JP6930392B2 - Viscoelastic conduit design method, design program, and evaluation method - Google Patents

Description

The present invention relates to a method for designing a viscoelastic body conduit, a design program, and an evaluation method.

Conventionally, the behavior of a viscoelastic body has been simulated, and the conduit of the viscoelastic body has been evaluated based on the result. Evaluation based on such a simulation is mainly useful for the design of an industrial machine having a viscoelastic body conduit. A viscoelastic body is an object having both properties of an elastic body and a viscous body, and a polymer material is typical. A more specific example is rubber before vulcanization.

For example, Patent Document 1 discloses that the cross-sectional shape of a flow path such as a mouthpiece used for extrusion molding of unvulcanized rubber is efficiently designed based on the flow simulation result of a viscoelastic body. More specifically, Patent Document 1 discloses that the design is made so as to reduce the velocity gradient of the viscoelastic body in the flow path. Further, Patent Document 2 discloses an analysis of behavior when a plastic material such as rubber or resin before cross-linking is kneaded with a Banbury mixer or the like.

Patent No. 5946627 Patent No. 5564074

However, as in Patent Document 1, there is a possibility that the processing accuracy of extrusion molding or the like cannot be sufficiently improved only by the approach of reducing the velocity gradient. Therefore, there has been a demand for a method for designing a viscoelastic material, which can analyze the viscoelastic material more quantitatively and form a viscoelastic material into a desired shape.

The present invention has been made to solve the above problems, and is used to design a viscoelastic body conduit, a design program, and a conduit for forming a viscoelastic body into a desired shape with higher accuracy. An evaluation method is provided.

The method for designing a pipeline according to the first aspect of the present invention is a method for designing a pipeline through which a viscoelastic body flows, and includes the following steps.
(1) Step of setting the initial shape of the inner wall surface of the pipeline (2) Step of modeling the viscoelastic body as a fluid (3) Step of dividing the flow path defined by the inner wall surface into predetermined elements (4) Steps for setting boundary conditions in the inner wall surface, the inlet cross section and the outlet cross section defined by the inner wall surface (5) Steps for setting initial values of physical quantities including the velocity and pressure of the fluid in each element (5) 6) Step of calculating the physical quantity of the fluid in each of the elements (7) Step of generating a plurality of streamlines or trace lines in the flow path (8) Along each of the streamlines or trace lines Step to calculate the cumulative extension strain Ε, which indicates the degree of elongation deformation received by the viscoelastic body flowing in from the inlet cross section until it flows out from the outlet cross section, based on the calculated physical quantity (9). Alternatively, a step of calculating the distribution of the cumulative viscoelastic strain Ε in the vicinity of the outlet cross section (10) a step of changing the initial shape of at least a part of the inner wall surface so that the distribution of the cumulative viscoelastic strain Ε changes.

The pipeline design method according to the second aspect of the present invention is the pipeline design method according to the first aspect, and the step of calculating the cumulative elongation strain Ε includes the following steps.
Wherein on each streamline or trajectories, a plurality of points _{Q k (1 ≦ k ≦ N} , N ≧ 2) a step wherein the fluid to be set in order to move from the point Q _k to a point next to the point Q _k based on the step the time t _k and the calculated physical quantity for calculating the time t _k required to undergo during the viscoelastic body from the point Q _k until you reach the point next to the point Q _{k Step to calculate extension strain ε k} indicating the degree of elongation deformation Step to calculate the cumulative extension strain Ε using the _{extension strain ε k Note that either point Q 1} or point Q _N is on the entrance cross section. Alternatively, it is set near the entrance cross section, and _{the other point Q 1} or the other point Q _N is set on the exit cross section or near the exit cross section.
It should be noted that the step of calculating the _{time t k here also includes setting the unit time t.} Further, the order of the steps for setting the plurality of points Q _{k in order and the steps for calculating the time t k} is not limited to the above order.

ただし、式（１）中の“Ｔ_O”は前記流体が前記各流線又は流跡線に沿って前記点Ｑ₁と前記点Ｑ_Nとの間を移動するのに要する時間を表し、“Ｔ_k”は前記流体が前記各流線又は流跡線に沿って前記点Ｑ₁又は前記点Ｑ_Nから前記点Ｑ_kまで移動するのに要する時間を表す。 The method for designing a pipeline according to a third aspect of the present invention is a method for designing a pipeline according to the second aspect, the relaxation time of the viscoelastic body is τ, and the cumulative elongation strain Ε is as follows. It is calculated by the formula (1).

However, equation (1) "T _O" in represents the time required to move between the point Q _N and the point Q ₁ along said fluid each streamline or trajectories, ""T _k " represents the time required for the _{fluid to move from the point Q 1} or the point Q _N to the point Q _k along each of the streamlines or trace lines.

The pipeline design method according to the fourth aspect of the present invention is the pipeline design method according to the second aspect, and the cumulative elongation strain Ε is calculated by the following equation (2).

The method for designing a pipeline according to a fifth aspect of the present invention is a method for designing a pipeline according to any one of the second to fourth aspects, and further includes the following steps.
Based on the distribution of the step the elongation strain epsilon _k to calculate the distribution of the elongation strain epsilon _k, among the inner wall surface, determining a range of changing the initial shape

The method for designing a pipeline according to a sixth aspect of the present invention is a method for designing a pipeline according to any one of the first to fifth aspects, and is a step of changing the initial shape of at least a part of the inner wall surface. Is a step of changing the initial shape of at least a part of the inner wall surface so that the distribution of the cumulative elongation strain Ε becomes uniform, and is in the vicinity of the streamline or the streamline for which the cumulative elongation strain Ε is desired to be increased. In the case where the initial shape of the inner wall surface is changed so that the change in the cross-sectional shape of the flow path becomes large, and the streamline or the trace line where the cumulative elongation strain Ε is to be reduced is desired. It includes at least one of changing the initial shape of the inner wall surface so that the change in the cross-sectional shape of the flow path is small.

The pipeline design method according to the seventh aspect of the present invention is the pipeline design method according to the sixth aspect, and the cross section of the flow path defined by the inner wall surface after the initial shape is changed is The area is smaller than the cross section of the flow path of the initial shape.

The method for designing a pipeline according to the eighth aspect of the present invention is a method for designing a pipeline according to any one of the first to seventh aspects, and further includes the following steps.
Step of calculating the velocity distribution in the exit cross section or in the vicinity of the exit cross section A step of changing the distance between the inlet cross section and the exit cross section in at least a part of the inner wall surface so that the velocity distribution becomes uniform.

The method for designing a pipeline according to a ninth aspect of the present invention is a method for designing a pipeline according to any one of the first to fifth aspects, and further includes the following steps.
Step to calculate the velocity distribution of the fluid in or near the outlet cross section Step to calculate the distribution of the relative index value of the cumulative elongation strain Ε with respect to the velocity in the outlet cross section or near the outlet cross section The velocity distribution changes. As described above, in at least a part of the inner wall surface, a step of changing the distance between the inlet cross section and the exit cross section. The step of changing the initial shape is a step of changing the initial shape of at least a part of the inner wall surface so that the relative index value distribution changes, and the cross section of the flow path after the initial shape is changed is The area is smaller than the cross section of the flow path of the initial shape.

ただし、式（３）中の“ｖ”は前記出口断面又は前記出口断面付近における前記流体の速度である。 The pipeline design method according to the tenth aspect of the present invention is the pipeline design method according to the ninth aspect, and the relative index value is calculated by the following formula (3).

However, "v" in the formula (3) is the velocity of the fluid in the outlet cross section or in the vicinity of the outlet cross section.

The method for designing a pipeline according to the eleventh aspect of the present invention is a method for designing a pipeline according to any one of the first to tenth aspects, and the conduit is a gold provided at a discharge port of an extruder. It is a mold, and the viscoelastic body is a rubber or resin material before cross-linking.

The pipeline design program according to the twelfth aspect of the present invention is a pipeline design program in which a viscoelastic body flows, and causes a computer to perform the following steps.
(1) Step of setting the initial shape of the inner wall surface of the pipeline (2) Step of modeling the viscoelastic body as a fluid (3) Step of dividing the flow path defined by the inner wall surface into predetermined elements (4) Steps for setting boundary conditions in the inner wall surface, the inlet cross section and the outlet cross section defined by the inner wall surface (5) Setting initial values of physical quantities including the velocity and pressure of the viscoelastic body in each element. Step (6) Calculate the physical quantity of the fluid in each of the elements (7) Generate a plurality of streamlines or trace lines in the flow path (8) Along each stream line or trace line The step (9) of calculating the cumulative elongation strain Ε, which indicates the degree of elongation deformation received by the viscoelastic body flowing in from the inlet cross section until it flows out from the outlet cross section, based on the calculated physical quantity (9). Step of calculating the distribution of the cumulative viscoelasticity Ε in or near the outlet cross section (10) A step of changing the initial shape of at least a part of the inner wall surface so that the distribution of the cumulative viscoelasticity Ε changes.

The method for evaluating a pipeline according to the thirteenth aspect of the present invention is a method for evaluating a pipeline through which a viscoelastic body flows, and includes the following steps.
(1) Step of modeling the shape of the inner wall surface of the pipeline (2) Step of modeling the viscoelastic body as a fluid (3) Step of dividing the flow path defined by the inner wall surface into predetermined elements (4) Steps for setting boundary conditions in the inner wall surface, the inlet cross section and the outlet cross section defined by the inner wall surface (5) Steps for setting initial values of physical quantities including the velocity and pressure of the fluid in each element (5) 6) Step of calculating the physical quantity of the fluid in each of the elements (7) Step of generating a plurality of streamlines or trace lines in the flow path (8) Along each of the streamlines or trace lines Step to calculate the cumulative extension strain Ε, which indicates the degree of elongation deformation received by the viscoelastic body flowing in from the inlet cross section until it flows out from the outlet cross section, based on the calculated physical quantity (9). Alternatively, a step of calculating the distribution of the cumulative viscoelasticity Ε in the vicinity of the outlet cross section (10) a step of evaluating the variation in the distribution of the cumulative viscoelasticity Ε based on a predetermined threshold value.

According to the present invention, there is provided a method for designing a viscoelastic body pipeline, a design program, and a method for evaluating a viscoelastic body, which can form a viscoelastic body into a desired shape with higher accuracy.

The schematic diagram of the extruder including the pipeline which is the object of the design method which concerns on this embodiment. (A) Schematic perspective view showing the shape of a pipeline that is the target of the design method according to the present embodiment. (B) End view of the pipeline seen from the left. (C) End view of the pipeline seen from the right. Explanatory drawing which shows an example of the mesh created in the initial flow path D1. Explanatory drawing which shows an example of the generated streamline. Explanatory drawing of the point to be set on the streamline. The explanatory view explaining the distribution of the extension strain ε in the initial flow path D1. Explanatory drawing explaining the distribution of the cumulative elongation strain Ε in the exit cross section O. (A) Schematic perspective view of the initial flow path D1 as viewed from the right side. (B) Explanatory drawing of velocity change of fluid model. (C) Explanatory drawing of velocity change of fluid model. Explanatory drawing explaining the velocity distribution in the exit cross section O. (A) Schematic perspective view of flow path D1'. (B) Schematic perspective view of the modified flow path D2. The figure explaining the rubber composition 1 discharged from the mold 2. Explanatory drawing of ideal distribution of velocity and relative index value in exit cross section O. (A)-(h) The figure which shows the example of the initial flow path and the change flow path. The figure which shows the model of the pipeline and the generated mesh in an Example. The figure which shows the simulation result in (a)-(c) Examples. The figure which shows the simulation result in (a)-(c) Examples. The figure which shows the example of the initial flow path and the change flow path created in an Example. (A)-(h) Graphs showing simulation results in Examples.

Hereinafter, an embodiment of a method for designing a viscoelastic body conduit according to the present invention will be described with reference to the drawings.

[Principle of pipeline design method according to this embodiment]
Before explaining the design method according to the present embodiment, the principle or the logical background targeted by the present embodiment will be described. When the material is extruded by an extruder or the like, the finished cross-sectional shape of the material is determined by the outlet cross-sectional shape of the mold installed at the discharge port of the extruder. However, when the material is a viscoelastic body such as rubber or resin exhibiting viscoelasticity, this material may partially shrink after being discharged from the mold. As a result, the material may be curved as a whole, or the cross-sectional shape may not be the intended shape. Therefore, in order to solve this problem, the present inventor describes the extension deformation in the streamline or trace line (hereinafter, referred to as “streamline or the like”) direction of the viscoelastic body flowing in the pipeline. , Focused on the cumulative amount of elongation strain. That is, in order to analyze the elongation deformation in the flow direction, a model fluid that models a viscoelastic body is set, the fluid analysis of the model fluid in the pipeline is performed, and a streamline or the like is generated. Then, along this streamline, the elongation strain representing the degree of elongation and deformation of the viscoelastic body under pressure from the original length is calculated. Further, the cumulative amount of elongation strain between the time when the viscoelastic body is injected into the mold and the time when the viscoelastic body is discharged is calculated. As a result, the elongation strain varies for each streamline, etc., and the cumulative amount of elongation strain (hereinafter referred to as "cumulative elongation strain") becomes non-uniform at the mold outlet. It was found that the material shrinks after withdrawal. As a result of intensive research and study based on this knowledge, the pipeline design method according to the present invention has been completed.

More specifically, for example, if there is a rapidly shrinking portion in the flow path through which the viscoelastic body flows (flows), the velocity of the viscoelastic body increases in the vicinity of the shrinking portion, and elongation deformation occurs. Elongation strain occurs. Further, if the stress due to the elongation deformation is not relaxed between the time when the elongation deformation is received and the time when the mold reaches the outlet, the elongation strain is accumulated by that amount. Then, they found that after the material was discharged from the mold, the portion having a relatively large cumulative elongation strain contracted more, and the portion having a relatively small cumulative elongation strain did not shrink more than that. Therefore, in order to improve the finishing accuracy of extrusion molding, it has been found that it is necessary not only to make the velocity distribution of the material at or near the outlet of the mold uniform, but also to make the cumulative elongation strain distribution uniform. Obtained. In addition to improving the accuracy of finish dimensions, if you want to bend the material after extrusion molding in a specific direction, design the mold so that a specific cumulative elongation strain distribution occurs, and the material is desired. It was also confirmed that it can be bent in the direction of.

Hereinafter, a specific method of the pipeline design method according to the present embodiment will be described based on the above findings. In the following, an extruder will be described as an example as a target of the pipeline design method according to the present embodiment.

<1. Overview of extruder>
FIG. 1 is a schematic view of the entire extruder 100. As shown in FIG. 1, this extruder includes a cylindrical main body 101, a screw 102 arranged inside the main body 101, and a hopper 103 arranged on the outer peripheral surface of the main body 101. ing. A discharge port 104 is formed at the axial end of the main body 101, and the hopper 103 described above is arranged on the outer peripheral surface of the end opposite to the discharge port 104. Then, when the rubber composition 1 is charged into the main body 101 from the hopper 103, the rubber composition 1 is kneaded by the screw 102 and moves to the discharge port 104. A preformer and a die plate (hereinafter referred to as a mold 2) are attached to the head portion 100a around the discharge port 104. The inlet 21 of the mold 2 communicates with the discharge port 104, and the rubber composition 1 discharged from the discharge port 104 moves from the inlet 21 into the mold 2 and is molded into a predetermined shape of the mold. It is discharged from the outlet 22 of 2. Hereinafter, the design method of the mold 2 will be described.

<2. Pipeline design method>
In the following, there are two methods, that is, A) a method of designing the shape of the mold 2 so that the finished cross-sectional shape of the rubber composition 1 matches the shape of the outlet cross-section O of the mold 2 (design method 1). , And B) A method of bending the rubber composition 1 after ejection in a desired direction (design method 2) will be described. First, the method of A) will be described.

<A. Design method 1>
<A-1. Initial shape setting>
A computer simulation can be used as a method for designing a pipeline according to the present embodiment. Therefore, the target pipeline (mold 2) is modeled. First, the shape of the inner wall surface 20 of the mold 2 having the inlet 21 and the outlet 22 is set. The inlet 21 is an opening defined by the peripheral edge of the inner wall surface 20 and communicates with the discharge port 104 of the extruder 100. On the other hand, the outlet 22 is an opening defined by another peripheral edge of the inner wall surface 20, and the rubber composition 1 is molded and discharged. Therefore, the shape of the outlet 22 (the shape seen from the axial direction of the screw 102) is the finished shape of the rubber composition 1. Conventionally used dimensional data of the mold 2 and the like can be used to set the modeled shape. The shape of the inner wall surface 20 set here and the flow path of the rubber composition 1 defined by the inner wall surface 20 are referred to as an initial shape and an initial flow path D1, respectively. Further, the surface surrounded by the peripheral edge of the inner wall surface 20 defining the entrance 21 is referred to as an inlet cross section I, and the surface surrounded by the peripheral edge of the inner wall surface 20 defining the exit 22 is referred to as an exit cross section O (see FIG. 2). In the initial flow path D1, the inlet cross section I and the outlet cross section O are parallel. The initial flow path D1 is a model of the pipeline defined by the mold 2, but for convenience of explanation, the reference numerals of the inner wall surface 20, the inlet 21, the outlet 22, and the like are used in common with the mold 2. I will do it.

FIG. 2A shows a schematic perspective view of an example of the initial flow path D1. Then, based on the result of the calculation described later, the modified flow path D2 in which the shape of the initial flow path D1 is changed is designed so that the rubber composition 1 is discharged in a desired shape. The inlet cross section I of the initial flow path D1 has a rectangular shape, and the inlet 21 communicates with the discharge port 104 of the extruder 100. The outlet cross section O has a triangular shape extending in the left-right direction and having the sharpest acute angle on the left side, and the rubber composition 1 formed from the outlet 22 is discharged.

FIG. 2B is an end view of the initial flow path D1 when viewed from the left. As shown in FIG. 2B, the left end surface has a horizontal portion 23a in which the upper surface 20a is horizontally continuous in the flow direction, and a rapidly expanding portion 23b in which the upper surface 20a rapidly expands upward from the horizontal portion 23a. Then, the upper surface 20a inclines from the rapidly expanding portion 23b toward the outlet 22 with a constant gradient, and the initial flow path D1 shrinks in the vertical direction. On the other hand, FIG. 2C is an end view of the initial flow path D1 when viewed from the right. As shown in FIG. 2C, on the right end surface, the upper surface 20a is inclined with a constant gradient toward the flow direction, so that the initial flow path D1 is reduced in the vertical direction. When the upper surface 20a reaches the bent portion 24, the upper surface 20a is inclined with a gentler gradient, and the initial flow path D1 is further reduced in the vertical direction. In the vicinity of the bent portion 24, there is a sharply reduced portion 20b in which the initial flow path D1 is locally reduced by forming the upper surface 20a in a stepped shape (see FIG. 2A). Hereinafter, unless otherwise specified, the "flow direction" refers to the direction in which the mold 2 extends from the inlet cross section I toward the outlet cross section O. Further, the surface viewed from the direction substantially orthogonal to the flow direction and the direction orthogonal to the vertical direction is referred to as the "side surface" of the mold 2, and when it is referred to as "upper", "lower", "left" or "right", FIG. It shall mean the direction shown in a). The same applies to the rubber composition 1 existing in the mold 2.

<A-2. Mesh generation>
Next, the initial flow path D1 is divided into a plurality of elements (Euler elements) composed of a predetermined three-dimensional space. The mode of dividing the elements is not particularly limited, and the elements are divided into three-dimensional elements such as a tetrahedron, a hexahedron, and a polyhedron cell (polyhedral grid). In addition, the volume (size) of the element can be set as appropriate. This set of elements is called a mesh. FIG. 3 is an example of a mesh generated for the initial flow path D1. In this embodiment, a polyhedral mesh as shown in FIG. 3 is generated. By dividing the area to be analyzed into such elements and discretizing the basic equations of the fluid, it becomes possible to calculate physical quantities such as the velocity and pressure of the fluid. As the discretization method, a known method such as a finite element method, a finite difference method, a finite volume method, or a boundary element method can be appropriately used.

<A-3. Modeling of rubber composition>
Subsequently, the rubber composition 1 is modeled for analysis. In the analysis described later, the rubber composition 1 is treated as an incompressible viscous fluid. Therefore, physical property values such as the density and viscosity coefficient of the rubber composition 1 are set as necessary. In this embodiment, the density, viscosity coefficient, specific heat, and thermal conductivity of the rubber composition 1 are set. Hereinafter, the rubber composition 1 modeled as a viscous fluid will be referred to as a fluid model 1, but the reference numerals will be the same for convenience of explanation.

The method for measuring the specific heat and thermal conductivity of the rubber composition 1 is not particularly limited, and a known method can be used. For example, the heat insulating continuous method can be used for the specific heat, and the hot wire method can be used for the thermal conductivity.

ただし、ａ、ｂ、ｃはそれぞれ正の定数であり、粘弾性体に固有の値である。 The viscosity coefficient μ set in this embodiment is set as a function including the temperature F of the rubber composition 1 and the strain rate V of the rubber composition 1. In the present specification, the "strain rate" means the rate at which the strain when the viscoelastic body is pulled changes with time, and when the strain continues to be increased at a constant rate, the strain rate becomes a constant. Specifically, the viscosity coefficient μ is defined by the following equation.

However, a, b, and c are positive constants, respectively, and are values peculiar to the viscoelastic body.

<A-4. Setting simulation conditions>
Subsequently, the conditions necessary for performing simulation / analysis are set. Specifically, the boundary conditions on the inlet cross section I, the exit cross section O, the inner wall surface 20 of the initial flow path D1, and the initial conditions for each element are set. In the present embodiment, the pressure, mass flow rate, and temperature of the fluid model 1 are set as the boundary conditions in the inlet cross section I, and the pressure of the fluid model 1 is set as the boundary conditions in the outlet cross section O (atmospheric pressure opening). As the boundary conditions on the inner wall surface 20, the wall surface temperature of the inner wall surface 20 and the speed of the fluid model 1 are set. In particular, when the viscosity coefficient of the fluid model 1 is large and it is necessary to consider the velocity in the flow direction on the inner wall surface 20, the slip velocity of the fluid model 1 is set. The method of setting the slip speed is not particularly limited, but in the present embodiment, the slip speed v _slip is set as follows by using the method described in Japanese Patent No. 5564704 of the applicant.
v _slip = _{α v t} + (1-α) ・ v _wall
However, v _slip is the slip velocity, v _t is the velocity component parallel to the inner wall surface 20 of the fluid model 1 at a position separated by a _{distance d wall in the} normal direction from _{the inner wall surface 20, v wall} is 0, and α is the slip rate. Then, the following formula is satisfied.
α / (1-α) = μ / {(d _wall / F _slip ) | v _slip −v _wall | ^eslip-1 } (0 ≦ α ≦ 1)
However, μ is the viscosity coefficient of the fluid model 1, and F _slip and brief are constants peculiar to the material.

As the initial condition for each element, the initial value of the physical quantity of the fluid model 1 is set. In this embodiment, the physical quantities are velocity, pressure and temperature.

<A-5. Execution of analysis calculation>
A fluid analysis by simulation is performed using the initial flow path D1, the boundary condition, and the initial condition, which are the models of the mold 2 described above. The physical quantity calculated as a result of the analysis is the velocity, pressure, temperature, etc. of the fluid model 1 in each element, although it depends on the set conditions and the equation used. In this embodiment, the Navier-Stokes equation in the case of an incompressible flow, the equation of conservation of mass (continuity equation), and the energy equation, which are disclosed in Patent Document 2, are used as equations, and a fluid model in the initial flow path D1 is used. The velocity distribution and pressure distribution of 1 are calculated. In Patent Document 2, the VOF method is used, and a multiphase flow model in which a gas phase model (air) and a material model (plastic material) are mixed is treated as one fluid. In this embodiment, analysis is performed for a single-phase flow, that is, a case where the volume fraction of the fluid model 1 in each element of the initial flow path D1 is 100%. However, a multiphase flow model in which the rubber composition 1 and air or the like are mixed in the initial flow path D1 may be separately set, and the analysis may be performed by the method disclosed in Patent Document 2. The specific equation is shown below.

ただし、ρは混相流モデルの密度、ｕは混相流モデルの速度、ｐは混相流モデルの圧力、Ｔは混相流モデルの絶対温度、ｇは重力加速度、Ｆは外力である。 [Navier-Stokes equation]
It is an equation of motion set for each of the three-dimensional (x, y, z) directions.

However, ρ is the density of the multiphase flow model, u is the velocity of the multiphase flow model, p is the pressure of the multiphase flow model, T is the absolute temperature of the multiphase flow model, g is the gravitational acceleration, and F is the external force.

[Conservation of mass]
In this embodiment, the density of the fluid model 1 is constant. Therefore, the continuity equation of incompressible fluid is used.

ただし、Ｈはエンタルピ、ｋは熱伝導率、Ｓはソース項である。 [Energy equation]
It is an equation that governs the heat transfer of the fluid model 1, and in the present embodiment, the temperature of the fluid model 1 is calculated by this equation.

However, H is the enthalpy, k is the thermal conductivity, and S is the source term.

<A-6. Streamline generation>
Next, a predetermined number of streamlines are generated in the initial flow path D1 based on the velocity distribution calculated by the analysis. The start point of the streamline is set on the entrance cross section I, and a line is created so that the direction of the velocity vector in each element is the direction of the tangent line. Such streamlines can be created using various programs and the like. The number of streamlines can be appropriately set according to the dimensions of the initial flow path D1 and the like. FIG. 4 is an example thereof. A streamline is a line connecting the velocity vectors of each point at a certain moment. The rubber composition 1 in the initial flow path D1 can be considered to be elongated and deformed in the direction of the velocity vector at each point. That is, the rubber composition 1 undergoes elongation deformation in the direction along the streamline before flowing in from the inlet cross section I and flowing out from the outlet cross section O. Therefore, streamlines are generated to evaluate the cumulative distribution of elongation deformation.

In general, the streamline is a line connecting the velocity vectors of each point at a certain moment. On the other hand, the track line is a locus through which a specific particle has flowed. When the flow does not change with time, that is, when the fluid flow is a steady flow, the streamline and the trace line coincide with each other. On the other hand, when the flow changes with time, that is, when it is an unsteady flow, the streamline and the trace line do not match. In this embodiment, it is assumed that the flow of the fluid model 1 is steady, and a streamline (trace line) is generated. However, the present invention is not limited to this, and either streamlines or trace lines may be generated. In the following, for convenience of explanation, a case where a streamline is generated will be described.

_{Subsequently, a plurality of points Q 1} , ..., Q _N (N ≧ 2) are set in order on each of the above-mentioned streamlines. Specifically, as shown in FIG. 5, the point Q ₁ is set at a position on the inlet cross section I on the streamline or near the inlet cross section I, and on the same streamline, from the point Q ₁ toward the exit cross section О. Points Q ₂ , ..., Q _N are sequentially arranged, and the points Q _N are set so as to be located on the exit cross section O or near the exit cross section O. Although one streamline is shown in FIG. 5, the same operation is actually performed for each of the generated streamlines. By this operation, each streamline is divided into (N-1) sections. Note that N may be different for each streamline. The distance L between adjacent points Q differs depending on the position of the points Q, and in the present embodiment, the distance L is set to a degree that roughly corresponds to the size of the element. This is because if the distance L is too large with respect to the size of the element, the calculation accuracy of the extension strain described later is lowered, and if it is too small, the calculation of the significant extension strain is hindered. From a point Q _K on certain streamlines the distance between the points Q _{K + 1} and L _K, the distance L _K is extended deformation encountered during the rubber composition 1 is moved from point Q _K to the point Q _{K + 1} Can be the reference length for. As will be described later, in order to evaluate the distribution of the cumulative elongation strain Ε in the exit cross section O, it is desirable that the position of the _{point Q N is closer to the exit cross section O.}

In the setting of the above-mentioned point Q, first, the point Q ₁ is set at a position on the outlet cross section О on the streamline or near the exit cross section О, and then the point Q _{is sequentially set from the point Q 1} toward the inlet cross section I on the same streamline. _{It is also possible to arrange 2} , ..., Q _N so that the point Q _N is located on the entrance cross section I or near the entrance cross section I. In this case, the cumulative elongation strain Ε on the outlet cross section O or near the outlet cross section O, which will be described later, is calculated by calculating the elongation deformation that the _{rubber composition 1 receives while moving from the point Q K + 1} to the point Q _K. be able to.

Further, as a method of setting the point Q, a unit time is set, and a point separated by the distance _{that the rubber composition 1 moves on the streamline from the point Q k in the unit time is set as the point Q k + 1.} Is also possible.

<A-7. Calculation of elongation strain>
At the stage of fluid analysis, the rubber composition 1 is treated as a viscous fluid, but here, the rubber composition 1 is treated as a viscoelastic body. As described above, the rubber composition 1 in the initial flow path D1 undergoes elongation deformation in the same direction as the direction of the velocity vector, and the degree thereof corresponds to the rate of change in the magnitude of the velocity of the model fluid. That is, at the place where the speed rapidly increases, the rubber composition 1 undergoes a larger elongation deformation, and the degree of shrinkage after ejection of that part becomes larger. By paying attention to which part of the initial flow path D1 the elongation strain is generated and how the elongation strain affects the cumulative elongation strain in the outlet cross section O, the rubber composition after ejection The contraction of 1 can be controlled efficiently.

Following the setting of the point Q, the _{elongation strain ε k} , which indicates the degree of elongation deformation received by the rubber composition 1 during the movement _{from the point Q k} to the point Q _{k + 1} described above, is set for each streamline section. calculate. That is, the elongation strain ε _k indicates the degree of elongation deformation in the local streamline direction of the rubber composition 1. Therefore, by calculating the distribution of the elongation strain ε _k in the initial flow path D1, the history of the elongation deformation received by the rubber composition 1 in the initial flow path D1 can be grasped in relation to the position in the initial flow path D1. It becomes possible to do. On the same flow line, during the time t _k to the rubber composition 1 is moved from point Q _k to the point Q _{k + 1,} when the speed is changed to v _{k + 1} from v _k, the rubber composition 1 The elongation of _{can be expressed as (v k + 1 −} v _k ) × t _{k, and the elongation strain ε k} is evaluated with respect to the _{distance L K} , which is the reference length. Therefore, the elongation strain ε _k is expressed by the following equation. Incidentally, the speed v _k is the velocity v _k of the viscous fluid in the element point Q _k is present, the time t _k is calculated as L _K / v _k.

_{By calculating the distribution of the elongation strain ε k} in the initial flow path D1 in this way, it is possible to identify a region in which the elongation strain ε _k is larger than the other portions, or conversely, a region in which the elongation strain ε k is smaller. FIG. 6 shows an example of a region specified by the initial flow path D1. The region R1 surrounded by the broken line is a region in which the elongation strain ε _k is relatively large. The upper surface 20a of the region R1 is formed in a stepped shape (see FIG. 8B), and the region R1 exists in the vicinity of the sharply reduced portion 20b where the initial flow path D1 locally shrinks. Since the velocity of the fluid model 1 rapidly increases on the inner wall surface 20 in the vicinity of the sharply reduced portion 20b, the rubber composition 1 undergoes a large elongation deformation in the vicinity of the sharply reduced portion 20b. As a result, the region R1 becomes a region in which the elongation strain ε _k is relatively large.

On the other hand, the region R2 surrounded by the alternate long and short dash line is a region in which the extension strain ε _k is relatively small. The region R2 exists in the vicinity of the horizontal portion 23a where the upper surface 20a is horizontally continuous. Since the shape of the inner wall surface 20 of the initial flow path D1 does not change in the vertical direction due to having the horizontal portion 23a, the velocity change of the fluid model 1 in the region R2 is relatively small. Therefore, the elongation deformation received by the rubber composition 1 is relatively small, and the region R2 is a region in which the elongation strain ε _k is relatively small. Based on the region specified in this way and _{the magnitude of the elongation strain ε k} in that region, the location where the shape of the initial flow path D1 is changed can be determined, and the change flow path D2 can be designed.

<A-8. Calculation of cumulative elongation strain>
Subsequently, the cumulative extension strain Ε, which is the cumulative amount of the extension strain ε _{k, is calculated for each streamline.} The cumulative elongation strain Ε is an amount indicating the degree of elongation and deformation of the rubber composition 1 flowing in from the inlet cross section I while finally flowing out from the outlet cross section O. The shrinkage of the rubber composition 1 after discharge occurs due to the residual cumulative elongation strain Ε, and the degree of shrinkage increases as the cumulative elongation strain Ε increases. Further, as the distribution of the cumulative elongation strain Ε in the outlet cross section O varies, the degree of shrinkage of the rubber composition 1 after discharge also varies depending on the portion, so that the entire rubber composition 1 may be bent.

By the way, the rubber composition 1 has a unique relaxation time τ. The relaxation time τ means that the stress generated when a tensile force is applied to the rubber composition 1 decreases with the passage of time to a certain threshold value or less (about 1 / e of the initial stress, where e is the natural logarithm). It means the time until it is relaxed. That is, the shorter the relaxation time τ, the shorter the stress of the stretch-deformed rubber composition 1 is relaxed, and the influence of the stretch deformation received by the rubber composition 1 on the cumulative stretch strain Ε tends to decrease. On the other hand, the longer the relaxation time τ, the more easily the stress of the stretch-deformed rubber composition 1 remains, and the greater the influence of the stretch deformation received by the rubber composition 1 on the cumulative stretch strain Ε. Therefore, as will be described later, the elongation deformation exerts on the cumulative elongation strain Ε according to the length of the time T from the entrance 21 of the mold 2 to the exit 22 of the rubber composition 1 with respect to the relaxation time τ. It is desirable to consider the impact. The method for defining the relaxation time τ is not particularly limited. For example, a method based on stress relaxation measurement using a Mooney viscometer, a method based on NMR relaxation measurement, a method based on simulation, or the like can be used.

ただし、“Ｔ_O”はゴム組成物１が金型２の入口２１から入り、前記流線又は流跡線上を移動して出口２２から吐出されるまでに要する時間を表す。“Ｔ_k”は前記粘弾性体が前記入口断面から前記点Ｑ_kまで前記流線又は流跡線上を移動するのに要する時間を表す。
“Ｔ_O”は流体モデル１が点Ｑ₁から点Ｑ_Nまで流れる時間（Σｔ_k）とすることができる。また、“Ｔ_k”は、流体モデル１が点Ｑ₁から点Ｑ_kまで流れる時間（ｔ₁＋・・・＋ｔ_k-1）とすることができる。式（１）は、例えば、（Ｔ_k−Ｔ_O）がτと等しい場合、ゴム組成物１が点Ｑ_k-1と点Ｑ_kとの間で受ける伸長ひずみε_k-1は、出口２２から吐出される時点で、概ね１／ｅ倍に緩和されることを表している。 When the relaxation time τ is relatively short with respect to the time T and it is considered that the stress generated by the elongation deformation is partially relaxed by the time the rubber composition 1 is discharged from the outlet 22, the cumulative elongation strain Ε is determined. It can be expressed by the following equation (1).

However, "T _O" rubber composition 1 enters from the die 2 of the inlet 21, represents the time required until discharged from the outlet 22 by moving the streamlined or Nagareato line. “T _k ” represents the time required for the viscoelastic body to move on the streamline or trace line from the inlet cross section to the point Q _k.
“ _TO ” can be the time (Σt _k ) that the fluid model 1 flows from the point Q _{1 to the point Q N.} Further, "T _k " can be the time (t ₁ + ... + t _k-1 ) at which the fluid model 1 flows from the point Q _{1 to the point Q k.} Equation (1) is, for example, when (T _k -T _O) is equal to tau, elongation strain epsilon _k-1 receiving between the rubber composition 1 is the point Q _k-1 and the point Q _k is the outlet 22 It means that it is relaxed by about 1 / e times when it is discharged from.

On the other hand, when the relaxation time τ is sufficiently long with respect to the time T and the stress generated by the elongation deformation is considered to remain in the rubber composition 1 discharged from the outlet 22, the cumulative elongation strain Ε is as follows. It can be expressed by the equation (2).

In the present embodiment, the distribution of the cumulative elongation strain Ε and the cumulative elongation strain Ε in the outlet cross section O is calculated using the above equation (2). From this distribution, it is possible to examine how the partially generated elongation strain ε _k eventually affects the finished shape of the rubber composition 1. FIG. 7 shows an example of the distribution of the cumulative elongation strain Ε in the outlet cross section O calculated for the initial flow path D1. The region S1 is a region where the cumulative elongation strain Ε is relatively large, and is shown by a shaded portion in FIG. The region S2 is a region where the cumulative elongation strain Ε is relatively small, and is shown by a shaded portion shown in FIG. 7. The region S1 is generated on the upper surface 20a from the right side of the exit cross section O, the right side surface and a part of the lower surface surface of the inner wall surface 20, and the one generated on the upper surface 20a is remarkable. The region S2 is formed at the left end of the exit cross section O so as to be surrounded by the inner wall surface 20. When confirmed together with the distribution of the _{extension strain ε k} shown in FIG. 6 described above, it can be seen _{that the large extension strain ε k} generated in the region R1 affects the cumulative extension strain Ε in the region S1 corresponding to the downstream side thereof. I understand. Further, it can be seen that the cumulative extension strain Ε is also small in the region S2 corresponding to the downstream of the region R2 in which the extension strain ε _{k is relatively not generated.}

In the present embodiment, if the variation in the values of all the cumulative elongation strains Ε in the outlet cross section O is within ± 5%, it is judged to be substantially uniform. In the method of designing the shape of the mold 2 so that the finished cross-sectional shape of the rubber composition 1 matches the shape of the outlet cross-section O of the mold 2 (design method 1), the distribution of the cumulative elongation strain Ε is uniform. If it is determined that, the shape of the initial flow path D1 is not changed in order to make the distribution of the cumulative elongation strain Ε uniform. On the other hand, when the variation exceeds ± 5%, it is judged that the distribution of the cumulative elongation strain Ε is not uniform and the shape of the initial flow path D1 needs to be changed. Therefore, it can be said that calculating the distribution of the cumulative elongation strain Ε and comparing the variation with a predetermined threshold value or the variation in other pipelines is to evaluate the pipeline from the viewpoint of processing accuracy. The threshold value of variation is not limited to this, and can be appropriately changed depending on the properties of the rubber composition 1 and the like. Further, the shape of the initial flow path D1 may be changed so that the distribution of the cumulative elongation strain Ε becomes more uniform without setting a specific threshold value. Hereinafter, a specific procedure for designing the changed flow path D2 by changing the initial flow path D1 will be described.

<A-9. Channel shape design>
In order to make the distribution of the cumulative elongation strain Ε uniform, the cumulative elongation strain Ε in the region S1 is made smaller, while the cumulative elongation strain Ε in the region S2 is made larger. Alternatively, depending on the degree of variation in the cumulative elongation strain Ε, only the cumulative elongation strain Ε in any region may be adjusted to make the distribution uniform. Then, for that purpose, the shape of the inner wall surface 20 is changed in the vicinity of the streamline whose end is included in the area S1 and the area S2. Various portions can be considered as the vicinity of the streamline, but it is desirable to change the shape of the inner wall surface 20 in the vicinity of the region R1 and the region R2 that affect the cumulative elongation strain Ε. Depending on the relaxation time τ of the rubber composition 1, it is possible to omit the shape change of the region where the _{elongation strain ε k, which} is considered to have almost no effect on the cumulative elongation strain Ε, is generated as a result.

FIG. 8A is a schematic perspective view of the initial flow path D1 as viewed from the right side. As described above, the region R1 exists in the vicinity of the sharp reduction portion 20b in which the initial flow path D1 sharply shrinks in the flow direction. In the present embodiment, _{in order to reduce the elongation strain ε k} in the vicinity of the region R1, the shape in the vicinity of the region R1 is changed to a shape in which a rapid increase in velocity is unlikely to occur. That is, as shown in FIG. 8C, the shape of the region R is changed to a shape that gradually shrinks in the flow direction by eliminating the suddenly shrinking portion 20b. _{By doing so, the elongation strain ε k} in the region R1 becomes small, and as a result, the cumulative elongation strain Ε in the region S1 existing downstream of the region R1 is reduced.

The distribution of the cumulative elongation strain Ε is also adjusted by changing the shape of the initial flow path D1 near the region R2 where the cumulative elongation strain Ε is relatively small. In the region R2, _{almost no elongation strain ε k} is generated, and the cumulative elongation strain Ε is relatively small also in the region S2 existing in the downstream region of the region R2. Therefore, the shape of the horizontal portion 23a is changed to a shape in which the initial flow path D1 gradually shrinks in the flow direction. In this way, since the velocity of the fluid model 1 in the region R2 becomes larger than the original, the elongation strain ε _k is generated, and the cumulative elongation strain Ε in the region S2 on the left side of the outlet cross section O can be increased. .. _{Alternatively, a larger extension strain ε k} may be generated by forming at least one protrusion on the inner wall surface 20 of the initial flow path D1 so as to resist the flow. The flow path changed so that the distribution of the cumulative elongation strain Ε becomes uniform (for example, the variation within 5% described above) is referred to as the flow path D1'(see FIG. 10A).

When changing the cross-sectional shape of the initial flow path D1, it is desirable that the flow path cross-sectional area of the flow path D1'is smaller than the flow path cross-sectional area of the initial flow path D1. It is desirable to make changes so that it shrinks in the direction. In the present embodiment, when the shape of the inner wall surface 20 is changed for the purpose of changing the distribution of the cumulative elongation strain Ε, the distance or the positional relationship of the exit cross section O with respect to the inlet cross section I is changed. The shape of the inner wall surface 20 shall not be changed. When a part or all of the inner wall surface 20 is extended or shortened in the flow direction to change the distance or positional relationship of the exit cross section O with respect to the inlet cross section I, the flow path length of the initial flow path D1 is changed. Although such a change slightly changes the distribution of the cumulative elongation strain Ε, it has a far greater effect on the velocity distribution of the fluid model 1 at the outlet cross section O. Therefore, it is more suitable for shape change (described later) for the purpose of changing the velocity distribution.

Further, in order to accurately form the finished dimension of the rubber composition 1 after discharge, the shape of the flow path D1'is changed so that the velocity distribution of the fluid model 1 in the outlet cross section O becomes uniform. Since the threshold value of the variation of the velocity distribution regarded as uniform can be appropriately set, the description thereof is omitted here. In the present embodiment, the shape of the inner wall surface 20 of the flow path D1'is changed so that the variation in the speed of the outlet cross section O in the initial flow path D1 becomes smaller. Specifically, the distance from the inlet cross section I to the outlet cross section O, that is, the flow path length of the flow path D1'is changed. For example, as shown in FIG. 7, the exit cross section O has a shape in which the left side is narrow and the right side is wide. Therefore, the pressure loss due to the wall friction of the fluid model 1 is large on the left side of the inner wall surface 20 near the outlet 22, and the pressure loss is relatively small on the right side. Therefore, the velocity of the fluid model 1 is small on the left side of the exit cross section O and large on the right side. When the velocity distribution in the exit cross section O is calculated by actually performing the analysis, the velocity increases from the left side to the right side, and the part slightly from the right side has the highest velocity distribution (see FIG. 9). Therefore, the velocity distribution can be made more uniform by shortening the inner wall surface 20 on the left side of the flow path D1'in the flow direction and / or extending the inner wall surface 20 on the right side in the flow direction. FIG. 10B shows a modified flow path D2 designed by extending the inner wall surface 20 on the right side. In the initial flow path D1 and the flow path D1', the inlet cross section I and the outlet cross section O were parallel, but in the modified flow path D2, the outlet cross section O was positioned so as to form a constant angle with respect to the inlet cross section I. has been changed. Further, except for the left side, from Ia point on the periphery of the wall 20 defining the inlet section O, up Oa point on the periphery of the wall 20 inner defining an outlet cross-section O, the distance K _IO in the inner wall surface 20 on Is changed in the flow path D1'and the changed flow path D2.

It is considered that the velocity distribution also changes by changing the shape of the initial flow path D1 so as to suppress the increase in the cumulative elongation strain Ε. Therefore, for the flow path D1', the velocity distribution in the exit cross section O may be obtained again, and the flow path length of the flow path D1'may be changed so as to make the velocity distribution uniform.

In this way, by calculating the distribution of the elongation strain ε _{k and} the distribution of the cumulative elongation strain Ε, it is possible to confirm in which part on which streamline the rubber composition 1 has undergone more elongation deformation. can. As a result, it is possible to determine the portion of the initial flow path D1 where the shape of the inner wall surface 20 is changed and how the shape of the inner wall surface 20 is changed. As a result, it is not necessary to design the pipeline based on experience and repeat the test experiment, so that the efficient pipeline design becomes possible. Further, the extrusion molding process can be performed with higher accuracy than simply making the velocity distribution in the outlet cross section of the pipeline uniform. Further, in this method, since it is not necessary to install a structure different from the pipeline on the inner wall surface of the pipeline, there is no possibility of contamination due to the viscoelastic body adhering to the structure.

<B. Design method 2>
Next, as a design method 2, a case where the material after discharge is bent in a predetermined direction will be described. Also in the design method 2, the process of modeling the rubber composition 1, performing the fluid analysis on the fluid model 1, and calculating the distribution of the cumulative elongation strain Ε in the outlet cross section O is the same as that of the design method 1. In the following, as an example, a case where the extruded rubber composition 1 is bent to the right side by using the mold 2 (initial flow path D1) of FIG. 2 will be described. FIG. 11 is a view showing how the rubber composition 1 discharged from the mold 2 bends in a predetermined direction when viewed from below the mold 2. In this case, as shown in FIG. 11, it is necessary that the right side of the extruded rubber composition 1 causes a larger shrinkage than the left side, and the left side is extruded earlier than the right side. Therefore, the distribution of the cumulative elongation strain Ε in the exit cross section O needs to be such that the cumulative elongation strain Ε increases from the left side to the right side. Further, the distribution of the velocity v in the exit cross section O needs to be such that the velocity v decreases from the left side to the right side (see FIG. 12).

However, in general, when the velocity of the fluid model 1 increases sharply, a large elongation strain ε _k tends to occur in the rubber composition 1. Then, when the velocity v in the exit cross section O is increased, the elongation strain ε _k tends to increase accordingly. That is, there is a trade-off relationship between increasing the velocity v and decreasing the cumulative elongation strain Ε.

すなわち、指標値αが、概ね出口断面Ｏの左側から右側に向かって増加していくような分布に変更流路Ｄ２を設計することが必要になる（図１２参照）。このような変更流路Ｄ２の設計方法としては、以下の態様が考えられる。速度分布の観点からは、出口断面Ｏの右側で速度ｖが相対的に小さくなるよう、初期流路Ｄ１の左側の流路長を短縮する、及び／又は右側の流路長を延長する。また、累積伸長ひずみΕの分布の観点からは、累積伸長ひずみΕが出口断面Ｏの右側で相対的に大きくなるよう、出口断面Ｏの右側付近に存在する流線の上流に、急縮小部分を付加する、等の方法が考えられる。なお、指標値αの分布は出口断面Ｏの全体に亘って算出されてもよいが、上下方向の所定の位置における分布のみが算出されてもよい。本実施形態では、図１２に示すような直線ｍ上の分布を算出している。直線ｍは、出口断面Ｏを上下方向に概ね二分する直線である。しかしながら、算出する位置はこれに限定されるものではなく、出口断面Ｏの形状によって、適宜変更が可能である。また、左右方向の同じ位置における上下方向の指標値αの平均や加重平均等を算出することもできる。 Therefore, it is assumed that the distribution of the velocity v and the cumulative elongation strain Ε in the exit cross section O is handled by the relative index value α of the cumulative elongation strain Ε with respect to the velocity v in the outlet cross section O. The index value α [s / m] is defined by the following equation (3).

That is, it is necessary to design the modified flow path D2 so that the index value α increases from the left side to the right side of the exit cross section O (see FIG. 12). The following aspects can be considered as a design method for such a modified flow path D2. From the viewpoint of velocity distribution, the flow path length on the left side of the initial flow path D1 is shortened and / or the flow path length on the right side is extended so that the velocity v is relatively small on the right side of the exit cross section O. Further, from the viewpoint of the distribution of the cumulative elongation strain Ε, a sharp reduction portion is provided upstream of the streamline existing near the right side of the exit cross section O so that the cumulative elongation strain Ε becomes relatively large on the right side of the exit cross section O. A method such as adding is conceivable. The distribution of the index value α may be calculated over the entire exit cross section O, but only the distribution at a predetermined position in the vertical direction may be calculated. In this embodiment, the distribution on the straight line m as shown in FIG. 12 is calculated. The straight line m is a straight line that roughly divides the exit cross section O in the vertical direction. However, the calculated position is not limited to this, and can be appropriately changed depending on the shape of the exit cross section O. It is also possible to calculate the average of the index values α in the vertical direction, the weighted average, and the like at the same position in the horizontal direction.

FIG. 13 shows an example of changing the shape of the flow path. FIG. 13A is an initial flow path D1. 13 (b) to 13 (h) are the changed flow path D2b to the changed flow path D2h, respectively, and are seven examples of the changed flow path D2. The main shape-changing portions of the inner wall surface 20 are shown by being surrounded by dotted lines. The features of the modified flow path D2b to the modified flow path D2h are as shown in Table 1 below.

In this way, by introducing an index called the relative index value α, it becomes possible to determine the magnitude of the cumulative elongation strain Ε with respect to the velocity. As a result, at the same position of the outlet cross section O, the cumulative elongation strain Ε is decreased while substantially increasing the velocity v of the model fluid, and the cumulative elongation strain Ε is increased while substantially decreasing the velocity v of the model fluid. can do. Thereby, the rubber composition 1 after discharge can be bent in a desired direction. According to this design method 2, for example, when there is a step of winding the rubber composition 1 after ejection in a ring shape, the rubber composition 1 can be bent in the same direction as the winding direction. , The winding work is streamlined.

<Modification example>
Although the embodiments of the present invention have been described in detail above, the present invention is not limited to the above-described embodiments, and can be changed to various embodiments.

For example, the formula for calculating the cumulative elongation strain Ε is not limited to the formulas (1) and (2). If the cumulative elongation strain Ε is calculated based on physical quantities such as velocity, pressure, and temperature calculated by fluid analysis of the fluid model, equations (1) and (2) may be appropriately modified. It is possible.

In the present embodiment, the formula (5) is used as a formula for calculating the local elongation strain ε _{k of the rubber composition 1.} Using an analysis result of Equation (5) is fluid model 1, calculate the elongation strain epsilon _k of the rubber composition 1 from the time t _k to move from the speed v _k and the point Q _k at point Q _k to the point Q _{k + 1} It is an expression to do. However, the _{method for calculating the elongation strain ε k} is not limited to the method according to the equation (5). For example, it is also possible to calculate the _{elongation strain ε k} by calculating the streamline direction component (velocity direction component) of the strain tensor at a point on the streamline or trace line.

In the above embodiment, the method of designing the pipeline has been described. However, the present invention can be used not only as a method for designing a pipeline but also as a method for evaluating an existing pipeline or a pipeline under design. As described above, the performance of the pipeline can be evaluated by calculating the variation in the distribution of the cumulative elongation strain Ε in the outlet cross section O and comparing it with the threshold value. It is also possible to compare the variation in the distribution of the cumulative elongation strain Ε for each pipeline, and evaluate the one with a small variation as a pipeline with high processing accuracy.

Hereinafter, examples of the present invention will be described. However, the present invention is not limited to the following examples.

(Example 1. Example of improving the processing accuracy of the rubber composition)
As an example according to the present invention, the mold model as shown in FIG. 14 was used as the initial flow path D1, and the modified flow path D2 was designed based on the above analysis. Hereinafter, a detailed description will be given.

The main conditions of the analysis are as follows.
Rubber composition density [kg / m ³ ]: 1121
Specific heat of rubber composition [J / (kg ・ K)]: 1430
Thermal conductivity of rubber composition [W / mK]: 0.32
Viscosity coefficient of rubber composition: 10.797 × exp (4220.2 / Temperature) × Strain ^{rate -0.833}
However, Temperature is the temperature of the rubber composition, and Strain rate is the strain rate.
Initial temperature of rubber composition [K]: 356
Wall surface temperature of initial flow path D1 [K]: 353
Inlet temperature [K]: 356
Inlet flow rate [Kg / s]: 0.0227
_{Constant F slip} that gives the slip speed on the wall surface: 496342
_{Constant e slip} that gives the slip speed on the wall surface: 0.121105
Mesh element size [mm]: 0.2-4
Streamline [book]: 1306
The analysis program uses star ccm +.

The time from the rubber composition 1 of the present embodiment entering the mold 2 from the inlet 21 and being discharged from the outlet 2 is about ten and several seconds. On the other hand, the relaxation time of the rubber material before vulcanization depends on the type, but in most cases, it is about several minutes to several tens of minutes. Therefore, it is considered that the influence of the relaxation time τ of the rubber composition 1 on the cumulative elongation strain Ε is limited. For this reason, in this embodiment, the above equation (2) is used to calculate the cumulative elongation strain Ε.

FIG. 14 shows an example of the initial flow path D1 set under the above conditions and the mesh generated in the initial flow path D1. However, in this embodiment, the initial flow path D1 includes the head portion 100a (see FIG. 1) of the extruder 100. Then, based on the above analysis, the cumulative elongation strain Ε in the initial flow path D1 and the velocity of the fluid model 1 were calculated. The results are as shown in FIGS. 15 and 16. Here, FIG. 15A is a perspective view showing a part of the head portion 100a and the distribution of the extension strain ε of each streamline in the pipeline corresponding to the mold 2, and FIG. 15B is an exit cross section. The distribution of the cumulative elongation strain Ε, FIG. 15 (c) shows the distribution of the velocity v in the exit cross section. As shown in FIG. 15A, a relatively large region G1 having an elongation strain ε of about 0.12 to 0.2 is formed in the vicinity of the rapidly contracting portion 20b of the flow path. On the other hand, in the vicinity of the horizontal portion 23a of the flow path, a relatively small region G2 is formed in which the elongation strain ε is about 0.0000 to 0.0267. Then, as shown in FIG. 15B, a plurality of regions H1 having an extremely large cumulative elongation strain Ε of about 4.000 are generated on the inner wall surface on the right side of the exit cross section O. On the other hand, on the left side of the exit cross section O, the cumulative elongation strain Ε is relatively small, about 3.000 to 3.2000. Further, as shown in FIG. 15 (c), in the region J1 on the right side of the exit cross section O, the velocity v is relatively large, about 0.12 to 0.15 (m / s), whereas in the region J2 on the left side, the velocity v is relatively large. v is relatively small, about 0.030 to 0.060. That is, there are variations in the velocity v and the cumulative elongation strain Ε in the exit cross section. As a result, in the mold of the initial flow path D1, shrinkage occurs in the rubber composition after extrusion, and the finished cross-sectional shape is different from the shape of the outlet cross-section O.

Therefore, the modified flow path D2 as shown in FIG. 10B was designed. Here, the inner wall surface F on the right side of the initial flow path D1 is lengthened, the cross section of the flow path near the region G1 (rapid reduction portion 20b) is gradually reduced, and the rapid increase in the velocity of the fluid model 1 is alleviated. Further, the cross section of the flow path near the region G2 (horizontal portion 23a) is reduced as compared with the initial flow path D1 so that the velocity and the elongation strain Ε increase in the vicinity of the region G2. The modified flow path D2 was analyzed in the same manner as the initial flow path D1, and the distribution of the extension strain ε in the modified flow path D2, the cumulative extension strain Ε in the exit cross section O, and the distribution of the velocity v were calculated. As a result, the distribution of the elongation strain ε is as shown in FIG. 16 (a). The elongation strain ε of the region G2 is about 0.04000 to 0.0533, and the elongation strain ε of the region G1 is about 0.02000 to 0.04667, and the difference in the elongation strain ε between the region G1 and the region G2 is almost eliminated. As for the distribution of the cumulative elongation strain Ε in the outlet cross section O, as shown in FIG. 16B, the cumulative elongation strain Ε increases to about 3.8000 to 3.95000 in the region on the left side of the mold, and about 3.6000 to 3.8000 in the other regions. Converges in the range of. In addition, the region H1 having a large cumulative elongation strain Ε disappeared on the inner wall surface on the right side of the mold. As a result, the cumulative elongation strain Ε in the exit cross section of the mold became a substantially uniform distribution (in FIG. 16B, for convenience of explanation, one scale of the diagram showing the cumulative elongation strain Ε was enlarged. Therefore, in reality, the variation of the cumulative elongation strain Ε is even smaller than that shown in FIG. 16 (b)). Further, as shown in FIG. 16C, as a result of the velocity v on the right side of the exit cross section decreasing and the velocity v on the left side increasing, the velocity v becomes about 0.090 to 0.15 (m / s) as a whole, and the initial flow. It can be seen that the variation is reduced as compared with the road D1. Therefore, in the mold of the modified flow path D2, the variation in shrinkage of the rubber composition after extrusion is largely eliminated, and the finished cross-sectional shape matches the shape of the outlet cross-section.

(Example 2. When the rubber composition is bent in a predetermined direction)
Next, an embodiment of the design method 2 will be described. In the second embodiment, the mold 2 is designed so that the rubber composition 1 is bent in the direction shown in FIG. 11 by causing a non-uniform shrinkage in the rubber composition 1 after ejection. Here, the initial flow path D1, the rubber composition 1 (model fluid 1), the boundary conditions, and the initial conditions are the same as those in the first embodiment. Further, the procedure for calculating the velocity distribution and the cumulative elongation strain Ε distribution of the fluid model 1 in the outlet cross section O is the same as that of the first embodiment. In this embodiment, the above equation (2) is used to calculate the cumulative elongation strain Ε for the same reason as in Example 1.

In the second embodiment, the velocity distribution and the distribution of the relative index value α on the straight line m that roughly divides the exit cross section O in the vertical direction as shown in FIG. 12 are evaluated. In order for the rubber composition 1 to bend in the direction shown in FIG. 11, as shown in FIG. 12, the velocity v decreases from the left to the right of the exit cross section O, and the relative index value α decreases from the left of the exit cross section O. The change flow path D2 is designed so that it becomes larger toward the right.

When the distribution of the velocity v and the relative index value α was calculated for the initial flow path D1, it was as shown in FIG. 18 (a). The horizontal axis of FIG. 18A indicates the position of the standardized exit cross section O in the left-right direction, and the left end is 0 and the right end is 1. The vertical axis represents the velocity v and the relative index value α, both of which are standardized to values from 0 to 1. The velocity v is indicated by a chain double-dashed line, and the relative index value α is indicated by a solid line. As described above, in the initial flow path D1, the velocity v increases from the left to the right of the outlet cross section O, whereas the relative index value α becomes smaller, so that the contracted portion of the rubber composition 1 after ejection And the degree of contraction is difficult to predict.

Next, based on the result of FIG. 18A, seven modified flow paths D2 were created and compared with the results of the initial flow path D1. However, the seven types of change flow paths D2 are merely examples. The top row of FIG. 17 shows the shapes of the initial flow path D1 and the modified flow paths D2b to D2h created below. However, the shape of the portion corresponding to the head portion 100a of the extruder 100 is not changed, and all are common to the initial flow path D1. The shapes of the mold portions of the changed flow paths D2b to D2h are the shapes shown in FIGS. 13 (b) to 13 (h), respectively, and the changed parts from the initial flow paths D1 are as described in the embodiment. The same analysis as that of the initial flow path D1 was performed for each of the changed flow paths D2b to D2h, and the distributions of the velocity v and the relative index value α were compared. As a result, the distribution was as shown in FIGS. 18 (b) to 18 (h), respectively. The modified flow path D2b has a shape in which the rapidly expanding portion 23b in the initial flow path D1 is eliminated, but as shown in FIG. 18B, the distribution of the velocity v and the relative index value α is that of the initial flow path D1. There are few remarkable changes in comparison. On the other hand, as shown in FIG. 18 (h), the distribution of the velocity v and the relative index value α in the changed flow path D2h is close to the distribution shown in FIG. The modified flow path D2h has a shape in which the rapid expansion portion 23b is eliminated from the initial flow path D1 and the inner wall surfaces 20 on both sides are the shortest, and the flow path is generally shorter than the initial flow path D1. It also has a sharply reduced portion 25. In this way, by evaluating the distributions of the velocity v and the relative index value α together, how much the shape of the mold can be changed, such as the addition of a sharply reduced portion and the increase / decrease in the flow path length, of the rubber composition 1 after ejection. It is possible to know whether it affects the shape. As a result, it becomes possible to efficiently design a mold that controls the elongation strain generated in the rubber composition 1 and bends the rubber composition 1 after ejection in a specific direction.

1 Rubber composition (model fluid)
2 Mold 20 Inner wall surface 20a Top surface 20b Rapid reduction part 21 Inlet 22 Exit 23a Horizontal part 23b Rapid expansion part 100 Extruder 100a Extruder head 102 Screw 103 Supply port 104 Discharge port D1 Initial flow path D2 Change flow path L Distance I Inlet Cross section O Exit cross section v _k Speed v Speed at exit cross section O ε Elongation strain Ε Cumulative extension strain α Index value τ Relaxation time

Claims (13)

It is a method of designing a conduit through which a viscoelastic body flows.
The step of setting the initial shape of the inner wall surface of the pipeline and
The step of modeling the viscoelastic body as a fluid and
A step of dividing the flow path defined by the inner wall surface into predetermined elements,
A step of setting boundary conditions in the inner wall surface, the entrance cross section and the exit cross section defined by the inner wall surface, and
A step of setting an initial value of a physical quantity including the velocity and pressure of the fluid in each of the elements, and
A step of calculating the physical quantity of the fluid in each of the elements, and
A step of generating a plurality of streamlines or trace lines in the flow path,
The calculation of the cumulative elongation strain Ε indicating the cumulative amount of the degree of elongation deformation that the viscoelastic body flowing in from the inlet cross section receives from the outlet cross section along each streamline or trace line. Steps to calculate based on the physical quantity and
A step of calculating the distribution of the cumulative elongation strain Ε in or near the exit cross section, and
A step of changing the initial shape of at least a part of the inner wall surface so that the distribution of the cumulative elongation strain Ε changes, and
A method of designing a pipeline. The step of calculating the cumulative elongation strain Ε is
_{A step of sequentially setting a plurality of points Q k} (1 ≦ k ≦ N, N ≧ 2) on each of the streamlines or trace lines, and
A step of said fluid to calculate the time t _k required to move from point Q _k to a point next to the point Q _k,
Based on the time t _k and the calculated physical quantity, elongation strain epsilon _k the viscoelastic body indicates the degree of elongation deformation experienced between the said point Q _k until you reach the point next to the point Q _k And the steps to calculate
The step of calculating the cumulative extension strain Ε using the extension strain ε _{k, and}
Including
Either point Q ₁ or point Q _N is set on or near the entrance cross section.
The other point Q ₁ or the other point Q _N is set on or near the exit cross section.
The method for designing a pipeline according to claim 1. The relaxation time of the viscoelastic body is τ,
The method for designing a pipeline according to claim 2, wherein the cumulative elongation strain Ε is calculated by the following formula (1).

However, equation (1) "T _O" in represents the time required to move between the point Q _N and the point Q ₁ along said fluid each streamline or trajectories, ""T _k " represents the time required for the _{fluid to move from the point Q 1} or the point Q _N to the point Q _k along each of the streamlines or trace lines. The method for designing a pipeline according to claim 2, wherein the cumulative elongation strain Ε is calculated by the following formula (2).

The step of calculating the distribution of the elongation strain ε _{k and}
A step of determining the range in which the initial shape is changed in the inner wall surface based on the distribution of the elongation strain ε _{k, and}
Further prepare,
The method for designing a pipeline according to any one of claims 2 to 4. The step of changing the initial shape of at least a part of the inner wall surface is a step of changing the initial shape of at least a part of the inner wall surface so that the distribution of the cumulative elongation strain Ε becomes uniform.
In the vicinity of the streamline or trace line for which the cumulative elongation strain Ε is desired to be increased, the initial shape of the inner wall surface is changed so that the change in the cross-sectional shape of the flow path becomes large, and the cumulative elongation strain Ε is changed. In the vicinity of the streamline or trace line for which Ε is desired to be reduced, at least one of changing the initial shape of the inner wall surface so as to reduce the change in the cross-sectional shape of the flow path is included.
The design method according to any one of claims 1 to 5. The pipeline according to claim 6, wherein the cross section of the flow path defined by the inner wall surface after the initial shape is changed has a smaller area than the cross section of the flow path defined by the inner wall surface of the initial shape. Design method. A step of calculating the velocity distribution of the fluid in or near the outlet cross section, and
A step of changing the distance between the inlet cross section and the outlet cross section on at least a part of the inner wall surface so that the velocity distribution becomes uniform.
Further prepare,
The design method according to any one of claims 1 to 7. A step of calculating the velocity distribution of the fluid in or near the outlet cross section, and
A step of calculating the distribution of the relative index value of the cumulative elongation strain Ε with respect to the velocity at or near the exit cross section, and
A step of changing the distance between the inlet cross section and the exit cross section on at least a part of the inner wall surface so that the velocity distribution changes.
With more
The step of changing the initial shape of at least a part of the inner wall surface so that the distribution of the cumulative elongation strain Ε changes changes the initial shape of at least a part of the inner wall surface so that the relative index value distribution changes. Is a step to do
The cross section of the flow path after the initial shape is changed has a smaller area than the cross section of the flow path of the initial shape.
The method for designing a pipeline according to any one of claims 1 to 5. The method for designing a pipeline according to claim 9, wherein the relative index value is calculated by the following formula (3).

However, "v" in the formula (3) is the velocity of the fluid in the outlet cross section or in the vicinity of the outlet cross section. The pipeline is a mold provided at the discharge port of the extruder.
The viscoelastic body is a rubber or resin material before cross-linking.
The method for designing a pipeline according to any one of claims 1 to 10. It is a design program of a conduit through which a viscoelastic body flows.
On the computer
The step of setting the initial shape of the inner wall surface of the pipeline and
The step of modeling the viscoelastic body as a fluid and
A step of dividing the flow path defined by the inner wall surface into predetermined elements,
A step of setting boundary conditions in the inner wall surface, the entrance cross section and the exit cross section defined by the inner wall surface, and
A step of setting an initial value of a physical quantity including the velocity and pressure of the fluid in each of the elements, and
A step of calculating the physical quantity of the fluid in each of the elements, and
A step of generating a plurality of streamlines or trace lines in the flow path,
A cumulative elongation strain Ε indicating the cumulative amount of elongation deformation received by the viscoelastic body flowing in from the inlet cross section and flowing out from the outlet cross section along each streamline or trace line is described above. Steps to calculate based on the calculated physical quantity,
A step of calculating the distribution of the cumulative elongation strain Ε in or near the exit cross section, and
A step of changing the initial shape of at least a part of the inner wall surface so that the distribution of the cumulative elongation strain Ε changes, and
A pipeline design program to execute. It is an evaluation method of the conduit through which the viscoelastic body flows.
Steps to model the shape of the inner wall surface of the pipeline,
The step of modeling the viscoelastic body as a fluid and
A step of dividing the flow path defined by the inner wall surface into predetermined elements,
A step of setting boundary conditions in the inner wall surface, the entrance cross section and the exit cross section defined by the inner wall surface, and
A step of setting an initial value of a physical quantity including the velocity and pressure of the fluid in each of the elements, and
A step of calculating the physical quantity of the fluid in each of the elements, and
A step of generating a plurality of streamlines or trace lines in the flow path,
The calculation of the cumulative elongation strain Ε indicating the cumulative amount of the degree of elongation deformation that the viscoelastic body flowing in from the inlet cross section receives from the outlet cross section along each streamline or trace line. Steps to calculate based on the physical quantity and
A step of calculating the distribution of the cumulative elongation strain Ε in or near the exit cross section, and
A step of evaluating the variation in the distribution of the cumulative elongation strain Ε based on a predetermined threshold value, and
A method for evaluating a pipeline.

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