Method for determining mass of rubber component and method for evaluating flow of rubber material

Abstract

To reduce simulation time.SOLUTION: A method for determining the mass of a rubber component molded by extruding a rubber extrusion profile containing air, the method using Moving Particle Simulation, wherein the model used for the simulation fills the space inside an extruder that extrudes the rubber material with particles of the same volume, the particles including particles of the rubber material and particles of the air, the density of the rubber material being used as the density of the air particles, and the kinematic viscosity of the rubber material being used as the kinematic viscosity of the air, positions of the particles of the rubber material and the particles of the air in the extruder being determined by the simulation, the particles of the rubber material and the particles of the air contained in the rubber component being identified, and the mass of the rubber component being determined by multiplying the number of the particles of the rubber material contained in the rubber component, the volume of each particle, and the density of the rubber material.SELECTED DRAWING: Figure 6

Description

Technical Field

[0001] The present invention relates to a method for determining the mass of a rubber member and a method for evaluating the flow of a rubber material.

Background Art

[0002] As a method for molding a rubber member, for example, a method is known in which a rubber roll is introduced into an extruder including a cylinder, a piston, and a die and extruded at a predetermined temperature and pressure. When molding a rubber member by such a method, the rubber roll contains air at its center and around it. Due to the influence of this air, the mass of the extruded rubber member may vary. Alternatively, due to the influence of this air, cracks may occur in the extruded rubber member. In order to solve the mass variation and cracks, the manufacturing conditions are optimized. The manufacturing conditions may be optimized by grasping the behavior of the pressurized and heated rubber member in the extruder. Optimizing while changing the pressure, temperature, and die shape of an actual extruder requires time and cost. For this reason, the manufacturing conditions may also be optimized by grasping the behavior by simulation (Patent Document 1).

[0003] Since pressurized and heated rubber becomes fluidized, the behavior of rubber is treated as a fluid. As a fluid simulation method, for example, there is the particle method. As the particle method, the MPS method (Moving Particle Simulation or Semi-implicit) (Patent Document 2) is known. The particle method is a method in which a fluid is replaced with particles and calculated as a collection of particles.

Prior Art Documents

Patent Documents

[0004]

Patent Document 1

Patent Document 2

Summary of the Invention

Problems to be Solved by the Invention

[0005] However, when determining the behavior of rubber when extruding a rubber roll containing air into the central space by an extruder using the MPS method, the calculation time for the simulation may become long. When using the MPS method, the simulation is performed by replacing the rubber material and air with particles. The density and kinematic viscosity of air are significantly different from those of the rubber material. A simulation in which the density and kinematic viscosity of the rubber material are applied to the rubber particles and the density and kinematic viscosity of air are applied to the air particles is a two-component system simulation that deals with two types of particles having different physical properties (density, kinematic viscosity). The calculation time for the two-component system simulation is longer than the calculation time for the one-component system simulation that deals with particles having the same physical properties.

[0006] Therefore, an object of the present disclosure is to shorten the calculation time for simulation in the case of a rubber roll containing air.

Means for Solving the Problems

[0007] (1) In the method for obtaining the mass of the rubber member of the present disclosure, The extruder includes a cylinder formed of steel, a piston, a spider, an outer die, and an inner die. The piston is inserted into the inner circumference of the cylinder from the first side in the axial direction. The outer circumferential surface of the piston slides in the axial direction on the inner circumferential surface of the cylinder. The spider is attached to the second side in the axial direction of the cylinder. The inner die is provided at the center of the second side in the axial direction of the spider. The annular outer die is provided radially outside the center of the spider. The spider has a plurality of holes penetrating axially between a portion where the inner die of the spider is fixed and a portion where the outer die is fixed. The total cross-sectional area of the plurality of holes is smaller than the cross-sectional area of the piston. The rubber extruded profile includes a rubber material having a density of ρ and a kinematic viscosity of ν, and air contained between the rubber materials. The outer diameter of the rubber extruded profile is smaller than the inner diameter of the cylinder. An extruder that inserts the rubber extruded profile into the space formed by the cylinder and the piston and pushes the piston from the first side in the axial direction to the second side, thereby extruding a predetermined amount of an annular rubber member from between the inner die and the outer die. The method for obtaining the mass of the rubber member uses Moving Particle Simulation. The model used for the Moving Particle Simulation is With the rubber extruded profile inserted into the space formed by the cylinder and the piston and the state where the piston contacts the rubber extruded profile from the first side in the axial direction to the second side as the initial state, the space in the extruder is filled with particles of the same volume. The particles include particles of the rubber material and particles of air. The density of the air particles uses the ρ that is the density of the rubber material, and the kinematic viscosity of the air uses the ν that is the kinematic viscosity of the rubber material. The piston is moved from the first side in the axial direction to the second side with respect to the cylinder. By the Moving Particle Simulation, The positions of the particles of the rubber material and the positions of the particles of air in the extruder are obtained, and the particles of the rubber material and the particles of air included in the rubber member are specified. The mass of the rubber member is obtained by multiplying the number of particles of the rubber material included in the rubber member, the volume of each particle, and ρ that is the density of the rubber material.

[0008] This makes it possible to shorten the calculation time for simulations in cases such as rubber rolls containing air.

[0009] (2) Preferably, the ν that is the kinematic viscosity of the rubber material is 1600 m2 is / s or more. This reveals the preferred application range of the method according to the present disclosure.

[0010] (3) In the method for evaluating the flow of the rubber material of the present disclosure, the extruder includes a cylinder formed of steel, a piston, a spider, an outer die, and an inner die, the piston is inserted into the inner circumference of the cylinder from the first side in the axial direction, the outer circumference of the piston slides axially on the inner circumference of the cylinder, the spider is attached to the second side in the axial direction of the cylinder, the inner die is provided at the center of the second side in the axial direction of the spider, the annular outer die is provided radially outside the center of the spider, the spider has a plurality of holes penetrating axially between the portion where the inner die of the spider is fixed and the portion where the outer die is fixed, the total cross-sectional area of the plurality of holes is smaller than the cross-sectional area of the piston, the rubber extruded profile includes a rubber material having a density of ρ and a kinematic viscosity of ν and air contained between the rubber materials, the outer diameter of the rubber extruded profile is smaller than the inner diameter of the cylinder, an extruder that inserts the rubber extruded profile into the space formed by the cylinder and the piston and pushes the piston from the first side in the axial direction to the second side to extrude a predetermined amount of an annular rubber member from between the inner die and the outer die, the method for evaluating the flow of the rubber material uses Moving Particle Simulation, the model used for the Moving Particle Simulation is, with the rubber extruded profile inserted into the space formed by the cylinder and the piston and the state where the piston contacts the rubber extruded profile from the first side in the axial direction to the second side as the initial state, the space in the extruder is filled with particles of the same volume, The particles include particles of the rubber material and particles of air. Using the density ρ of the rubber material as the density of the air particles and the kinematic viscosity ν of the rubber material as the kinematic viscosity of the air particles, The piston is moved from a first side in the axial direction to a second side with respect to the cylinder. By the Moving Particle Simulation, The positions of the particles of the rubber material and the positions of the particles of air in the extruder are determined.

[0011] This can reduce the calculation time required for simulation in the case of a rubber roll containing air.

[0012] Preferably, the kinematic viscosity ν of the rubber material is 1600 m 2 / s or more. This clarifies the preferred application range of the method according to the present disclosure.

Advantages of the Invention

[0013] According to the method of the present disclosure, even in the case of a rubber roll containing air, it is possible to perform a simulation in a short calculation time.

Brief Description of the Drawings

[0014]

Figure 1

Figure 2

Figure 3

Figure 4

Figure 5

Figure 6

Figure 7

Figure 8

Figure 9

Figure 10

Figure 11

MODE FOR CARRYING OUT THE INVENTION

[0015] 〔Explanation of Terms〕

[0016] Rubber: A material with a high elastic limit and a low elastic modulus mainly composed of organic polymers such as natural rubber and synthetic rubber. Viscosity: When a fluid is sandwiched between flat plates with an area S and a distance h, and the flat plates are moved parallel to each other at a relative velocity U, a shear stress τ is generated in the direction opposite to the moving direction. If the force generated between the object and the plate is F, F is proportional to the reciprocal of the distance h and the relative velocity U, and is expressed as τ = F / S = μ × U / h. This proportionality coefficient μ is the viscosity. Kinematic viscosity: The value ν = μ / ρ (m 2 / s) obtained by dividing the viscosity by the density of the liquid under the same conditions (temperature, pressure), which is a physical property value that governs the state of flow. Power-law fluid: Among non-Newtonian fluids, a fluid in which the apparent viscosity increases or decreases exponentially with the increase or decrease of the shear rate (the magnitude of flow).

[0017] 〔1. Extruder〕 The present disclosure relates to a method for obtaining the mass of a rubber member in an extruder that extrudes a rubber member formed from a rubber material by heating and pressurizing and forming it from a die, and evaluating the flow of the rubber material. First, the extruder will be described.

[0018] FIG. 1 is a schematic diagram showing an overview of an extruder. The extruder 1 includes a cylinder 2, a piston 3, a spider 4, an outer die 5, and an inner die 6. The cylinder 2, the piston 3, the spider 4, the outer die 5, and the inner die 6 are formed of a steel material. The steel material is an alloy mainly composed of iron such as stainless steel, for example.

[0019] <Cylinder> The cylinder 2 has a cylindrical shape. The cylinder 2 guides the piston 3 described later on the inner peripheral surface of the cylinder 2. The cylinder 2 constitutes a first space for pressurizing the rubber extruded profile 7 together with the piston 3. The extending direction of the inner peripheral surface of the cylinder 2 is the axial direction. The first space holds the rubber extruded profile 7 containing the rubber material which is the raw material of the rubber member described later. The cylinder 2 has the strength necessary for holding the rubber extruded profile 7 at a predetermined temperature and pressure. The cylinder 2 includes a heating device (not shown) for heating the rubber extruded profile 7. The heating device is, for example, an electric heater. The heating device is not limited to an electric heater and may be one that circulates a heated liquid. Further, a temperature sensor (not shown) for measuring the temperature is attached to the cylinder 2. The temperature sensor is, for example, a thermocouple.

[0020] <Piston> The piston 3 is a member for pressing the rubber extrusion molding 7. The piston 3 has a rod-shaped outer peripheral surface that follows the shape of the inner peripheral surface of the cylinder 2. The extending direction of the outer peripheral surface of the piston 3 is also the axial direction. The piston 3 is fitted into the cylinder 2 with the outer peripheral surface of the piston 3 aligned with the inner peripheral surface of the cylinder 2. The piston 3 can move slidably in the axial direction with respect to the cylinder 2. When the piston 3 slides with respect to the cylinder 2, the piston 3 is arranged with a predetermined clearance with respect to the cylinder 2 so that the heated and pressurized and fluidized rubber extrusion molding 7 does not leak out. The piston 3 is inserted into the inner peripheral surface of the cylinder 2 from the first side in the axial direction. In FIG. 1, the axial direction is the left-right direction, and the first side is the left side in FIG. 1. In FIG. 1, the piston 3 is slid from the left side (the first side in the axial direction) toward the right side (the second side in the axial direction) with respect to the inner peripheral surface of the cylinder 2 by an actuator (not shown), and the rubber extrusion molding 7 is pressed by reducing the first space. The actuator is, for example, a hydraulic actuator. The actuator may be an electric actuator.

[0021] <Spider> The spider 4 is a member for fixing and supporting the outer die 5 and the inner die 6. The spider is called a spider because its shape resembles a spider. The spider 4 is attached to the second side in the axial direction of the cylinder 2. The second side in the axial direction is the right side. The spider 4 includes an inner die at the center of the second side in the axial direction, and an annular outer die 5 on the radially outer side of the center of the spider 4. The spider 4 has a plurality of holes penetrating axially between the portion where the inner die 6 of the spider 4 is fixed and the portion where the outer die 5 is fixed. The plurality of holes penetrate in the axial direction of the cylinder 2. The plurality of holes are arranged in the circumferential direction of the cylinder 2. The plurality of holes are the inner peripheral surface of a cylinder. The total cross-sectional area of the plurality of holes in a cross-section perpendicular to the axial direction is smaller than the cross-sectional area of the piston 3 in a cross-section perpendicular to the axial direction. The sum of the spaces of the plurality of holes and the sum of the spaces formed between the outer die 5 and the inner die 6 described later are the second space.

[0022] <Outer die, inner die> FIG. 2 is a perspective view showing the positional relationship between the spider 4, the inner wall 21 of the outer die 5, and the outer wall 22 of the inner die 6. The outer die 5 and the inner die 6 are fixed in a predetermined positional relationship by being attached to the spider 4. The inner wall 21 of the outer die 5 includes a first conical surface that tapers from the second side in the axial direction to the first side in the axial direction, a flat surface that is connected to the first conical surface and whose diameter decreases from the first conical surface, and a cylindrical surface that extends from the flat surface to the first side in the axial direction. The outer wall 22 of the inner die 6 includes a part of a second conical surface that tapers from the second side in the axial direction to the first side in the axial direction, and a third conical surface that is connected to the second conical surface and whose diameter increases from the second conical surface toward the first side in the axial direction. A part of the second space formed between the outer die 5 and the inner die 6 has a shape in which the cross-sectional area in a cross-section perpendicular to the axial direction gradually decreases from the upper left (the first side in the axial direction) to the lower right (the second side in the axial direction) in FIG. 2. The shape of the outlet side of the space, in other words, the shape of the lower right side (the second side in the axial direction) in FIG. 2, is a shape that transfers the inner peripheral surface and the outer peripheral surface of the rubber member 8. That is, the shape of the inner wall 21 on the radially inner side of the outer die 5 and the shape of the outer wall 22 on the radially outer side of the inner die 6 are determined so as to be the shape of the rubber member 8. The outer die 5 and the inner die 6 are attached to the spider 4. The temperature of the outer die 5 is maintained at a predetermined temperature. The temperature of the outer die 5 may be different from the temperature of the cylinder 2. The temperature of the outer die 5 is maintained at a predetermined temperature to control the behavior of the rubber material. A heating device and a temperature sensor may be provided on the outer die 5 to control the temperature so that the temperature of the outer die 5 is maintained at a predetermined temperature.

[0023] <Rubber Extrusion Molding> The rubber extruded profile 7 is, for example, a product in which a plurality of rubber materials formed into a sheet shape are wound into a roll shape. The rubber extruded profile 7 is not limited to such a shape. For example, it may be a cylindrical block shape. The rubber extruded profile 7 may be composed of one piece or a plurality of pieces. In the case of the rubber extruded profile 7 in which the rubber material is wound into a roll shape and arranged in the first space, there is a third space at the center of the wound sheet-shaped rubber material, and the third space contains air 9. Among the wound sheets, a fourth space is formed between the sheets, and the fourth space contains air 9. There is also a fifth space between the outer side of the sheet-shaped rubber material and the inner peripheral surface, end surface of the cylinder 2, and end surface of the piston 3, and the fifth space contains air 9. Since the sheet-shaped rubber materials are arranged side by side in the axial direction on the inner peripheral surface of the cylinder, a sixth space is also formed between the sheet-shaped rubber material adjacent to the sheet-shaped rubber material, and the sixth space contains air 9. The rubber extruded profile 7 includes the rubber material and the air 9 in the third space, the air 9 in the fourth space, the air 9 in the fifth space, and the air 9 in the sixth space. Such a rubber extruded profile 7 contains air 9 between the rubber materials, so the rubber extruded profile 7 inserted into the first space formed by the cylinder 2 and the piston 3 includes the rubber material and the air 9.

[0024] 〔2. Manufacture of Rubber Member〕 The rubber member 8 is manufactured as follows. The spider 4 is removed from the cylinder 2. The rubber extruded profile 7 is arranged on the inner peripheral surface of the cylinder 2 of the extruder. The spider 4 is attached to the cylinder 2. The rubber extruded profile 7 arranged in the first space formed by the cylinder 2 and the piston 3 is pushed into the holes of the spider 4 by the piston 3 being pushed from the first side in the axial direction to the second side, and the rubber extruded profile 7 is manufactured by being extruded little by little from between the inner die 6 and the outer die 5.

[0025] Specifically, first, the rubber extrusion profile 7 is disposed on the inner peripheral surface of the cylinder 2 that forms a first space which is opened by removing the spider 4 from the cylinder 2. FIG. 3 is a schematic diagram showing the state of the rubber extrusion profile inserted into the extruder. As shown in FIG. 3, three rubber extrusion profiles 7 with the rubber material wound in a roll shape are arranged in the first space. The spider 4 is attached to the cylinder 2. When the rubber extrusion profile 7 is arranged in the first space, a sixth space is formed between each of the rubber materials wound in a roll shape, and this sixth space contains air 9. Also, in order to easily insert the rubber material wound in a roll shape into the inner peripheral surface of the cylinder 2, the outer diameter of the rubber material wound in a roll shape is smaller than the inner diameter of the cylinder 2. In this case, a fifth space is formed between the rubber material wound in a roll shape and the cylinder 2, and the fifth space contains air 9.

[0026] After the rubber extrusion profile 7 is arranged in the first space, the spider 4 is attached to the cylinder 2, and the first space is closed, the cylinder 2 and the outer die 5 are heated to a predetermined temperature, the rubber material softens, and the rubber extrusion profile 7 becomes fluidized. Then, the piston 3 is pushed from the first side in the axial direction to the second side, from the left side to the right side in FIG. 1, so that pressure is applied to the rubber extrusion profile. The rubber extrusion profile 7 that has become fluidized and is under pressure is extruded from between the outer die 5 and the inner die 6 through the holes of the spider 4 and the second space formed by the outer die 5 and the inner die 6. The extruded rubber extrusion profile 7 is cut by a cutter (not shown) provided at the outlets of the outer die 5 and the inner die 6 when a predetermined amount has been extruded, and an annular rubber member is completed. As described above, the rubber extrusion profile 7 contains the rubber material and air 9.

[0027] [3. Fluid Analysis Method] Next, the fluid analysis method will be described. In an extruder for molding a rubber member, the fluidized rubber material is simulated as a fluid. As methods for simulating a fluid, there are the lattice method and the particle method.

[0028] [Lattice Method] Figure 4 is a conceptual diagram showing the concept of the lattice method. The lattice method is a technique that divides the region where the fluid exists into a lattice pattern as shown in Figure 4, and obtains the physical quantities of each divided element by a system of simultaneous equations. The arrows shown in Figure 4 indicate the moving directions of the lattice points where the lattices intersect. The lattice method is, for example, the finite element method. However, when using the lattice method, the divided lattices cannot be greatly displaced or split. In the case of an extruder, the rubber extrusion profile 7 containing the rubber material and air 9 arranged in the first space is fluidized and fills the entire interior of the extruder including the first space and the second space. The rubber extrusion profile 7 is pressurized by the piston 3, and the rubber extrusion profile 7 is pushed out through the holes of the spider 4 and the annular space formed by the outer die 5 and the inner die 6, and is greatly displaced. Therefore, for the rubber extrusion profile 7 in the extruder, the analysis results obtained by performing a simulation by the lattice method may deviate from the actual situation.

[0029] <Particle method> Figure 5 is a conceptual diagram showing the concept of the particle method. The arrows shown in Figure 5 indicate the moving directions of the particles. As shown in Figure 5, the particle method divides the fluid into particles and calculates them as a collection of particles. Therefore, the particle method can perform more accurate analysis than the lattice method in cases where the displacement of the fluid is large or when it splits. The particle method is, for example, the MPS method. The MPS method is a method proposed to handle incompressible fluids in the particle method. The basic equations governing the MPS method are the continuity equation and the Navier - Stokes equation, which will be described later.

[0030] <Continuity equation> The continuity equation is applied generally in physics and represents that "substances do not suddenly appear or disappear without any trigger", and is also called the law of conservation of mass. The law of conservation of mass in the MPS method is expressed by Equation (1). Dρ / Dt = 0 ···(1) ρ means density. D / Dt means the time derivative representing the time change of the physical quantity associated with particles or the like, and is also called the Lagrange derivative.

[0031] <Navier - Stokes equation> The Navier-Stokes equations are non-linear partial differential equations that describe the motion of fluids and represent the law of conservation of momentum in fluids. The Navier-Stokes equations in the MPS method are represented by Equation (2). Du / Dt = ∇P / ρ + ν∇ 2 u + g ··· (2) u is the velocity, P is the pressure, ν is the kinematic viscosity, and g is the external force field (acceleration due to gravity) acting per unit mass of the fluid.

[0032] <Flow of simulation> Under the control of the continuity equation and the Navier-Stokes equations, the MPS method determines the tentative positions of the particles from the forces between the particles at a certain time, and using the determined tentative positions, calculates the pressure at the next time under the condition of keeping the density of the particles constant. The velocity of each particle is calculated from the pressure gradient obtained based on the calculated pressure. The position of each particle at that time is obtained from the calculated velocity of each particle.

[0033] 〔4. Method for evaluating the flow of rubber materials〕 Next, a method for evaluating the flow of rubber materials using the MPS method will be described.

[0034] The inventor of the present disclosure has intensively studied the behavior of rubber materials when extruding a rubber extruded profile 7 containing air 9 arranged in a first space by an extruder using the MPS method. However, the physical properties including the density and kinematic viscosity of the rubber material and the physical properties including the density and kinematic viscosity of air 9 are significantly different. A simulation using the MPS method with the actual density and kinematic viscosity of rubber and the actual density and kinematic viscosity of air is a two-component system simulation that deals with rubber material particles and air particles, and takes a long calculation time.

[0035] In view of such problems, when the inventor extrudes the rubber extruded profile 7 by an extruder, since the kinematic viscosity of the rubber material is high, the air between the rubber materials in the first space and the second space does not rise vertically upward in the fluid like the bubbles in water, and in the fluidized rubber extruded profile 7, the inventor considered that the initial shape of the fluidized rubber material gradually deforms. In other words, the inventor considered that the regions of the third space, the fourth space, the fifth space, and the sixth space are supported by the surrounding rubber material, and the rubber material supporting the third space, the fourth space, the fifth space, and the sixth space behaves in such a way that it moves in the first space and the second space while gradually deforming the shape of the third space, the fourth space, the fifth space, and the sixth space without significantly changing the volume.

[0036] Furthermore, the inventor further considered that if the air 9 in the third space, the fourth space, the fifth space, and the sixth space gradually deforms its initial shape between the fluidized rubber materials in the first space and the second space, then the particle density and kinematic viscosity of the air 9 should be made the same as those of the rubber material respectively. The inventor considered that if the particle density and kinematic viscosity of the air are made the same as those of the rubber material respectively, the density and kinematic viscosity of all the particles will be the same as those of the rubber material, resulting in a single-component system simulation dealing with one type of particle, and the calculation time can be shortened. In order to distinguish between the particles of the rubber material and the particles of the air, the inventor decided to assign identification information for identifying whether each particle is a particle of the rubber material or a particle of the air in the analysis.

[0037] <Evaluation of Rubber Material Flow by MPS Method> Next, a method for evaluating the flow of rubber material by the MPS method will be described. FIG. 3 is a schematic diagram showing a state where a rubber extruded profile is inserted into an extruder. FIG. 3 shows an example in which a rubber extruded profile 7 including three rubber rolls is arranged in the first space formed by a cylinder 2 and a piston 3. The following description will proceed along the example of FIG. 3.

[0038] FIG. 6 is a schematic diagram showing a state where the fluid is replaced with particles in a simulation using the MPS method. FIG. 6 shows a state where the example shown in FIG. 3 is replaced with particles. The particles indicated by the hatched circles are particles 61 of a rubber material. The particles indicated by the white circles are particles 62 of air 9. FIG. 6 shows the state of the particles immediately after the rubber extruded material 7 is inserted into the first space formed by the cylinder 2 and the piston 3. The rubber member region 63 is a region where the rubber extruded material 7 extruded from the extruder 1 is formed as the rubber member 8.

[0039] FIG. 7 is a schematic diagram showing a state where the fluid is replaced with particles. FIG. 7 shows the simulation result after a predetermined time has elapsed from FIG. 6. The piston 3 is moved from left (the first side in the axial direction) to right (the second side in the axial direction) in FIG. 7 by an actuator to pressurize the rubber extruded material 7. The pressurized rubber extruded material 7 starts to be extruded out of the extruder 1 through the holes of the spider 4 and the annular second space formed by the outer die 5 and the inner die. The particles 61 of air 9 between the rubber materials do not rise vertically upward in the fluid like bubbles in water, so they are extruded out of the extruder 1 together with the particles 61 of the rubber material.

[0040] FIG. 8 is a schematic diagram showing a state where the fluid is replaced with particles. FIG. 8 shows an example of the simulation result after a predetermined time has elapsed from FIG. 7. The pressurized rubber extruded material 7 is further extruded out of the extruder 1 through the annular second space, and the particles 61 of the rubber material and the particles 62 of air 9 fill the rubber member region 63. The rubber extruded material 7 extruded out of the extruder 1 is separated from the extruder by the above-described cutter and becomes the rubber member 8.

[0041] When a simulator that executes the MPS method is configured to display schematic diagrams such as FIGS. 6, 7, and 8 on a display as computer graphics, a person performing the simulation can evaluate the flow of the rubber member by looking at the displayed computer graphics. Displaying the particles of the rubber material and the particles of air 9 in different colors makes the behavior of the particles of the rubber material and the particles of air easier to understand and facilitates the evaluation for the person performing the simulation.

[0042] <Operation Procedure> FIG. 9 is a flowchart showing the operation procedure of the simulation using the MPS method. Before starting the simulation, a person performing the simulation first inputs material property data, simulation conditions, and modeling data into the simulator (S01).

[0043] The material property data S01a is data indicating the physical properties of the constituent members appearing in the simulation. The data indicating the physical properties of the rubber material treated as a fluid includes density ρ, kinematic viscosity ν, and thermal conductivity. Since the kinematic viscosity changes depending on the temperature, the material property data S01a also includes a coefficient expressing the change in kinematic viscosity with respect to temperature and a calculation formula for obtaining the kinematic viscosity with respect to temperature. At this time, the density and kinematic viscosity applied to the particles of air 9 are the density and kinematic viscosity applied to the particles of the rubber material, respectively. Thereby, the simulator executes the simulation as a one-component system. When the fluid is treated as a power-law fluid, the material property data S01a includes coefficients representing the properties of the power-law fluid. The data indicating the physical properties of solid constituent members such as the cylinder 2 and the piston 3 includes the heat transfer coefficient and the like.

[0044] The simulation conditions S01b are the conditions for causing the simulator to execute the simulation. The conditions for execution include, for example, the temperatures of the cylinder 2 and the outer die 5, the extrusion speed of the piston 3, and the size of the particles replacing the fluid.

[0045] The modeling data S01c is data indicating the physical shape such as the cylinder 2. Based on the physical shape such as the cylinder 2, the simulator determines boundary conditions and the like indicating the range in which the fluid flows.

[0046] Next, the person performing the simulation causes the simulator to execute the simulation (S02). For example, the simulator outputs computer graphics data at predetermined time intervals. The computer graphics data shows the flow of the rubber material particles and air particles represented by replacing the rubber material and air arranged in the first space with particles. The person performing the simulation evaluates the flow of the rubber material based on the computer graphics data. After outputting the data, the simulator ends the simulation (S03).

[0047] <Mass calculation of rubber member> After the simulation is completed, the person performing the simulation calculates the mass of the rubber member based on the data (S04). The mass of the rubber member 8 is calculated by multiplying the number of rubber material particles included in the rubber member 8, the volume of a single particle, and the density of the rubber material. In FIG. 8, the rubber material particles 61 and air particles 62 fill the rubber member region 63 and have the shape of the formed rubber member 8. Before executing the simulation, the volume of a single particle and the density of the rubber material are determined. Therefore, if the number of rubber material particles 61 included in the rubber member 8 among the rubber material particles 61 and air particles 62 filling the rubber member region 63 can be obtained, the mass of the rubber member 8 can be calculated.

[0048] Figure 10 is a schematic diagram of the rubber member 8 when viewed from the right direction (the second side in the axial direction) in Figure 8. The particles indicated by the hatched circles are the particles 61 of the rubber material. The particles indicated by the white circles are the particles 62 of the air 9. The rubber member 8 on the left side in Figure 10 is an example of the rubber member 8 with fewer particles 62 of the air 9. The rubber member 8 on the right side in Figure 10 is an example of the rubber member 8 with more particles 62 of the air 9. Figures 10 and 8 show the states of the particles 61 of the rubber material and the particles 62 of the air 9 included in the rubber member 8 in the rubber member region 63. Therefore, by counting the number of particles 61 of the rubber material in the rubber member region 63, the number of particles 61 of the rubber material included in the rubber member 8 can be obtained. The person performing the simulation may count the number of particles 61 of the rubber material in the rubber member region 63. The simulator may count the number of particles 61 of the rubber material in the rubber member region 63. If the number of particles 61 of the rubber material in the rubber member region 63 can be obtained, the person performing the simulation or the simulator can calculate the mass of the rubber member 8 by multiplying this number by the volume of a single particle and the density of the rubber material.

[0049] [5. Comparison between Simulation Results and Actual Measurement] Figure 11 is a graph comparing the simulation results with the mass (actual measurement results) of the actually manufactured rubber member 8. The horizontal axis indicates the experiment number, and each is as follows. Experiment number 1: Actual measurement result, high extrusion speed Experiment number 2: Actual measurement result, low extrusion speed Experiment number 3: Simulation result, high extrusion speed Experiment number 4: Simulation result, low extrusion speed A high extrusion speed means that the extrusion speed of the piston 3 is 0.37 mm / sec. A low extrusion speed means that the extrusion speed of the piston 3 is 0.35 mm / sec.

[0050] The vertical axis in FIG. 11 indicates the 3σ interval of the normal distribution as the variation in the mass of the rubber member when conducting experiments multiple times. As shown in FIG. 11, the simulation results are in good agreement with the measured results. That is, the method according to the present disclosure can accurately predict the mass variation of the rubber member 8.

[0051] 〔6. Scope of application〕 The method of the present disclosure is a method premised on a fluid with a high kinematic viscosity in which air particles do not rise in the fluid like bubbles in water. The inventor of the present disclosure has conducted research and found that the lower limit of the kinematic viscosity to which the method of the present disclosure can be applied is 1600 m 2 / s. If the kinematic viscosity is 1600 m 2 / s or more, the air particles in the fluid move while gradually deforming their initial shape without significantly changing their volume.

[0052] All the embodiments disclosed this time are illustrative in all respects and not restrictive. The scope of the rights of the present invention is not limited to the above-described embodiments, but includes all modifications within the scope equivalent to the configurations described in the claims.

Explanation of reference numerals

[0053] 1 Extruder 2 Cylinder 3 Piston 4 Spider 5 Outer die 6 Inner die 7 Rubber extruded profile 8 Rubber member 9 Air 21 Inner wall of the outer die 22 Outer wall of the inner die 61 Particles of rubber material 62 Particles of air 63 Rubber member region

Claims

1. The extruder includes a cylinder formed of steel, a piston, a spider, an outer die, and an inner die, wherein the piston is inserted into the inner circumference of the cylinder from a first side in the axial direction, the outer circumference of the piston slides axially on the inner circumferential surface of the cylinder, the spider is attached to a second side in the axial direction of the cylinder, the inner die is provided at the center of the second side in the axial direction of the spider, the annular outer die is provided radially outside the center of the spider, the spider has a plurality of holes penetrating axially between a portion where the inner die of the spider is fixed and a portion where the outer die is fixed, the total cross-sectional area of the plurality of holes is smaller than the cross-sectional area of the piston, the rubber extruded profile includes a rubber material having a density of ρ and a kinematic viscosity of ν and air contained between the rubber materials, the outer diameter of the rubber extruded profile is smaller than the inner diameter of the cylinder, an extruder for extruding a predetermined amount of an annular rubber member from between the inner die and the outer die by inserting the rubber extruded profile into the space formed by the cylinder and the piston and pushing the piston from a first side in the axial direction to a second side, the method for obtaining the mass of the rubber member uses Moving Particle Simulation, the model used for the Moving Particle Simulation is with the state where the piston contacts the rubber extruded profile when the rubber extruded profile is inserted into the space formed by the cylinder and the piston and the piston is moved from the first side in the axial direction to the second side as the initial state, filling the space in the extruder with particles of the same volume, the particles include particles of the rubber material and particles of air, the density of the air particles uses the ρ which is the density of the rubber material, and the kinematic viscosity of air uses the ν which is the kinematic viscosity of the rubber material, moving the piston from a first side in the axial direction to a second side with respect to the cylinder, by the Moving Particle Simulation, obtaining the positions of the particles of the rubber material and the positions of the particles of air in the extruder, and identifying the particles of the rubber material and the particles of air included in the rubber member, the mass of the rubber member is obtained by multiplying the number of particles of the rubber material included in the rubber member, the volume of each particle, and the density ρ which is the density of the rubber material, A method for obtaining the mass of a rubber member.

2. The method for obtaining the mass of the rubber member according to claim 1, wherein the ν, which is the kinematic viscosity of the rubber material, is 1600 m2 / s or more.

3. The extruder includes a cylinder formed of a steel material, a piston, a spider, an outer die, and an inner die. The piston is inserted into the inner circumference of the cylinder from the first side in the axial direction. The outer circumference of the piston slides in the axial direction on the inner circumference surface of the cylinder. The spider is attached to the second side in the axial direction of the cylinder. The inner die is provided at the center of the second side in the axial direction of the spider. The annular outer die is provided radially outside the center of the spider. The spider has a plurality of holes penetrating in the axial direction between a portion where the inner die of the spider is fixed and a portion where the outer die is fixed. The total cross-sectional area of the plurality of holes is smaller than the cross-sectional area of the piston. The rubber extruded profile includes a rubber material having a density of ρ and a kinematic viscosity of ν, and air contained between the rubber materials. The outer diameter of the rubber extruded profile is smaller than the inner diameter of the cylinder. An extruder that inserts the rubber extruded profile into the space formed by the cylinder and the piston and pushes the piston from the first side in the axial direction to the second side, thereby extruding a predetermined amount of an annular rubber member from between the inner die and the outer die. The method for evaluating the flow of the rubber material uses Moving Particle Simulation. The model used for the Moving Particle Simulation is as follows: The rubber extruded profile is inserted into the space formed by the cylinder and the piston, and with the state where the piston contacts the rubber extruded profile from the first side in the axial direction to the second side as the initial state, the space in the extruder is filled with particles of the same volume. The particles include particles of the rubber material and particles of air. The density of the air particles uses the ρ, which is the density of the rubber material, and the kinematic viscosity of the air uses the ν, which is the kinematic viscosity of the rubber material. The piston is moved from the first side in the axial direction to the second side with respect to the cylinder. By the Moving Particle Simulation, The positions of the particles of the rubber material and the positions of the particles of air in the extruder are obtained. A method for evaluating the flow of a rubber material.

4. The method for evaluating the flow of the rubber material according to claim 3, wherein ν, which is the kinematic viscosity of the rubber material, is 1600 m2 / s or more.

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