JP2019093566A - Engineering method of duct line of viscoelastic body, engineering program, and evaluation method - Google Patents

Abstract

To provide an engineering method of a duct line good in process tolerance in extrusion molding of a viscoelastic body.SOLUTION: The invention has: a step for setting an initial shape of an inner wall surface of a duct line; a step for modeling the viscoelastic body as a fluid; a step for dividing a flow pass defined by the inner wall surface into prescribed elements; a step for setting a boundary condition at an inner wall surface, an inlet cross section and an outlet cross section defined by the inner wall surface; a step for setting an initial value of physical value at each element; a step for calculating the physical value of the fluid at each element; a step for generating a plurality of flow lines; a step for calculating cumulative elongation strain E showing the degree of elongation deformation which the viscoelastic body flowed in from the inlet cross section receives until it flows out from the outlet cross section based on the calculated physical amount; a step for calculating the distribution of the cumulative elongation strain E at the outlet cross section; and a step for changing at least a part of the initial shape of the inner wall surface so that the distribution of the cumulative elongation strain E is changed.SELECTED DRAWING: Figure 8

Description

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

  Conventionally, it has been practiced to simulate the behavior of a visco-elastic body and to evaluate the conduit of the visco-elastic body based on the result. Such simulation-based evaluation is mainly useful for the design of industrial machines having lines of viscoelastic material. The viscoelastic body is an object having properties of an elastic body and a viscous body, and a polymer material is representative. More specific examples include rubber before vulcanization and the like.

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

Patent No. 5946627 Patent No. 5564074

  However, as in the case of Patent Document 1 described above, there is a possibility that the processing accuracy such as extrusion molding may not be sufficiently improved only by the approach of reducing the speed gradient. For this reason, there has been a demand for a conduit design method that can analyze the conduit of the viscoelastic body more quantitatively and form the viscoelastic material into a desired shape.

  The present invention has been made to solve the above-mentioned problems, and a method of designing a conduit of a viscoelastic body, a design program, and a conduit for forming a viscoelastic body into a desired shape with higher accuracy. Provide an evaluation method.

A method of designing a conduit according to a first aspect of the present invention is a method of designing a conduit through which a viscoelastic body flows, and includes the following steps.
(1) setting an initial shape of the inner wall surface of the pipe line (2) modeling the viscoelastic body as a fluid (3) dividing the flow path defined by the inner wall surface into predetermined elements (4) setting boundary conditions in the inlet cross section and the outlet cross section defined by the inner wall surface and the inner wall surface (5) setting initial values of physical quantities including velocity and pressure of the fluid in each element 6) calculating the physical quantity of the fluid in each of the elements (7) generating a plurality of streamlines or trajectories in the flow path (8) along the respective streamlines or trajectories, Based on the calculated physical quantity, the cumulative elongation strain 伸長, which indicates the degree of elongation and deformation that the viscoelastic body flowing from the inlet cross section receives during the time it flows out from the outlet cross section, is calculated (9) calculating the distribution of the accumulated elongation strain Ε at or near the outlet cross section (10) initial shape of at least a part of the inner wall surface so that the distribution of the accumulated elongation strain 変 化 changes Step to change

A method of designing a conduit according to a second aspect of the present invention is the method of designing a conduit according to the first aspect, wherein the step of calculating the cumulative elongation strain 含 む 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 of calculating extension strain ε _k indicating degree of extension deformation Step of calculating the cumulative extension strain Ε using the extension strain ε _k Note that any _{one of} the point Q _{1 and the} point Q _N is on the inlet cross section or said set near the entrance section, the other of the point Q ₁ or the point Q _N is set near or on the outlet sectional said outlet section.
Note that the step of calculating the time t _k includes setting a unit time t. Further, the order of setting the plurality of points Q _k in order and calculating the time t _k is not limited to the above order.

A method of designing a conduit according to a third aspect of the present invention is the method of designing a conduit according to the second aspect, wherein the relaxation time of the visco-elastic body is τ, and the cumulative elongation strain Ε is It is calculated by equation (1).
However, “T _O ” in the equation (1) represents the time required for the fluid to move between the point Q ₁ and the point Q _N along the streamlines or the trajectory, “ T _k ′ ′ represents the time it takes for the fluid to travel from the point Q ₁ or the point Q _N to the point Q _k along the streamlines or trajectory lines.

The method for designing a conduit according to a fourth aspect of the present invention is the method for designing a conduit according to the second aspect, wherein the accumulated elongation strain Ε is calculated by the following equation (2).

A method for designing a conduit according to a fifth aspect of the present invention is a method for designing a conduit 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

  A method of designing a conduit according to a sixth aspect of the present invention is the method of designing a conduit according to any one of the first through fifth aspects, wherein 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 accumulated elongation strain 均一 becomes uniform, and the vicinity of the streamline or trajectory to which the accumulated elongation strain た い is to be increased Changing the initial shape of the inner wall surface so that the change in the cross-sectional shape of the flow path is large, and in the vicinity of the streamline or trajectory where the accumulated elongation strain is to be reduced. Changing at least one of the initial shape of the inner wall surface so as to reduce a change in the cross-sectional shape of the flow path.

  The method for designing a conduit according to the seventh aspect of the present invention is the method for designing a conduit according to the sixth aspect, wherein 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 channel in the initial shape.

A method of designing a conduit according to an eighth aspect of the present invention is a method of designing a conduit according to any one of the first through seventh aspects, and further includes the following steps.
Calculating the velocity distribution near the outlet cross section or the outlet cross section changing the distance between the inlet cross section and the outlet cross section on at least a portion of the inner wall surface so that the velocity distribution is uniform

A method for designing a conduit according to a ninth aspect of the present invention is a method for designing a conduit according to any one of the first to fifth aspects, and further includes the following steps.
Calculating velocity distribution of the fluid in the outlet cross section or in the vicinity of the outlet cross section; calculating in the distribution of the relative index value of the accumulated extension strain に 対 す る relative to the velocity in the outlet cross section or in the vicinity of the outlet cross section; And changing the distance between the inlet cross section and the outlet cross section in at least a portion of the inner wall surface, wherein at least a portion of the inner wall surface is changed such that the distribution of the accumulated elongation strain Ε changes. 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 channel in the initial shape.

The pipe design method according to a tenth aspect of the present invention is the pipe design method according to the ninth aspect, wherein the relative index value is calculated by the following formula (3).
Where "v" in equation (3) is the velocity of the fluid at or near the outlet cross section.

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

A conduit design program according to a twelfth aspect of the present invention is a conduit design program in which a viscoelastic body flows, and causes a computer to execute the following steps.
(1) setting an initial shape of the inner wall surface of the pipe line (2) modeling the viscoelastic body as a fluid (3) dividing the flow path defined by the inner wall surface into predetermined elements (4) setting boundary conditions in the inlet cross section and the outlet cross section defined by the inner wall surface and the inner wall surface (5) setting initial values of physical quantities including velocity and pressure of the viscoelastic body in each element Step (6) Step of calculating the physical quantity of the fluid in each element (7) Step of generating a plurality of streamlines or trajectory lines in the flow path (8) Along each of the streamlines or trajectory lines Based on the calculated physical quantity, based on the calculated physical quantity, indicating the degree of extensional deformation received by the viscoelastic body flowing from the inlet cross section until it flows out from the outlet cross section (9) calculating the distribution of the accumulated elongation strain in the outlet cross section or the vicinity of the outlet cross section (10) initial stage of at least a part of the inner wall surface so that the distribution of the accumulated elongation strain is changed Step of changing shape

The conduit evaluation method according to a thirteenth aspect of the present invention is an evaluation method of a conduit through which a visco-elastic body flows, and includes the following steps.
(1) modeling the shape of the inner wall surface of the pipeline (2) modeling the viscoelastic body as a fluid (3) dividing the flow path defined by the inner wall into predetermined elements (4) setting boundary conditions in the inlet cross section and the outlet cross section defined by the inner wall surface and the inner wall surface (5) setting initial values of physical quantities including velocity and pressure of the fluid in each element 6) calculating the physical quantity of the fluid in each of the elements (7) generating a plurality of streamlines or trajectories in the flow path (8) along the respective streamlines or trajectories, Based on the calculated physical quantity, the cumulative elongation strain 伸長, which indicates the degree of elongation and deformation that the viscoelastic body flowing from the inlet cross section receives during the time it flows out from the outlet cross section, is calculated Step be evaluated based on that step (9) the outlet cross section or step (10) for calculating a distribution of the accumulated elongation strain Ε near the outlet section the accumulated elongation strain predetermined threshold variation in the distribution of Ε

  According to the present invention, it is possible to provide a method of designing a conduit of a visco-elastic body, a design program, and a method of evaluating a conduit, which can form a visco-elastic body into a desired shape more accurately.

BRIEF DESCRIPTION OF THE DRAWINGS The schematic of the extruder containing the pipeline used as the object of the design method which concerns on this embodiment. (A) The schematic perspective view which shows the shape of the pipeline used as the object of the design method which concerns on this embodiment. (B) An end view of the pipeline viewed from the left direction. (C) End view of the pipeline viewed from the right. Explanatory drawing which shows an example of the mesh created to the initial stage flow path D1. Explanatory drawing which shows an example of the produced streamline. Explanatory drawing of the point set to a streamline. Explanatory drawing explaining distribution of the elongation distortion (epsilon) in the initial stage flow path D1. Explanatory drawing explaining distribution of the accumulation elongation strain Ε in the exit cross section O. FIG. (A) The schematic perspective view which looked at the initial stage flow path D1 from the right side. (B) Explanatory drawing of the speed change of a fluid model. (C) Explanatory drawing of the speed change of a fluid model. Explanatory drawing explaining the velocity distribution in the exit cross section O. FIG. (A) Schematic perspective view of flow path D1 '. (B) The schematic perspective view of the change flow path D2. FIG. 2 is a view for explaining a rubber composition 1 discharged from a mold 2; Explanatory drawing of the ideal distribution of the speed | velocity and relative index value in the exit cross section O. FIG. (A)-(h) The figure which shows the example of an initial stage flow path and a change flow path. The figure which shows the model of the pipeline in the Example, and the generated mesh. (A)-(c) The figure which shows the simulation result in an Example. (A)-(c) The figure which shows the simulation result in an Example. The figure which shows the example of the initial stage flow path created in the Example, and a change flow path. (A)-(h) The graph which shows the simulation result in an Example.

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

[Principle of pipeline design method according to the present embodiment]
Before describing the design method according to the present embodiment, the principle or 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 visco-elastic body such as rubber or resin exhibiting visco-elasticity, 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 inventor of the present invention relates to extension deformation in the direction of streamlines or trajectories (hereinafter referred to as “streamlines etc.”) of a visco-elastic body flowing in a pipeline. And focused on the accumulated amount of elongation strain. That is, in order to analyze the extension deformation in the flow direction, a model fluid obtained by modeling a visco-elastic body is set, fluid analysis of the model fluid in the conduit is performed, and streamlines and the like are generated. Then, along this streamline, an elongation strain is calculated that represents the degree to which the visco-elastic body has been subjected to pressure and has been stretched and deformed from its original length. Furthermore, the accumulated amount of elongation strain during injection and discharge of the viscoelastic body is calculated. As a result, variations in elongation strain occur for each streamline, etc., and the amount of accumulated extension strain (hereinafter referred to as "accumulated elongation strain") becomes uneven at the die exit, so that the mold The material was found to shrink after detachment. Based on this finding, as a result of intensive studies and studies, we have completed the conduit design method according to the present invention.

  More specifically, for example, if there is a rapidly shrinking portion in the flow (flowing) flow path of the visco-elastic body, the velocity of the visco-elastic body becomes large near the shrinking portion, and elongation deformation occurs. Stretch strain occurs. Furthermore, if the stress due to the elongation deformation is not relieved during the time from the elongation deformation to the exit of the mold, the elongation strain of that amount accumulates. And, after the material was discharged from the mold, it was found that the portion where the accumulated elongation strain is relatively large shrinks more, and the portion where the accumulated elongation strain is relatively smaller shrinks less. For this reason, in order to improve the finishing accuracy of extrusion molding, it has been found that it is necessary to make not only the velocity distribution of the material at or near the die exit uniform, but also the cumulative elongation strain distribution uniform. It was obtained. Also, if you want to bend the material after extrusion molding in a specific direction other than to improve the accuracy of finishing dimensions, design the mold so that a specific cumulative elongation strain distribution occurs, and the material is desired. It was also confirmed that it could be bent in the direction of.

  Hereinafter, based on the said knowledge, the concrete method of the design method of the pipeline concerning this embodiment is demonstrated. Below, an extruder is demonstrated as an example as an object of the design method of the pipe line which concerns on this embodiment.

<1. Outline of extruder>
FIG. 1 is a schematic view of the entire extruder 100. As shown in FIG. 1, the extruder includes a cylindrical main body portion 101, a screw 102 disposed inside the main body portion 101, and a hopper 103 disposed on the outer peripheral surface of the main body portion 101. ing. A discharge port 104 is formed at an end portion in the axial direction of the main body portion 101, and the hopper 103 described above is disposed on the outer peripheral surface of the end portion on the opposite side. Then, when the rubber composition 1 is introduced into the main body portion 101 from the hopper 103, the rubber composition 1 is moved to the discharge port 104 while being kneaded by the screw 102. In addition, 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 while the mold It is discharged from the outlet 22 of 2. Below, the design method of this metal mold | die 2 is demonstrated.

<2. Pipe design method>
In the following, there are two methods: A) A method of designing the shape of the mold 2 such 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 (design method 2) of bending the rubber composition 1 after discharge in a desired direction will be described. First, the method A) will be described.

<A. Design method 1>
<A-1. Initial shape setting>
A computer simulation can be used for the method of designing a conduit 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 periphery 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 formed and discharged. Therefore, the shape of the outlet 22 (the shape viewed from the axial direction of the screw 102) is the finished shape of the rubber composition 1. For setting of the modeled shape, dimension data and the like of the mold 2 used conventionally can be used. The flow path of the rubber composition 1 defined by the shape of the inner wall surface 20 set here and the inner wall surface 20 is referred to as an initial shape and an initial flow passage D1, respectively. Further, a surface surrounded by the peripheral edge of the inner wall surface 20 defining the inlet 21 is referred to as an inlet cross section I, and a surface surrounded by the peripheral edge of the inner wall surface 20 defining the outlet 22 is referred to as an outlet 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. Although the initial flow path D1 is a model of a pipeline defined by the mold 2, for convenience of explanation, the reference numerals of the inner wall surface 20, the inlet 21, the outlet 22, etc. are used in common with the mold 2. To be.

  FIG. 2A shows a schematic perspective view of an example of the initial flow path D1. And based on the result of the calculation mentioned later, the change flow path D2 which changed the shape of this initial flow path D1 is designed, and the rubber composition 1 is discharged in a desired shape. The inlet cross section I of the initial flow passage D1 is rectangular, and the inlet 21 communicates with the discharge port 104 of the extruder 100. The outlet cross section O is in the form of a triangle extending in the left-right direction and having the most acute angle on the left side, and the rubber composition 1 molded from the outlet 22 is discharged.

  FIG. 2B is an end view of the initial flow passage D1 as viewed from the left. As shown in FIG. 2B, the left end surface has a horizontal portion 23a in which the upper surface 20a continues horizontally in the flow direction, and a rapidly expanding portion 23b in which the upper surface 20a is rapidly expanded upward from the horizontal portion 23a. Then, the upper surface 20a is inclined at a constant gradient from the rapidly expanding portion 23b toward the outlet 22, and the initial flow passage D1 is reduced in the vertical direction. On the other hand, FIG. 2 (c) is an end view of the initial flow passage D1 as viewed from the right. As shown in FIG. 2C, in the right end face, the initial flow path D1 is reduced in the vertical direction by the upper surface 20a being inclined at a constant slope in the flow direction. When the upper surface 20a reaches the bent portion 24, the initial flow passage D1 is further reduced in the vertical direction by being inclined at a gentle gradient. The upper surface 20a is formed in a step shape in the vicinity of the bent portion 24, so that there is a sharply reduced portion 20b in which the initial flow passage D1 is locally reduced (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. In addition, a surface viewed from a direction substantially orthogonal to the flow direction and a direction orthogonal to the vertical direction is referred to as a “side surface” of the mold 2 and “upper”, “lower”, “left”, “right”, FIG. We shall refer to the direction shown in a). The same applies to the rubber composition 1 present in the mold 2.

<A-2. Mesh generation>
Next, the initial flow path D1 is divided into a plurality of elements (Euler elements) consisting of a predetermined three-dimensional space. The division mode of the element is not particularly limited, and it is performed by a three-dimensional element such as a polyhedral cell (polyhedral grid) other than a tetrahedron, a hexahedron or the like. Also, the volume (size) of the element can be set appropriately. This set of elements is called a mesh. FIG. 3 is an example of a mesh generated for the initial flow path D1. In the present 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 equation of the fluid, it becomes possible to calculate physical quantities such as fluid velocity and pressure. As a method of discretization, known methods such as a finite element method, a finite difference method, a finite volume method, and a boundary element method can be appropriately used.

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

  The measuring method of the specific heat of the rubber composition 1 or a thermal conductivity is not specifically limited, A well-known method can be used. For example, an adiabatic continuous method can be used for specific heat, and a heat wire method can be used for thermal conductivity.

The coefficient of viscosity μ set in the present 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, “strain rate” refers to a rate at which strain when a viscoelastic body is pulled changes with time, and when the strain is continuously 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 unique to the visco-elastic body.

<A-4. Setting simulation conditions>
Subsequently, conditions necessary for performing simulation and analysis are set. Specifically, boundary conditions of the inlet cross section I, the outlet cross section O, and the inner wall surface 20 of the initial channel D1, and initial conditions of the respective elements are set. In the present embodiment, the pressure, mass flow rate, and temperature of the fluid model 1 are set as boundary conditions in the inlet cross section I, and the pressure of the fluid model 1 is set as boundary conditions in the outlet cross section O (atmospheric pressure release). As boundary conditions in the inner wall surface 20, the wall surface temperature of the inner wall surface 20 and the velocity of the fluid model 1 are set. In particular, when the viscosity coefficient of the fluid model 1 is large and the velocity in the flow direction on the inner wall surface 20 needs to be taken into consideration, 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 using the method described in the applicant's patent 5564074.
v _slip = αv _t + (1-α) · v _wall
Where v _slip is the slip velocity, v _t is a velocity component parallel to the inner wall surface 20 of the fluid model 1 at a position separated by a distance d _wall from the inner wall surface 20 in the normal direction, v _wall is 0, and α is the slip ratio In the following formula.
α / (1-α) = μ / {(d _wall · F _slip ) | v _slip −v _wall | ^{es lip-1} } (0 ≦ α ≦ 1)
Where μ is the viscosity coefficient of fluid model 1, and F _slip and es lip are constants inherent to the material.

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

<A-5. Execution of analysis calculation>
Fluid analysis by simulation is performed using the initial flow path D1 which is a model of the mold 2 described above, the boundary conditions, and the initial conditions. As a result of analysis, the physical quantities calculated are the velocity, pressure, temperature, etc. of the fluid model 1 in each element, depending on the set conditions and the equation used. In this embodiment, a Navier-Stokes equation in the case of incompressible flow disclosed in Patent Document 2 as an equation, an equation of mass conservation (an equation of continuity), an energy equation, and a fluid model in the initial flow passage D1. 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 on a single-phase flow, that is, a case where the volume fraction of the fluid model 1 in each element of the initial flow passage D1 is 100%. However, a multiphase flow model in which the rubber composition 1 and air are mixed in the initial flow path D1 may be separately set, and analysis may be performed by the method disclosed in Patent Document 2. Specific equations are shown below.

[Navier-Stokes equation]
It is an equation of motion set for each of the three-dimensional (x, y, z) directions.
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.

[Form of mass conservation]
In the present embodiment, the density of the fluid model 1 is made constant. Therefore, the equation of continuity of incompressible fluid is used.

[Energy equation]
The equation governs the heat transfer of the fluid model 1, and in this embodiment, the temperature of the fluid model 1 is calculated by this equation.
Where H is enthalpy, k is the thermal conductivity, and S is the source term.

<A-6. Streamline generation>
Next, based on the velocity distribution calculated by analysis, a predetermined number of streamlines are generated in the initial flow passage D1. The starting point of the streamline is set on the inlet cross section I, and a line is created such that the direction of the velocity vector in each element is in the tangential direction. Such streamlines can be created using various programs and the like. The number of streamlines can be appropriately set in accordance with the size and the like of the initial flow passage D1. FIG. 4 is an example thereof. A streamline is a line connecting the velocity vectors of each point at a certain moment. It can be considered that the rubber composition 1 in the initial flow passage D1 elongates and deforms in the direction of the velocity vector at each point. That is, before the rubber composition 1 flows in from the inlet cross section I and flows out from the outlet cross section O, the rubber composition 1 is subjected to elongation deformation in the direction along the streamline. Therefore, streamlines are generated to evaluate the distribution of cumulative elongational deformation.

  In general, a streamline refers to a line connecting the velocity vectors of each point at a certain moment. On the other hand, a trajectory refers to a trajectory in which a specific particle flows. If there is no time change in the flow, that is, if the fluid flow is a steady flow, the streamlines and the trajectories coincide. On the other hand, when there is a time change in the flow, that is, in the case of an unsteady flow, the streamlines and the trajectories do not coincide. In the present embodiment, assuming that the flow of the fluid model 1 is steady, streamlines (trajectories) are generated. However, it is not limited to this, and any of streamlines or trajectories may be generated. Below, the case where a streamline is produced | generated is demonstrated for convenience of explanation.

Subsequently, a plurality of points Q ₁ ,..., Q _N (N ≧ 2) are sequentially set on each of the aforementioned streamlines. Specifically, as shown in FIG. 5, and set the point Q ₁ on the inlet section I of the flow line or at a position near the inlet section I, on the same flow line, from the point Q ₁ to the outlet section О The points Q ₂ ,..., Q _N are sequentially arranged, and set so that the point Q _N is located on the outlet cross section O or near the outlet cross section O. Although one streamline is shown in FIG. 5, the same operation is actually performed on each generated streamline. By this operation, the streamlines are divided into (N-1) sections respectively. N may be different for each streamline. The distance L between adjacent points Q differs depending on the position of the point Q, and in the present embodiment, the distance L is set to approximately correspond to the size of the element. If the distance L is too large relative to the size of the element, the calculation accuracy of elongation strain to be described later is reduced, and if it is too small, the calculation of significant elongation 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 a reference length for Incidentally, as described later, in order to evaluate the distribution of Ε strain accumulated elongation at the outlet cross section O, the position of the point Q _N is desirable closer to the outlet cross-section O.

Setting Q points described above, first set the point Q ₁ to the outlet section О on or a position near the outlet section О on streamline, on the same flow line, successively the point Q from the point Q ₁ toward the inlet section I It is also possible to arrange ₂ ,..., Q _N so that the point Q _N is located on or near the inlet cross section I. By this the rubber composition 1 If calculates the elongation deformation experienced during the movement from point Q _{K + 1} to the point Q _K, to calculate the cumulative elongation strain Ε at the outlet cross-section O on or outlet cross section near O below be able to.

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

<A-7. Calculation of elongation strain>
In the fluid analysis stage, the rubber composition 1 is treated as a viscous fluid, but here, the rubber composition 1 is treated as a visco-elastic body. As described above, the rubber composition 1 in the initial flow passage D1 undergoes extension deformation in the same direction as the direction of the velocity vector, and the degree thereof corresponds to the rate of change of the velocity of the model fluid. That is, at a portion where the speed increases rapidly, the rubber composition 1 is subjected to a larger elongation and deformation, and the degree of contraction after discharge of that portion becomes larger. The rubber composition after discharge by noticing how much elongation strain occurs in which part of the initial flow path D1 and how much the elongation strain affects the cumulative elongation strain at the outlet cross section O The contraction of 1 can be efficiently controlled.

Subsequent to setting of point Q, an elongation strain ε _k indicating the degree of elongation deformation received by the rubber composition 1 while moving from the point Q _k to the point Q _{k + 1 as} described above, for each section of each streamline 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 extension strain ε _k in the initial flow passage D1, the history of the extension deformation received by the rubber composition 1 in the initial flow passage D1 is grasped in relation to the position in the initial flow passage D1. It will be possible to 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 elongation is _{(v k + 1 -v k)} × t k and may be represented, elongation strain epsilon _k is to evaluate this for the distance L _K reference length. Therefore, the extension 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.

Thus, when the distribution of the extension strain ε _k in the initial flow passage D1 is calculated, it is possible to identify a region in which the extension strain ε _k is large compared to the other part, and a region in which the extension strain ε _k is small. FIG. 6 shows an example of the area specified by the initial flow path D1. The region R1 enclosed by the broken line is a region where the extension strain ε _k is relatively large. In the region R1, the upper surface 20a is formed in a step-like shape (see FIG. 8B), and the initial flow passage D1 is present in the vicinity of the sharply reduced portion 20b which is locally reduced. Since the velocity of the fluid model 1 increases rapidly on the inner wall surface 20 near the rapid contraction portion 20b, the rubber composition 1 is subjected to a large elongation deformation near the rapid contraction portion 20b. Thus, the region R1 is a region where the extension 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 is present near 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 passage D1 does not change in the vertical direction by having the horizontal portion 23a, the change in velocity of the fluid model 1 in the region R2 is relatively small. Therefore, the elongation deformation to which the rubber composition 1 is subjected is relatively small, and the region R2 is a region where the elongation strain ε _k is relatively small. Based on the region thus identified and the magnitude of the extension strain ε _k in that region, it is possible to determine the location where the shape of the initial flow passage D1 is to be changed, and to design the changed flow passage D2.

<A-8. Calculation of cumulative elongation strain>
Subsequently, an accumulated elongation strain で あ る, which is a cumulative amount of the elongation strain ε _k , is calculated for each streamline. The cumulative elongation strain Ε is an amount that indicates the degree to which the rubber composition 1 flowing from the inlet cross section I undergoes elongation deformation while finally flowing out from the outlet cross section O. The contraction of the rubber composition 1 after discharge is caused by the residual of the cumulative elongation strain, and the degree of the contraction becomes larger as the accumulated elongation strain is larger. Further, as the variation in the distribution of the cumulative elongation strain に お け る at the outlet cross section O is larger, the degree of contraction of the rubber composition 1 after discharge also varies depending on the part, and thus the entire rubber composition 1 may be bent.

  By the way, the rubber composition 1 has an inherent relaxation time τ. The relaxation time τ is the stress generated when tensile force is applied to the rubber composition 1 decreases with the passage of time to a certain threshold or less (about 1 / e of the initial stress, where e is a natural logarithm) It is the time until it is alleviated. That is, as the relaxation time τ is shorter, the stress of the elongated and deformed rubber composition 1 is relieved in a short time, and the influence of the extension deformation received by the rubber composition 1 on the cumulative extension strain tends to be reduced. On the other hand, as the relaxation time τ is longer, the stress of the stretched and deformed rubber composition 1 is more likely to remain, and the effect of the stretching deformation received by the rubber composition 1 on the cumulative extension strain 大 き く becomes larger. Therefore, as described later, the elongation deformation affects the cumulative elongation strain 応 じ according to the length with respect to the relaxation time τ of the time T until the rubber composition 1 enters from the inlet 21 of the mold 2 and exits from the outlet 22. It is desirable to consider the impact. The method of defining the relaxation time τ is not particularly limited. For example, a method by stress relaxation measurement with a Mooney viscometer, a method by NMR relaxation measurement, a method by simulation, etc. can be used.

If the relaxation time τ is relatively short relative to the time T, and it is considered that the stress caused by the elongation deformation is partially relieved before the rubber composition 1 is discharged from the outlet 22, the cumulative elongation strain Ε is It can be represented by the following equation (1).
However, “T _O ” represents the time required for the rubber composition 1 to enter from the inlet 21 of the mold 2, move on the streamline or the trajectory, and be discharged from the outlet 22. “T _k ” represents the time it takes the visco-elastic body to travel on the streamline or trajectory from the inlet cross section to the point Q _k .
“T _o ” can be the time (Σt _k ) at which fluid model 1 flows from point Q ₁ to point Q _N. Further, “T _k ” can be set to the time (t ₁ +... + T _k−1 ) in which the fluid model 1 flows from the point Q ₁ to the point Q _k . Equation (1) shows that, for example, when (T _k −T _o ) is equal to τ, the elongation strain ε _k-1 that the rubber composition 1 receives between the point Q _k-1 and the point Q _k is the outlet 22 At the time of discharge from the ink, it is shown to be relaxed by approximately 1 / e.

On the other hand, when it is considered that the relaxation time τ is sufficiently long relative to the time T, and the stress caused by the elongation deformation substantially remains in the rubber composition 1 discharged from the outlet 22, the cumulative elongation strain Ε is It can be expressed by equation (2).

In the present embodiment, the distributions of the cumulative elongation strain Ε and the cumulative elongation strain に お け る at the outlet cross section O are calculated using the above equation (2). This distribution makes it possible to study how the partially generated elongation strain ε _k consequently affects the finished shape of the rubber composition 1. An example of the distribution of the accumulated extension strain Ε at the outlet cross section O calculated for the initial flow passage D1 is shown in FIG. The region S1 is a region where the accumulated elongation strain Ε is relatively large, and is shown by hatched portions in FIG. The region S2 is a region where the cumulative elongation strain Ε is relatively small, and is indicated by a shaded portion shown in FIG. The region S1 is generated on the right of the outlet cross section O on the right side 20a and a part of the right side surface and the lower surface of the inner wall surface 20, and among them, the generation on the upper surface 20a is remarkable. The region S2 is formed at the left end of the outlet 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, the large extension strain ε _k generated in the region R1 affects the cumulative extension strain に お い て in the region S1 corresponding to the downstream thereof. I understand. In addition, in the region S2 corresponding to the downstream of the region R2 in which the extension strain ε _k is not relatively generated, it is understood that the cumulative extension strain 小 さ く な る also becomes small.

  In the present embodiment, if the variation of all the values of the accumulated elongation strain Ε in the outlet cross section O is in the range of ± 5% or less, it is judged as substantially uniform. In the method (design method 1) 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 exit cross section O of the mold 2, the distribution of cumulative elongation strain Ε is uniform If it is determined that the shape of the initial flow passage D1 is not changed in order to make the distribution of the accumulated elongation strain 均一 uniform. On the other hand, when the variation exceeds ± 5%, it is judged that the distribution of the accumulated elongation strain Ε is not uniform, and it is necessary to change the shape of the initial flow passage D1. Therefore, it can be said that the calculation of the distribution of the accumulated elongation strain Ε and the comparison of the variation with the predetermined threshold value or the variation in other pipelines is to evaluate the pipeline from the viewpoint of processing accuracy. Note that the threshold value of variation is not limited to this, and can be changed as appropriate depending on the properties of the rubber composition 1 and the like. Further, the shape of the initial flow passage D1 may be changed so as to make the distribution of the accumulated elongation strain Ε even more without setting a specific threshold value. Below, the specific procedure which changes the initial stage flow path D1 and designs the change flow path D2 is demonstrated.

<A-9. Flow path shape design>
In order to make the distribution of the cumulative elongation strain 均一 uniform, the cumulative elongation strain 領域 in the region S2 is made larger while the cumulative elongation strain Ε in the region S1 becomes smaller. Alternatively, depending on the degree of variation of the accumulated elongation strain Ε, only the accumulated elongation strain Ε in any region may be adjusted to make the distribution uniform. And for that purpose, the shape of the inner wall surface 20 is changed in the vicinity of the streamline which an end includes in area | region S1 and area | region S2. Although various portions can be considered as the vicinity of the streamline, desirably, the shapes of the inner wall surface 20 in the vicinity of the region R1 and the region R2 which affect the cumulative elongation strain are changed. Depending on the relaxation time τ of the rubber composition 1, it is possible to omit the change in shape of the region in which the extension strain ε _k is considered to have little influence on the cumulative extension strain Ε.

FIG. 8A is a schematic perspective view of the initial flow passage D1 as viewed from the right side. As described above, the region R1 is present in the vicinity of the sharply reduced portion 20b where the initial flow passage D1 sharply shrinks in the flow direction. In the present embodiment, in order to reduce the extension 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 less likely to occur. That is, as shown in FIG. 8C, the shape of the region R is changed to a shape in which the sharp reduction portion 20b is eliminated and the shape is gradually reduced in the flow direction. In this way, the extension strain ε _k in the region R1 is reduced, and as a result, the cumulative extension strain に お け る in the region S1 located downstream of the region R1 is reduced.

Further, the distribution of the accumulated elongation strain Ε is also adjusted by changing the shape of the initial flow passage D1 in the vicinity of the region R2 where the accumulated elongation strain Ε is relatively small. In the region R2, the extension strain ε _k hardly occurs, and the cumulative extension strain Ε is relatively small also in the region S2 existing in the lower region of the region R2. Therefore, the shape of the horizontal portion 23a is changed to a shape such that the initial flow passage D1 gradually reduces 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 extension strain ε _k is generated, and the cumulative extension strain に お け る in the region S2 on the left side of the outlet cross section O can be increased. . Alternatively, by forming at least one protrusion on the inner wall surface 20 of the initial flow passage D1 so as to be resistant to flow, a larger elongation strain ε _k may be generated. Thus, the flow channel changed so that the distribution of the accumulated elongation strain 均一 becomes uniform (for example, the variation within 5% described above) is referred to as a flow channel D1 ′ (see FIG. 10A).

  When a change is made to the cross-sectional shape of the initial flow passage D1, it is desirable that the flow passage cross-sectional area of the flow passage D1 'be smaller than the flow passage cross-sectional area of the initial flow passage D1. It is desirable to make changes to shrink in the direction. In the present embodiment, when changing the shape of the inner wall surface 20 for the purpose of changing the distribution of the accumulated elongation strain Ε, the distance or the positional relationship of the outlet cross section O with respect to the inlet cross section I is changed. The shape change of the inner wall surface 20 is not performed. When a part or all of the inner wall surface 20 is extended in the flow direction or shortened to change the distance or positional relationship of the outlet cross section O 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 accumulated strain strain, the influence on the velocity distribution of the fluid model 1 at the outlet cross section O is much larger. For this reason, it is because it is more suitable for shape change (described later) for the purpose of changing the velocity distribution.

Furthermore, in order to accurately shape the finished dimensions 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 at the outlet cross section O becomes uniform. In addition, since the threshold value of the variation of the velocity distribution regarded as uniform can be set appropriately, the description is omitted here. In the present embodiment, the shape of the inner wall surface 20 of the flow passage D1 'is changed so that the variation in the velocity of the outlet cross section O in the initial flow passage D1 is further reduced. 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 outlet cross section O is narrow on the left side and wide on the right side. Therefore, on the left side of the inner wall 20 near the outlet 22, the pressure loss due to the wall friction of the fluid model 1 is large, and on the right side, the pressure loss is relatively small. Therefore, the velocity of the fluid model 1 is small on the left side of the outlet cross section O and large on the right side. When the velocity distribution in the outlet cross section O is calculated by actually performing the analysis, the velocity is generally increased from the left to the right, and the portion slightly more to the right has the largest velocity distribution (see FIG. 9). Therefore, the velocity distribution can be made more uniform by shortening the left inner wall surface 20 of the flow path D1 'in the flow direction and / or extending the right inner wall surface 20 in the flow direction. FIG. 10 (b) shows a modified flow passage D <b> 2 designed by extending the right inner wall surface 20. 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 has a certain angle with the inlet cross section I has been changed. In addition, the distance K _IO on the inner wall 20 from the point Ia on the periphery of the inner wall 20 defining the inlet cross section O to the point Oa on the periphery of the inner wall 20 defining the outlet cross section O except for the left side Is changed between the flow path D1 'and the change flow path D2.

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

Thus, by calculating the distribution of the extension strain ε _{k and} the distribution of the cumulative extension strain 確認, it is confirmed which part of the flow line the rubber composition 1 is subjected to more extension deformation. it can. As a result, it is possible to determine a portion for changing the shape of the inner wall surface 20 in the initial flow path D1 and how to change the shape of the inner wall surface 20. This makes it possible to design an efficient conduit because it is not necessary to design a conduit based on experience etc. and repeat test experiments. In addition, it is possible to perform extrusion molding with higher accuracy than simply making the velocity distribution in the outlet cross section of the conduit uniform. Furthermore, in this method, there is no need to install a structure different from the conduit on the inner wall surface of the conduit, so there is no possibility of causing contamination due to the adhesion of the visco-elastic body to the structure.

<B. Design method 2>
Next, as Design Method 2, the 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 at the outlet cross section O is the same as the design method 1. Below, the case where the rubber composition 1 after extrusion is bent to the right direction is demonstrated as an example using the metal mold | die 2 (initial stage flow path D1) of FIG. FIG. 11 is a view when the rubber composition 1 discharged from the mold 2 is bent in a predetermined direction as viewed from the lower side of the mold 2. In this case, as shown in FIG. 11, it is necessary that the right side of the extruded rubber composition 1 shrinks more than the left side, and the left side is extruded earlier than the right side. Therefore, the distribution of the accumulated elongation strain 累積 at the outlet cross section O needs to be a distribution such that the accumulated elongation strain 大 き く increases from the left side to the right side. Furthermore, the distribution of the velocity v at the outlet cross section O needs to be a distribution such that the velocity v becomes smaller from the left side to the right side (see FIG. 12).

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

Therefore, the distribution index of the velocity v and the cumulative elongation strain に お け る at the outlet cross section O is treated by the relative index value α of the cumulative elongation strain に 対 す る with respect to the velocity v at 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 passage D2 in such a distribution that the index value α generally increases from the left side to the right side of the outlet cross section O (see FIG. 12). The following aspect can be considered as a design method of such a change flow path D2. From the viewpoint of the velocity distribution, the channel length on the left side of the initial channel D1 is shortened and / or the channel length on the right side is extended so that the velocity v becomes relatively small on the right side of the outlet cross section O. In addition, from the viewpoint of the distribution of the accumulated elongation strain Ε, a rapidly shrinking portion is provided upstream of the streamline existing near the right side of the outlet cross section O so that the accumulated elongation strain Ε becomes relatively large on the right side of the outlet 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 the present embodiment, the distribution on the straight line m as shown in FIG. 12 is calculated. The straight line m is a straight line which roughly divides the outlet cross section O in the vertical direction. However, the position to be calculated is not limited to this, and can be changed as appropriate depending on the shape of the outlet cross section O. Further, it is also possible to calculate an average or weighted average of the index values α in the vertical direction at the same position in the horizontal direction.

FIG. 13 shows an example of changing the shape of the flow path. FIG. 13A shows an initial flow passage D1. FIGS. 13 (b) to 13 (h) show the modified flow channel D2b to the modified flow channel D2h, respectively, and there are seven examples of the modified flow channel D2. The main shape change parts of the inner wall surface 20 are shown surrounded by dotted lines. The features of the change flow path D2b to the change flow path D2h are as shown in Table 1 below.

  Thus, by introducing the index of the relative index value α, it becomes possible to determine the magnitude of the accumulated elongation strain Ε with respect to the speed. As a result, at the same position of the outlet cross section O, the cumulative elongation strain モ デ ル is reduced while the velocity v of the model fluid is substantially increased while the velocity v of the model fluid is substantially reduced while the cumulative elongation strain 大 き く is increased. can do. By this, 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 discharge into a ring, the rubber composition 1 can be bent in the same direction as the winding direction. , The winding work is streamlined.

<Modification>
As mentioned above, although the embodiment of the present invention was explained in full detail, the present invention is not limited to the above-mentioned embodiment, and can be changed into various modes and can carry out.

  For example, the equation for calculating the cumulative elongation strain Ε is not limited to the equations (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, it is also possible to use equations obtained by appropriately modifying the equations (1) and (2) It is possible.

In the present embodiment, the equation (5) is used as a equation 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 that However, the method of calculating the extension strain ε _k is not limited to the method by equation (5). For example, it is also possible to calculate the extension strain ε _k by calculating the component (component in the velocity direction) of the strain tensor in the streamline direction at a point on the streamline or trajectory.

  In the above embodiment, the method of designing a conduit has been described. However, the present invention can be used not only as a method of designing a pipeline, but also as a method of evaluating an existing pipeline or a pipeline being designed. As described above, it is possible to evaluate the performance of the conduit by calculating the variation in the distribution of the accumulated elongation strain Ε at the outlet cross section O and comparing with the threshold value. Moreover, it is also possible to compare the variation in the distribution of the accumulated elongation strain Ε for each pipe line, and to evaluate a pipe line with small variation as a pipe line 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 Processing Accuracy of Rubber Composition
As an example according to the present invention, a mold model as shown in FIG. 14 was used as an initial flow path D1, and a change flow path D2 was designed based on the above analysis. The details will be described below.

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

  The time taken for the rubber composition 1 of this embodiment to enter the mold 2 from the inlet 21 and to be discharged from the outlet 2 is about a dozen seconds. On the other hand, the relaxation time of the rubber material before vulcanization, which depends on the type, is mostly 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 限定 is limited. For this reason, in the present embodiment, the above-mentioned equation (2) is used to calculate the cumulative elongation strain Ε.

  An example of the initial flow path D1 set under the above conditions and the mesh generated in the initial flow path D1 is shown in FIG. However, in the present embodiment, the initial flow passage D1 includes the head portion 100a (see FIG. 1) of the extruder 100. Then, based on the above analysis, the accumulated elongation strain に お け る in the initial flow path D1 and the velocity of the fluid model 1 were calculated. The results are as shown in FIG. 15 and FIG. Here, FIG. 15 (a) is a perspective view showing a part of the head portion 100a and distribution of the extension strain ε of each streamline in the pipeline corresponding to the mold 2, and FIG. 15 (b) is an outlet cross section. FIG. 15 (c) shows the distribution of the velocity v at the exit cross section. As shown in FIG. 15 (a), a relatively large region G1 having an extension strain ε of about 0.12 to 0.2 is formed near the rapid contraction portion 20b of the flow passage. On the other hand, in the vicinity of the horizontal portion 23a of the flow passage, a relatively small region G2 of about 20000 to 0.0267 in the extension strain ε is formed. And as shown in FIG.15 (b), in the inner wall surface of the right side of the outlet cross section O, multiple area | region H1 with extremely large accumulated extension strain (xi) is generated with about 4.0000. On the other hand, on the left side of the outlet cross section O, the cumulative elongation strain 相 対 的 に is relatively small at about 3.0000 to 3.2000. Further, as shown in FIG. 15C, in the region J1 on the right side of the outlet cross section O, the velocity v is relatively large at about 0.12 to 0.15 (m / s), while in the region J2 on the left side v is relatively small, about 0.030 to 0.060. That is, there is a variation in the velocity v and the cumulative elongation strain に お け る at the outlet cross section. As a result, in the mold of the initial flow passage 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, a modified flow passage D2 as shown in FIG. 10 (b) was designed. Here, the inner wall F on the right side of the initial flow passage D1 is lengthened, the cross section of the flow passage near the region G1 (the rapidly shrinking portion 20b) is gradually reduced, and the rapid increase in the velocity of the fluid model 1 is alleviated. Furthermore, the cross section of the flow path in the vicinity of the region G2 (horizontal portion 23a) is reduced as compared with the initial flow passage D1, and the velocity and the extension strain Ε are increased in the vicinity of the region G2. The same analysis as in the initial flow passage D1 was performed on the changed flow passage D2, and the distribution of the extension strain ε in the changed flow passage D2 and the distribution of the cumulative extension strain Ε and the velocity v in the outlet cross section O were calculated. As a result, the distribution of the extension strain ε was as shown in FIG. The extension strain ε of the area G2 is about 0.04000-0.533, and the extension strain ε of the area G1 is about 0.02000-0.04667, and the difference between the extension strain ε between the area G1 and the area G2 is almost eliminated. As shown in FIG. 16 (b), the distribution of the cumulative elongation strain に お け る at the outlet cross section O is increased 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 region. It converges to the range of In addition, the region H1 where the accumulated elongation strain 大 き い is large almost 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 becomes a substantially uniform distribution (note that in FIG. 16B, one scale of the diagram showing the cumulative elongation strain 大 き く is enlarged for convenience of explanation). Therefore, in fact, the variation in the cumulative strain strain is smaller than that shown in FIG. Also, as shown in FIG. 16C, the velocity v at the right side of the outlet cross section decreases and the velocity v at the left side increases, resulting in an overall velocity v of about 0.090 to 0.15 (m / s), and an initial flow It can be seen that the variation is reduced compared to the road D1. Therefore, in the mold of the modified flow passage D2, the variation in shrinkage of the rubber composition after extrusion is substantially eliminated, and the finished cross-sectional shape matches the shape of the outlet cross-section.

(Example 2. In the case of bending a rubber composition in a predetermined direction)
Next, an embodiment of the design method 2 will be described. In Example 2, the die 2 is designed such that the rubber composition 1 after discharge is caused to generate non-uniform shrinkage and the rubber composition 1 bends in the direction shown in FIG. Here, the initial channel D1, the rubber composition 1 (model fluid 1), the boundary conditions and the initial conditions are the same as in the first embodiment. Further, the procedure up to the step of calculating the velocity distribution of the fluid model 1 and the distribution of the accumulated elongation strain に お け る at the outlet cross section O is the same as that of the first embodiment. In the present embodiment, for the same reason as that of the first embodiment, the above-mentioned equation (2) is used to calculate the cumulative elongation strain Ε.

  In the second embodiment, the velocity distribution and the distribution of the relative index value α in a straight line m which roughly divides the outlet 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 outlet cross section O, and the relative index value α from the left of the outlet cross section O The modified flow passage D2 is designed to be larger toward the right.

  When the distribution of the velocity v and the relative index value α was calculated for the initial flow passage D1, the results are as shown in FIG. The horizontal axis in FIG. 18A indicates the position in the left-right direction of the normalized outlet cross section O, where 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 normalized to values from 0 to 1. The velocity v is indicated by a two-dot chain line, and the relative index value α is indicated by a solid line. As described above, in the initial flow passage D1, the velocity v increases as going from the left to the right of the outlet cross section O, but the relative index value α decreases, so the contraction portion of the rubber composition 1 after discharge It is difficult to predict the degree of contraction.

  Next, seven modified flow channels D2 were created based on the results of FIG. 18A, and compared with the results of the initial flow channel D1. However, seven types of change flow paths D2 are just an example. The top row of FIG. 17 shows the shapes of the initial flow passage D1, and the changed flow passages D2b to D2h created below. However, the shape of the portion corresponding to the head portion 100 a of the extruder 100 is not changed, and all is common to the initial flow passage D 1. The shapes of the mold portions of the change flow channels D2b to D2h are the shapes shown in FIGS. 13B to 13H, respectively, and the change from the initial flow channel D1 is as described in the embodiment. For the change channels D2b to D2h, the same analysis as in the initial channel D1 was performed to compare the distribution of the velocity v and the relative index value α. As a result, the distributions were as shown in FIGS. 18 (b) to 18 (h), respectively. The changed 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. 18 (b), the distribution of the velocity v and the relative index value .alpha. 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 passage D2h is close to the distribution shown in FIG. The changed flow path D2h is a shape in which the rapidly expanding portion 23b is eliminated from the initial flow path D1 and the inner wall surfaces 20 on both sides are shortened most, and the flow path is shorter overall than the initial flow path D1. Also, it has a sharp reduction portion 25. As described above, by evaluating the distribution of the velocity v and the relative index value α together, the rubber composition 1 after the discharge is added to the extent of the change of the shape of the mold such as the addition of the rapid contraction and the increase or decrease of the flow path length. You can know if it affects the shape. As a result, it is possible to control the elongation strain generated in the rubber composition 1 and efficiently design a mold that causes the rubber composition 1 after discharge to bend in a specific direction.

1 Rubber composition (model fluid)
2 mold 20 inner wall surface 20a upper surface 20b sudden contraction portion 21 inlet 22 outlet 23a horizontal portion 23b abrupt expansion portion 100 extruder 100a extruder head 102 screw 103 supply port 104 discharge port D1 initial flow path D2 changed flow path L distance I entrance Cross-section O Outlet cross-section v _k Speed v Outlet cross-section O Speed ε Elongation strain 累積 Cumulative extension strain α Index value τ Relaxation time

Claims (13)

It is a design method of a pipeline through which a viscoelastic body flows,
Setting an initial shape of the inner wall surface of the pipeline;
Modeling the visco-elastic body as a fluid;
Dividing the flow path defined by the inner wall surface into predetermined elements;
Setting boundary conditions in the inlet cross section and the outlet cross section defined by the inner wall surface and the inner wall surface;
Setting an initial value of a physical quantity including the velocity and pressure of the fluid in each of the elements;
Calculating the physical quantity of the fluid in each of the elements;
Generating a plurality of streamlines or trajectories in the flow path;
The calculated physical quantity is a cumulative elongation strain 示 す, which indicates the degree of elongation and deformation that the visco-elastic body that has flowed in from the inlet cross section along the streamlines or the trajectory line receives during the time it flows out from the outlet cross section. Calculating on the basis of
Calculating a distribution of the accumulated elongation strain Ε at or near the outlet cross section;
Changing an initial shape of at least a part of the inner wall surface so as to change a distribution of the accumulated elongation strain 変 化;
A method of designing a conduit comprising: The step of calculating the accumulated elongation strain Ε
Setting a plurality of points Q _k (1 ≦ k ≦ N, N ≧ 2) in order on the streamlines or the trajectory;
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 Calculating the
Calculating the accumulated elongation strain Ε using the elongation strain ε _k ;
Including
Either the point Q ₁ or the point Q _N is set on the inlet cross section or in the vicinity of the inlet cross section,
The other of the point Q ₁ or the point Q _N is set on or near the outlet cross section,
A method of designing a conduit according to claim 1. The relaxation time of the viscoelastic body is τ,
The method for designing a conduit according to claim 2, wherein the cumulative elongation strain Ε is calculated by the following equation (1).
However, “T _O ” in the equation (1) represents the time required for the fluid to move between the point Q ₁ and the point Q _N along the streamlines or the trajectory, “ T _k ′ ′ represents the time it takes for the fluid to travel from the point Q ₁ or the point Q _N to the point Q _k along the streamlines or trajectory lines. The method for designing a conduit according to claim 2, wherein the cumulative elongation strain Ε is calculated by the following equation (2).
Calculating a distribution of the elongation strain ε _k ;
Determining the range in which the initial shape is changed among the inner wall surfaces based on the distribution of the extension strain ε _k ;
Further comprising
A method of designing a conduit 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 accumulated elongation strain Ε becomes uniform,
In the vicinity of the streamline or trajectory where it is desired to increase the cumulative elongation strain 変 更, changing the initial shape of the inner wall surface so that the change in cross-sectional shape of the flow path becomes large, and the cumulative elongation strain Changing at least one of the initial shape of the inner wall surface so as to reduce the change in the cross-sectional shape of the flow path in the vicinity of the streamline or trajectory where it is desired to reduce wrinkles;
A method of designing a conduit according to any one of claims 1 to 5.   The conduit according to claim 6, wherein the cross section of the flow path defined by the inner wall surface after the change of the initial shape has a smaller area than the cross section of the flow passage defined by the inner wall surface of the initial shape. How to design. Calculating the velocity distribution of the fluid at or near the outlet cross section;
Changing the distance between the inlet cross section and the outlet cross section at least in part of the inner wall surface so that the velocity distribution is uniform;
Further comprising
The design method of the pipeline according to any one of claims 1 to 7. Calculating the velocity distribution of the fluid at or near the outlet cross section;
Calculating a distribution of relative indicator values of the accumulated elongation strain に 対 す る with respect to the velocity at or near the outlet cross section;
Changing the distance between the inlet cross section and the outlet cross section on at least a portion of the inner wall surface such that the velocity distribution changes.
And further
The step of changing the initial shape of at least a part of the inner wall surface so as to change the distribution of the accumulated elongation strain 、 changes the initial shape of at least a part of the inner wall surface so as to change the relative index value distribution Step to
The cross section of the flow path after the change of the initial shape has a smaller area than the cross section of the flow path of the initial shape,
A method of designing a conduit according to any one of claims 1 to 5. The method of designing a conduit according to claim 9, wherein the relative index value is calculated by the following equation (3).
Where "v" in equation (3) is the velocity of the fluid at or near the outlet cross section. The pipe line is a mold provided at the discharge port of the extruder,
The viscoelastic body is a rubber or resin material before crosslinking.
A method of designing a conduit according to any one of claims 1 to 10. It is a design program of a pipeline through which a viscoelastic body flows,
On the computer
Setting an initial shape of the inner wall surface of the pipeline;
Modeling the visco-elastic body as a fluid;
Dividing the flow path defined by the inner wall surface into predetermined elements;
Setting boundary conditions in the inlet cross section and the outlet cross section defined by the inner wall surface and the inner wall surface;
Setting an initial value of a physical quantity including the velocity and pressure of the fluid in each of the elements;
Calculating the physical quantity of the fluid in each of the elements;
Generating a plurality of streamlines or trajectories in the flow path;
The accumulated elongation strain 示 す, which indicates the degree of the elongation deformation received during the time when the visco-elastic body flowing from the inlet cross section flows out from the outlet cross section, is calculated along the streamlines or the trajectories. Calculating based on physical quantities;
Calculating a distribution of the accumulated elongation strain Ε at or near the outlet cross section;
Changing an initial shape of at least a part of the inner wall surface so as to change a distribution of the accumulated elongation strain 変 化;
A pipeline design program that lets you run It is an evaluation method of a pipeline through which a viscoelastic body flows, and
Modeling the shape of the inner wall surface of the pipeline;
Modeling the visco-elastic body as a fluid;
Dividing the flow path defined by the inner wall surface into predetermined elements;
Setting boundary conditions in the inlet cross section and the outlet cross section defined by the inner wall surface and the inner wall surface;
Setting an initial value of a physical quantity including the velocity and pressure of the fluid in each of the elements;
Calculating the physical quantity of the fluid in each of the elements;
Generating a plurality of streamlines or trajectories in the flow path;
The calculated physical quantity is a cumulative elongation strain 示 す, which indicates the degree of elongation and deformation that the visco-elastic body that has flowed in from the inlet cross section along the streamlines or the trajectory line receives during the time it flows out from the outlet cross section. Calculating on the basis of
Calculating a distribution of the accumulated elongation strain Ε at or near the outlet cross section;
Evaluating the variation in the distribution of the accumulated strain strain based on a predetermined threshold value;
A method of evaluating a conduit comprising: