛｝. In addition, the arrow in the figure has shown the relationship (relationship) between tables, and has shown that the foreign key in the table by the end side of an arrow refers to the primary key in the table at the origin of an arrow. In addition, between the two tables, the corresponding relationship between the primary key and the foreign key is indicated by Cardinality (number of rows), and the arrow indicates that the origin has 0 or 1 and the cardinality with many endpoints. It is shown. In addition, the table shown may exist logically, and may represent the same data group physically by a plurality of tables, or may represent a plurality of data groups by the same table. In addition, the column set to each table only lists what is important in order to demonstrate this embodiment with respect to this table, and may have a column other than the illustrated item.

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

The web table 211 is a table for registering the specifications of the web 10. For each web number (primary key), the thickness h _f , the width W, the critical friction force Fcr, the radial elongation modulus E _r , and the circumferential elongation modulus E _θ , RMS composite roughness σ _ff , static friction coefficient ㎲, radial Poisson's ratio υ _θr , circumferential Poisson's ratio υ _θr , thermal conductivity K _f , specific heat Cf, density ρ _f , radial linear expansion coefficient α _r , circumferential linear expansion coefficient α _θ It is possible to register parameters including. In particular, in the present embodiment, since the linear expansion coefficient α _r and the linear expansion coefficient α _θ are employed as the parameters of the basic equation 28 and calculated, the extension in the radial direction and the circumferential direction due to the heat received by the winding roll 5 is calculated. It is possible to calculate the internal stresses considered.

The winding table 212 registers the specifications of the winding core, and for each winding number (main key), the elastic modulus of elasticity E _c , the core thickness t _c , the Poisson's ratio υ _c , the core υ _c , the radius r _c , the thermal conductivity K _c , and the specific heat C It is possible to register parameters including _c , density ρ _f , and coefficient of linear expansion α _c .

The air table 213 registers the specifications of the air, and contains the air code as the main key, ｛atmospheric pressure, thermal conductivity K _a , specific heat C _a , density ρ _a , gauge pressure Pg, and viscosity η｝ as heat. The air table 213 is provided in the storage unit 21, where the air specifications are registered, and it is possible to precisely calculate the internal stress and the heat distribution in the equivalent layer between the air layer and the web.

The nip roller table 214 registers the specifications of the nip roller 4, and for each nip roller number (primary key), the radius r _n of the nip roller 4, the elongation elastic modulus E _n , the initial taper tension, and the Poisson's ratio It is possible to register parameters including _n .

Next, as a transaction table for operating the winding apparatus 100, in this embodiment, the winding plan table 215, the winding plan specification table 216, the web product management table 217, the temperature change map ( 218, a winding control table 220 is provided.

The winding plan table 215 memorizes the specifications for managing the plan of a winding process, and it is possible to register the item including an order of manufacture date and manufacture code for every winding plan code (primary key).

The winding plan specification table 216 registers the specification of the winding roll 5 produced by a winding plan and the general specification of a process for every winding plan code, and of the nip roller 4 used for every specification code for every winding plan. It is possible to register an article number, an article number of the winding core 5a, an article number of the web 10, a winding length, the number of turns n, the outermost layer roll radius r _out , and the number of winding rolls 5. In addition, in order to achieve the winding control in consideration of the temperature change after the winding, the air cord is provided as an external key, and information about the air from the air table 213 can be specified for each specification of the production plan. Further, the winding plan specification table 216 sets the specifications of the core 5a such as the core radius (core diameter) r _c from the core table 212 since the relation ship is also established with the core table 212. It is in a form that can be referenced.

The web product management table 217 is for managing the production conditions of the individual concrete products (the winding rolls 5) produced for each specification determined by the winding plan specification table 216, and the winding plan specification table 216 and The main key is a composite key consisting of an external key ｛production plan code, a specification code｝ and a serial number for association, and allows the registration of the manufacturing date, initial temperature T ₀ (see Eq. (36)), and the specified time T _k . It is. Further, in order to register the temperature prediction for the individual products, the web product management table 217, and is able to register the time step and the heat transfer coefficient α _h. The time step is a time interval of temperature change, and is a column (item) for registering a numerical value that can be arbitrarily selected by a user by the optimization control described later. In addition, heat transfer rate (alpha) _h is a parameter for solving Formula (33) (34), It is possible to register the value computed based on the value determined by experiment and the value measured in the environment of the winding roll 5 ,. . 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.

The temperature change map 218 is for registering the specifications of the environment in which the winding roll 5 is placed (map data). The temperature change map 218 stores the environmental temperature T _∞ for each time T _j for the temperature change map code. It is possible to set within the range of the designated time T _k set at (216).

The winding control table 220 sets specifications required for optimal winding control, and the composite key between the main key ｛winding plan code, the specification code｝ and the winding control code of the winding plan specification table 217 is used as the primary key. Winding tension Tw, winding speed (motor revolutions) V, nip wire load L, dimensionless roll radius position r / r _{c for} each winding plan specification Etc. can be set.

In accordance with the use of the tables 211 to 220 as described above, various screens or view tables can be created to enable the operator to realize the optimization operation.

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

On the screen 300, a command button 303 for setting the method of optimization calculation based on the condition set by the command button 301 for setting the web and machine conditions and the command button 302 for setting the temperature condition. ) Is ready. In the text box 304, the winding control code of the winding control table 220 is displayed as a result of the setting of the optimization calculation, and at the same time, the driving speed (the number of rotations of the motor 7) and the nip line load of the winding device 100 are displayed. This is displayed in the text boxes 305 and 306, respectively. Viewing the numerical values displayed in these text boxes, the operator judges whether the correction is necessary, and when it is determined that the correction is not necessary, operates the command button 307 for transmission and instructs the control unit 20 of the setting result. . Based on the set result, the control unit 20 winds up the web 10, processes it to the winding roll 5, and registers the transaction result in each table 215-217 shown in FIG. . In addition, a command button 308 is prepared on the screen 300 as necessary to switch to the main menu.

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

Referring to FIG. 8, the screen 310 displays a combo box 311 for selecting an article number of the web 10, and a list window displaying specifications of the web 10 selected by the combo box 311. 312) is installed. In the combo box 311, the web numbers registered in the web table 211 of FIG. 6 are listed up, and each specification regarding the selected item number is displayed in the list window 312. FIG. When it is necessary to register a new article number, it returns to a main menu and registers from the registration screen which is not shown in figure.

The screen 310 is provided with a combo box 313 for selecting an article number of the core 5a and a list window 314 for displaying the specifications of the core 5a selected by the combo box 313. In the combo box 313, the core article number registered in the core table 212 of FIG. 6 is listed up, and each specification regarding the selected article number is displayed in the list window 314. FIG. When it is necessary to register a new article number, it returns to the main menu and registers from a registration screen not shown.

The screen 310 is provided with a combo box 315 for selecting the part number of the nip roller 4 and a list window 316 displaying the specifications of the nip roller 4 selected by the combo box 315. It is. In the combo box 315, the nip roller article numbers registered in the nip roller table 214 of FIG. 6 are listed up, and each specification regarding the selected article number is displayed in the list window 316. FIG. When it is necessary to register a new article number, it returns to a 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 if there is no change in the displayed contents, the operator operates the command button 317 for execution to switch to the next screen. When the command button 317 is operated, the screen is switched to the screen 320 for setting the temperature condition of FIG.

Referring to FIG. 9, the 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, and designation. A text box 324 for displaying time, 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. Equipped

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

The heat transfer rate is a value used in equations (33) and (34) set as boundary conditions of the basic equation (32). Since the heat transfer rate can be measured by calculating the environmental temperature, and calculated, it is preferable to pattern the temperature according to the temperature setting conditions, register it separately for easy selection by the operator (user), and select it from a combo box or the like.

The temperature change map code calls data registered in the temperature change map table 218 of FIG. 6, and selects the temperature change map code registered in the temperature change map table 218 from the combo box 323. According to the work, it is possible to arbitrarily set the environmental temperature T _∞ for each time T _j . When it is necessary to register a new temperature change map code, it returns to the main menu and registers from the registration screen which is not shown in figure.

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

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 equation (36). Alternatively, the initial environment temperature may be set in this screen 320 and registered in the web product management table 217 of FIG. 6, and the air temperature may be controlled by the air conditioner when the web 10 is wound. 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 example shown, the example which performs a winding process in 25 _degreeC state of initial _stage environment temperature _T∞ , and _{heats the} winding roll 5 after completion | finish of a process to 20K high temperature for 2 hours is shown.

The operator checks the specifications set on the screen 320, and if there is no change in the displayed contents, the operator 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 correction is necessary, and when it is determined that no correction is 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 an optimal winding condition in consideration of the temperature change in the following procedure.

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

The control unit 20 reads out necessary data from each table of FIG. 6 based on the transmitted setting condition (step S101). Next, the control unit 20 calculates a temperature distribution to be generated in the winding roll 5 based on the read data, the basic equations 26, and the prices related to the basic equations 26 (step) S102). Next, the control unit 20 initializes the counter variable k to 0 (step S103), calculates by giving an initial taper tension to the tension function Tw (r), and calculates the winding tension Tw in the sections r0 to rs. Compute (step S104). In this first step (k = 0), the winding tension Tw is set at the 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 tensions Tw (ΔTw1, ΔTw2, ΔTw3, ??? ΔTwn) of the design variable vectors obtained in this step. Specifically, the r coordinate of each contact P ^(k) is fixed, and only the ΔTwi is changed in the positive or negative direction to obtain a new contact P ^(k) . For example, when the initial winding tension T _wo shown by an imaginary line evolves, the tension function Tw (r) evolves to the winding tension T _wk shown by a solid line.

Then, the control unit 20 verifies whether or not the searched objective function f (X) is a minimum value (step S107), and if it is not the minimum value, increments step k (step S108) and step S6. The following steps are repeated and if the minimum value is reached, the process proceeds to the control process.

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 equation (45) evolving until the objective function f (X) becomes the minimum value. (Step S109). As a result, even after the winding, even after the temperature change has occurred, it becomes possible to obtain the winding roll 5 in which neither the star defect, the plastic deformation, and the telescope occur.

As explained above, according to this embodiment, when processing the web 10 with the winding roll 5 wound around the core 5a, the winding tension of the winding web 10 is adjusted according to the winding diameter. It is a winding apparatus provided with the control unit 20 to make, The control unit 20 changes the environmental temperature _T∞ which affects the motor control part 23 and the winding roll 5 as a winding tension adjustment apparatus, and predetermined | prescribed | designated. Based on the time Tk, temperature distribution calculating means for calculating the temperature distribution after the specified time Tk in the winding roll 5, and the internal stress σr, σ _θ of the winding roll 5 based on the calculated temperature distribution. And logically calculating the optimum value calculating means for calculating the optimum value of the winding tension based on the internal stress? R and? _Theta calculated by the stress calculating means. Therefore, to set in the present embodiment, the take-up roll 5, the web product management table 217, or a temperature change map table of the storing section 21 to change and a point in time Tk of the ambient temperature T _∞ be the 218, etc. According to the work, the temperature distribution calculating means calculates the temperature distribution of the winding roll 5 after the specified time Tk has passed (temperature distribution calculating step). Then, the stress calculating means calculates the internal stress σr, σ _θ taking into account the calculated temperature distribution of the winding roll 5 (internal stress calculating step). The optimum value calculating means calculates the optimum value of the winding tension based on the internal stresses σr and σ _θ calculated in consideration of the temperature distribution of the winding roll 5 (optimum value calculating step). Therefore, when the winding roll 5 receives the heat influence after a process, the internal stress (sigma) r and ( _theta ) _theta of the winding roll 5 will change based on the predicted characteristic of the temperature distribution calculating means. As a result, due to the internal stresses sigma r and sigma _θ that are changed on the basis of the thermal effect, it is possible to prevent post-expected winding failures, such as blocking, buckling wrinkles, or tensile wrinkles, which are fixed to the films.

Moreover, in this embodiment, the temperature distribution calculation means is equipped with the function or step which calculates the temperature distribution of the said winding roll 5 based on the thermal conductivity analysis model containing the abnormal heat conductivity differential equation 32. As shown in FIG. For this reason, in this embodiment, since the temperature distribution which acts on the winding roll 5 can be computed in consideration of the heat conduction characteristic in the winding roll 5, and the heat transfer characteristic from the environment, the change of the environmental temperature _T∞ . Even when a gap occurs in the temperature distribution of the winding roll 5 accompanying, it becomes possible to ensure necessary interlayer frictional force F _i and circumferential stress σ _θ . 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 calculating means can optimize the calculated value to a more suitable winding tension.

In addition, in this embodiment, a temperature distribution calculation means evaluates the layer of the air which intervenes between the layer of the web 10 which comprises the winding roll 5, and the layer of the web 10 as an equivalent layer, and the said winding roll ( 5) has the function of calculating the temperature distribution. For this reason, in this embodiment, it becomes possible to calculate the precise temperature distribution which considered 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, the thermal resistance of the winding roll 5 decreases with the increase of the contact pressure, so that the temperature distribution around the air does not become linear. On the other hand, since the roughness exists on the surface of the web 10, a part of the contact surface between the web 10 layers is in contact with each other, and other parts are in contact with each other in a distributed contact. Air is interposed in the non-contact part. In addition, when the air layer becomes thick, the web 10 is separated and non-contacted at the front surface. In such a form, when the air layer exists in the winding roll 5, the thermal conductivity K _eq of the external appearance of the winding roll 5 changes. In this embodiment, since the abnormal thermal conductivity differential equation 32 is solved using the thermal conductivity K _eq of the equivalent layer in consideration of the thermal resistance according to the presence of this air layer, it is possible to calculate a precise temperature distribution.

In addition, in this embodiment, the stress calculation means evaluates the layer of the air which intervenes between the layer of the web 10 which comprises the winding roll 5, and the layer of the web 10 as an equivalent layer, and the said winding roll 5 It has a function of calculating the internal stress σ r, σ _θ of. 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 addition, in this embodiment, the stress calculation means includes the function which calculates the differential equation which contains the linear expansion coefficient (alpha) r, (sigma) _theta of the web 10 as a parameter as stress calculation 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 It is possible to keep the value as needed.

In the present embodiment, the stress analysis model is given the boundary condition of the innermost layer by the differential equation 29 having the linear expansion coefficient α _c of the core 5a as a parameter. For this reason, in this embodiment, it becomes possible to calculate the internal stress of the winding roll 5 precisely in consideration of the linear expansion coefficient (alpha) _c of the core 5a.

Further, in the present embodiment, the optimum value calculating means includes the objective function of equation (47) for solving the tension and the objective function of equation (47) for solving the tension function of this equation (45) and the objective function of the equation (47). It stores a design variable of the equation (46) included, and has the function of calculating the minimum value of the equation (47) at every predetermined step related to the winding diameter. For this reason, in this embodiment, the minimum tension which considers the change of the environmental temperature _{T∞ which} the winding roll 5 will receive for every predetermined step of the winding diameter is calculated, and it is optimized to optimize the tension every time the step increases. It becomes possible.

In the present embodiment, the objective function of the equation (47) of the optimum value calculating means is that the circumferential stress σ _θ acting on the winding roll 5, the frictional force between the web 10, and the slip of the web 10 start. It includes either of the parameters resulting from the critical frictional force Fcr. For this reason, in this embodiment, it becomes 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 winding roll 5 is calculated in accordance with the change of the environmental temperature T _∞ to be received by the winding roll 5 and the designated time Tk, and the internal stress σr in consideration of the thermal stress, Since σ _θ can be optimized, it is possible to prevent post-expected winding failures, such as blocking, buckling wrinkles, or tensile wrinkles, caused by film sticking, due to the internal stresses σr and σ _θ that are changed based on thermal effects. It has a significant effect that can be prevented.

In addition, in this embodiment mentioned above, although the nip wire load L is included as a parameter in a design variable as a parameter of a constraint function, the form which does not use nip wire load L as a control parameter may be sufficient. In the Example shown below, the form which omitted the nip line load L is shown.

[Example]

Next, the Example of this invention is described, comparing with a comparative example. This inventor set several analysis conditions, and confirmed the effect by the above-described prediction theory model and embodiment for every analysis condition. For any analysis condition, the designated time Tk is 12 hours.

[Interpretation condition A]

In 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 _θ [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 Poisson's Ratio υ _r 0 Thermal conductivity λ _w 0.115 specific heat c _pw 936 density ρ _w 1400 Radial linear expansion coefficient α _r 15.5 × 10 ^-5 Circumferential linear expansion coefficient α _θ 2.08 × 10 ^-5 Heart Outer diameter r _c [m] 0.451 Bore r _cin [m] 0.0381 Elongation Modulus E _c [Pa] 17.0 × 10 ⁹ Poisson's υ _c 0.3 Coefficient of linear expansion α _c [1 / K] 1.4 × 10 ^-5

The coiling conditions, the nip rollers, and the heat transfer coefficients around the winding rolls in the analysis condition A are shown in the following table.

Item sign unit Specifications Winding condition




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

Elongation Modulus E _n [Pa] 4.12 × 10 ⁶ Radius R _n [m] 0.0738 Poisson's ν _n 0.5 Heat transfer coefficient
(Environment of the winding roll)
When heating h _h [W / m ² K] 33.1 During cooling h _c [W / m ² K] 33.1

For analysis condition A, design variables, objective functions, and constraints are shown below.

[Jos 42]

(52)

(52)

(53)

(53)

는、미끄럼이 생기는 마찰력의 참조치only,

Is a reference value of the sliding friction

(54)

(54)

The objective function in the above example minimizes the equation (53) of the objective function regarding the frictional force F _i and the circumferential stress σ _θ after a specified time T _k (= 12 hours) when the winding roll 5 receives a temperature change. I do it. In addition, the formula (54) of a constraint condition changes + 20K or -20K from the initial roll temperature T _r0 at the time of winding | winding during the elapsed time T _k = 0 hour-12 hours, and it rolls up the roll state. In the process of changing, the condition that wrinkles and slip does not occur is restricted.

In addition, the design conditions in 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: Verification result at the time of heat processing in analysis condition A)

In Example 1, the winding roll wound up under analysis condition A was heated. As for the temperature change conditions at the time of heating, as shown to FIG. 11A, the roll temperature was 25 degreeC, the temperature difference at the time of heating was 20K, and the heating time was 12 hours. As shown in FIG. 11A, the calculation result based on the thermal stress basic equation 23 shows that the winding roll 5 heated in the aging room increases in temperature from the outer circumferential side as the heating time elapses. Later, the temperature distribution over the entire floor became almost the same as the room. It is thought that the temperature rises from the outer layer side is because the heat transfer rate is higher on the outer circumferential side than on the inner circumferential side. In addition, the winding tension Tw calculated in consideration of the temperature change as shown in FIG. 11A is slightly higher and gently falls on the inner circumferential side than in the case of not considering the temperature change.

When the optimization of the winding tension Tw was computed based on the said calculation result, the winding tension characteristic shown in FIG. 12 was obtained. 12, the solid line X is a characteristic of the winding tension Tw which concerns on a present Example, and the broken line Y is compared when it calculates using general winding equation, without using Formula (28), Formula (32), etc. Example characteristics.

Regarding the frictional force F _i and the radial stress sigma, as shown in Figs. 13A and 13B, in the characteristic X (X1 to X3, hereinafter equal) of the present embodiment, a good frictional force F and a radial stress are applied over all the temperature distribution changes. represents σr.

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 characteristic Y (Y1-Y3, below) of the comparative example which does not consider temperature change, as the internal temperature rises (longer heating time), the circumferential stress? Tended to be.

(Example 2: Verification result at the time of cooling process in analysis condition A)

The winding roll of analysis condition A was cooled. As a temperature change condition at the time of cooling, as shown to FIG. 14A, the roll temperature was 25 degreeC, the temperature difference at the time of cooling was 20K, and the cooling time was 12 hours. As shown in Fig. 14A, the calculation result based on the thermal stress basic equation 23 shows that the cooled winding roll 5 is cooled at the outermost layer side, and after 12 hours, the temperature distribution over the entire layer is changed to the environmental temperature. Became almost the same as

When the optimization of the winding tension Tw was computed based on the said calculation result, the result similar to FIG. 15 was obtained. The characteristic X of this Example rose slightly abruptly from the inner circumferential side, assumed the same characteristic to the vicinity of the outermost circumference, and became a characteristic that greatly increased again after the outermost circumference. On the other hand, the characteristic Y of the comparative example fell as the winding tension fell in the inner peripheral side, and after estimating to the low level near the outermost circumference, it rose to the predetermined level from 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 could be maintained regardless of the temperature change. On the other hand, in the characteristic Y of the comparative example, a friction coefficient fell with the temperature change becoming large (as cooling time becomes long), and it became a characteristic which slips easily at a wide roll radius position.

Regarding the radial stress sigma, as shown in Fig. 16B, in the characteristic X of the present embodiment, the necessary radial stress sigma 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 stress fall in the wide roll radius position.

In addition, about the circumferential stress, as shown in FIG. 16C, in the characteristic X of the Example, the required circumferential stress (sigma) ( _theta) was maintained with respect to all the roll radius positions and all the temperature distributions. In contrast, in the characteristic Y of the comparative example, the circumferential stress became negative on the outermost circumferential side.

[Interpretation condition B]

Next, in the analysis condition B, the case where the temperature conditions were set so that winding failure might not generate | occur | produce even if a temperature change generate | occur | produced after winding up (that is, even if the temperature difference is + 20K or -20K) was verified. For the required verification, among the analysis conditions A, the objective function and the constraints were changed as follows.

[Jos 43]

(56)

(56)

は、미끄러짐이 발생하는 마찰력의 참조값only,

･ Reference value of frictional force that causes slip

(57)

(57)

The equation (55) of the objective function in the analysis condition B is calculated in such a manner that the frictional force and the circumferential stress immediately after the winding are minimized. As a result, the result of FIG. 17 which was the same also in cooling also in temperature conditions was obtained. In the embodiment of characteristic X, the take-up the initial dimensionless roll radial position r / r _c is the coiling tension Tw rises from the range of 1.0 from, and thereafter, while it returned to the initial value slightly lowered toward the outer layer is assumed that a gradual, non- After the dimensional roll radius position r / r _c passed 2.0, the behavior rapidly increased again. On the other hand, in the characteristic Y of a comparative example, it is estimated that the winding tension Tw falls in the range of about 1.0 from the beginning of a winding to the dimensionless roll radius position r / r _{c, and} is gentle to the outer layer side as it is, and the dimensionless roll radius position r / r _c passed 2.0 and then rose again.

Next, the result after heat processing is as follows.

(Example 3: Verification result at the time of heat processing in analysis condition B)

As shown in FIG. 18A, the temperature difference was set to 10K and heated for 12 hours with respect to the initial roll temperature T _r0 at the time of winding as heat processing. The calculation result based on the thermal equation basic equation 23 is as shown in Fig. 18B.

With reference to FIG. 18B, as for the temperature distribution of the winding roll 5 after heating, the temperature rises from the outer peripheral side as a heating time passes, and after 12 hours, the temperature distribution became almost the same as the room | room over the whole layer.

Regarding the frictional force and the radial stress sigma, as shown in Figs. 19A and 19B, good frictional force F _i and the radial stress sigma r were shown over all the 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: Verification result at the time of cooling process in analysis condition B)

As shown in FIG. 20A, as the cooling treatment, the temperature difference was set to −10 K with respect to the initial roll temperature T _r0 at the time of winding and cooled for 12 hours. The calculation result based on the thermal equation (23) was as shown in FIG. 20B.

Referring to FIG. 20B, the temperature distribution of the winding roll 5 after cooling decreases from the outer circumferential side as the cooling time elapses, and after 12 hours, the temperature distribution becomes almost the same as that of the room over the entire layer. .

Regarding the frictional force, as shown in FIG. 21A, in the characteristic X of the embodiment, the necessary frictional force F _i could 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, as temperature change became large (as cooling time becomes long), a friction coefficient fell and it became the behavior which slips easily at a wide roll radius position.

Regarding the radial stress σ r, as shown in FIG. 21B, in the characteristic X of the embodiment, the required radial stress σ 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, it was in the wide roll radius position and showed the stress fall.

As for the circumferential stress, as shown in Fig. 21C, in the characteristic X of the embodiment, necessary circumferential stress σ _θ could be maintained for all the roll radius positions and all the temperature distributions. In contrast, 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 depending on the difference of the heat transfer coefficients, an example in which the heat transfer coefficients are changed as shown in Table 6 in the analysis condition A was investigated.

Item sign unit Specifications Heat transfer coefficient
(Environment of the 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: Verification result at the time of heat processing in analysis condition C)

In Example 5, the winding roll wound up under analysis condition C was heated. As for the temperature change condition at the time of heating, as shown to FIG. 22A, the roll temperature was 25 degreeC, the temperature difference at the time of heating was 20K, and the heating time was 2 hours. In addition, 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, the calculation result based on the thermal stress basic equation 23 shows that the winding roll 5 heated in the aging room increases in temperature from the outer circumferential side as the heating time elapses. After the passage, the temperature tended to decrease from the outer layer side. Moreover, after 7 hours, while the temperature was relatively maintaining the temperature at the end of heating on the core side, the phenomenon that the temperature was lowered on the outer layer side than the core side was seen. This phenomenon can also be considered to be because the heat transfer rate is higher on the outer circumferential side than on the inner circumferential side. Based on this calculation result, the optimization of the winding tension Tw was calculated and the result of FIG. 23 was obtained.

Referring to Fig. 23, the characteristic X of the winding tension Tw calculated in consideration of the same temperature change as in Fig. 22A is set slightly higher than the characteristic Y of the comparative example which does not consider the temperature change.

As shown in Figs. 24A and 24B, in the characteristic X of the present embodiment, in addition to showing the good frictional force F _i and the radial stress σ r over all the temperature distribution changes, the circumferential stress σ _θ is also shown in Fig. 24C. As described above, it was possible to obtain the characteristic that no sagging occurred for all the dimensionless roll radius positions r / r _c over all the temperature distribution changes. On the other hand, in the characteristic Y of the comparative example, when the difference of the temperature distribution between the core side and the outer layer side is large, the circumferential stress (sigma) ( _theta) fell and the tendency to become negative was seen.

(Example 6: Verification result at the time of heat processing in analysis condition C)

The winding roll of analysis condition C was cooled. As upper conditions of the temperature distribution in the core side and the outer layer side at the time of cooling, as shown to FIG. 25A, the roll temperature was 25 degreeC, the temperature difference at the time of cooling was 20K, and the cooling time was 2 hours. Moreover, after cooling time passed, the environmental temperature of the winding roll 5 was returned to the same temperature as roll temperature. As a result of the calculation based on the thermal equation (23), as shown in Fig. 25B, the cooled winding roll 5 was cooled at the outermost layer side and showed a tendency for the temperature to fall from the outer layer side. In addition, after 7 hours, the temperature was relatively maintained at the core side at the end of the heating, while the temperature on the outer layer side was higher than that at the core side. Based on this calculation result, the optimization of the winding tension Tw was calculated and the result of FIG. 26 was obtained.

Referring to Fig. 26, for characteristic X related to the present embodiment, the winding tension Tw rises as the dimensionless roll radius position r / r _c increases at the first predetermined gradient, and the predetermined dimensionless roll radius position r It stopped after / r _c (about 1.0) and showed a sharp rise after the outer periphery (about 2.0). In contrast, in Comparative Example Y, the winding tension Tw decreases until the predetermined dimensionless roll radius position r / r _c (about 1.0) passes, and then stops and rises after the outer circumference (about 2.0). Showed action.

Regarding the frictional force, as shown in Fig. 27A, in the characteristic X of the embodiment, it was possible to maintain the required frictional force F _i regardless of the difference in the temperature distribution at the core side and the outer layer side. On the other hand, in the characteristic Y of a comparative example, when the difference of the temperature distribution in a core side and an outer layer side becomes large, a friction coefficient will fall and it becomes a characteristic which slips easily at a wide roll radius position.

Regarding the radial stress sigma, as shown in Fig. 27A, in the characteristic X of the present embodiment, the required radial stress sigma r could be maintained irrespective of the difference in the temperature distribution on the core side and the outer layer side. On the other hand, in the characteristic Y of the comparative example, the stress fall in the wide roll radius position at the time of cooling.

In addition, about the circumferential stress, as shown in FIG. 16C, in the characteristic X of the Example, the required circumferential stress (sigma) ( _theta) was maintained with respect to all the roll radius positions and all the temperature distributions. On the other hand, in the characteristic Y of the comparative example, when the difference of the temperature distribution in the core side and the outer layer side became large, the circumferential stress became negative in the outermost peripheral side.

In a form also apparent from the above-described embodiment, since the heat transfer rate has a great influence on the roll temperature in an abnormal state, it is difficult to calculate the temperature distribution of the winding roll 5 using an abnormal thermal conductivity analysis model including the basic equation 28. It was found to be extremely valid.

Referring to FIGS. 28A and 28B, when the web 10 of the winding roll 5 has an anisotropic linear expansion coefficient that tends to extend in the circumferential direction, the web 10 expands in the radial direction by heating. Phosphorus acts. As a result, when temperature rises, a gap tends to arise in each layer in the outer layer side, and a radial stress falls. As a result, slip easily occurs where the change in temperature distribution is large. In addition, on the winding side, the web does not extend, and compression occurs, whereby wrinkle wrinkles are likely to occur. On the other hand, when a temperature decrease occurs, since it shrinks in the radial direction, the radial stress increases, but because it is stretched without shrinking on the winding core 5a side, the circumferential stress does not become negative.

In addition, as shown in (c) and (d) of FIG. 28, when the web 10 of the winding roll 5 has an anisotropic linear expansion coefficient that tends to extend in the radial direction, the web 10 is radially heated by heating. The expanding stress acts on the outside of each layer. As a result, when temperature rises, the thickness of each layer increases, the radial stress increases, and wrinkles and blocking tend to occur. On the other hand, when a temperature fall has occurred, the stress which a web reduces in the radial direction acts, and the outer side of each layer reduces a shaft diameter. As a result, when a temperature fall occurs, the radial stress on the inner circumferential side is forcibly reduced, and the circumferential stress is converted to positive.

Therefore, in the basic equation or the like of Equation (28), including the coefficient of linear expansion as a parameter is extremely important in order to obtain an appropriate winding tension in the case of the difference in the temperature distribution of the web, particularly the case where the linear expansion coefficient of the web has anisotropy. It was confirmed to be valid.

Moreover, based on the above knowledge, even if the linear expansion coefficient is anisotropic in the circumferential direction and the radial direction of the wound web, it can also be controlled intermittently. In other words, when an increase in the environmental temperature is expected after winding, even if either the circumferential linear expansion coefficient or the radial linear expansion coefficient is high, circumferential stress is not applied to the diameter between the core diameter and the winding diameter or less. It is also preferable to give tension beforehand. On the other hand, in the case where a decrease in the environmental temperature is expected after the winding, even when either the circumferential linear expansion coefficient or the radial linear expansion coefficient is high, the tension is given in advance so that the interlaminar frictional force does not exceed the limiting frictional force for the entire diameter. It is also preferable. In the case of adopting such a form, when an increase in the environmental temperature is expected after winding or when a decrease in the environmental temperature is expected after the winding, the winding tension Tw considering the change of the internal stress accompanying the temperature change intermittently is obtained. It can be given. In the above aspect, after calculating the internal stress in the general state equation as shown in Equation (7), optimizing the winding tension function based on the calculation result, etc., a temperature rise is expected or a temperature drop is expected. In addition, since a very suitable winding tension corresponding to the temperature change can be obtained only by correcting the respective calculation results, it is possible to greatly simplify the calculation and to complete a highly suitable winding roll.

This invention is not limited to embodiment mentioned above, Needless to say that various changes can be added in the range which does not deviate from the summary of this invention.

For example, in the embodiments and examples described above, a stress analysis model and a thermal conductivity analysis model mainly used in consideration of the air layer are used, but when the air layer is so small that the influence on the actual phenomenon is very small, the air layer between the web layers does not need to be considered. .

In addition, in the above-described embodiment, the radial elongation modulus E _ral of the air layer is treated as a constant without depending on the temperature. However, it is also preferable to configure the air elongation modulus E _ral in such a manner that the change in elongation modulus E _ral due to temperature is taken into consideration.

1: roll 2: guide roller
3: pinch roller 4: nip roller
5: winding roll 5a: winding
6: nip load adjuster 7: motor
8: temperature sensor 10: Web
21: memory 22: calculator
23: motor control unit 24: nip load adjustment unit
25: display unit 26: input / output unit
45: nip 100: winding device
101: unwinding device

Claims (18)

In the winding apparatus provided with the winding tension adjustment apparatus which adjusts the winding tension of the wound web according to a winding diameter, when winding a web around a core and processing with a winding roll,
The winding tension adjusting device,
Temperature distribution calculating means for calculating a temperature distribution after the designated time elapses in the winding roll based on a change in environmental temperature affecting the winding roll and a predetermined designated time;
Stress calculation means for calculating an internal stress of the winding roll based on the calculated temperature distribution,
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. The method according to claim 1,
And said temperature distribution calculating means has a function of calculating a temperature distribution of said winding roll based on a thermal conductivity analysis model including an abnormal thermal conductivity differential equation. The method according to claim 2,
The temperature distribution calculating means has a function of calculating the temperature distribution of the winding roll by 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. Winding device. The method according to claim 3,
The said stress calculating means has the function of calculating the internal stress of the said winding roll by evaluating the layer of the web which comprises the said winding roll, and the layer of air interposed between the layers of the said web as an equivalent layer. Device. The method according to claim 1,
And said stress calculating means includes a function of calculating a differential equation including a linear expansion coefficient of a web as a parameter as a stress analysis model. The method according to claim 5,
The said stress analysis model is a winding apparatus characterized by the boundary condition of an innermost layer given by the differential equation which makes the linear expansion coefficient of a winding core a parameter. 7. The method according to any one of claims 1 to 6,
The optimum value calculating means stores a tension function for calculating the tension, an objective function for solving the tension function, and a design variable included in the objective function, so that a predetermined value associated with the winding diameter of the minimum value of the objective function is stored. A winding apparatus comprising a function for calculating each step. The method of claim 7,
The objective function of the optimum value calculating means includes any one of parameters including a circumferential stress acting on the winding roll, a friction force between the webs, and a critical frictional force at which slipping of the webs starts. Device. In the winding control method for controlling the winding apparatus which adjusts the winding tension of the wound web according to a winding diameter, when winding a web around a core and processing with a winding roll,
A temperature distribution calculating step of calculating a temperature distribution after the designated time elapses in the winding roll, based on a change in environmental temperature affecting the winding roll and a predetermined designated time;
A stress calculation 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 according to claim 9,
And said temperature distribution calculating step comprises calculating a temperature distribution of said winding roll based on a thermal conductivity analysis model including an abnormal thermal conductivity differential equation. The method of claim 10,
The temperature distribution calculating step includes 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. Winding control method. The method of claim 11,
The stress calculation step includes 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 an internal stress of the winding roll. Winding control method. The method according to claim 9,
The stress calculation step includes winding the differential equation including the linear expansion coefficient of the web as a parameter as a stress analysis model. The method according to claim 13,
And said stress calculation step calculates said stress analysis model on the basis of boundary conditions of the innermost layer given by a differential equation with the linear expansion coefficient of the core as a parameter. The method according to any one of claims 9 to 14,
The optimum value calculating step includes storing a tension function for calculating a tension, an objective function for solving the tension function, and a design variable included in the objective function, so that a predetermined value associated with the winding diameter is obtained. Winding control method characterized in that it comprises a step for calculating each step. The method according to claim 15,
The objective function of the optimum value calculating step includes any one of a parameter consisting of a circumferential stress acting on the winding roll, a friction force between the webs, and a critical frictional force at which the slip of the web starts. Control method. In the winding control method for controlling the winding apparatus which adjusts the winding tension of the wound web according to a winding diameter, when winding a web around a core and processing with a winding roll,
In the case where the change in the environmental temperature affecting the winding roll is expected to be higher than the environmental temperature at the time of winding, the circumferential stress of the winding roll does not become negative, from the inner peripheral side to the winding intermediate layer. A winding control method, wherein the winding tension is set high in advance. In the winding control method for controlling the winding apparatus which adjusts the winding tension of the wound web according to a winding diameter, when winding a web around a core and processing with a winding roll,
In the case where a change in the environmental temperature affecting the winding roll is expected to be lower than the environmental temperature at the time of winding, the interlayer frictional force of the winding roll does not fall below a predetermined limit frictional force to the entire winding diameter. A winding control method, wherein the winding tension is set high in advance.

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