JP2013180879A - Method for manufacturing web roll, method for winding web roll, and method for calculating inner stress - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a method for manufacturing a web roll, and a method for winding a web roll with consideration of stress change in a web in a width direction.SOLUTION: A method for manufacturing a web roll includes: a dummy roll manufacturing step for manufacturing a dummy roll for evaluation; a model creation step for creating a divided model by dividing a web roll into a plurality of sections in a width direction; a calculation step for calculating stress for each divided model, and for each winding diameter; a defect generating stress range determination step for calculating a defect generating stress range in which a defect may occur; a stress recalculation step for redoing the calculation step by changing winding conditions until the stress in a predetermined winding diameter range is not included in the defect generating stress range; and a winding step for winding a web under the winding conditions in which the stress in the predetermined winding diameter range is not included in the defect generating stress range found in the stress recalculation step.

Description

  The present invention relates to a web roll manufacturing method and a web roll winding method that are manufactured by winding a web around a winding core, and in particular, by calculating the internal stress of a web wound in a roll shape, The present invention relates to a web roll manufacturing method and a web roll winding method for winding a web under the determined winding conditions.

  Conventionally, webs made of plastic or the like are wound up, rolled, and shipped to customers. By winding up as long a web as possible and making it into a roll, it is possible to carry a large number of webs by carrying one roll, and efficient carrying becomes possible.

  However, the longer the web is wound, the greater the possibility that a winding misalignment will occur in the formed roll. Here, the winding misalignment refers to a defect in which the positions of both side ends of the roll wound with the web are partially deviated from the initial position after winding. This winding misalignment occurs not only when winding, but also when transporting a rolled roll.

  Conventionally, there have been many empirical trial experiments for web winding conditions that do not cause such defects. This is because there is no effective prediction method (simulation) with few errors. In addition, when evaluating the conditions, it takes two weeks or more for the evaluation period, and a sample for evaluation takes up several hundred to several thousand meters of web, so the evaluation period is long and the cost of the evaluation sample is enormous. Because it becomes. For this reason, it has been difficult to evaluate many conditions.

  Therefore, a method for obtaining the winding condition by theoretically predicting the internal stress of the roll without conducting many experiments has been studied. For example, the web winding method described in Patent Document 1 introduces a radial equivalent Young's modulus that takes into account the air film thickness interposed between the webs, thereby providing a radial stress (or a good agreement with the actual value) (or (Referred to as surface pressure) is calculated by a theoretical formula, and a method of determining an excellent winding tension pattern so that the radial stress or the lateral displacement resistance force becomes a desired value over the winding radius is disclosed.

  Non-Patent Document 1 discloses a formula for calculating the internal stress of the roll.

Japanese Patent Publication No. 7-33198

Z. Hakiel, “Nonlinearmodel for wound roll stresses”, J. Tech. Assoc. Paper Pulp. Ind., Vol. 70, pages 113-117, 1987

  However, the web winding method disclosed in Patent Document 1 has a problem that the web thickness distribution and the knurling are not taken into consideration, and thus the error becomes large and cannot be practically used. Here, knurls (also known as knurling) are minute uneven portions for preventing slippage formed at both ends in the width direction of the web.

Reference is now made to FIG. FIG. 20 is a roll perspective view for explaining the stress inside the roll. As shown in FIG. 20, the roll 10 has a radial stress σ _r that is a stress applied to the film 31 in the radial direction of the roll 10 and a stress applied to the film 31 in the circumferential direction of the film 31. There is a certain circumferential stress σ _t . As shown in the partial enlarged view 400, the product of the radial stress multiplied by the area is the normal resistance N, and the frictional force F = μN when the friction coefficient of the film is μ. Therefore, if the radial stress is different, the frictional force is also different. Therefore, when the radial stress changes in the width direction of the roll, it is necessary to consider the radial stress. If knurls are formed, the stress in the radial direction is greatly different. Therefore, the stress cannot be calculated using the same model as the part where knurls are not formed.

  In view of such circumstances, the present invention intends to provide a web roll manufacturing method and a web roll winding method that also take into account stress changes in the width direction of the web.

  The problems of the present invention can be solved by the following inventions.

  That is, the web roll manufacturing method of the present invention is a web roll manufacturing method for manufacturing a web roll obtained by winding a web around a core, and the core is formed using the same web as that used for the web roll. For each of the divided models, a dummy roll production process for producing a dummy roll for evaluation by winding the web on, a model creation process for creating a plurality of divided models obtained by dividing the web roll into a plurality of sections in a width direction, and And at least one of the circumferential stress and the radial stress based on the circumferential Young's modulus, the radial Young's modulus, and the winding tension profile for each winding diameter. A calculation step for obtaining a defect, a defect occurrence winding diameter of a defect generated in the dummy roll in the dummy roll preparation step, and a winding obtained in the calculation step A failure occurrence stress range determination step for obtaining a failure occurrence stress range in which the failure can occur from the stress for each diameter, and winding until a stress in a predetermined winding diameter range is not included in the failure occurrence stress range. A stress recalculation step in which at least one of a winding tension pattern, a thickness distribution in the width direction of the film, a height of the knurled portion, and an amplitude of oscillating is changed, and the stress recalculation is performed. And a winding step of winding the web under a winding condition that is found in the process and does not include a stress within a predetermined winding diameter range.

  Thereby, since the model divided | segmented into the width direction of the roll is created and stress calculation is performed for every divided model, the stress distribution of the whole width direction of a roll can be obtained. For this reason, it is possible to accurately know the stress, and even when a plurality of types of defects occur in the production of the dummy roll, it is possible to manufacture a web roll that solves all of the plurality of defects.

  The web winding method of the present invention is a web winding method for forming a web roll in which a web is wound around a winding core, and the winding is performed using the same web as that used for the web roll. A dummy roll manufacturing process for manufacturing a dummy roll for evaluation by winding the web around a core, a model creating process for creating a plurality of divided models obtained by dividing the web roll into a plurality of sections in the width direction, and the divided model For each winding diameter, and based on the circumferential Young's modulus, radial Young's modulus, and winding tension profile, at least one of circumferential stress and radial stress. The calculation process for obtaining stress, the defect occurrence winding diameter of the defect generated in the dummy roll in the dummy roll manufacturing process, and the winding determined in the calculation process A failure occurrence stress range determination step for obtaining a failure occurrence stress range in which the failure can occur from the stress for each diameter, and winding until a stress in a predetermined winding diameter range is not included in the failure occurrence stress range. A stress recalculation step in which at least one of a winding tension pattern, a thickness distribution in the width direction of the film, a height of the knurled portion, and an amplitude of oscillating is changed, and the stress recalculation is performed. And a winding step of winding the web under a winding condition that is found in the process and does not include a stress within a predetermined winding diameter range.

  Thereby, since the model divided | segmented into the width direction of the roll is created and stress calculation is performed for every divided model, the stress distribution of the whole width direction of a roll can be obtained. For this reason, it is possible to accurately know the stress, and to obtain a winding condition that can improve all of the plurality of defects even when a plurality of types of defects occur in the production of the dummy roll.

  Furthermore, the internal stress calculation method of the present invention is a method for calculating internal stress of a web roll in which a web is wound around a winding core, and is a calculation for creating a plurality of divided models in which the web roll is divided into a plurality of sections in the width direction. Circumferential stress and radial stress based on the model creation process, the circumferential Young's modulus, the radial Young's modulus, and the winding tension profile for each of the split models and for each winding diameter. And a calculation step for obtaining at least one of the stresses.

  It is possible to provide a web roll manufacturing method and a web roll winding method that take into account the stress change in the width direction of the web.

It is a conceptual diagram of the three-dimensional model of a roll. It is explanatory drawing explaining each parameter of the divided | segmented roll. It is the schematic which shows the cross section of the two webs in a roll. It is a figure which shows tension distribution of the width direction of Eb. It is explanatory drawing which shows the condition which draws in air between films. It is the schematic of a part of roll cross section of the direction parallel to a central axis. It is a schematic diagram of a part of a cross section in the ring direction of the roll. It is a graph showing a stress calculation result and an actual measurement value. It is a graph showing a stress calculation result and an actual measurement value. It is a graph showing a stress calculation result and an actual measurement value. It is the flowchart which showed the procedure of the winding method of a web. FIG. 4 is a schematic cross-sectional view in a ring direction of a roll for explaining cut-out projection. It is a graph which shows the relationship between a winding diameter and film tension. (A) It is a three-dimensional graph which shows the relationship between the winding length of a dummy roll, and radial direction stress. (B) It is a graph which shows the relationship between the winding length of the axial center part of a dummy roll, and radial direction stress. (A) It is a three-dimensional graph which shows the relationship between the winding diameter of a dummy roll, and radial direction stress. (B) It is a graph which shows the relationship between the winding diameter of the knurled part of a dummy roll, and radial direction stress. It is a graph which shows the relationship between the winding diameter-center radial direction stress in an initial condition and derivation conditions. It is a graph which shows the relationship between the initial condition and the winding diameter-knurling radial direction stress in the same participation right. It is a graph which shows derived winding diameter-film tension conditions. 4 is a table summarizing conventional conditions, derivation conditions, and winding quality. (A) is the one part schematic of the cross section of the three-dimensional model of a roll. (B) is a schematic view when the knurled part is close to the lower film in (A). (A) is the one part schematic of the cross section of the three-dimensional model of a roll. (B) is a schematic diagram of a part of a cross section of a three-dimensional model when a portion having the maximum “film thickness + air film thickness” is close to the lower film in (A). It is a roll perspective view for demonstrating the stress inside a roll. It is a figure which shows the simulation result in the two-dimensional model of roll internal stress. It is the schematic which shows arrangement | positioning in the roll of a pressure sensor. It is a figure which shows the actual value of roll internal stress.

  Hereinafter, embodiments for carrying out the present invention will be described in detail with reference to the accompanying drawings. Here, in the drawing, portions indicated by the same symbols are similar elements having similar functions. In addition, in the present specification, when a numerical range is expressed using “˜”, upper and lower numerical values indicated by “˜” are also included in the numerical range.

<Method for calculating radial stress of web in roll>
The calculation method of the internal stress of the web wound by the roll shape of this invention is demonstrated with reference to drawings.

(1) Conventional two-dimensional model When the internal stress of a web wound in a roll (hereinafter simply referred to as a roll) is obtained by simulation, a highly accurate result can be obtained by creating a finely cut three-dimensional model. Can be expected. However, if a simple 3D model is created, or a finely meshed 3D model is created, the calculation becomes very complicated, and the winding equation, which is an equation for determining the internal stress of the roll, is used. The constituting nonlinear ordinary differential equation may not be easily solved, and even if solved, it may take too much time.

  Therefore, in order to investigate the accuracy of the simulation with the conventional two-dimensional model (hereinafter referred to as the conventional simulation), the conventional simulation is performed and the simulation value of the internal stress of the roll is compared with the actual measurement value. And then examined. The conventional simulation was performed based on Non-Patent Document 1. The result is shown in FIG. FIG. 21 is a diagram showing a simulation result in a two-dimensional model of roll internal stress.

  In addition, as shown in FIG. 22, the actually measured values were obtained by sandwiching a plurality of pressure sensors 302 while winding the web 304 and measuring the pressure with the plurality of pressure sensors 302. FIG. 22 is a schematic view showing the arrangement of the pressure sensor in the roll. A plurality of pressure sensors 302 were installed in the roll 306 at predetermined intervals in the width direction for each predetermined winding diameter. The measurement result with the pressure sensor 302 is shown in FIG. FIG. 23 is a diagram showing actual measured values of roll internal stress.

  Referring to FIG. 21, since it is a two-dimensional model (a cross-sectional model in which the roll is cut into round sections), the influence of the roll in the width direction (presence of knurling, web thickness distribution in the width direction) is not taken into consideration. The radial stress in the width direction is constant. Here, the radial stress indicates the radial stress of the web. Hereinafter, it is also simply referred to as radial stress.

  On the other hand, referring to FIG. 23 showing actual measurement values, the radial stress at both ends in the width direction of the roll on which the knurl is formed is large. Thus, it has been found that the two-dimensional model does not accurately represent actual stress.

(2) Three-dimensional model used in the present invention (1) Outline of three-dimensional model In the present invention, a three-dimensional model is created in order to improve the inaccuracy of the conventional two-dimensional model. As shown in FIG. 1, the three-dimensional model was prepared by dividing a roll 10 around which a web (band-like flexible support) was wound into a plurality of pieces in the width direction and discretizing them. Here, the roll has a spiral cross section originally, but a concentric model was created in the three-dimensional model of the present invention. FIG. 1 is a conceptual diagram of a three-dimensional model of a roll.

  Next, the three-dimensional model used in the present invention will be described in more detail with reference to the drawings. FIG. 2 is an explanatory diagram for explaining each parameter of the divided rolls. FIG. 3 is a schematic diagram showing a cross section of two webs in a roll. FIG. 4 is a diagram showing a tension distribution in the width direction of the web.

  As shown in FIG. 2, the three-dimensional model used in the present invention has a roll 10 in which a web (also referred to as a film) is wound around a winding core 18 with widths W1, W2, W3, W4. These are divided into a divided roll 11, a divided roll 12, a divided roll 13, a divided roll 14 (hereinafter omitted). Here, in this description, only four divisions from W1 to W4 are explicitly described, but this is only described by way of example for convenience of explanation, and is limited to four divisions. Instead, a model with an arbitrary number of divisions can be created according to the form of the roll to be simulated and the accuracy desired to be obtained.

  The divided rolls 11, 12, 13, 14... (Hereinafter omitted) are considered to be rolls wound with the divided webs 21, 22, 23, 24... (Hereinafter omitted), and the divided webs 21, 22, 23, 24. (Omitted) tensions are considered as tensions T1, T2, T3, T4. The thicknesses of the divided webs 21, 22, 23, 24 (hereinafter omitted) are considered as a1, a2, a3, and a4, respectively.

  Further, the winding speed V, the winding length L, the total film width Wa, and the winding diameter r are considered as common parameters for each of the divided rolls 11, 12, 13, 14,. The winding speed V is a speed at which the web is wound. The winding length L is the length of the wound web. The total film width Wa is the total width of the web, that is, W1 + W2 + W3 + W4 + (hereinafter omitted) (hereinafter, the film and the web are used as the same meaning). The winding diameter r is the radius of the roll.

  Here, when stress analysis is performed with a three-dimensional model, the calculation becomes very complicated, and there is a problem that a nonlinear partial equation called a winding equation cannot be easily solved. However, due to the diligent research of the present inventor, it is possible to obtain and obtain the winding equation of the three-dimensional model by not considering the width direction stress and the displacement connection condition which are the connection conditions between the divided rolls. The value was found to be close to the experimental value. That is, a stress value close to the experimental value can be obtained easily by solving the winding equation separately for each divided roll to obtain the stress.

  Next, a description will be given with reference to FIG. FIG. 3 is a schematic view showing a cross section parallel to the roll rotation center axis of two films (webs) overlapped in the roll. As shown in FIG. 3, the thickness of the film (web) 31 is often formed so as to be thinner toward the outer side (though not limited to this). In addition, air 32 that is entrained exists between the films 31. The interval between the dividing lines 33 that divide the roll 10 into divided rolls is wider toward the center and narrows toward both ends.

  As a result, the stress calculation result can be brought closer to the experimental value by finely dividing the portion where the change in thickness is large, particularly the end portions where the knurled portion 34 is formed and the change in thickness is large.

  Next, a description will be given with reference to FIG. FIG. 4 is a diagram showing the relationship between the position in the width direction of the film and the tension. The horizontal axis of FIG. 4 shows the position of the film in the width direction, and the vertical axis shows the tension of the film. Referring to FIG. 3 together with FIG. 4, the tension is set so that the tension increases in proportion to the thickness of the film as shown in FIG. This is because a greater tension is applied to a region where the film thickness is thicker (divided roll). The film tension is divided for each of the divided rolls so that the tension of all the regions (all divided rolls) is summed up to be the film tension.

Specifically, when the thickness of the film of each split roll is t _n (m), the tension applied to the full width of the film is T (N), and the cross sectional area of the full width of the film is A (m ² ), The tension is T / A (N / m ² ). When the thickness of the film of each divided roll is multiplied by this, the tension Tn per unit width of each divided roll can be calculated as Tn = [T × t _n / A] (N / m).

(2) Calculation of thickness of air layer wound between films Next, in the process of winding a film to form a roll, the thickness of the air layer formed between the films by the air wound between the films The calculation method will be described with reference to the drawings. FIG. 5 is an explanatory diagram showing a situation in which air is involved between films. FIG. 5 shows an outline of a cross section of the roll 10 winding the film 31. The thickness of the air entrained between the films is calculated using foil bearing theory as shown below.

  As shown in FIG. 5, the film 31 is conveyed in the arrow direction and wound around the roll 10. At this time, air is entrained between the outermost film (the uppermost film in the drawing) and the lower film, and the thickness of the air layer at that time is defined as ho.

  In order to exclude the entrained air to the outside, that is, in order to reduce the thickness ho of the air layer, the air is blown from the air press device 50 onto the outermost film surface and pressed against the outermost film. (The effect of squeezing the air from between the films to the outside of the take-up roll is referred to as an incompressible squeeze action). The thickness of the air layer after being pressed by the air press device 50 is defined as ha.

  Here, in order to produce the squeeze effect, the use of the air press device 50 has been described as an example. However, not only the air press device but also various devices such as a contact roll can be used as long as pressure can be applied to the film surface. The air layer thickness can be calculated in the same manner.

  Further, when the film is wound around the roll 10 and several layers of the film are wound around the outside, the same squeezing action is applied to the internal air engulfed by those stresses (stress in the direction perpendicular to the film surface). Let h be the thickness of the air layer when (squeezed out) is performed. A method for calculating ho, ha, and h will be described below.

  The thickness ho of the air layer flowing into the winding is obtained by the following formula 1.

Here, R, η, Vr, Vw, and T are shown below.
R: radius of roll 10 η: viscosity coefficient of air Vr: rotational speed of roll (linear velocity outside roll)
Vw: Conveying speed of film to be wound

T: film tension
Next, using the calculated ho, the thickness ha of the air layer at the start of entrainment after being pressed down by the air press device 50 is obtained by the following formula 2.

Here, L, W, and t are shown below.
L: Force for pressing the film wound around the roll 10 by the air jetted from the air press device 50 against the roll 10 W: Web width t: Time

(3) Application to the model of the entrained air layer Next, the application to the model of the thickness h of the air layer after the entrainment (inside the winding) is shown in FIG. 6, FIG. 18 (A), (B), FIG. ) And (B) will be described. FIG. 6 is a schematic view of a part of a roll section in a direction parallel to the central axis. FIG. 18A is a schematic diagram of a part of a cross section of the three-dimensional model when there is no other film having “film thickness + air film thickness” larger than the total thickness including the film of the knurled portion. FIG. 18B is a schematic view when the knurled portion is close to the lower film in FIG. FIG. 19A is a schematic diagram of a part of a cross section of the three-dimensional model in the case where there is another film having “film thickness + air film thickness” larger than the entire thickness including the film of the knurled portion. FIG. 19B is a schematic diagram of a part of a cross section of the three-dimensional model when the portion having the maximum “film thickness + air film thickness” in FIG. 19A is close to the lower film.

  In the present invention, the film is considered as a rigid body. Moreover, about the surface of a film, and a back surface, let the surface of the center side of a roll be a surface, and let the surface of the outer side of a roll be a back surface. Here, as shown in FIG. 6, description will be made by taking as an example a film 31 that is formed such that the thickness of the film increases from the central portion toward both end portions. However, the present invention is not limited to the thickness pattern shown on the film 31, and the present invention can be applied to any thickness pattern and belongs to the scope of the present invention.

  In the case of a film having a thickness distribution, the upper and lower films try to contact (approach) at the upper two places of the thick part in the width direction. As shown in FIG. 18 (A), the “film thickness + air thickness ha” is larger than the maximum thickness among the film thicknesses of the respective divided rolls when the knurled portion 34 is also considered as a part of the film. When there is no other split roll film 50 having a value (referred to simply as a split film 60), the knurled portion 34 is squeezed without being disturbed by the entrained air, as shown in FIG. As a result, the distance between the upper and lower films is determined, and the air film thickness in other zones is also determined.

  Regarding the air film between the winding layers, at this time, the air film thickness h under the knurled portion 34 (or the film having the maximum film thickness among the divided films 60) is obtained by the following formula 3A or formula 3B. 6. As shown in FIG. 18 (B), the air film thickness under the other divided film 60 is equal to the distance between the surface of the divided film and the back surface of the film underneath caused by the film thickness distribution. Think.

  Instead of Equation 3A, the following Equation 3B that can be easily derived from Boyle's Law may be used.

σ: Radial stress (calculation result when rolled up to the i-th layer with Hakiel)
σ0: Initial radial stress (calculation result when rolled up to i-1th layer with Hakiel)
Pap: Atmospheric pressure ha: The thickness of the air layer after being pressed with an L force in the radial direction by an air press. After entrainment, the air layer thickness h involved when winding up to the i-1th layer with Hakiel.

  As shown in FIG. 19A, “film thickness + air thickness” is larger than the thickness of the film having the maximum thickness among the films of the division model when the knurled portion 34 is also considered as a part of the film. When there is a split film 60 having a value of “ha”, as shown in FIG. 19 (B), the air trapped in the other ring-cutting zones is obstructed and the air is hardly pushed out, and the distance between the upper and lower films is as follows: To decide.

  There are two methods. (1) As shown in FIG. 19B, the divided film having the largest “film film thickness + air film thickness ha” other than the knurled part and the film below it are the air film. When arranged at an interval of thickness ha, the distance between the upper and lower divided films (the distance between the upper film surface and the lower film back surface) is defined as the air film thickness.

Or (2) The total cross-sectional area of the entrainment air of each divided film shown in FIG. 19B is the same as the cross-sectional area of the gap between the upper and lower films (between the upper film surface and the lower film back surface). The distance between the upper film surface and the lower film surface is determined, and the distance between the upper and lower divided films at that time (the distance between the upper film surface and the lower film back surface) is defined as the air film thickness.
As described above, it is desirable that the calculation is performed by comparing the thickness in the width direction with good accuracy, but the squeeze calculation is uniformly performed by Formula 3A or Formula 3B over the entire width direction without comparing the thickness. It is also possible to calculate h and calculate the thickness of the air film (when there is no knurling or when it is low and has little influence).

  In this way, by taking into account the thickness of the air that has been involved, the influence of the air that has been involved can be numerically analyzed easily and accurately, and the stress distribution in the width direction of the roll can be accurately calculated.

(4) Oscillating in the width direction The oscillating in the width direction (hereinafter simply referred to as “oscillate”) is a film formed by winding the film relative to the roll. It is to reciprocate in the width direction.

  A method of applying this oscillation to the model will be described with reference to FIG. FIG. 7 is a schematic view of a part of a roll in a cross-section direction. 7A shows a case where the amplitude of the oscillate is 10 mm, and FIG. 7B shows a case where the amplitude of the oscillate is 5 mm. Here, the amplitude is a distance moved in the width direction by the oscillation. In FIG. 7, a range surrounded by a dotted line can be considered as a range corresponding to one divided roll divided by a three-dimensional model, for example.

  At this time, the portion where the knurled portion 34 is formed is larger in the case where the amplitude is 5 mm than in the case where the amplitude is 10 mm within the range of the dotted line. This indicates that the radial stress is increased. In order to consider the influence of such an oscillate, for example, when the film and the air layer of the adjacent split roll B enter the range of the split roll A due to the oscillate, the length of the intruded portion and the original The equivalent film thickness and the equivalent air layer thickness are calculated by proportionally allocating the film of the split roll A and the length of the air layer.

  At this time, both film thickness and air layer thickness are calculated. Thereby, the influence of the oscillation rate can be sufficiently taken into consideration. Here, the oscillate swings the film in the width direction at a constant cycle, and this cycle includes a winding length cycle and a winding diameter cycle. The winding length cycle is a winding length when one reciprocating oscillation is performed for every fixed winding length. The winding diameter cycle is an increment of the roll diameter when the reciprocating oscillation is performed every time the roll diameter is increased by a certain length. In either case, the calculation can be performed in consideration of the influence of oscillation by applying the above method.

(3) Calculation of web radial stress and circumferential stress According to the model described so far, the radius is solved by solving the following modified Hakir formula (see Non-patent Document 1) that takes into account the air film between the films to be wound. The directional stress σ _r and the circumferential stress σ _t are obtained.

Here, r, E _t , and E _r are shown below.
r: Winding diameter E _t : Circumferential Young's modulus E _r : Radial Young's modulus E _r is calculated by the following Equation 6.

tw: Web thickness h: Air layer thickness E1: Web radial Young's modulus E2: Air layer radial Young's modulus Here, Et is a physical property value obtained by a general tensile test method. Pull the web in the circumferential direction (tangential direction) and measure strain and stress. The slope of strain-circumferential stress is Et.

  The radial Young's modulus E1 of the web is a physical property value obtained by a compression test in which webs are laminated in the radial direction, which is called a known K2 factor test (established by J.D. Pfeiffer in Tappi Journal). Obtained from strain and radial stress gradient when a compressive load is applied.

(4) Web Radial Stress Calculation Value and Actual Measurement Value Next, the evaluation of the calculation value and the actual measurement value by the web radial stress calculation method according to the present invention will be described with reference to the drawings. 8A, 8B, and 8C are graphs showing the stress calculation results and the actual measurement values. Hereinafter, FIGS. 8A, 8B, and 8C are collectively referred to as FIG.

The radial stress was calculated by a computer under the following conditions 1 to 3. At that time, the film was actually wound under conditions 1 to 3, and the radial stress was measured using a pressure sensor as shown in FIG.
Condition 1: Oscillation amplitude 5 mm, tension 580 N, knurl thickness 8 μm, film thickness distribution of width direction 79.0-81.5 μm Condition 2: Oscillation amplitude 10 mm, tension 580 N, knurl thickness 8 μm, width direction 79.0 Film thickness distribution of ˜81.5 μm / Condition 3: Oscillation amplitude 0 mm (no oscillate), tension 580 N (, knurled thickness 8 μm, width direction 79.0-81.5 μm film thickness distribution Stress under conditions 1 to 3 The calculation results are (A), (B), and (C), respectively, in Fig. 8. The actual measurement values under conditions 1 to 3 are (a), (b), and (c) in Fig. 8, respectively. It is.

  Comparing (A) and (a) of FIG. 8 shows that the calculated value is very close to the actually measured value. In particular, the change in radial stress due to the influence of knurls at both ends in the width direction of the film is also calculated close to the actually measured value.

  As can be seen from the fact that (B) and (b) and (C) and (c) in FIG. 8 are the same, even if the conditions are changed, a value close to the actual measurement value can be calculated. ing. That is, by using the stress calculation method according to the present invention, a value close to the actual measurement value can be obtained.

<Web winding method using radial stress of web in roll>
Next, a method of winding the web using the radial stress and the circumferential stress of the web in the roll obtained by the above-described method will be described with reference to the drawings. FIG. 9 is a flowchart showing the procedure of the web winding method.

  Referring to FIG. 8, first, a dummy roll that is an evaluation roll is manufactured (S1: dummy roll manufacturing step). The production of the dummy roll is performed by winding the same film (web) as that used for the product around the winding core. However, the conditions for winding may be appropriate. Here, the conditions for winding are a winding tension profile, an oscillating amplitude, a knurl height, a web thickness pattern, and the like.

  The winding tension profile is a change pattern of the winding tension from the start to the end of winding. The oscillation amplitude is a movement width due to oscillation. The knurl height is the height from the web surface where the knurl is not formed to the apex of the convex portion due to the knurl formation. The web thickness pattern is a thickness change pattern in the width direction of the web.

  Before, after or simultaneously with S1, a split model in which a roll is divided into a plurality of round sections in the width direction is created by the above-described method (model creation step), and the same circumferential direction Young as the product (ie, the same as the dummy roll) By solving Equations 4 and 5 using the ratio and the radial Young's modulus, the radial stress and the circumferential stress of the dummy roll are obtained for each winding diameter and for each divided model (S2: calculation step) ). In the following description, stress calculation refers to radial stress calculation or circumferential stress calculation by the above-described method.

Next, critical stress evaluation is performed (S3: critical stress determination step). The critical stress evaluation refers to how many meters from the core side each of the defects that occurred when the dummy roll was manufactured, ie, winding misalignment, cut-out images, bevel, black belt, wrinkle, chrysanthemum pattern, etc. In other words, the number of mm of the winding diameter) is investigated, and the radial stress σ _r and the circumferential stress σ _{t at} that time are evaluated from the stress calculation result performed in S2. That is. Each defect will be described below.

(1) Winding misalignment The winding misalignment is a defect in which the positions of both side ends of the roll wound with the web are partially deviated from the initial position after winding. As a countermeasure against this defect, it is necessary to adjust the radial stress σ _r high.

(2) Cut-out copy As shown in FIG. 8, the cut-out copy is obtained by winding the film over the step portion 80 at the start of winding when the film 31 starts to be wound around the core. A step that occurs in film. As a countermeasure against this defect, it is necessary to adjust the radial stress σ _r low. FIG. 10 is a schematic cross-sectional view in a ring direction of a roll for explaining cut-out projection. A step always occurs at the beginning of winding, and the step generated by the effect of the step becomes smaller as the film is wound, and finally becomes a level at which there is no product-like problem. In this way, it is desirable that the film winding length until the level of the product-like problem or less is as short as possible, because many good products can be obtained.

(3) Chrysanthemum pattern A defect in which the film is buckled due to compression in the circumferential direction and the film becomes wavy. This defect looks like a chrysanthemum pattern when viewed from the end face side of the roll. As a countermeasure against this defect, it is necessary to adjust the circumferential stress σ _t so that it is as close to a positive value as possible in the event that the circumferential stress σ _t is negative (negative).

(4) Beko / Depression Deformation Beco / Depression Deformation is a defect in which the web falls and deforms due to depression on the surface of Robeco / Depression Deformation Roll. This countermeasure against defects needs to be adjusted so that the entrained air film thickness becomes small.

(5) Black belt When the film is wound, the convex portions of the film may overlap at the same position. In this case, as the product is wound many times, pressure is applied strongly to the convex part, and this part adheres, or extension occurs due to the pressure, resulting in a decrease in product quality. Become. Moreover, when this part is seen from the outside, it looks like a black belt. This is a black belt defect. To deal with this defect, it is necessary to adjust the amplitude of the oscillation to be large or to adjust the radial stress σ _r to be low.

(6) Winding wrinkle The winding wrinkle defect is a defect in which wrinkles are generated when the film is wound. To prevent this defect, it is necessary to adjust the circumferential stress σ _t to a low level.

Next, the defect generated in the dummy roll is within a predetermined winding diameter range (the range of the winding diameter in which defects should not occur in the product specifications is referred to as the predetermined winding diameter range). Then, in order to find the winding condition that will disappear, the following operation is performed. That is, the failure occurrence stress range which is the stress range in which the failure can occur is obtained from the failure occurrence radial stress and the failure occurrence circumferential stress which are the radial stress and the circumferential stress when the failure occurs (failure Generation stress range determination step). Specifically, this is as follows.
In the case of winding misalignment failure, the stress range below the failure occurrence radial stress is the failure occurrence stress range.
-In the case of poor cut-out projection, the stress range above the failure generation radial direction stress is the failure generation stress range.
-In the case of a chrysanthemum pattern defect, the stress range below the defect-occurring circumferential stress is the defect-occurring stress range.
-In the case of a bevel defect, the film thickness range equal to or greater than the defect occurrence entrained air film thickness is the defect occurrence air film thickness range.
-In the case of a black belt defect, the stress range above the defect occurrence radial stress is the defect occurrence stress range.
-In the case of winding wrinkle failure, the stress range not less than the failure occurrence circumferential stress is the failure occurrence stress range.

  Next, stress (radial stress, circumferential stress) within the predetermined winding diameter range is included in the defective generation stress range so that no defect occurs within the predetermined winding diameter range. The stress calculation is performed while changing at least one of the winding tension pattern, the thickness distribution in the width direction of the film, the height of the knurled portion, and the amplitude of the oscillate, so as to be eliminated (S4: stress recalculation) Process). This stress calculation is performed until a winding condition in which a defect does not occur in a predetermined winding diameter range (a winding condition in which the stress of the roll within the predetermined winding diameter range is not included in the failure generating stress range) Repeatedly changing the winding condition. As a result, it is possible to derive a winding condition in which the stress within a predetermined winding diameter range is not included in the failure-generating stress range.

  A web roll of a product can be manufactured by winding a film (web) on a winding core using the derived winding conditions.

  Here, the winding tension pattern is a change pattern of film tension at the time of winding according to the winding diameter when the film is wound up, as shown in FIG. FIG. 11 is a graph showing the relationship between the winding diameter and the film tension.

  Finally, the film is actually wound under the required winding conditions (S5).

  In this way, by using the calculation of the stress inside the roll based on the three-dimensional model to determine the winding condition, it is possible to obtain a winding condition that does not cause a defect with little actual evaluation. The calculation of stress and the winding condition can be obtained using a computer. By causing the computer to execute the above calculation formula and calculation procedure, it is possible to perform stress calculation and graph it by simply inputting the winding condition.

<Evaluation>
Next, regarding the winding method according to the present invention, two types of optical films of type A and type B were evaluated.

(1) Evaluation of Variety A First, a dummy roll of Variety A was produced. As a result, a cut-off portion of the dummy roll of Variety A occurred up to a winding length of 100 m, and winding deviation occurred at a location having a roll diameter of φ520 mm. The winding conditions at this time are as follows.
-The winding start tension was 650 N and the winding end tension was 580 N, and the tension was changed linearly from the start of winding to the end of winding.
-Knurl height 6μm (The thickness of the knurled part is the film thickness plus the knurled height 6μm)
・ Oscillate amplitude 10mm
Therefore, based on the production conditions of the dummy roll, the change in the radial stress when the film winding length and the winding diameter were changed by the stress calculation method according to the present invention was determined. The results are shown in FIGS.

  FIG. 12A is a three-dimensional graph showing the relationship between the winding length of the dummy roll and the radial stress. (B) It is a graph which shows the relationship between the winding length of the axial center part of a dummy roll, and radial direction stress. FIG. 13A is a three-dimensional graph showing the relationship between the winding diameter of the dummy roll and the radial stress. (B) It is a graph which shows the relationship between the winding diameter of the knurled part of a dummy roll, and radial direction stress.

  The cut-out image defect is more likely to occur as the stress in the effective product portion (other than both ends of the roll) increases. Therefore, FIG. 12B is a graph in which the horizontal axis is the winding length (m) and the vertical axis is the radial stress on the central portion representing the effective product portion in the width direction, and FIG. .

  Referring to FIG. 12 (b), since the cut-out image failure occurred when the winding length was 100 m, the radial stress when the winding length was 100 m was read from the graph (solid line) (calculated by calculation). 0.088 MPa.

  Therefore, in order to reduce the occurrence winding length of the cut edge to a target value of 30 m or less, for example, as shown by the dotted line in FIG. 12B, the radial stress value is only when the winding length is 30 m or less. Thus, it is only necessary to obtain a winding condition that is equal to or higher than the radial stress at which the cut edge defect occurs, and to perform winding under that condition. Here, as the target value, an arbitrary value can be selected depending on the product. The above value is an example, and the present invention is not limited to this value.

  Further, one of the purposes for forming the knurled portion is to increase the frictional force by increasing the radial stress by the convex portion of the knurled portion, thereby preventing winding deviation. Therefore, it is important to examine the radial stress of the knurled portion with respect to the winding deviation.

  Therefore, a graph shown in FIG. 13A, in which the radial stress at both ends (knurled portions) in the width direction of the roll is plotted on the vertical axis and the winding diameter (mm) is plotted on the horizontal axis, is shown in FIG. It is a solid line. Since winding deviation occurred at a roll diameter of 520 mm, the radial stress at the time of winding deviation was obtained from this solid line graph (calculated by calculation) and found to be 0.15 MPa.

  In order to set the winding diameter at which winding deviation occurs to, for example, 575 mm or more, which is 93.5% of the total winding diameter as a target value, when the winding diameter is larger than 575 mm as shown by the dotted line in FIG. Only the winding condition such that the radial stress is less than 0.15 MPa is obtained, and the winding should be performed under that condition. Here, the target value of the winding diameter at which winding deviation occurs can be set to an arbitrary% value depending on the product, and the above value is an example, and the present invention is not limited to this value.

  Here, the alternate long and short dash line in FIG. 13B shows the stress of the knurled portion under the condition of the dotted line in FIG. That is, when the take-up tension is changed so that the radial stress indicated by the dotted line in FIG. 12B is taken as a countermeasure against the cut defect, the cut defect is reduced, but the dashed line in FIG. As shown, it is understood that the winding misalignment worsens.

  Thus, changing the take-up tension to reduce cut end defects and winding misalignment is in a trade-off relationship with each other. In view of this, defective cutting edges were dealt with by changing the winding tension, and poor winding deviations were dealt with by changing the oscillation width. This is because even if the winding tension is not changed, if the oscillating width is changed, the radial stress of the knurled portion is changed.

  In this way, the winding tension is changed in order to prevent cut defects, and the oscillation width is changed in order to prevent winding deviation. In this case, a total of 100 or more simulations are performed to prevent both cut and winding deviation simultaneously. The winding condition that can be derived was derived. The results are shown in FIGS.

  FIG. 14 is a graph showing the relationship between the winding diameter and the central radial stress under the initial condition and the derivation condition. FIG. 15 is a graph showing the relationship between the initial condition and the winding diameter-knurling radial stress under the same entry rights. The dotted line in FIG. 14 shows the winding result under an initial condition in which the tension is linearly changed from the winding start tension 650N to the winding end tension 580N and the knurling amplitude is 10 mm. Further, the solid line in FIG. 14 shows the winding result at the oscillation amplitude of 5 mm when the tension is linearly changed from the winding start tension 550N to the winding end tension 550N, which is a newly derived condition.

  Also, the dotted line in FIG. 15 shows the winding result under the same initial conditions as the dotted line in FIG. 14, and the solid line in FIG. 15 shows the winding result under the newly derived conditions same as the solid line in FIG. As shown in FIGS. 14 and 15, by changing the tension and the knurl amplitude, the radial stress at the center of the roll can be reduced and the radial stress at the knurl can be increased. As a result, we succeeded in improving both cut-off and winding misalignment at the same time.

  As described above, according to the present invention, it is possible to derive a winding condition free from defects using a simulation that does not require cost and labor.

(2) Evaluation of product type B Next, evaluation of product type B will be described. For the product type B, a dummy roll was produced in the same manner as the product type A, and the roll diameter range in which the cut end defect occurred and the roll diameter in which the winding misalignment occurred were evaluated. Next, simulation (stress calculation according to the present invention) was repeated to derive a winding condition for improving the defect.

  Here, unlike the breed A, the breed B is a breed in which the oscillation amplitude cannot be changed due to the design of the product. Therefore, a winding condition for deriving both a cut edge defect and a winding shift defect by changing only the film winding tension was derived.

  The result is shown in FIG. FIG. 16 is a graph showing the derived winding diameter-film tension condition. A dotted line in FIG. 16 indicates an initial condition, and a solid line indicates a newly derived winding condition.

  As shown in FIG. 16, the newly derived condition is that the tension is increased linearly every time winding is started, and then the tension is decreased linearly for a while from the start of winding. By adopting such a winding tension profile, it is possible to improve both the cut end defect and the winding misalignment which are in a trade-off relationship with respect to the tension without changing the knurling amplitude.

  The reason for this is that the cutting edge failure occurs around the beginning of winding, so the tension at the beginning of winding was reduced from the initial condition, and after winding for a while the winding deviation occurred, the tension was higher than the initial condition. It is done.

  However, there are innumerable winding condition profiles of the winding diameter and tension, and it is practically impossible to derive which conditions are appropriate by conventional evaluation. According to the method of the present invention, it is possible not only to derive a winding condition profile that has been impossible in the past, but also to greatly reduce the evaluation cost and the evaluation / experiment time. For example, in the derivation of the winding conditions for the varieties A and B, the evaluation time can be reduced to about 1/6 (300 hours to 50 hours).

  FIG. 17 shows a summary of the conventional winding conditions and the winding conditions derived in the present invention, including the winding quality. FIG. 17 is a table summarizing conventional conditions, derivation conditions, and winding quality.

  In FIG. 17, the multipoint tension pattern means a pattern (becomes a broken line) whose inclination changes a plurality of times in the middle when the tension pattern is linearly changed. The conventional film thickness pattern means a pattern in which the central portion in the width direction is thin and both ends are thick, and the flat means that the thickness is constant in the width direction.

  In addition, the failure evaluation level of each winding quality is shown below.

・ Winding misalignment Evaluate the alignment and disorder of the end face (side face) of the take-up roll.
Excellent: Wound neatly with no gap in the width direction. (Deviation within 3mm)
Good: Misalignment in the width direction is observed. (3mm-10mm)
Impossible: There is a part that is greatly displaced in the width direction.

・ Cut-out image Failure where the step at the beginning of winding is transferred to the overwound film and deformed.
Excellent: Almost 15m or more from the core is not seen.
Good: The cut-out image is weak at 15m or more from the core.
Impossible: The cut-out image is seen strongly at 15m or more from the core.

-Black belt It is also called blocking, and as a result of the film layer and the film layer adhering to each other in the take-up roll, a portion that becomes sticky and transparent appears. It worsens when the winding radial stress is large. State without any entrained air layer.
Yu: No black belt.
Good: Some black belts are seen.
Impossible: A black belt is generated on most of the wound surface.

-Wrinkles (horizontal winding wrinkles) Failures that cause wrinkle deformation in the direction parallel to the winding shaft as a result of the web being compressed in the circumferential direction.
Yu: There are no wrinkles.
Good: Weak wrinkles are seen.
Impossible: Strong wrinkles with broken web deformed.

・ Depression / Square winding A failure in which the winding surface falls down and the cross section is not a beautiful curvature, and some angular deformations are seen.
Excellent: Square winding deformation is not seen on the winding surface.
Good: Each winding deformation is weak on the winding surface.
Impossibility: Strong angular winding deformation is seen in a wide range on the winding surface.

  As shown in FIG. 17, by winding under the winding conditions derived according to the present invention, it becomes possible to produce a roll having good winding quality and no defects.

  In the above evaluation, the winding misalignment failure and the cut edge failure have been described as examples to evaluate the failure. However, in the present invention, the present invention is not limited to these failures, and the winding misalignment is not limited. In addition, it is possible to obtain a winding condition that makes any defect such as cut-out, black belt, winding wrinkle, depression / square winding good.

  This is because any defect can be improved by setting conditions for any of radial stress, circumferential stress, and entrained air film, and the winding conditions for that can be simulated in the present invention. is there.

  DESCRIPTION OF SYMBOLS 10 ... Roll, 11 ... Split roll, 12 ... Split roll, 13 ... Split roll, 14 ... Split roll, 18 ... Core, 21 ... Split web, 31 ... Film, 32 ... Air, 33 ... Split line, 34 ... Knurl, DESCRIPTION OF SYMBOLS 50 ... Air press apparatus, 60 ... Dividing film, 80 ... Step part, 302 ... Pressure sensor, 304 ... Web, 306 ... Roll, 400 ... Partial enlarged view

Claims (12)

A web roll manufacturing method for manufacturing a web roll in which a web is wound around a core,
Using the same web as that used for the web roll, a dummy roll making step for actually producing a dummy roll for evaluation by winding the web around the core;
A calculation model creating step for creating a plurality of divided models obtained by dividing the web roll into a plurality of pieces in the width direction;
For each split model and for each winding diameter, at least one of circumferential stress and radial stress based on the circumferential Young's modulus, the radial Young's modulus, and the winding tension profile. A calculation process for determining one of the stresses,
Defect occurrence that determines the defect occurrence stress range in which the defect can occur from the defect occurrence winding diameter of the defect generated in the dummy roll in the dummy roll manufacturing process and the stress for each winding diameter obtained in the calculation process A stress range determination step;
Until the stress in the range of the predetermined winding diameter is not included in the failure generation stress range, the winding conditions are the winding tension pattern, the air press pressing force pattern, the thickness distribution in the width direction of the film, and the height of the knurl portion. A stress recalculation step in which at least one of the amplitude and period of the oscillate is changed and the calculation step is repeated;
A winding step of winding the web under a winding condition in which the stress in a predetermined winding diameter range determined in the stress recalculation step is not included in the failure occurrence stress range;
A web roll manufacturing method comprising: In the calculation step, σ _r that is the radial stress is derived by the following equation derived from a modified haquile considering the entrained air film:

r: winding diameter Et: circumferential Young's modulus Er: calculated by radial Young's modulus
Σ _t , which is the circumferential stress, is derived by the following formula derived from a modified haquile considering the entrained air film:

The web roll manufacturing method of Claim 1 calculated | required by. When obtaining the thickness of the entrained air film, the thickness ho of the outermost air layer of the roll is obtained by the following formula 1,


R: radius of roll 10 η: viscosity coefficient of air Vr: rotational speed of roll (linear velocity outside roll)
Vw: Conveying speed of the film to be wound T: Tension value obtained by distributing the tension of the entire film in proportion to the film thickness of the division model for each division model. In order to reduce the outermost air thickness, the thickness ha of the air layer after pressing a part of the outermost web with the force of L in the radial direction over the entire width direction is obtained by the following equation 2.


L: force for pressing the film against the roll W: width of the roll “film thickness + air” larger than the thickness of the film having the maximum thickness among the films of the split model when the knurling is also considered as a part of the film When there is no film of another split roll having the value of “film thickness ha”, the air film thickness h under the film having the maximum film thickness is obtained by the following formula 3A or formula 3B, and the maximum film thickness The film thickness of the air under the film other than the film is considered as a rigid body, and the thickness between the film surface caused by the film thickness distribution and the back surface of the film underneath is the thickness of the entrained air film,


σ: Radial stress (calculation result when rolled up to the i-th layer with Hakiel)
σ0: Initial radial stress (calculation result when rolled up to i-1th layer with Hakiel)
Pap: Atmospheric pressure ha: The thickness of the air layer after being pressed with an L force in the radial direction by an air press. After entrainment, the air layer thickness h involved when winding up to the i-1th layer with Hakiel.
Of the other split rolls having a value of “film film thickness + air film thickness ha” larger than the film thickness of the film having the maximum film thickness among the films of the split model when the knurling is also considered as a part of the film When there is a film, the film is considered as a rigid body, and the divided film having the largest “film film thickness + air film thickness ha” of the part other than the knurled part and the film below it have an air film thickness ha. The distance between the surface of each upper film and the back surface of the lower film is the thickness of the entrained air film, or the total cross-sectional area of entrained air in each divided model and the surface of the upper film Find the distance between the upper film surface and the lower film surface so that the cross-sectional area of the gap between the upper film surface and the lower film back surface is the same, and the distance between the upper film surface and the lower film back surface at that time Serial winding the thickness of the air film, the web roll process according to claim 2.   When determining the thickness of the entrained air film and the film thickness, if the film and the air layer of another division model adjacent to the range of a certain division model enter due to the oscillate, from the other division model The web roll manufacturing method according to claim 3, wherein the length of the part that has intruded and the length of the film and the air layer of the certain division model are proportionally distributed to obtain an equivalent film thickness and an equivalent air film thickness. A web roll winding method for forming a web roll in which a web is wound around a winding core,
Using the same web as that used for the web roll, a dummy roll making step for actually producing a dummy roll for evaluation by winding the web around the core;
A calculation model creating step for creating a plurality of divided models obtained by dividing the web roll into a plurality of pieces in the width direction;
For each split model and for each winding diameter, at least one of circumferential stress and radial stress based on the circumferential Young's modulus, the radial Young's modulus, and the winding tension profile. A calculation process for determining one of the stresses,
Defect occurrence that determines the defect occurrence stress range in which the defect can occur from the defect occurrence winding diameter of the defect generated in the dummy roll in the dummy roll manufacturing process and the stress for each winding diameter obtained in the calculation process A stress range determination step;
Until the stress in the range of the predetermined winding diameter is not included in the failure generation stress range, the winding conditions are the winding tension pattern, the air press pressing force pattern, the thickness distribution in the width direction of the film, and the height of the knurl portion. A stress recalculation step that changes at least one of the amplitude and period of the oscillate and repeats the calculation step;
A winding step for winding the web under a winding condition that is found in the stress recalculation step, and a stress in a range of a predetermined winding diameter is not included in the failure generation stress range;
A web roll winding method comprising: In the calculation step, σ _r that is the radial stress is derived by the following equation derived from a modified haquile considering the entrained air film:

r: winding diameter Et: circumferential Young's modulus Er: calculated by radial Young's modulus
Σ _t , which is the circumferential stress, is derived by the following formula derived from a modified haquile considering the entrained air film:

The web roll winding method according to claim 5, which is obtained by: When obtaining the thickness of the entrained air film, the thickness ho of the outermost air layer of the roll is obtained by the following formula 1,


R: radius of roll 10 η: viscosity coefficient of air Vr: rotational speed of roll (linear velocity outside roll)
Vw: Conveying speed of the film to be wound T: Tension value obtained by distributing the tension of the entire film in proportion to the film thickness of the division model for each division model. In order to reduce the outermost air thickness, the thickness ha of the air layer after pressing a part of the outermost web with the force of L in the radial direction over the entire width direction is obtained by the following equation 2.


L: force for pressing the film against the roll W: width of the web roll “film thickness + larger than the thickness of the film having the maximum thickness among the films of the split model when the knurling is also considered as part of the film” When there is no film of another split roll having the value of “air film thickness ha”, the air film thickness h under the film having the maximum film thickness is obtained by the following formula 3A or formula 3B, and the maximum film The film thickness of the air under the film other than the film having the thickness is considered as a rigid body, and the thickness between the film surface generated by the film thickness distribution and the back surface of the film underneath is the thickness of the entrained air film,


σ: Radial stress (calculation result when rolled up to the i-th layer with Hakiel)
σ0: Initial radial stress (calculation result when rolled up to i-1th layer with Hakiel)
Pap: Atmospheric pressure ha: The thickness of the air layer after being pressed with an L force in the radial direction by an air press. After entrainment, the air layer thickness h involved when winding up to the i-1th layer with Hakiel.
Of the other split rolls having a value of “film film thickness + air film thickness ha” larger than the film thickness of the film having the maximum film thickness among the films of the split model when the knurling is also considered as a part of the film When there is a film, the film is considered as a rigid body, and the divided film having the largest “film film thickness + air film thickness ha” of the part other than the knurled part and the film below it have an air film thickness ha. The distance between the surface of each upper film and the back surface of the lower film is the thickness of the entrained air film, or the total cross-sectional area of entrained air in each divided model and the surface of the upper film Find the distance between the upper film surface and the lower film surface so that the cross-sectional area of the gap between the upper film surface and the lower film back surface is the same, and the distance between the upper film surface and the lower film back surface at that time Serial winding the thickness of the air film, the web roll winding process according to claim 6.   When determining the thickness of the entrained air film and the film thickness, if the film and the air layer of another division model adjacent to the range of a certain division model enter due to the oscillate, from the other division model 8. The web roll winding method according to claim 7, wherein the length of the part that has entered and the length of the film and air layer of the certain division model are proportionally distributed to obtain an equivalent film thickness and an equivalent air film thickness. An internal stress calculation method for a web roll in which a web is wound around a winding core,
A calculation model creating step for creating a plurality of divided models obtained by dividing the web roll into a plurality of pieces in the width direction;
For each split model and for each winding diameter, at least one of circumferential stress and radial stress based on the circumferential Young's modulus, the radial Young's modulus, and the winding tension profile. A calculation process for determining one of the stresses,
Internal stress calculation method with In the calculation step, σ _r that is the radial stress is derived by the following equation derived from a modified haquile considering the entrained air film:

r: winding diameter Et: circumferential Young's modulus Er: calculated by radial Young's modulus
Σ _t , which is the circumferential stress, is derived by the following formula derived from a modified haquile considering the entrained air film:

The internal stress calculation method according to claim 9, which is obtained by: When obtaining the thickness of the entrained air film, the thickness ho of the outermost air layer of the roll is obtained by the following formula 1,


R: radius of roll 10 η: viscosity coefficient of air Vr: rotational speed of roll (linear velocity outside roll)
Vw: Conveying speed of the film to be wound T: Tension value obtained by distributing the tension of the entire film in proportion to the film thickness of the division model for each division model. In order to reduce the outermost air thickness, the thickness ha of the air layer after pressing a part of the outermost web with the force of L in the radial direction over the entire width direction is obtained by the following equation 2.


L: force for pressing the film against the roll W: width of the web roll “film thickness + larger than the thickness of the film having the maximum thickness among the films of the split model when the knurling is also considered as part of the film” When there is no film of another split roll having the value of “air film thickness ha”, the air film thickness h under the film having the maximum film thickness is obtained by the following formula 3A or formula 3B, and the maximum film The film thickness of the air under the film other than the film having the thickness is considered as a rigid body, and the thickness between the film surface generated by the film thickness distribution and the back surface of the film underneath is the thickness of the entrained air film,


σ: Radial stress (calculation result when rolled up to the i-th layer with Hakiel)
σ0: Initial radial stress (calculation result when rolled up to i-1th layer with Hakiel)
Pap: Atmospheric pressure ha: The thickness of the air layer after being pressed with an L force in the radial direction by an air press. After entrainment, the air layer thickness h involved when winding up to the i-1th layer with Hakiel.
Of the other split rolls having a value of “film film thickness + air film thickness ha” larger than the film thickness of the film having the maximum film thickness among the films of the split model when the knurling is also considered as a part of the film When there is a film, the film is considered as a rigid body, and the divided film having the largest “film film thickness + air film thickness ha” of the part other than the knurled part and the film below it have an air film thickness ha. The distance between the surface of each upper film and the back surface of the lower film is the thickness of the entrained air film, or the total cross-sectional area of entrained air in each divided model and the surface of the upper film Find the distance between the upper film surface and the lower film surface so that the cross-sectional area of the gap between the upper film surface and the lower film back surface is the same, and the distance between the upper film surface and the lower film back surface at that time Serial winding the thickness of the air film, the internal stress calculation method according to claim 10.   When determining the thickness of the entrained air film and the film thickness, if the film and the air layer of another division model adjacent to the range of a certain division model enter due to the oscillate, from the other division model The internal stress calculation method according to claim 11, wherein the length of the invading portion and the length of the film and the air layer of the certain division model are proportionally distributed to obtain an equivalent film thickness and an equivalent air film thickness.