JP2010280083A - Calculation method for calculating neck-in width, and calculator - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a calculation method for calculating a neck-in width precisely considering a viscoelastic change of a resin due to thermal deterioration of the resin by extrusion lamination processing or the like. <P>SOLUTION: The calculation method for calculating the neck-in width of the resin extruded by the extrusion processing contains: a visco-elasticity acquisition step of acquiring a viscoelasticity distribution in the widthwise direction in case of extruding the resin from a processing machine 1; a layer ratio calculation step of calculating, based on the viscoelasticity distribution, a layer ratio distribution in the widthwise direction of one layer of a plurality of layers used for modeling the resin by a multi-layer model which has a layer structure including a plurality of layers each showing single viscoelasticity and shows different viscoelasticity depending on the position in the widthwise direction; a modeling step of modeling the resin by the multi-layer model based on the layer ratio; a neck-in calculation step of analyzing the modeled resin by a finite element method and calculating the neck-in width by the analysis; and an output step of outputting the calculated neck-in width. <P>COPYRIGHT: (C)2011,JPO&INPIT

Description

  The present invention relates to a calculation method and a calculation apparatus for calculating a neck-in width. In particular, the present invention relates to a calculation method and a calculation device for calculating a neck-in width in an object extruded from a processing machine by extrusion processing such as extrusion lamination processing and cast film processing.

  When extruding and laminating a thermoplastic resin to a substrate such as a plastic film, aluminum foil, or paper, or when processing a plastic film with a T-die film processing machine, the exit width of the die that extrudes the thermoplastic resin A phenomenon that the coat width of the thermoplastic resin is shortened may occur. Thus, shortening the film width with respect to the die width is called a neck-in phenomenon, and this shortened width is called a neck-in width NI. When the neck-in phenomenon occurs, the product width is limited or the yield is lowered.

  As measures to reduce the film width due to the neck-in phenomenon, there is a method of reflecting the influence of the neck-in phenomenon in the extrusion die design in advance, or a method of adjusting the die width or the air gap by the deckle at the time of extrusion. is there. However, when there are restrictions on the type of thermoplastic resin and the extrusion process conditions, it is difficult to appropriately control the neck-in width NI due to the neck-in phenomenon.

  The reason why it is difficult to appropriately control the width NI of such a neck-in is that as the residence time of the thermoplastic resin that is heat-treated in the processing machine becomes longer, the resin tends to be deteriorated, such as extrusion lamination. In some cases, the resin may deteriorate due to the high temperature conditions. For example, Non-Patent Document 1 describes that the influence of such resin degradation is relatively large. This Non-Patent Document 1 discloses that the viscoelasticity is changed as compared with the unprocessed resin when the resin extruded from the processing machine in the extrusion laminating process is collected and the viscoelasticity is measured. Has been.

Naoki Sato, “Numerical analysis of film cast molding”, “Molding”, Japan Society for Plastic Molding Processing, November 2000, Vol. 12, No. 11, pp. 689-694

  By the way, in order to appropriately control the neck NI width NI, even if the extrusion of the resin is performed with the deterioration of the thermoplastic resin or the like being uniform, due to the structure of the processing machine, for example, the central portion and the end portion of the extrusion die Therefore, the residence time of the resin in the processing machine is inevitably varied. That is, it has been difficult to prevent the viscoelasticity of the resin from changing depending on the position in the width direction of the extrusion die. For example, in extrusion laminating using polyethylene as a thermoplastic resin, the resin may be extruded at a high temperature of 300 to 340 ° C. in order to improve the adhesion between the resin and the substrate. When the resin is actively thermally deteriorated, it is assumed that the variation in viscoelasticity increases.

  On the other hand, the calculation of the neck-in width NI due to the neck-in phenomenon is performed, for example, by analyzing the extruded resin using the finite element method or the like, but differs depending on the position in the width direction as described above. Conventionally, a method of reflecting viscoelasticity in the analysis by the finite element method has not been provided. As a result, although Non-Patent Document 1 discloses that the viscoelasticity changes, there is no suggestion of the application method, and the problem that it is difficult to appropriately calculate the neck-in width NI remains unresolved. Met.

  Therefore, the present invention provides a calculation method and a calculation device for accurately calculating the neck-in width in consideration of changes in viscoelasticity due to thermal degradation of resin in extrusion lamination processing, T-die film processing, and the like. Objective.

  In order to solve the above-mentioned problems, the present inventor has focused on the fact that the subject resin can be applied to the finite element method as long as the target resin is a layer composed of a single viscoelasticity. Then, further considering the layer consisting of this single viscoelasticity, when a plurality of layers consisting of this single viscoelasticity are provided to form a multi-layer model, the viscoelasticity is increased in the width direction by multiplying by a predetermined ratio. It has been found that changing workpieces can be modeled by a multilayer model. Therefore, the present inventor considered a change in viscoelasticity due to thermal degradation of the resin by adopting a multi-layer model in which a single viscoelastic layer applicable to the finite element method is multiplied by a predetermined ratio. The knowledge that the width of in can be calculated was obtained, and the present invention was completed.

  In order to solve the above problem, a calculation method according to the present invention is a calculation method for calculating a neck-in width in an object extruded from a processing machine by extrusion while heating, and the object is removed from the processing machine. Based on the viscoelasticity acquisition step for acquiring the viscoelasticity distribution in the width direction when extruding and the viscoelasticity distribution acquired in the viscoelasticity acquisition step, and having a layer configuration including a plurality of layers showing a single viscoelasticity A layer ratio calculating step for calculating a layer ratio distribution in the width direction of at least one of a plurality of layers used for modeling an object by a multilayer model having different viscoelasticity depending on the position in the width direction; A modeling step for modeling an object to be pushed out from a processing machine by processing using a multilayer model based on the layer ratio calculated in the layer ratio calculation step, and a model in the modeling step Neck-in calculation step of analyzing the target object using the finite element method, calculating a neck-in width in the target object by the analysis, and an output step of outputting the neck-in width calculated in the neck-in calculation step It is characterized by including these.

  Further, the calculation device according to the present invention is a calculation device for calculating the width of the neck-in in the object extruded from the processing machine by extrusion while heating, and the width direction when the object is extruded from the processing machine The viscoelasticity acquisition means for acquiring the viscoelasticity distribution of the material and the viscoelasticity distribution acquired by the viscoelasticity acquisition means have a layer configuration including a plurality of layers exhibiting a single viscoelasticity and at a position in the width direction. A layer ratio calculating means for calculating a layer ratio distribution in the width direction of at least one layer among a plurality of layers used for modeling an object by a multilayer model showing different viscoelasticity, and from a processing machine by extrusion Modeling means for modeling the object to be pushed out by a multilayer model based on the layer ratio calculated by the layer ratio calculation means, and analyzing the object modeled by the modeling means using the finite element method Characterized in that it comprises a neck-calculating means for calculating the width of the neck-in the object by the analysis, and output means for outputting the width of the neck-calculated in neck-calculating means.

  In the calculation method and the calculation apparatus according to the present invention, when an object is modeled by a multilayer model having a layer configuration including a plurality of layers exhibiting a single viscoelasticity and exhibiting different viscoelasticity depending on the position in the width direction. Modeled by a multilayer model based on the layer ratio calculated by the layer ratio calculation step or the layer ratio calculation means based on the viscoelastic distribution in the width direction, taking into account changes in the viscoelasticity in the width direction due to thermal degradation of the resin Thus, analysis by the finite element method can be performed. Therefore, the neck-in width can be calculated with high accuracy. The “width direction” used here is the longitudinal direction of the extrusion port for extruding the object from the processing machine, and is the direction intersecting the extrusion direction for extruding the object.

  Further, in the calculation method according to the present invention, the viscoelasticity acquisition step includes an acquisition step of acquiring thermal behavior information indicating the viscoelasticity change of the target object according to the heating time for the target object, and when extruding the target object. In the residence time calculation step for calculating the residence time distribution in the width direction in which the object stays in the processing machine, and the residence time in the residence time distribution calculated in the residence time calculation step, in the thermal behavior information obtained in the acquisition step It is preferable to include a calculation step of calculating a viscoelastic distribution in the width direction when the object is pushed out of the processing machine by making the heating time correspond. Since the viscoelastic distribution in the width direction is calculated based on the thermal behavior information that affects the change in the viscoelasticity of the object and the residence time distribution in the width direction, it is possible to accurately calculate the viscoelastic distribution in the width direction. it can. As a result, the neck-in width can be calculated more accurately.

  The neck-in calculation method according to the present invention has an effect that the width of the neck-in can be predicted with high accuracy in extrusion processing, particularly extrusion lamination processing.

It is a figure which shows the processing machine used for an extrusion lamination process, (a) is a perspective view, (b) is a side view. It is a figure which shows the function structure of the calculation apparatus which concerns on this embodiment. It is a flowchart which shows the calculation method of the neck in width | variety NI which concerns on this embodiment. It is a figure which shows the heat deterioration behavior of resin. It is a flowchart which shows the calculation method of residence time distribution in a processing machine. It is a figure which shows the finite element mesh used for calculation of the residence time distribution in a processing machine. It is a figure which shows the shear viscosity used for calculation of residence time distribution in a processing machine. It is a figure which shows the residence time distribution in a processing machine according to the position of die exit. It is a figure which shows the relative viscosity distribution in a processing machine according to the position of die exit. It is a figure which shows the layer ratio of the center layer in a multilayer model according to the position of die | dye exit. It is a finite element mesh figure used for neck-in calculation, (a) is a figure at the time of an analysis start, (b) is a figure at the time of the end of analysis. It is a figure which shows the viscoelasticity of the resin of the center layer and end layer in a multilayer model. It is a flowchart which shows the calculation method of the width NI of the neck-in in a comparative example. It is a figure which shows the viscoelasticity of resin in a comparative example.

  Hereinafter, a calculation device and a calculation method of a neck-in width NI according to the present invention will be described in detail with reference to the drawings.

  First, extrusion processing by the extrusion laminating machine 1 and the extrusion laminating machine 1 (hereinafter also referred to as “processing machine 1”) according to the calculation device and the calculation method will be briefly described with reference to FIG. The extrusion laminating machine 1 includes a single screw 2, an extrusion die 3, a nip roll 4, a chill roll 5, and a base material supply roll 6. The uniaxial screw 2 is a part for sending the molten resin to the extrusion die 3 from a melting part (not shown) for melting the resin, and is connected to the central part of the upper surface of the extrusion die 3 in the figure. The extrusion die 3 is a device for extruding the molten resin R sent from a die outlet 3a formed on the lower surface in the figure while maintaining a predetermined heating temperature. In a region facing the die outlet 3a, the nip roll 4 and the chill roll 5 are arranged substantially in parallel in the horizontal direction so that the nip roll 4 and the chill roll 5 are partially in contact with each other so that the nip roll 4 and the chill roll 5 rotate in cooperation. It has become. A base material supply roll 6 for supplying a base material is disposed at a position that is a predetermined distance away from the nip roll 5 in the horizontal direction.

The extrusion lamination machine 1, for example, there are Shigeru Sumitomo Industries Modern, Ltd.-made machine, in this machine, the single screw 2 diameter 65 mm, the outlet width W _D is 600 mm, the gap length H _D is The air gap L between the die outlet 3a and the nip roll 4 / chill roll 5 is 160 mm.

In the processing machine 1 having the above-described configuration, for example, when polyethylene is used as an object, the molten resin R melted at about 320 ° C. in the melting part is extruded from the single screw 2 at an extrusion rate of 60 kg / h. The molten resin R that has been fed out and spreads in the width direction while being heated at about 320 ° C. in the extrusion die 3 and is pushed out from the die outlet 3a. Extruded molten resin R is the nip roll 4 / chill roll 5, for example, Hikito as take-up speed is 120 m / min, the draw ratio is the ratio of the thickness of the resin of the gap length H _D and after take-off of 40 Then, the base material supplied from the base material supply roll 6 is adhered to the base material, and the base material on which the resin R is laminated is obtained. The resin R extruded from the die outlet. 3a, the neck-in phenomenon, as shown in FIG. 1, is reduced from the outlet width W _D of the die with the web width W _F. In this embodiment, a half of the difference of the web width _{W F} of the outlet width _{W D} and nip roll 4 of die _{(W D -W F) / 2} , but the width of the neck-NI (mm), the neck-in The width NI may be defined by another formula.

  Next, the configuration of a calculation device for calculating the neck-in width NI in the extrusion laminating machine 1 described above will be briefly described with reference to FIG. A detailed calculation method by this calculation apparatus will be described later.

  The calculation device 10 is a calculation device that calculates the neck-in width NI of the molten resin extruded from the processing machine 1 by extrusion while heating. Functionally, the calculation device 10 includes a viscoelasticity acquisition unit 11 and a layer ratio calculation unit. 12, a modeling unit 13, a neck-in calculation unit 14, and an output unit 15. Such a computing device 10 is configured from an information processing device such as a workstation or a PC (Personal Computer) in terms of hardware, and the following functions are performed by operating components such as a CPU and a memory. And the detailed calculation method mentioned later by these each function is performed.

The viscoelasticity acquisition unit 11 acquires information on the viscoelasticity distribution η (x) in the width direction when the molten resin is extruded from the processing machine 1. As used herein, "width direction" means a longitudinal direction of the die outlet 3a extruding molten resin from machine 1 (the direction of the outlet width W _D), perpendicular to the extrusion direction of extruding the molten resin. In this embodiment, the shear viscosity is used as information indicating the viscoelasticity acquired by the viscoelasticity acquisition unit 11, but the information indicating the viscoelasticity is not limited to this.

  The layer ratio calculation unit 12 is based on the information on the viscoelasticity distribution η (x) in the width direction acquired by the viscoelasticity acquisition unit 11, and at least of a plurality of layers used for modeling the molten resin by a multilayer model. A layer ratio distribution h (x) in the width direction of one layer is calculated. This multi-layer model has a layer configuration (for example, a two-layer configuration) including a plurality of layers each having a different single viscoelasticity, and by changing the thickness of each layer according to the position in the width direction, The viscoelasticity varies depending on the position. In other words, in the analysis by the finite element method, it is difficult to directly change the viscoelasticity of the molten resin according to the position in the width direction as a parameter, but the change in the viscoelasticity according to the position in the width direction is a virtual layer configuration. By replacing it with a change in the thickness of each layer, it can be used as a parameter. As a result, a change in viscoelasticity according to the position in the width direction can be taken into the analysis by the finite element method.

  The “layer ratio” used here is a ratio coefficient for increasing or decreasing the thickness of each layer for replacing the above-described change in viscoelasticity, and is represented by a value between 0 and 1, for example (see FIG. 10). . The layer ratio distribution h (x) is a distribution in which this layer ratio is indicated according to the position in the width direction, and corresponds to a change in viscoelasticity according to the position in the width direction.

  The modeling unit 13 models the molten resin extruded from the processing machine 1 by extrusion processing using a multilayer model based on the layer ratio distribution h (x) calculated by the layer ratio calculation unit 12. The neck-in calculation unit 14 analyzes the object modeled by the modeling unit 13 using a finite element method, and calculates the neck-in width NI in the molten resin by the analysis. The output means 15 outputs the neck-in width NI calculated by the neck-in calculator 14.

  Next, a method of calculating the neck-in width NI by the calculation apparatus 10 having the above-described configurations will be described with reference to FIG. In this embodiment, as described above, the neck-in width NI can be accurately calculated by adopting a calculation method that takes into account a change in viscoelasticity due to thermal degradation of the resin. .

  First, the viscoelasticity acquisition unit 11 acquires thermal behavior information indicating the thermal degradation behavior of the target resin used for extrusion (acquisition step, step S01). The thermal behavior information is information indicating a change in viscoelasticity of the resin according to the heating time for the resin, for example, data indicating the relationship between the heating time and the relative viscosity as shown in FIG. This thermal behavior information is obtained, for example, by performing the following measurement in advance, and the obtained measurement result is input to the calculation device 10 by the user and stored in the storage unit or the like of the calculation device 10. It is like that.

  In order to obtain thermal behavior information, for example, a capillary type rheometer (Toyo Seiki Co., Ltd., Capillograph II) is used as a measurement device, the measurement temperature is 320 ° C., which is the processing temperature, the capillary length is 40 mm, the diameter is 1 mm, The thermal degradation behavior of the target resin is measured under measurement conditions such that the inflow angle from the reservoir to the capillary is 90 °. As the resin to be measured, for example, unprocessed low-density polyethylene (manufactured by Sumitomo Chemical Co., Ltd., trade name: Sumikasen CE4009) is used.

この式（１）に示されるように、計算装置１０に入力されて記憶部に記憶されている熱挙動情報は、二次関数で示される情報となる。また、粘弾性取得部１１が、相対粘度と経過時間との複数のデータを入力して、最小二乗法により、上記の式のパラメータを求めてもよい。なお、図４に、低密度ポリエチレンの相対粘度η_ｒ（ｔ）と式（１）で回帰される曲線とを示す。粘弾性取得部１１によって取得されて計算装置１０に記憶される情報は、他の機能部からも利用可能である（以降の情報についても同様である）。ステップＳ０１における対象樹脂の熱挙動情報の取得が終了したら、ステップＳ０２に進む。 As a measurement procedure, first, the above-described resin is filled in a rheometer reservoir and then preheated for 5 minutes. Then, the shear viscosity η is measured at a shear rate of 60.8 s ^{−1 with} the time after the completion of preheating as the measurement start time. Thereafter, the resin is left in the rheometer, and the shear viscosity η is measured at intervals of 30 minutes. In this way, the change with time of the shear viscosity η is measured. Here, the shear viscosity at time 0 (that is, equivalent to the shear viscosity of the unprocessed resin) is converted to a relative viscosity η _r with a reference value of 1 to obtain a relative viscosity η _r (t) indicating a change with time. Here, t represents time (s). What approximated the obtained relative viscosity (eta) _r (t) by the least squares method is shown to following formula (1).

As shown in the equation (1), the thermal behavior information input to the calculation device 10 and stored in the storage unit is information indicated by a quadratic function. Moreover, the viscoelasticity acquisition part 11 may obtain | require the parameter of said formula by the least square method by inputting the some data of relative viscosity and elapsed time. FIG. 4 shows the relative viscosity η _r (t) of the low density polyethylene and the curve regressed by the equation (1). Information acquired by the viscoelasticity acquisition unit 11 and stored in the calculation device 10 can be used from other functional units (the same applies to the subsequent information). When the acquisition of the thermal behavior information of the target resin in step S01 is completed, the process proceeds to step S02.

Subsequently, the viscoelasticity acquisition unit 11 calculates data of the residence time distribution t _R (x) in the width direction at the outlet of the processing machine 1 (extrusion die 3) (residence time calculation step, step S02). The residence time is the time that the molten resin stays in the processing machine 1 (extrusion die 3) when the molten resin is extruded. As shown in FIG. 5, the calculation of the residence time distribution t _R (x) in step S02 is as follows. First, in step S11, a finite element mesh is created by the same technique as in the prior art, and then in step S12. Create a data file for flow analysis in the processing machine 1 (extrusion die 3), and finally calculate the flow state in the processing machine 1 (extrusion die 3) based on the set conditions in step S13. Data of residence time distribution t _R (x) in the machine is obtained. Details will be described below. Note that information and software necessary for performing the flow analysis are stored in advance in the calculation device 10 by the user's input or the like with the following contents (the following functions are also performed by each function of the present embodiment). The same applies except for the calculated information).

First, in step S11, a finite element mesh is created. For example, modeling software Gambit version 2.4.6 (manufactured by ANSYS Inc.) is used to create the mesh. Specifically, from the tip of the single screw 2 of the extrusion laminating machine 1 to the exit of the extrusion die 3 is modeled. In consideration of symmetry in the width direction and the thickness direction, it is preferable to use a ¼ model in which the configurations in the width direction and the thickness direction are each halved. In addition, as this 1/4 model, there exists a model as shown in FIG. 6, for example, and it is displayed on the display part etc. of the calculation apparatus 10. FIG. In the 1/4 model shown in FIG. 6, the adapter pipe (Adapter) from the tip of the single screw 2 to the extrusion die 3 has a diameter of 20 mm and a length of 600 mm, and the extrusion die 3 (Die) has a length. 125 mm, the outlet width _{W D1} is 300 mm, the gap length _{H D} is a 0.4 mm.

After the finite element mesh is created in step S11, a data file for flow analysis in the processing machine 1 is created (step S12). For creating the data file, for example, heat flow analysis software Polyflow version 3.11.0 (manufactured by ANSYS Inc.) based on the finite element method is used. First, the following boundary conditions are set. The boundary condition is input and stored in the calculation device 1 in advance.
Boundary 1: Corresponds to the inlet (Inlet) of the processing machine. As the flow rate corresponding to the resin extrusion rate of 60 kg / h, 5447 mm ³ / s is given. The temperature is 320 ° C.
Boundary 2: Corresponds to the die outlet. At this boundary, the condition of the fully developed flow of resin is given.
Boundary 3: Corresponds to a wall surface (Die right end surface in FIG. 6). At this boundary, a speed of 0 m / s is given. The temperature is 320 ° C.
Boundary 4: Corresponds to a symmetry plane (Die left end face in FIG. 6). At this boundary, 0 m / s is given as the speed in the width direction, and 0 Pa is given as the stress in the take-up direction, and heat insulation conditions are established.

ここで、η_∞は第二Ｎｅｗｔｏｎ粘度を、η_０はゼロせん断粘度を、λは特性時間を、上にドットが付いたγはせん断速度を，ａおよびｎはモデルパラメータをそれぞれ表す。η_∞には０Ｐａ・ｓ、η_０には２８．８５Ｐａ・ｓ、λには０．２７５５ｓ、ａには０．３２８３６、ｎには０．１０９６がそれぞれ設定されている。 The resin used for the analysis is treated as a viscous fluid, and a Carreau-Yasuda model (hereinafter referred to as “CY model”) is used as a flow model. The CY model is stored in advance in the storage unit of the calculation apparatus 10. The CY model is shown in Formula (2).

Here, η _∞ represents the second Newton viscosity, η ₀ represents the zero shear viscosity, λ represents the characteristic time, γ with a dot above represents the shear rate, and a and n represent the model parameters. eta 0 Pa · s to _∞, eta ₀ The 28.85Pa · s, the λ 0.2755s, in a 0.32836, .1096 is set respectively to n.

ここで、Ｔは温度を、Ｔ_αは基準温度を、αは温度依存パラメータをそれぞれ表す。αには０．０２８８、Ｔ_αには１３０℃がそれぞれ与えられている。このような、式（２）、（３）によって特定される低密度ポリエチレンの３２０℃におけるＣＹモデルのせん断粘度データ（図７参照）は、計算装置１０の記憶部に予め記憶されている。 As the temperature dependency of the CY model, an Arrheniusapproximate shear stress model shown in Expression (3) is used. This model is also stored in advance.

Here, T represents a temperature, T _α represents a reference temperature, and α represents a temperature dependent parameter. α is 0.0288, and T _α is 130 ° C. Such shear viscosity data (see FIG. 7) of the CY model at 320 ° C. of the low density polyethylene specified by the equations (2) and (3) is stored in advance in the storage unit of the calculation device 10.

Finally, calculation is performed using the above-described Polyflow version 3.11.0 (step S13). A finite element mesh shown in FIG. 6 is used for the calculation by the viscoelasticity acquisition unit 11. The boundary conditions 1 to 4 are given as boundary conditions. As the resin data, the CY model shown in the formula (1) is used. As the temperature dependency of the resin viscosity, an Arrhenius appreciate shear stress model shown in Formula (2) is used. Under these conditions, calculation is performed using the same method as in the prior art. Then, from the residence time in the processing machine 1 (extrusion die 3) obtained by this calculation, data of the residence time distribution t _R (x) in the width direction at the outlet of the extrusion die 3 is calculated. FIG. 8 shows data of the residence time distribution t _R (x) calculated in this way. The data of the residence time distribution t _R (x) is a set of data indicating the residence time of the resin according to the position in the width direction of the die width (for example, the position at intervals of about 0.02 m). In the data of the residence time distribution t _R (x), x represents a coordinate in the width direction, and the die center is the origin of x. Thereby, calculation of the data of the residence time distribution t _R (x) in the processing machine 1 (extrusion die 3) in step S02 ends, and the process proceeds to step S03.

Subsequently, the viscoelasticity acquisition unit 11 calculates the viscosity distribution of the die outlet 3a (calculation step, step S03). Specifically, the viscoelasticity acquisition unit 11 retains the die outlet 3a obtained in step S02 in the width direction with respect to the equation (1) indicating the relative viscosity η _r (t) obtained in step S01. Substituting the time distribution t _R (x), a relative viscosity distribution η _r (x) in the width direction of the extrusion die 3 is obtained. The obtained relative viscosity distribution η _r (x) is shown in FIG. When the calculation of the viscosity distribution at the die outlet 3a is completed in step S03, the process proceeds to step S04.

ここで、層比ｈ_Ｃ（ｘ）は中央側から押出された樹脂からなる層（中央層）の層比の幅方向分布を、η_ｒＣは中央層の未加工樹脂に対する相対粘度を、η_ｒEは端側から押出された樹脂からなる層（以下、「端層」と略する。）の未加工樹脂に対する相対粘度を、それぞれ表す。具体的には、η_ｒＣは、図９におけるダイ中央での滞留時間ｔ_ＲＣに相当する、図４における相対粘度η_ｒを表す。またη_ｒＥは、図８においてダイ端部側の幅５０ｍｍの範囲で平均した滞留時間ｔ_ＲＥに相当する、図４における相対せん断粘度η_ｒを表す。層比算出部１２は、式（４）を用いて、中央層の層比分布ｈ_Ｃ（ｘ）を式（５）より求める。ここで、幅方向分布η_ＭＬ（ｘ）を、ステップＳ０３で取得された相対粘度分布η_ｒ（ｘ）の値とし、ダイ幅の幅方向の位置（上述した一定間隔の位置と同様）毎に層比分布ｈ_Ｃ（ｘ）を求める。

このようにステップＳ０４で得られた、中央層の幅方向への層比分布ｈ_Ｃ（ｘ）のデータを図１０に示す。ステップＳ０４で中央層の幅方向への層比ｈ_Ｃ（ｘ）が算出されたら、ネックインの幅ＮＩの計算の準備段階が終了し、ネックインの幅ＮＩを算出するステップＳ０５以降に進む。 Subsequently, the layer ratio calculation unit 12 is based on the information on the relative viscosity distribution η _r (x) in the width direction acquired in step S03, and among the plurality of layers used to model the molten resin using a multilayer model. A layer ratio distribution h (x) in the width direction of at least one layer is calculated (layer ratio calculating step, step S04). As described above, the multi-layer model used here has a layer structure (for example, a two-layer structure) including a plurality of layers each having a different single viscoelasticity, and the thickness of each layer is changed according to the position in the width direction. Thus, different viscoelasticity is exhibited depending on the position in the width direction. In the present embodiment, for example, the multilayer model is set to include two layers (referred to as “center layer” and “end layer”, respectively) extruded from the center and end of the extrusion die 3. In step S04, specifically, using the relative viscosity distribution η _r (x) in the width direction of the extrusion die 3, the width direction distribution η _ML (x) of the relative shear viscosity of the multilayer model is _expressed by Equation (4). To represent. This equation (4) is stored in the storage unit of the computing device 10.

Here, the layer ratio h _C (x) is the width direction distribution of the layer ratio of the resin (center layer) made of resin extruded from the center side, η _rC is the relative viscosity of the center layer with respect to the raw resin, η _rE Represents the relative viscosity of the layer made of resin extruded from the end side (hereinafter abbreviated as “end layer”) with respect to the raw resin. Specifically, η _rC represents the relative viscosity η _r in FIG. 4 corresponding to the residence time t _RC at the die center in FIG. Further, η _rE represents the relative shear viscosity η _r in FIG. 4 corresponding to the residence time t _RE averaged in the range of the width of 50 mm on the die end side in FIG. Layer ratio calculation unit 12, using equation (4), a layer ratio of the middle layer distribution _h C (x) is obtained from equation (5). Here, the width direction distribution η _ML (x) is set as the value of the relative viscosity distribution η _r (x) obtained in step S03, and the position in the width direction of the die width (similar to the above-described fixed interval positions) The layer ratio distribution h _C (x) is obtained.

The data of the layer ratio distribution h _C (x) in the width direction of the central layer obtained in step S04 is shown in FIG. When the layer ratio h _C (x) in the width direction of the central layer is calculated in step S04, the preparation stage for calculating the neck-in width NI is completed, and the process proceeds to step S05 and subsequent steps for calculating the neck-in width NI.

Subsequently, the modeling unit 13 models the molten resin extruded from the processing machine 1 by extrusion using a multilayer model based on the layer ratio distribution h _C (x) calculated in step S04 (modeling step, step S05). Specifically, in step S05, the web in the air gap is first modeled and a finite element mesh is created using conventional methods. For creating the mesh, modeling software Gambit version 2.4.6 (manufactured by ANSYS Inc.) is used. A quasi-three-dimensional model is used in which changes in physical quantities in the web thickness direction are averaged. In consideration of symmetry in the width direction, a ½ model in which the configuration in the width direction is halved is used. The above finite element mesh is shown in FIG. Outlet width _{W D} is 600 mm, the gap length _{H D} of the extrusion die 3 of the extrusion die 3 is 0.8 mm, the air gap L is set to 160 mm. Although an analysis method will be described later, the finite element mesh is repeatedly calculated and transformed into the model shown in FIG. 11A shows a finite element mesh in an initial calculation state, and FIG. 11B shows a finite element mesh after deformation. The origin (X = 0, Y = 0) corresponds to the central portion of the die outlet 3 a of the Oshida die 3.

Subsequently, a data file for extrusion processing analysis is created (modeling step, step S06). For the calculation, heat flow analysis software Polyflow version 3.11.0 (manufactured by ANSYS Inc.) based on the finite element method is used. The following boundary conditions are set.
Boundary 1: Corresponds to the die exit (line along the Y axis where X = 0, Inlet). 0.05 m / s as the take-up direction velocity _{V n,} 0 m / s is the width direction velocity _{V t,} 320 ° C. as the temperature T is, the gap length _H D 0.8 mm are respectively given as thickness H.
Boundary 2: Corresponds to the edge of the web (Free Surface). Treated as free surface, 0 m / s as the normal direction velocity _{V n,} 0 Pa as the normal direction stress _{F n} is, also, adiabatic conditions are given, respectively.
Boundary 3: Corresponds to a position (Outlet) where the web is taken up by the chill roll 4 and the nip roll 5. The heat insulation condition is given as 2 m / s as the take-up direction speed V _{n and 0} Pa as the width direction stress F _t .
Boundary 4: Corresponds to an axis of symmetry in the web width direction. The heat insulation condition is given as 0 m / s as the width direction velocity V _n and 0 Pa as the take-up direction stress F _t . Further, a heat flow rate f = 60 W / (mK2) is given on the web surface.

ここで、ηは粘度を、τは異方性応力テンソルを、Ｄは変形速度テンソルを、λは緩和時間を、ξ及びεは非線形パラメータを表す。△はｌｏｗｅｒ−ｃｏｎｖｅｃｔｅｄ時間微分を、▽はｕｐｐｅｒ−ｃｏｎｖｅｃｔｅｄ時間微分をそれぞれ表す。本実施形態で用いた中央層のＰＴＴモデルのパラメータを表１に、端層のパラメータを表２にそれぞれ示す。これらのパラメータも記憶部に記憶されている。

In this embodiment, the resin used for analysis is treated as a viscoelastic fluid. A Phan-Thien / Tanner model (hereinafter referred to as “PTT model”) is used as the viscoelastic model. The PTT model is described in, for example, Phan-Thien, Journalof Rheology, Vol. 22, pp. 259-283 (1978). A PTT model is shown in Formula (6). This model is stored in the storage unit.

Here, η represents viscosity, τ represents anisotropic stress tensor, D represents deformation rate tensor, λ represents relaxation time, and ξ and ε represent nonlinear parameters. Δ represents a lower-connected time derivative, and ▽ represents an upper-connected time derivative. Table 1 shows parameters of the PTT model of the central layer used in this embodiment, and Table 2 shows parameters of the end layer. These parameters are also stored in the storage unit.

ここで、Ｔは温度を、Ｔ_０は摂氏温度の絶対温度への換算値を、Ｔ_αは基準温度を、αは温度依存パラメータをそれぞれ表す。本実施形態では、Ｔ_αとして１３０℃が、αとして６０００がそれぞれ与えられている。本ステップＳ０６で得られる、１３０℃におけるＰＴＴモデルの粘弾性データを実線及び点線で図１２に示す。物性値として、密度ｄ＝７３５ｋｇ／ｍ^３、熱伝導度ｋ＝０．１５Ｗ／ｍ・Ｋ、比熱Ｃ_ｐ＝３０００Ｊ／（ｋｇ・℃）が中央層、端層に設定されている。

Here, T represents a temperature, T ₀ represents a converted value of Celsius to an absolute temperature, T _α represents a reference temperature, and α represents a temperature-dependent parameter. In this embodiment, 130 ° C. is given as T _{α and} 6000 is given as α. The viscoelasticity data of the PTT model at 130 ° C. obtained in step S06 is shown in FIG. 12 as a solid line and a dotted line. As physical properties, density d = 735 kg / m ³ , thermal conductivity k = 0.15 W / m · K, specific heat C _p = 3000 J / (kg · ° C.) are set in the center layer and the end layer.

  In addition, as acquired viscoelasticity data, in addition to the data based on the above-described formula (7), actual measurement is performed in advance as shown below, and these measurement values are stored in the storage unit. Such measured values are shown, for example, as plotted data in FIG.

  As such an actual measurement method, first, the extrusion resin is recovered in the extrusion processing by the extrusion laminating machine 1. The processing conditions are the same as those described above. Under these processing conditions, the molten resin is extruded and coated on a PET film. The coated low density polyethylene is recovered by peeling the center of the die 5 cm wide and both ends of the die 3 cm apart. Next, the measurement of viscoelasticity in the molten state of the resin recovered after extrusion from the extrusion laminating machine 1 is performed. In order to prevent oxidation, 10,000 ppm of dibutylhydroxytoluene is added to the recovered resin, and then hot pressed at a temperature of 150 ° C. to prepare a sheet. The obtained sheet is cut into pellets and subjected to viscoelasticity measurement.

  In this viscoelasticity measurement, a complex viscosity η *, storage elastic modulus G ′, and loss elastic modulus G ″ are measured using a rotary rheometer (TA Instruments, ARES). A parallel disk having a diameter of 25 mm is used as the fixture of the sample. Viscoelasticity is measured at a temperature of 130 to 190 ° C. and an angular frequency of 0.01 to 100 rad / s. The obtained viscoelasticity is used by converting the angular frequency into a shear rate in accordance with Cox-Merz's rule of thumb. A capillary rheometer (Bohlin, Flowmaster RH7) is used for measurement of uniaxial elongational viscosity. FIG. 12 shows viscoelasticity data at 130 ° C. of low-density polyethylene obtained by such actual measurement. As is apparent from FIG. 12, the actual measurement value and the calculated value are substantially the same. In each of the following steps, for example, calculation is performed using the actual measurement value.

Subsequently, when viscoelastic data of the PTT model at 130 ° C. is obtained, the layer configuration of the multilayer model is set (modeling step). In this embodiment, as described above, the number of layers is set such that the center layer and the end layer are set for each finite element mesh, and the PTT model and the Arrhenius model of the center layer are set on one layer. Parameters, physical properties and thickness are set. The thickness distribution in the width direction of the central layer in the finite element mesh is obtained by multiplying 0.8 mm of the total thickness according to the position in the width direction by the layer ratio distribution h _C (x) in the width direction obtained in step S04. The obtained thickness distribution is set. In the other layer, parameters, physical properties and thicknesses of the PTT model and the Arrhenius model of the end layer are set. As the thickness distribution in the width direction of the end layer in the finite element mesh, a thickness distribution obtained by subtracting the thickness of the central layer from 0.8 mm of the total thickness is set according to the position in the width direction. That is, in each finite element mesh, information (such as the physical property value and thickness described above) associated with each layer is associated. In this way, the viscoelastic distribution in the width direction at the die exit due to the viscoelastic change in the flow in the extrusion die is expressed by a multilayer model including a plurality of layers having a single viscoelasticity. Thereby, in the analysis using the finite element method, it is possible to consider the influence of the viscoelastic distribution on the neck-in. In this way, when the creation of the data file for extrusion processing analysis (step S06) is completed, the process proceeds to step S07.

Subsequently, the neck-in calculating unit 14 analyzes the molten resin modeled in Steps S05 and 06 using the finite element method, and calculates the neck-in width in the molten resin by the analysis (neck-in calculating step, Step S07). Specifically, calculation is performed using the finite element mesh shown in FIG. 11 by the above-mentioned Polyflow version 3.11.0. As the boundary conditions, the conditions of boundaries 1 to 4 in step S06 are given. Further, as the resin data, a stored PTT model shown in Expression (6) is used. The values shown in Table 1 are given as parameters of the PTT model. As the temperature dependency of the resin, an Arrhenius model shown in Equation (7) is used. Moreover, the said physical-property value is given as a physical-property value of resin. Using these finite element meshes and resin data, finite element calculation is performed by the same analysis method under the given boundary conditions. Calculating initial, as the take-up speed V _n at the interface 3, the boundary 1 the same value is given and, repeating the calculation is performed while increasing the value of the take-up speed V _n of the boundary 3. The finite element mesh is deformed so as to satisfy the boundary condition every time the calculation is repeated, so that a final web shape as shown in FIG. 11B is obtained. By performing such an analysis, the speed, stress, temperature, and thickness in the web are obtained. Further, the neck-in width NI is calculated from the finite element mesh shape.

  When the neck-in width NI is calculated in step S07, the output unit 15 displays and outputs the calculated neck-in width NI (output step, step S08).

  As described above, according to the present embodiment, when a molten resin is modeled by a multilayer model having a layer configuration including two layers showing a single viscoelasticity and showing different viscoelasticity according to the position in the width direction, Modeled by a multilayer model based on the layer ratio distribution h (x) calculated in the layer ratio calculation step based on the viscoelastic distribution in the width direction, taking into account changes in the viscoelasticity in the width direction due to thermal degradation of the resin. Thus, analysis by the finite element method can be performed. Therefore, the neck-in width NI can be accurately calculated.

  In the present embodiment, when acquiring the viscoelastic distribution in the width direction, an acquisition step of acquiring thermal behavior information indicating a change in the viscoelasticity of the resin according to the heating time for the resin, and a resin when extruding the resin In the thermal behavior information acquired in the acquisition step with respect to the residence time in the residence time distribution step calculated in the residence time calculation step and the residence time distribution step calculated in the residence time calculation step. By making the heating time correspond, a calculation step for calculating the viscoelastic distribution in the width direction when the resin is extruded from the processing machine 1 is performed. In this way, the viscoelastic distribution in the width direction is calculated based on the thermal behavior information that affects the change in the viscoelasticity of the resin and the residence time distribution in the width direction, so the viscoelastic distribution in the width direction is accurately calculated. can do. As a result, the neck-in width can be calculated more accurately. Of course, the viscoelastic distribution in the width direction may be measured in advance and stored in the storage unit, and when the above calculation is performed, the stored viscoelastic distribution may be recalled and used.

  Examples will be shown below, and the embodiments of the present invention will be described in more detail. Of course, the present invention is not limited to the following examples, and it goes without saying that various aspects are possible in detail. Further, the present invention is not limited to the above-described embodiments, and various modifications can be made within the scope shown in the claims, and the present invention is also applied to the embodiments obtained by appropriately combining the disclosed technical means. It is included in the technical scope of the invention. Moreover, all the literatures described in this specification are used as reference.

[Example 1]
As Example 1, the neck-in width NI was calculated by the calculation method performed by the calculation device 10 based on the conditions described in the above-described embodiment. Table 4 shows the calculation results.

[Example 2]
A finite element mesh was prepared by changing the air gap L in Example 1 to 190 mm, and the calculation was performed by the calculation device 10 in the same manner as in Example 1. Table 4 shows the neck-in width NI of Example 2 obtained by the above calculation.

Example 3
A finite element mesh was prepared by changing the air gap L in Example 1 to 220 mm, and the calculation was performed by the calculation device 10 in the same manner as in Example 1. Table 4 shows the neck-in width NI of Example 3 obtained by the above calculation.

[Comparative Example 1]
Next, calculation of the neck-in width NI according to the comparative example will be described. First, the calculation procedure in the comparative example will be described with reference to FIG. In this calculation method, first, in step S21, the viscoelasticity of the resin used for extrusion processing in an unprocessed state is measured. And the viscoelasticity of the unprocessed low density polyethylene CE4009 was measured. FIG. 14 shows viscoelasticity data of low-density polyethylene at 130 ° C. together with prediction of viscoelasticity by a PTT model described later.

Then, the web in an air gap was modeled and the finite element mesh was created (step S22). Modeling software Gambit version 2.4.6 (manufactured by ANSYS Inc.) was used to create the mesh. Specifically, a pseudo three-dimensional model in which changes in physical quantities in the web thickness direction were averaged was used. In consideration of symmetry in the width direction, the 1/2 model was used. The above finite element mesh is shown in FIG. 11 together with the boundary conditions described later (note that the boundary conditions are the same as in the embodiment). 600mm outlet width _{W D} of the extrusion die 3, extruded 0.8mm gap length _{H D} of the die 3, and the air gap L and 160 mm. Thereafter, the finite element mesh was repeatedly calculated and deformed at a predetermined cycle.

Then, it progressed to step S23 and the data file for extrusion process analysis was created. For the calculation, heat flow analysis software Polyflow version 3.11.0 (manufactured by ANSYS Inc.) based on the finite element method was used. Next, the following boundary conditions were set.
Boundary 1: Corresponds to the die exit. The 0.05 m / s as a take-up direction velocity _{V n,} a 0 m / s the width direction velocity _{V t,} the 320 ° C. as the temperature T, gave respectively the gap length _H D 0.8 mm The thickness H.
Boundary 2: corresponds to the edge of the web. Treated as free surface, a 0 m / s in the normal direction velocity _{V n,} the 0Pa the normal direction stress _{V n,} also gave adiabatic conditions, respectively.
Boundary 3: Corresponds to a position where the web is taken up by the chill roll 4 and the nip roll 5. Adiabatic conditions were given as 2 m / s as the take-up direction speed V _n , 0 Pa as the width direction stress F _t , respectively.
Boundary 4: Corresponds to a symmetrical line in the web width direction. The 0 m / s the width direction velocity _{V n,} the 0Pa as take-up direction stress _{F t,} gave adiabatic conditions, respectively. Further, a heat flow rate f = 60 W / (mK2) was applied to the web surface.

A PTT model was used as a viscoelastic model. Table 3 shows the parameters of the PTT model used in Comparative Example 1.

As the temperature dependence of the PTT model, the Arrhenius model was used. In Comparative Example 1, 130 ° C. was given as T _{α and} 6000 was given as α. FIG. 14 shows the viscoelasticity data of the PTT model at 130 ° C. obtained in step S41. The physical properties were set as follows: density d = 735 kg / m ³ , thermal conductivity k = 0.15 W / m · K, specific heat Cp = 3000 J / (kg · ° C.).

  Finally, calculation was performed using the above-mentioned Polyflow version 3.11.0 (step S24). A finite element mesh shown in FIG. 11 was used. The boundary conditions 1 to 4 were given as boundary conditions. Moreover, the PTT model shown in Formula (6) was used as resin data. As the parameters of the PTT model, the values at 130 ° C. shown in Table 3 were given. As the temperature dependency of the resin, the Arrhenius model shown in the equation (7) was used. Moreover, the said physical-property value was given as a physical-property value of resin. Using these finite element meshes and resin data, finite element calculations were performed under given boundary conditions. At the beginning of the calculation, the same value as the boundary 1 was given as the take-up speed at the boundary 3. The calculation was repeatedly performed while gradually increasing the value of the take-up speed at the boundary 3. The finite element mesh was deformed to satisfy the boundary condition every time the calculation was repeated, and the final web shape was obtained. By executing such an analysis, the neck-in width NI according to the comparative example is calculated.

  Table 4 shows the neck-in NI of Comparative Example 1 obtained by the above calculation.

[Comparative Example 2]
A finite element mesh was prepared by changing the air gap L in Comparative Example 1 to 190 mm, and calculation was performed in the same manner as in Comparative Example 1. Table 4 shows the neck-in NI of Comparative Example 2 obtained by the above calculation.

[Comparative Example 3]
A finite element mesh was prepared by changing the air gap in Comparative Example 2 to 220 mm, and the same calculation as in Comparative Example 1 was performed. Table 4 shows the neck-in NI of Comparative Example 3 obtained by the above calculation.

  As is apparent from Table 4 described above, according to Examples 1 to 3, the neck-in width NI was able to be calculated with higher accuracy than Comparative Examples 1 to 3 in which changes in viscoelasticity were not taken into account.

Since the predicted value of neck-in in extrusion processing using the calculation method according to the present invention is high in accuracy, it can be suitably applied to extrusion lamination processing and the like.

Claims (3)

A calculation method for calculating a neck-in width in an object extruded from a processing machine by extrusion while heating,
A viscoelasticity acquisition step of acquiring a viscoelasticity distribution in the width direction when extruding the object from the processing machine;
Based on the viscoelastic distribution acquired in the viscoelastic acquisition step, the multilayer model has a layer configuration including a plurality of layers exhibiting a single viscoelasticity and exhibits different viscoelasticity according to the position in the width direction. A layer ratio calculating step of calculating a layer ratio distribution in a width direction of at least one of the plurality of layers used for modeling the object;
A modeling step of modeling the object to be extruded from the processing machine by extrusion processing using the multilayer model based on the layer ratio calculated in the layer ratio calculation step;
Neck-in calculating step of analyzing the object modeled in the modeling step using a finite element method, and calculating a neck-in width in the object by the analysis;
An output step of outputting the width of the neck-in calculated in the neck-in calculation step;
A method for calculating the width of a neck-in, characterized by comprising: The viscoelastic acquisition step includes
An acquisition step of acquiring thermal behavior information indicating a change in viscoelasticity of the object according to a heating time for the object;
A residence time calculating step for calculating a residence time distribution in the width direction in which the object stays in the processing machine when the object is extruded; and
When the object is pushed out from the processing machine by associating the heating time in the thermal behavior information acquired in the acquisition step with the residence time in the residence time distribution calculated in the residence time calculation step. A calculation step of calculating a viscoelastic distribution in the width direction of
The neck-in width calculation method according to claim 1, wherein: A calculation device for calculating a neck-in width in an object extruded from a processing machine by extrusion while heating,
Viscoelasticity acquisition means for acquiring a viscoelasticity distribution in the width direction when extruding the object from the processing machine;
Based on the viscoelastic distribution acquired by the viscoelastic acquisition means, a multilayer model having a layer configuration including a plurality of layers exhibiting a single viscoelasticity and exhibiting different viscoelasticity depending on the position in the width direction. A layer ratio calculating means for calculating a layer ratio distribution in the width direction of at least one of the plurality of layers used for modeling the object;
Modeling means for modeling the object to be extruded from the processing machine by extrusion processing by the multilayer model based on the layer ratio calculated by the layer ratio calculation means;
Neck-in calculation means for analyzing the object modeled by the modeling means using a finite element method, and calculating a neck-in width in the object by the analysis;
Output means for outputting a width of the neck-in calculated by the neck-in calculating means;
A computing device comprising:

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