JP2022181577A - Prediction method of cross-sectional shape of viscoelastic fluid - Google Patents

Abstract

To provide a method capable of predicting a cross-sectional shape of a viscoelastic fluid after expansion deformation.SOLUTION: A method for predicting a cross-sectional shape of a viscoelastic fluid passing through an extrusion channel having a discharge port through which a viscoelastic fluid is extruded and then discharged from the discharge port includes the steps of causing a computer to: make a fluid model flow toward a discharge port of a channel model, where the fluid model is placed in the channel model S6; calculate a shear speed of a flowing fluid model at the discharge port S7; and calculate a cross-sectional shape of a viscoelastic fluid discharged from the discharge port after expansion deformation based on a relation between a die swell ratio and a shear speed of the viscoelastic fluid, the shear speed of the fluid model, and an opening dimension of the discharge port S8.SELECTED DRAWING: Figure 8

Description

The present invention relates to a method for predicting the cross-sectional shape of a viscoelastic fluid.

Patent Literature 1 listed below describes a method for simulating a viscoelastic body. This method includes the steps of first setting a fluid analysis model having an inflow portion and an outflow portion and a viscoelastic model, executing a fluid analysis using the viscoelastic model, and calculating the viscosity on the streamline obtained as a result of the fluid analysis. calculating a stress for structural analysis input from the elastic stress. Furthermore, a step of setting a structural analysis model whose cross section is the shape of the outlet of the outlet of the fluid analysis model, and a step of setting the stress for structural analysis input as the initial stress for the structural analysis model and executing the structural analysis. and are included.

JP 2017-189957 A

The viscoelastic body as described above has a property of expanding and deforming (die swell) immediately after being discharged from the outlet. Therefore, it is important to consider such expansion deformation in order to predict the cross-sectional shape of the viscoelastic body discharged from the outlet.

SUMMARY OF THE INVENTION The present invention has been devised in view of the actual situation as described above, and a main object of the present invention is to provide a method capable of predicting the cross-sectional shape of a viscoelastic fluid after being expanded and deformed.

The present invention provides a method for predicting the cross-sectional shape of a viscoelastic fluid that has passed through an extrusion channel having an ejection port through which the viscoelastic fluid is extruded and is ejected from the ejection port, the extrusion channel and inputting a flow path model having the discharge port into a computer; inputting a fluid model modeling the viscoelastic fluid into the computer; a die swell ratio of the viscoelastic fluid; and inputting the relationship to shear rate into the computer, wherein the computer places the fluid model in the channel model and causes the fluid model to flow toward the outlet of the channel model. calculating a shear rate at the outlet of the flowing fluid model; based on the relationship, the shear rate of the fluid model, and the outlet opening size, the and calculating a cross-sectional shape of the viscoelastic fluid after expansion deformation discharged from the discharge port.

In the method for predicting the cross-sectional shape of the viscoelastic fluid according to the present invention, the step of calculating the cross-sectional shape includes specifying the die swell ratio corresponding to the shear rate of the fluid model based on the relationship; calculating a cross-sectional shape of the viscoelastic fluid based on the identified die swell ratio and the aperture dimensions.

The method for predicting the cross-sectional shape of the viscoelastic fluid according to the present invention further includes dividing the discharge port into a plurality of regions, wherein the step of calculating the cross-sectional shape includes: A step of calculating a cross-sectional shape of each of said viscoelastic fluids may be included.

In the method for predicting the cross-sectional shape of the viscoelastic fluid according to the present invention, the contour shape of the discharge port includes a predetermined length in a first direction and a length in a second direction orthogonal to the first direction. and the length in the second direction is smaller than the length in the first direction, and the step of calculating the cross-sectional shape is the step of calculating the cross-sectional shape of the viscoelastic fluid expanded and deformed at least in the second direction. may include

In the method for predicting the cross-sectional shape of the viscoelastic fluid according to the present invention, the step of inputting the relationship includes the step of measuring the die swell ratio based on the ratio of the capillary length to the capillary diameter of the extrusion channel. may contain.

In the method for predicting the cross-sectional shape of the viscoelastic fluid according to the present invention, the viscoelastic fluid may contain unvulcanized rubber.

The method for predicting the cross-sectional shape of a viscoelastic fluid according to the present invention makes it possible to predict the cross-sectional shape of the viscoelastic fluid after expansion and deformation discharged from the discharge port of the extrusion channel by adopting the above steps. .

1 is a perspective view showing a computer for executing a method for predicting a cross-sectional shape of a viscoelastic fluid according to this embodiment; FIG. FIG. 4 is a cross-sectional view showing a viscoelastic fluid passing through an extrusion channel; 3 is a perspective view of the extrusion channel of FIG. 2; FIG. 4 is a flow chart showing a processing procedure of a method for predicting the cross-sectional shape of a viscoelastic fluid according to the present embodiment; FIG. 2 is a conceptual diagram showing a channel model of this embodiment; FIG. 6 is a front view of a discharge port of the channel model of FIG. 5; 4 is a graph showing the relationship between the die swell ratio of a viscoelastic fluid and the shear rate; 5 is a flow chart showing a processing procedure of a cross section calculation step of the embodiment; It is a figure which shows the cross-sectional shape of the viscoelastic fluid after expansion deformation|transformation of this embodiment.

BEST MODE FOR CARRYING OUT THE INVENTION Hereinafter, embodiments of the present invention will be described based on the drawings. It should be understood that the drawings include exaggerated representations and representations that differ from the dimensional ratios of the actual structures in order to facilitate understanding of the content of the invention. In addition, throughout each embodiment, the same or common elements are denoted by the same reference numerals, and overlapping descriptions are omitted. Furthermore, the specific configurations shown in the embodiments and drawings are for understanding the content of the present invention, and the present invention is not limited to the illustrated specific configurations.

The method of predicting the cross-sectional shape of the viscoelastic fluid of the present embodiment (hereinafter sometimes simply referred to as the “prediction method”) is to pass through an extrusion channel having an ejection port through which the viscoelastic fluid is extruded, A method for predicting the cross-sectional shape of a dispensed viscoelastic fluid. A computer is used in the prediction method of this embodiment.

[Computer]
FIG. 1 is a perspective view showing a computer for executing a method for predicting the cross-sectional shape of a viscoelastic fluid according to this embodiment. A computer 1 of this embodiment includes a main body 1a, a keyboard 1b, a mouse 1c, and a display device 1d. The main body 1a is provided with, for example, an arithmetic processing unit (CPU), a ROM, a working memory, a storage device such as a magnetic disk, and disk drive devices 1a1 and 1a2. In addition, software and the like for executing the prediction method of this embodiment are stored in advance in the storage device.

[Viscoelastic fluid]
FIG. 2 is a cross-sectional view showing viscoelastic fluid 4 passing through extrusion channel 2 . The viscoelastic fluid 4 of the present embodiment contains unvulcanized rubber (fully kneaded rubber material before cross-linking). The viscoelastic fluid 4 is not limited to such unvulcanized rubber, and may include, for example, those having viscoelasticity such as resin materials and elastomers. In addition, the viscoelastic fluid 4 of the present embodiment is assumed to be sufficiently kneaded and in a state that can be regarded as a stable flow state (fluid). For example, if the viscoelastic fluid 4 is an unvulcanized rubber material, this state corresponds to a state in which the fluid is sufficiently kneaded and heated to approximately 80 to 100.degree.

[Extrusion channel]
The extrusion flow path 2 to be analyzed in this embodiment is formed in a cylindrical shape and is connected to the downstream side of the screw extruder 3 . The extrusion channel 2 of this embodiment is partitioned by a frame 2c.

The frame 2c of this embodiment includes a head 17 and a die (base) 18. As shown in FIG. Although the die 18 in this embodiment is removably fixed to the head 17, it may be fixed to the head 17 in a non-removable manner, for example. It should be noted that the extrusion channel 2 to be analyzed is not limited to an existing one, and may be, for example, one in the design stage (for example, one having only CAD data).

The extrusion channel 2 includes a first extrusion channel 2A defined by a head 17 and a second extrusion channel 2B defined by a die (or die) 18 . A supply port 5 connected to the extruder 3 is provided at one end of the first extrusion flow path 2A (extrusion flow path 2). A viscoelastic fluid 4 is supplied from the extruder 3 to the supply port 5 .

3 is a perspective view of the extrusion channel 2 of FIG. 2. FIG. The contour shape (opening dimension) 5s of the supply port 5 of the present embodiment includes a predetermined length L1 in the first direction x and a length L2 in the second direction y orthogonal to the first direction x. there is These lengths L1 and L2 are set to be substantially the same (variation such as manufacturing error (for example, ±5% of length L1) is allowed). In addition, although the contour shape 5s of the present embodiment is formed in a circular shape when viewed from the front, it is not limited to such a form.

A first connection port 21 connected to one end of the second extrusion flow path 2B is provided at the other end of the first extrusion flow path 2A of the present embodiment. The contour shape of the first connection port 21 of the present embodiment is set to be the same as the contour shape of the discharge port 6 (the contour shape of the second connection port 22), which will be described later.

A second connection port 22 connected to the first connection port 21 (the other end of the first extrusion flow path 2A) is provided at one end of the second extrusion flow path 2B of the present embodiment. The contour shape of the second connection port 22 of the present embodiment is set to be the same as the contour shape of the discharge port 6, which will be described later.

As shown in FIG. 2, a discharge port 6 through which the viscoelastic fluid 4 is extruded is provided at the other end of the second extrusion channel 2B (extrusion channel 2). As shown in FIG. 3, the contour shape (opening dimension) 6s of the ejection port 6 of this embodiment has a predetermined length L3 in the first direction x and a second direction y perpendicular to the first direction x. and the length L4 of . The length L4 in the second direction y in this embodiment is set smaller than the length L3 in the first direction x. The contour shape 6s of the present embodiment is formed in a trapezoidal shape when viewed from the front, but is not limited to such a form.

The extrusion channel 2 of the present embodiment is cut from the upstream side to the downstream side in the extrusion direction z (that is, from the supply port 5 side toward the first connection port 21 side) in the first extrusion channel 2A. The area is gradually decreasing. On the other hand, in the second extrusion channel 2B, the cross-sectional area of the extrusion channel 2 is constant from the upstream side to the downstream side in the extrusion direction z (that is, from the second connection port 22 side toward the discharge port 6 side). maintained at As a result, as shown in FIG. 2, the viscoelastic fluid 4 passing through the extrusion flow path 2 receives a large pressure from the first extrusion flow path 2A, and tends to expand and deform immediately after being discharged from the discharge port 6. be.

As shown in FIG. 3, in this embodiment, the length L3 of the discharge port 6 (the first connection port 21 and the second connection port 22) in the first direction x and the length L3 of the supply port 5 in the first direction x The ratio L4/L2 between the length L4 of the discharge port 6 in the second direction y and the length L2 of the supply port 5 in the second direction y is set smaller than the ratio L3/L1 of the length L1. . Therefore, the pressure in the second direction y acts on the viscoelastic fluid 4 passing through the first extrusion flow path 2A to be greater than the pressure in the first direction x, resulting in thread-like molecular chains (not shown). is strongly stretched. On the other hand, the cross-sectional area of the second extrusion channel 2B is kept constant. For this reason, in the viscoelastic fluid 4 passing through the second extrusion flow path 2B, the stretched molecular chains can be returned to the stringy state, but the original stringy state cannot be restored before reaching the discharge port 6. may not be possible. In such a case, the viscoelastic fluid 4 is likely to expand and deform (die swell) immediately after being discharged from the discharge port 6 . In this embodiment, the expansion deformation (die swell) in the first direction x tends to increase in the expansion deformation (die swell) in the second direction y where a large pressure acts. In addition, the tendency of such expansion deformation changes with the shape of the 2nd extrusion flow path 2B.

In this way, the viscoelastic fluid 4 has the property of expanding and deforming (die swell) immediately after being discharged from the discharge port 6 . Therefore, it is important to consider such properties when designing the second extrusion flow path 2B (die 18) capable of ejecting the viscoelastic fluid 4 having the desired cross-sectional shape 16. FIG.

[Prediction method of cross-sectional shape of viscoelastic fluid]
Next, the prediction method of this embodiment will be described. FIG. 4 is a flow chart showing the processing procedure of the method for predicting the cross-sectional shape of a viscoelastic fluid according to this embodiment.

[Input channel model]
In the prediction method of this embodiment, first, the extrusion channel 2 (shown in FIGS. 2 and 3) is modeled, and a channel model having a discharge port is input to a computer (step S1). FIG. 5 is a conceptual diagram showing the channel model 7 of this embodiment.

In step S1 of the present embodiment, based on the design data (design factors) of the extrusion flow path 2 to be analyzed (shown in FIGS. 2 and 3), the three-dimensional space of the extrusion flow path 2 has a finite number of elements e is modeled (discretized) with Thus, the channel model 7 is set. In this embodiment, modeling of the frame 2c (shown in FIGS. 2 and 3) that partitions the extrusion channel 2 is omitted.

The flow path model 7 of the present embodiment includes a first flow path model 7A modeling the first extrusion flow path 2A (shown in FIGS. 2 and 3) and a second extrusion flow path 2B (shown in FIGS. 2 and 3). shown) and a second flow path model 7B. A supply port 8 modeling the supply port 5 (shown in FIGS. 2 and 3) of the extrusion channel 2 is provided at one end of the first channel model 7A (channel model 7) of the present embodiment. The supply port 8 of the present embodiment is set to have the same shape (shown in FIG. 3) as the supply port 5 of the extrusion channel 2 when viewed from the front.

On the other hand, at the other end of the second flow channel model 7B (flow channel model 7) of the present embodiment, a discharge port 9 modeling the discharge port 6 (shown in FIGS. 2 and 3) of the extrusion flow channel 2 is provided. ing. The ejection port 9 of the present embodiment is set to have the same shape (shown in FIG. 3) as the ejection port 6 of the extrusion channel 2 when viewed from the front.

In the present embodiment, the supply port 8 and the discharge port 9 having the above-described shapes allow the flow path to flow from the upstream side toward the downstream side in the extrusion direction z (that is, from the supply port 8 side toward the discharge port 9 side). The cross-sectional area of model 7 is gradually decreasing.

The flow path model 7 (the first flow path model 7A and the second flow path model 7B) has, as shown in the partially enlarged view of FIG. 5, a space in which the fluid model 10 flows is divided ( discretized). The element division is performed by three-dimensional elements such as polyhedral cells (polyhedral grid) as well as tetrahedrons, hexahedrons, etc., and is modeled by Euler elements in this embodiment. At each element e, physical quantities such as pressure, temperature and velocity of the fluid model 10 are calculated. A channel model 7 is stored in the computer 1 .

[Dividing into multiple areas]
Next, in the prediction method of the present embodiment, the outlet 9 of the channel model 7 is divided into a plurality of regions (step S2). FIG. 6 is a front view of the outlet 9 of the flow path model 7 of FIG.

The plurality of regions 11 of the present embodiment are used to calculate the cross-sectional shape of the viscoelastic fluid 4 after expansion and deformation in the cross-section calculation step S8, which will be described later. The plurality of regions 11 can be appropriately divided, for example, according to the contour shape of the ejection port 9 or the like. In the present embodiment, a plurality of division lines 12 extending along the second direction y are spaced apart in the first direction x in the ejection port 9 (the area surrounded by the outline of the ejection port 9). It is divided into a plurality of regions 11 arranged along x.

The plurality of regions 11 can be specified by, for example, the coordinate values of the channel model 7 (element e shown in FIG. 5). In step S2 of the present embodiment, the computer 1 may divide the plurality of areas 11, or the operator may divide (input the areas 11). A plurality of partitioned areas 11 are stored in the computer 1 .

[Input fluid model]
Next, in the prediction method of this embodiment, the fluid model 10 (shown in FIG. 5) modeling the viscoelastic fluid 4 (shown in FIG. 2) is input to the computer 1 (step S3). The fluid model 10 is for incorporating the viscoelastic fluid 4 passing through the extrusion channel 2 into numerical calculation by the computer 1 . The fluid model 10 is arranged at the element e of the channel model 7 .

In the fluid model 10 of this embodiment, the shear viscosity, specific heat and thermal conductivity are defined based on the physical properties of the viscoelastic fluid. Details of shear viscosity, specific heat and thermal conductivity are as described in, for example, the patent document (Japanese Patent No. 5498523). A fluid model 10 is stored in the computer 1 .

[Enter boundary conditions]
Next, in the prediction method of this embodiment, boundary conditions for calculating the flow of the fluid model 10 are input to the computer 1 (step S4). As the boundary conditions of this embodiment, the flow velocity V and temperature of the fluid model 10 supplied to the supply port 8 of the flow channel model 7, and the pressure (=0) of the discharge port 9 of the flow channel model 7 are given. . For the flow velocity and temperature of the fluid model 10, for example, it is possible to appropriately perform actual measurements in the extrusion flow path 2 to be analyzed, and set the values with reference to these values. Further, a constant temperature is set for the wall surface 7w of the flow channel model 7 of the present embodiment.

A flow velocity boundary condition is set on the wall surface 7w of the channel model 7 . As with the patent document (Japanese Patent No. 5498523), the wall surface no-slip condition or the wall-slip condition can be set as the flow velocity boundary condition. Adopted. In this embodiment, wall slip conditions are set. As a result, the fluid model 10 is restrained by the wall surface 7w due to the friction between the fluid model 10 and the wall surface 7w, and the fluid model 10 can be prevented from generating excessive heat. Therefore, it is possible to prevent the temperature distribution, velocity distribution, etc. of the fluid model 10 from deviating from the actual temperature distribution, velocity distribution, etc. of the viscoelastic fluid 4 .

Other boundary conditions include the unit time (time step) of flow calculation (simulation), the number of iterations in internal processing, and the calculation end time. These conditions are arbitrarily determined according to the purpose of the simulation. These boundary conditions are stored in computer 1 .

[Enter the relationship between die swell ratio and shear rate]
Next, in the prediction method of this embodiment, the relationship between the die swell ratio of the viscoelastic fluid 4 and the shear rate is input to the computer 1 (step S5). FIG. 7 is a graph showing the relationship between the die swell ratio of the viscoelastic fluid 4 and the shear rate.

As shown in FIG. 2, the die swell ratio is the ratio between the opening dimension (for example, D5) of the ejection port 6 and the cross-sectional dimension (for example, D6) of the viscoelastic fluid 4 after expansion and deformation ejected from the ejection port 6. is the ratio (eg, D6/D5). In FIG. 7, the higher the shear rate, the higher the die swell ratio. Therefore, the die swell ratio has shear rate dependence.

The relationship between the die swell ratio of the viscoelastic fluid 4 and the shear rate can be obtained as appropriate. In this embodiment, the above relationship is obtained by measuring the die swell ratio at a plurality of shear rates. The die swell ratio can be measured using a capillary rheometer (for example, RG-50 manufactured by Gottfeld) in accordance with JIS-K7199. The temperature of the viscoelastic fluid 4 used for measuring the die swell ratio is appropriately set (eg, 100° C.) based on the temperature of the viscoelastic fluid 4 that is actually passing through the extrusion channel 2. It is desirable to be

It should be noted that the measurement of the die swell ratio requires setting the capillary length L and the capillary diameter D in the above-described capillary rheometer. For example, when the ratio L/D between the capillary length L and the capillary diameter D is set smaller than the ratio (L5/D5) of the extrusion channel 2 (second extrusion channel 2B) shown in FIG. There is a tendency to measure a die swell ratio that is greater than the die swell ratio in extrusion channel 2 (second extrusion channel 2B). Therefore, in step S5, the die swell ratio is preferably measured based on the ratio L5/D5 between the capillary length L5 of the extrusion channel 2 (second extrusion channel 2B) and the capillary diameter D5. As a result, in step S5, a die swell ratio equivalent to the die swell ratio of the viscoelastic fluid 4 actually discharged from the discharge port 6 of the extrusion channel 2 can be experimentally obtained.

As shown in FIG. 2, in this embodiment, the capillary length L5 is the second extrusion channel 2B (from the second connection port 22 to the discharge port) in the extrusion direction z of the viscoelastic fluid 4 in the extrusion channel 2. 6). Also, as shown in FIGS. 2 and 3, the capillary diameter D5 is specified as the length L4 in the second direction y for the contour shape 6s of the discharge port 6. As shown in FIG.

In step S5 of the present embodiment, the measured die swell ratio is plotted at each shear rate, as shown in FIG. Thereby, the relationship between the die swell ratio of the viscoelastic fluid 4 and the shear rate is obtained. In step S5, an approximate expression of the relationship between the die swell ratio and the shear rate may be obtained in order to uniquely identify the die swell ratio corresponding to the shear rate. The relationship between die swell ratio and shear rate is stored in computer 1 .

[Calculate flow of fluid model]
Next, as shown in FIG. 5, in the prediction method of the present embodiment, the computer 1 arranges the fluid model 10 in the flow path model 7 and moves the fluid model 10 toward the discharge port 9 of the flow path model 7. is allowed to flow (step S6). In step S6 of the present embodiment, a flow calculation for flowing the fluid model 10 from the supply port 8 to the discharge port 9 of the channel model 7 based on the boundary conditions described above is performed for each simulation unit time Tx. .

The VOF (Volume of Fluid) method used in the calculation of the flow on the free surface is used for the flow calculation of this embodiment. In the VOF method, instead of directly calculating the movement of the interface between two fluids (viscoelastic fluid 4 and gas (air)) with different shear viscosities, the filling rate of the fluid model 10 in the volume of each element e (i.e. , volume fraction) and expressed by averaging the free interface.

In step S6 of the present embodiment, calculations are performed until the flow of the fluid model 10 reaches a stable state (that is, until it converges). The flow calculation can be performed, for example, by a procedure similar to that of the patent document (Japanese Patent No. 5498523). Thereby, the stable state of the fluid model 10 can be obtained. For flow calculation, for example, commercially available fluid analysis software (eg, ANSYS FLUNET, CFX, etc.) can be used.

In this embodiment, since the wall surface slip condition is set for the wall surface 7w of the flow path model 7, it is possible to prevent the fluid model 10 from generating excessive heat due to the friction between the fluid model 10 and the wall surface 7w. can. As a result, in step S6, it is possible to prevent the temperature distribution, velocity distribution, etc. of the fluid model 10 from deviating from the actual temperature distribution, velocity distribution, etc. of the viscoelastic fluid 4 . Therefore, in step S6, in the flow calculation of the fluid model 10, the behavior of the viscoelastic fluid 4 (shown in FIG. 2) passing through the actual extrusion channel 2 can be reproduced.

[Calculate shear rate]
Next, in the prediction method of this embodiment, the computer 1 calculates the shear rate at the outlet 9 of the fluid model 10 in motion (step S7). In step S7 of the present embodiment, the shear rate at the outlet 9 is calculated in the fluid model 10 flowing in a stable state.

In step S7 of the present embodiment, the shear rate of the fluid model 10 is calculated for each element e (shown in FIG. 5) that constitutes the ejection port 9. FIG. Shear rates can be readily calculated by, for example, the fluid analysis software described above. In step S7, a shear rate for an arbitrary unit time Tx may be calculated, or an average value of multiple shear rates calculated for a plurality of unit times Tx may be calculated.

In the prediction method of this embodiment, even without using the actual extrusion flow path 2 (extruder 3) shown in FIG. Velocity can be simulated using computer 1 . The shear rate is stored in computer 1 .

[Calculate cross-sectional shape of viscoelastic fluid (cross-sectional calculation process)]
Next, in the prediction method of the present embodiment, the computer 1 calculates the cross-sectional shape of the viscoelastic fluid 4 after expansion and deformation discharged from the discharge port 6 shown in FIG. 2 (cross-section calculation step S8). In the cross section calculation step S8, based on the relationship between the die swell ratio of the viscoelastic fluid and the shear rate (shown in FIG. 7), the shear rate of the fluid model 10, and the opening size of the discharge port 9 (shown in FIG. 6) , the cross-sectional shape of the viscoelastic fluid 4 is calculated. FIG. 8 is a flow chart showing the processing procedure of the section calculation step S8 of this embodiment.

In the cross section calculation step S8 of the present embodiment, first, the die swell ratio corresponding to the shear rate of the fluid model 10 is specified based on the relationship between the die swell ratio of the viscoelastic fluid and the shear rate (shown in FIG. 7). (step S81). In step S81 of the present embodiment, the die swell ratio corresponding to the shear rate is specified in each of the plurality of regions 11 shown in FIG.

In step S81 of the present embodiment, first, the shear rates of the plurality of regions 11 are respectively specified. In this embodiment, the shear rate of each region 11 is specified based on the shear rate calculated by the element e (shown in FIG. 5) that configures each region 11 . For specifying the shear rate of each region 11, when there are a plurality of elements e constituting each region 11, the average value of the shear rates of those elements e may be specified, or the maximum value may be specified. and a minimum value may be specified. In the present embodiment, the average value of shear velocities of a plurality of elements e forming each region 11 is specified as the shear velocity of each region 11 .

Next, in step S81 of the present embodiment, the die swell ratio corresponding to the shear rate of each region 11 is specified. In this embodiment, the die swell ratio corresponding to the shear rate of each region 11 is specified based on the relationship between the die swell ratio of the viscoelastic fluid and the shear rate (shown in FIG. 7). The die swell ratio for each region 11 is stored in computer 1 .

Next, in the cross-sectional calculation step S8 of the present embodiment, the cross-sectional shape of the viscoelastic fluid is calculated based on the identified die swell ratio and opening dimensions (step S82). In step S82 of the present embodiment, the cross-sectional shape of the viscoelastic fluid 4 after expansion and deformation is calculated in each of the plurality of regions 11 . FIG. 9 is a diagram showing a cross-sectional shape 16 of the viscoelastic fluid 4 after being expanded and deformed in this embodiment.

As described above, the extrusion channel 2 of the present embodiment is subjected to expansion deformation (die swell) in the first direction x immediately after being discharged from the discharge port 6 shown in FIGS. Expansion deformation (die swell) in two directions y tends to increase. Therefore, in step S82, it is desirable to calculate the cross-sectional shape of the viscoelastic fluid 4 that has expanded and deformed at least in the second direction y.

In step S82 of the present embodiment, the shape (cross-sectional shape 15) obtained by enlarging each region 11 in the second direction y at the die swell ratio specified for each region 11 is specified. In the present embodiment, the length L4 of each region 11 in the second direction y is multiplied by the die swell ratio from the central portion 13 in the second direction y of each region 11 toward both sides in the second direction y. is expanded to From these expanded shapes, the cross-sectional shape 15 of the viscoelastic fluid 4 after expansion and deformation is calculated in each region 11 .

In the step S82 of the present embodiment, the cross-sectional shape 15 of each region 11 is arranged in the first direction x based on the arrangement of each region 11 in the ejection port 9, so that the cross-section of the viscoelastic fluid 4 after expansion and deformation is Each shape 16 is calculated.

In the prediction method of the present embodiment, it is possible to predict the cross-sectional shape 16 of the viscoelastic fluid in consideration of the property of expansion and deformation (die swell) immediately after being discharged from the discharge port 6 of the extrusion flow path 2 shown in FIG. can. Furthermore, in the prediction method of the present embodiment, the relationship between the die swell ratio and the shear rate (shown in FIG. 7), the shear rate of the fluid model 10, and the discharge port do not require the structural analysis of Patent Document 1. A simple calculation based on the opening dimensions of 6 can predict the cross-sectional shape 16 . Therefore, the prediction method of the present embodiment can predict the cross-sectional shape 16 in a short time.

In the prediction method of this embodiment, the relationship between the actual die swell ratio of the viscoelastic fluid 4 and the shear rate (shown in FIG. 7) is used to calculate the cross-sectional shape of the viscoelastic fluid 4 . Therefore, the prediction method of the present embodiment can calculate the cross-sectional shape 16 of the viscoelastic fluid 4 that approximates the actual expansion deformation.

As shown in FIGS. 6 and 9, in the prediction method of the present embodiment, the shear velocity of the fluid model 10 and the Each die swell ratio is specified. As a result, the prediction method of the present embodiment can consider the uneven expansion deformation of the viscoelastic fluid 4 at the discharge port 6 shown in FIGS. A cross-sectional shape 16 of the fluid 4 can be calculated. The number of regions 11 can be appropriately set according to the opening size of the ejection port 6 and the required prediction accuracy, and can be set to 50 to 150, for example.

[Evaluation of cross-sectional shape]
Next, as shown in FIG. 4, in the prediction method of the present embodiment, it is determined whether or not the predicted cross-sectional shape 16 (shown in FIG. 9) of the viscoelastic fluid 4 is satisfactory (step S9). . Whether or not the cross-sectional shape 16 is satisfactory may be determined by the computer 1 or by an operator.

Whether or not the cross-sectional shape 16 of the viscoelastic fluid 4 is satisfactory can be appropriately determined, for example, based on the design accuracy of the rubber product in which the viscoelastic fluid 4 is used. In this embodiment, the cross-sectional shape 16 of the viscoelastic fluid 4 is judged to be good when the die swell ratio (and/or the dimensions after expansion and deformation) of each region 11 is equal to or less than a predetermined threshold value. be. Note that the threshold may be set to a different value for each region 11 .

In step S9, if it is determined that the cross-sectional shape 16 of the viscoelastic fluid 4 is good ("Yes" in step S9), the extrusion flow path 2 (extruder 3) shown in FIG. 2 is manufactured ( step S10). As a result, the viscoelastic fluid 4 having the desired cross-sectional shape 16 can be discharged, so that it is possible to manufacture rubber products and the like capable of exhibiting desired performance.

On the other hand, in step S9, when it is determined that the cross-sectional shape 16 of the viscoelastic fluid 4 is not good ("No" in step S9), the extrusion flow path 2 (in this example, the second extrusion flow path 2B (the die 18 )) is changed (step S11), and steps S1 to S9 are performed again.

In the prediction method of the present embodiment, the design factor of the extrusion channel 2 is deformed until the cross-sectional shape 16 of the viscoelastic fluid 4 is improved. The flow path 2 can be reliably designed and manufactured. As a result, the prediction method of the present embodiment can reduce the time and cost required for prototyping and testing the extrusion flow path 2, so that the extrusion flow path 2 (extruder 3) and the rubber product using the viscoelastic fluid 4 It is possible to shorten the development period such as.

In the previous embodiments, the cross-sectional shape 16 (shown in FIG. 9) of the viscoelastic fluid expanded and deformed in the second direction y was calculated, but the present invention is not limited to such a mode. For example, the cross-sectional shape expanded and deformed in the first direction x may be calculated based on the contour shape of the discharge port 6 and the shape of the extrusion flow path 2 shown in FIG. A cross-sectional shape expanded and deformed in both y may be calculated.

As shown in FIG. 6, in the previous embodiments, the discharge port 9 of the flow channel model 7 was divided into a plurality of regions 11 arranged along the first direction x. Not limited. For example, considering the shape of the discharge port 6 (discharge port 9) and the direction in which expansion deformation (die swell) tends to increase, it may be divided into a plurality of regions 11 arranged in the second direction y. However, it may be divided into a plurality of regions 11 arranged in both the first direction x and the second direction y.

Although the particularly preferred embodiments of the present invention have been described in detail above, the present invention is not limited to the illustrated embodiments and can be modified in various ways.

According to the processing procedures shown in FIGS. 4 and 8, the cross-sectional shape of the viscoelastic fluid discharged from the discharge port of the extrusion channel was predicted (Example 1 and Example 2).

In Example 1, the die swell ratio of the viscoelastic fluid was measured without considering the ratio of the capillary length and diameter of the extrusion channel. On the other hand, in Example 2, the die swell ratio of the viscoelastic fluid was measured based on the ratio of the capillary length and diameter of the extrusion channel.

In Examples 1 and 2, the relationship between the die swell ratio of the viscoelastic fluid and the shear rate, the shear rate of the fluid model, and the opening size of the ejection port were used to determine the expansion deformation after being ejected from the ejection port. , the cross-sectional shape of the viscoelastic fluid was calculated.

In addition, in order to compare the effects of Examples 1 and 2, an extrusion channel (extruder) was manufactured, a viscoelastic fluid was discharged from the outlet of the extrusion channel, and the viscoelastic fluid after expansion and deformation was was measured (experimental example). Then, the cross-sectional shapes predicted in Examples 1 and 2 and the cross-sectional shapes measured in the experimental example were compared. Common specifications are as follows.
Viscoelastic fluid: natural rubber (carbon black compounded)
Die swell ratio measurement temperature: 100°C
Number of regions: 100

As a result of the test, the cross-sectional shape of the experimental example expanded and deformed relatively greatly at both ends of the ejection port in the first direction. On the other hand, in Examples 1 and 2, expansion deformation similar to that of the experimental example was predicted. Therefore, in Examples 1 and 2, the cross-sectional shape of the viscoelastic fluid after expansion and deformation could be predicted.

Furthermore, in Example 2, the die swell ratio was measured considering the ratio of the capillary length and the capillary diameter of the extrusion channel, so compared to Example 1 in which they were not taken into account, the cross-sectional shape was similar to that of the experimental example. could be predicted.

S6 Step of flowing the fluid model S7 Step of calculating the shear rate S8 Step of calculating the cross-sectional shape of the viscoelastic fluid after expansion and deformation

Claims (6)

A method for predicting a cross-sectional shape of a viscoelastic fluid that passes through an extrusion channel having an ejection port through which the viscoelastic fluid is extruded and is ejected from the ejection port, comprising:
a step of modeling the extrusion channel and inputting the channel model having the discharge port into a computer;
inputting a fluid model modeling the viscoelastic fluid into the computer;
inputting into the computer the relationship between the die swell ratio and the shear rate of the viscoelastic fluid;
the computer
arranging the fluid model in the flow path model and causing the fluid model to flow toward the outlet of the flow path model;
calculating a shear rate at the outlet of the flowing fluid model;
calculating a cross-sectional shape of the viscoelastic fluid after expansion and deformation discharged from the discharge port based on the relationship, the shear rate of the fluid model, and the opening size of the discharge port;
A method for predicting the cross-sectional shape of a viscoelastic fluid. calculating the cross-sectional shape includes determining the die swell ratio corresponding to the shear rate of the fluid model based on the relationship;
2. A method of predicting a cross-sectional shape of a viscoelastic fluid according to claim 1, comprising calculating a cross-sectional shape of the viscoelastic fluid based on the determined die swell ratio and the aperture size. further comprising dividing the outlet into a plurality of regions;
3. Prediction of the cross-sectional shape of the viscoelastic fluid according to claim 1, wherein the step of calculating the cross-sectional shape includes a step of calculating the cross-sectional shape of the viscoelastic fluid after expansion deformation in the plurality of regions. Method. The contour shape of the ejection port includes a predetermined length in a first direction and a length in a second direction orthogonal to the first direction, and the length in the second direction is the length in the first direction. less than length
The cross-section of the viscoelastic fluid according to any one of claims 1 to 3, wherein the step of calculating the cross-sectional shape includes calculating the cross-sectional shape of the viscoelastic fluid expanded and deformed at least in the second direction. Shape prediction method. 5. The viscosity of any one of claims 1 to 4, wherein the step of inputting the relationship comprises measuring the die swell ratio based on the ratio of capillary length to capillary diameter of the extrusion channel. A method for predicting the cross-sectional shape of an elastic fluid. The method for predicting a cross-sectional shape of a viscoelastic fluid according to any one of claims 1 to 5, wherein the viscoelastic fluid contains unvulcanized rubber.

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