JP2016043545A - Extrusion simulation method for plastic material - Google Patents

Abstract

PROBLEM TO BE SOLVED: To stably converge the fluidization calculation of a material model.SOLUTION: Provided is an extrusion simulation method for a plastic material where the manner of passing a plastic material through an extrusion flow passage 3 having a feed port to be fed with the plastic material at one end, also having a discharge port 3o from which the plastic material is extruded at the other edge and further having a changed cross section is calculated by a computer 1 and simulated. In the extrusion simulation method, a material model modeled with the plastic material and a flow passage model 11 modeled with the extrusion flow passage 3 are inputted into the computer 1. The shear viscosity η of the material model has shear speed dependency or temperature dependency. In the fluidization calculation of the material model, the definitions of the shear viscosity η are changed in a multistep in such a manner that the influence of the shear speed dependency or temperature dependency to the material model gradually expresses.SELECTED DRAWING: Figure 3

Description

  The present invention relates to a plastic material extrusion simulation method capable of accurately and stably calculating how a plastic material having fluidity such as a rubber material before cross-linking is extruded from a die plate or the like using a computer. .

  The following Patent Document 1 describes the extrusion of a plastic material in which the state of the plastic material passing through the extrusion channel is calculated by a computer in order to increase the development efficiency of the shape of a preformer, die plate, or the like that controls the cross-sectional shape of the rubber material. A simulation method is proposed. In the extrusion simulation, a material model that models a plastic material and a channel model that models an extrusion channel are defined. In the extrusion simulation, a material model is arranged in the flow channel model, and a flow calculation is performed to flow from the supply port to the discharge port based on a predetermined condition.

JP 2013-184367 A

  In the extrusion simulation, shear viscosity is defined in the material model. The shear viscosity has, for example, a shear rate dependency in which the viscosity changes according to the shear rate and a temperature dependency in which the viscosity changes according to the temperature. For example, if the shear viscosity of the material model is defined so that the effects of the shear rate dependency and the temperature dependency appear at the same time, the flow calculation may diverge and cannot be converged.

  For this reason, in the above-mentioned patent document 1, the step of calculating the shear viscosity so that one of the influence of the shear rate dependency or the temperature dependency appears and calculating until the material model becomes stable, and the shear rate dependency Alternatively, the step of defining the shear viscosity and calculating until the material model becomes stable is sequentially performed so that the other influence of temperature dependence appears.

  However, in Patent Document 1, although the flow calculation can be converged stably to some extent, there is room for further improvement.

  The present invention has been devised in view of the above circumstances, and the definition of shear viscosity is changed in multiple stages so that the influence of the shear rate dependency or temperature dependency on the material model gradually appears. The main object of the present invention is to provide a plastic material extrusion simulation method that can stably converge the flow calculation of the material model based on the flow calculation.

  The present invention has a state in which the plastic material passes through an extrusion passage having a supply port to which the plastic material is supplied at one end and a discharge port through which the plastic material is extruded at the other end, and having a change in cross-sectional area. A simulation method for extruding a plastic material that is calculated and simulated by a computer, comprising: inputting a material model obtained by modeling the plastic material into the computer; Discretizing and inputting a flow channel model, and flow calculation for causing the computer to place the material model in the flow channel model and to flow from the supply port to the discharge port based on a predetermined condition And the computer obtains a physical quantity from the material model, the material model The shear viscosity has a shear rate dependency in which the shear viscosity changes according to the shear rate, and the influence of the shear rate dependency on the material model gradually increases in the flow calculation. As shown, the step of changing the definition of the shear viscosity in multiple stages is included.

  The present invention has a state in which the plastic material passes through an extrusion passage having a supply port to which the plastic material is supplied at one end and a discharge port through which the plastic material is extruded at the other end, and having a change in cross-sectional area. A simulation method for extruding a plastic material that is calculated and simulated by a computer, comprising: inputting a material model obtained by modeling the plastic material into the computer; Discretizing and inputting a flow channel model, and flow calculation for causing the computer to place the material model in the flow channel model and to flow from the supply port to the discharge port based on a predetermined condition And the computer obtains a physical quantity from the material model, the material model The shear viscosity is defined, and the shear viscosity has a temperature dependency in which the shear viscosity changes according to the temperature, so that the influence of the temperature dependency on the material model gradually appears in the flow calculation. And changing the definition of the shear viscosity in multiple stages.

  In the plastic material extrusion simulation method according to the present invention, the shear viscosity has the shear rate dependency and the temperature dependency in which the shear viscosity changes according to temperature. The definition of the shear viscosity is changed in multiple stages so that the calculation result of the material model in which the influence of the speed dependence appears is the initial value, and the influence of the temperature dependence on the material model gradually appears. It is desirable to further include a step.

  In the plastic material extrusion simulation method according to the present invention, it is preferable that the flow calculation is performed until the material model is in a stable state at each stage where the shear viscosity is changed.

  In the plastic material extrusion simulation method according to the present invention, in the stable state, a difference between an amount of the material model at the supply port and an amount of the material model at the discharge port is a predetermined range. It is desirable that the state be within.

  The method for extruding a plastic material according to claim 1 includes a step of inputting, into a computer, a material model obtained by modeling a plastic material, and a step of discretizing the extrusion channel with a finite element and inputting a channel model. Contains. Further, in the extrusion simulation method for a plastic material according to claim 1, the computer performs a flow calculation in which the material model is arranged in the flow channel model and flows from the supply port to the discharge port based on a predetermined condition. And obtaining a physical quantity from the material model.

  The extrusion simulation method for a plastic material according to claim 1 includes a step of changing the definition of the shear viscosity in multiple stages so that the influence of the shear rate dependency on the material model gradually appears in the flow calculation. For this reason, in the extrusion simulation method of the plastic material according to the first aspect, for example, a change in the shear viscosity of the material model can be suppressed to suppress the divergence of the flow calculation.

  The method for simulating extrusion of a plastic material according to claim 2 includes a step of inputting, into a computer, a material model obtained by modeling the plastic material, and a step of inputting a channel model by discretizing the extrusion channel with finite elements. It is out. Further, in the extrusion simulation method for a plastic material according to claim 2, the computer performs a flow calculation in which the material model is arranged in the flow channel model and flows from the supply port to the discharge port based on a predetermined condition. A step and a computer obtaining a physical quantity from the material model.

  The plastic material extrusion simulation method according to claim 2 includes a step of changing the definition of the shear viscosity in multiple stages so that the influence of the temperature dependence on the material model gradually appears in the flow calculation. For this reason, in the extrusion simulation method for a plastic material according to claim 2, for example, a change in shear viscosity of the material model can be suppressed to suppress the divergence of the flow calculation.

It is a perspective view of the computer for performing the extrusion simulation method of this invention. It is sectional drawing explaining an extrusion flow path. It is a flowchart which shows an example of the process sequence of an extrusion simulation method. It is a graph which shows the relationship between a shear viscosity and a shear rate. It is a graph which shows the relationship between shear viscosity and temperature. (A), (b) is a perspective view which visualizes and shows a flow-path model. It is sectional drawing of a flow-path model. It is a flowchart which shows an example of the process sequence of flow calculation. It is a flowchart which shows an example of the process sequence of a 1st calculation step. It is a flowchart which shows an example of the process sequence of an exercise | movement calculation step. It is a flowchart which shows an example of the process sequence of a 2nd calculation step. It is a flowchart which shows an example of the process sequence of a 3rd calculation step.

Hereinafter, an embodiment of the present invention will be described with reference to the drawings.
The plastic material extrusion simulation method of the present embodiment (hereinafter sometimes simply referred to as “extrusion simulation method”) is a method for calculating and simulating a state of a plastic material passing through an extrusion flow path by a computer. It is.

  FIG. 1 is a perspective view of a computer for executing the extrusion simulation method of the present embodiment. The computer 1 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. The storage device stores in advance software or the like for executing the extrusion simulation method of the present embodiment.

  FIG. 2 is a cross-sectional view illustrating the extrusion channel 3. The extrusion flow path 3 is formed in the internal space of the screw type extruders 4a to 4c. The extrusion flow path 3 is provided with at least one, in this embodiment, three extrusion flow paths 3a to 3c. For example, differently blended rubber materials are supplied to the extrusion channels 3a to 3c.

  A supply port (not shown) through which a plastic material is supplied is provided at one end of each of the extrusion channels 3a to 3c. Moreover, the other end of each extrusion flow path 3a-3c is provided with the discharge port 3o from which a plastic material is extruded. Furthermore, the cross sections of the extrusion channels 3a to 3c change in the direction in which the rubber material flows. Each extrusion flow path 3a-3c of this embodiment has a cross-sectional area that gradually decreases from the upstream side toward the downstream side.

  A die plate 7 is disposed at the discharge port 3o of the extrusion channels 3a to 3c. The die plate 7 can finally extrude the rubber material supplied to the extrusion flow paths 3a to 3c in one extrusion cross section.

  The plastic material of this embodiment is a sufficiently kneaded rubber material before crosslinking. However, in addition to such a rubber material, a fluid material such as a resin material or an elastomer can be used as the plastic material. In the present invention, it is assumed that the plastic material is in a state that can be regarded as a stable fluid state (fluid) that is sufficiently kneaded. For example, in the case of an unvulcanized rubber material, a state where it is sufficiently kneaded and heated to about 80 ° C. corresponds to this state.

  FIG. 3 is a flowchart illustrating an example of a processing procedure of the extrusion simulation method of the present embodiment. In the present embodiment, first, a material model is input to the computer 1 (step S1). The material model is for incorporating a rubber material (not shown) flowing through the extrusion channels 3 a to 3 c (shown in FIG. 2) into the numerical calculation in the computer 1. In the present embodiment, material models simulating three types of rubber materials having different shear viscosities η are set. For each material model, specific heat, thermal conductivity, and shear viscosity η based on the physical properties of the rubber material are input to the computer 1.

  Specific heat is measured from the rubber material to be analyzed by, for example, an adiabatic continuous method (@ 25 ° C.). In the present embodiment, the same value is set as the specific heat of each rubber material. Such specific heat is input to the computer 1.

  The thermal conductivity is measured by, for example, a hot wire method (@ 25 ° C.) from the rubber material to be analyzed. The thermal conductivity is input to the computer 1. Note that specific heat and thermal conductivity have temperature dependence, and may be defined as a function of temperature. In addition, since the rubber discharge temperature is usually between 100 ° C. and 130 ° C., a value in the temperature range may be adopted.

  The shear viscosity η of the present embodiment is determined from, for example, a Cox-Merz law based on experimental results for obtaining viscoelastic properties (G ′ and G ″) of a sufficiently kneaded rubber material (not shown) under a plurality of temperature conditions. Can be defined by the following formula (1).

In the above formula (1), c · γ ′ ⁽ⁿ⁻¹⁾ is a term (Power Law) related to the speed dependency (shear rate dependency ⁾ of the viscosity. Parameters for controlling the shear rate dependency (hereinafter, simply referred to as “shear rate parameter”) c and n are used to adjust the shear rate dependency of the shear viscosity η (ie, the term relating to the shear rate dependency). belongs to.

The shear rate parameters c and n can be set as appropriate. For example, first, the shear rate dependence of viscosity is measured at a plurality of temperatures. Next, fitting to c · γ ′ ⁽ⁿ⁻¹⁾ is performed at each temperature. Then, based on the assumption that the shear rate dependence of the viscosity does not change even if the temperature changes, the shear rate parameters c and n can be obtained by approximating with an exponential function. In the present embodiment, the shear rate parameter c is set to a constant determined from the experimental results, and the shear rate parameter n is changed from the initial value 1 (no dependence on the shear rate) to the experimental value, thereby gradually fitting. ing.

In the above formula (1), O · em ^{· (T-273)} is a term relating to temperature dependence (Approximate Arrhenius Law). The parameter for controlling the temperature dependence (hereinafter, simply referred to as “temperature parameter”) m is a value obtained by measuring the shear viscosity under various conditions including, for example, the shear rate and the temperature, and curve the shear viscosity. It can be obtained by fitting. The term relating to the temperature dependency may be obtained by approximating a polynomial or other appropriate function. The shear viscosity can be measured using a capillary rheometer or a rotary rheometer.

  FIG. 4 is a graph showing the relationship between the shear viscosity η and the shear rate γ ′. In this graph, for example, the relationship between the shear rate η and the shear rate γ ′ in which the shear rate parameter n is varied in the range of “0 to 1” is shown. When the shear rate parameter n is “1”, the shear viscosity η can be set constant at all shear rates γ ′. On the other hand, when the shear rate parameter n is smaller than “1”, the shear viscosity η increases as the shear rate γ ′ decreases. Moreover, as the shear rate parameter n decreases, the rate of increase in the shear viscosity η increases.

  Therefore, the shear viscosity η defined by the above formula (1) has a shear rate dependency in which the shear viscosity η changes according to the shear rate γ ′ when the shear rate parameter n is smaller than “1”. ing. Further, in the above formula (1), the influence of the shear rate dependency can be gradually expressed (increased) as the shear rate parameter n is gradually decreased.

  The temperature parameter O is for adjusting the temperature dependence of the shear viscosity η (that is, the term relating to the temperature dependence). The temperature parameter O can be set as appropriate, and is set in the range of 0 to 1 in this embodiment.

  FIG. 5 is a graph showing the relationship between the shear viscosity η and the temperature T. In this graph, for example, the relationship between the shear viscosity η and the shear rate γ ′ in which the temperature parameter O is varied in the range of “0 to 1” is shown. When the temperature parameter O is “0”, the shear viscosity η can be set constant at all temperatures T. On the other hand, when the temperature parameter O is larger than “0”, the shear viscosity η increases as the temperature T decreases. In addition, the increase rate of the shear viscosity η increases as the temperature parameter O increases.

  Therefore, the shear viscosity η defined by the above formula (1) has a temperature dependency in which the shear viscosity η changes according to the temperature T when the temperature parameter O is larger than “0”. Furthermore, in the above formula (1), the influence of temperature dependency can be gradually expressed (increased) as the temperature parameter O is gradually increased. In the present embodiment, it is desirable that the temperature parameter O is set based on the following formula (2).

Here, the symbols are as follows.
M: Parameter for controlling the temperature parameter O a: Maximum value of the temperature parameter O b, d: Coefficients set from experimental results

  The above equation (2) is an equation representing a logistics curve. As with the temperature parameter O, the parameter M of the present embodiment is set in the range of 0 to 1. The maximum value “1” of the temperature parameter O is set as the maximum value a of the present embodiment. Further, the coefficient b and the coefficient d are appropriately set by the operator so that the flow calculation is easy to converge.

  As described above, the temperature parameter O is set based on the logistics curve, so that the temperature parameter O can be freely changed and set in the range of 0 to 1 while preventing a rapid increase. desirable.

  A different numerical value is set for each material model in the parameters c and m of the above formula (1). Thus, in the present embodiment, different shear viscosities η can be defined for each material model. In addition, it is desirable to set a lower limit value, an upper limit value, and the like for the shear viscosity η of each material model. These shear viscosities η are input to the computer 1.

  Next, as shown in FIG. 3, the flow channel model is input to the computer 1 (step S2). FIG. 6 is a perspective view showing the flow path model 11 in a visual manner. FIG. 7 is a cross-sectional view of the flow channel model 11. As shown in FIGS. 6 and 7, the flow channel model 11 is obtained by modeling (discretizing) the three-dimensional space of the extrusion flow channel 3 shown in FIG. 2 with a finite number of elements 13. The flow path model 11 is provided with a supply port 11i to which a material model is supplied at one end. The flow path model 11 is provided with a discharge port 11o through which the material model is pushed out at the other end.

  The channel model 11 of the present embodiment includes three channel models 11 each having an independent supply port 11i, that is, a first channel model 11a to a third channel model 11c. The material model that has passed through each flow channel model 11a to 11c is discharged from one discharge port 12 through each discharge port 11o.

  The cross-sectional areas of the respective channel models 11a to 11c change in the direction in which the material model flows, similarly to the extrusion channel 3 illustrated in FIG. In each of the flow path models 11a to 11c of this embodiment, the cross-sectional area gradually decreases from the upstream side toward the downstream side. Moreover, each flow path model 11a-11c of this embodiment is set so that a cross section may be halved as FIG.6 (b) shows. Thereby, in this embodiment, calculation time can be shortened. However, it is not limited to such an aspect.

  In each flow path model 11a to 11c, as shown in the partially enlarged view of FIG. 7, the space in which the material model flows is divided (discretized) by a plurality of elements 13. The element division is performed by a three-dimensional element such as a polyhedron cell (polyhedral grid) in addition to a tetrahedron, a hexahedron, and the like, and is modeled by an Euler element in this embodiment. In each element 13, physical quantities such as pressure, temperature and speed of the material model are calculated.

Next, as shown in FIG. 3, in this embodiment, boundary conditions and the like are set (step S3). In the present embodiment, flow rates and temperatures of the first material model to the third material model respectively supplied to the supply ports 11i (shown in FIG. 6) of the flow channel models 11a to 11c are set as boundary conditions. . Furthermore, in this embodiment, the pressure (= 0) of the discharge port 12 of each flow path model 11a-11c is set as a boundary condition.

  The flow velocity and temperature of each material model can be appropriately set with reference to, for example, values actually measured in the extrusion flow path 3 (shown in FIG. 2) to be analyzed. Further, for example, a constant temperature is applied to the wall surface 11e (shown in FIG. 7) of each of the flow path models 11a to 11c.

  Furthermore, a flow velocity boundary condition is set on the wall surface 11e (shown in FIG. 7) of each flow path model 11a to 11c. As the flow velocity boundary condition, a wall surface no-slip condition or a wall surface slip condition can be set. In the present embodiment, the wall surface no-slip condition is set from the same viewpoint as in Patent Document 1.

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

  Next, as shown in FIG. 3, the computer 1 arranges a material model in each of the flow path models 11 a to 11 c shown in FIG. 7 based on the boundary condition, from the supply port 11 i to the discharge port 11 o. The flow calculation for flowing is performed (step S4).

  In the flow calculation, similarly to the above-mentioned Patent Document 1, three directions (x, y, z) for specifying the motion state of the material model at the position of each element 13 (shown in FIG. 7) of each flow channel model 11a to 11c. And the pressure p and temperature T, which are unknown quantities that specify the internal state of the material model, are calculated. In the flow calculation of this embodiment, the Navier-Stoks equation in the case of incompressible flow is used, and the density of the material model is constant.

  In this embodiment, the material model is treated as a fluid in the entire temperature range. Therefore, the fluid equation (Navier-Stoks equation, mass conservation equation, and energy equation) is solved. In this embodiment, mixed phases of a plurality of types of material models having different shear viscosities η are handled. For this reason, in this embodiment, the VOF (Volume of Fluid) method used in the calculation of the flow of the free interface is used. In the VOF method, the movement of the interface between two fluids (material models) having different shear viscosities η and the like is not directly calculated, but the material model is filled in the volume of each element 13 (also referred to as “cell”). The ratio (ie volume fraction) is defined and the free interface is averaged and expressed. The governing equation is as follows.

[Equation of motion]
In the present embodiment, a three-phase mixed phase model in which three types of material models flow in each flow path model 11a to 11c (shown in FIG. 6) is handled as one fluid. In this case, the equation of motion only needs to be solved for one set of the following formulas (three directions of x, y, and z). This is realized by averaging three phases and treating them as a one-phase fluid by the VOF method.

In the above formula, the symbols are as follows.
u: Speed of multiphase flow model p: Pressure of multiphase flow model ρ: Density of multiphase flow model g: Gravitational acceleration T: Absolute temperature of multiphase flow model F: External force

  Further, the density ρ, shear viscosity η, etc. of the multiphase flow model are averaged by weighting each volume of the first material model to the third material model, as shown in the following equation. used.

In the above formula, the symbols are as follows.
α _q : Volume fraction of each phase in each cell ρ _q : Density of each phase in each cell η _q : Shear viscosity of each phase in each cell

[Mass conservation type]
Similarly, only one set of mass conservation (continuous equation) and pressure equation is sufficient. That is, in the simulation method of the present embodiment, the flow field calculation is the same as that of the single phase although it is multiphase, and the flow having different physical property values is solved depending on the location (volume fraction). The position of each phase can be determined from the volume fraction distribution obtained as a calculation result.

[Energy equation]
The energy equation is expressed by the following equation. Moreover, the temperature of a material model can be calculated | required by a following formula.

In the above formula, the symbols are as follows.
E: enthalpy k: thermal conductivity S: source term

[Volume transport equation]
The volume fraction distribution determines the interface position between the phases of each material model. This volume fraction αq can be obtained by accurately solving the following equation.

Here, in the arbitrary element 13 (shown in FIG. 7) of each flow path model 11a to 11c, when the volume fraction α _q = 0, it indicates that the q phase does not exist in the element 13. In addition, when the volume fraction α _q = 1, the element 13 indicates that the q phase is all satisfied. Further, when 0 <α _q <1, the element 13 is filled with the q phase and the other phase, that is, is a mixed phase and has an interface between the two. This equation can be solved by Modified-HRIC (Implicit), for example. Details are described in detail in ANSYS Fluent User's Manual, 26.2.9 Modified HRIC Scheme.

  In the present embodiment, the above equations are solved by a pressure-based separation type solution. For example, a SIMPLE (Semi-Implicit Method for Pressure-Linked Equations) algorithm is preferably used for the coupling between the pressure equation and the equation of motion.

  FIG. 8 is a flowchart illustrating an example of a flow calculation processing procedure according to the present embodiment. In this embodiment flow calculation, first, the flow of each material model in which the shear viscosity η is set to be constant is calculated (first calculation step S41). FIG. 9 is a flowchart illustrating an example of a processing procedure of the first calculation step S41.

  In the first calculation step S41, first, a constant shear viscosity η is set for each material model (step S101), and this material model is supplied to each flow path model 11a to 11c (shown in FIG. 6) (see FIG. 6). Step S102).

  In step S101, for example, “1” is substituted for the shear rate parameter n in the above equation (1) that defines the shear viscosity η. Furthermore, for example, “0.00001” is substituted into the temperature parameter O (in this embodiment, the parameter M in the above equation (2)). Thereby, in step S101, each shear viscosity η of the first material model to the third material model is a constant one that does not change even if the shear rate γ ′ and the temperature T change (that is, shear rate dependency and It is changed to one that does not have temperature dependence (or very small one). For the shear rate γ ′ and the temperature T, a typical shear rate (10 (1 / s)) and temperature (for example, 100 ° C.) are set based on the experimental results.

  Next, the motion (flow) of the material model is calculated based on each material model in which the shear viscosity η is set to be constant and each flow path model 11a to 11c (motion calculation step S103). ). FIG. 10 is a flowchart showing an example of the processing procedure of the motion calculation step S103 for each material model.

  In the motion calculation step S103 of the present embodiment, as in the above-mentioned Patent Document 1, first, the speed and the pressure gradient are calculated by setting the speed and the pressure gradient lower limit and upper limit of each material model (steps). S201).

  Next, a discrete equation of motion is set up from the latest pressure field, and the solution, that is, the velocity of the material model (or multiphase) in three directions is calculated using an iterative solver (step S202). Examples of the iterative method include the Gauss-Seidel method.

Next, the mass flow rate before correction of each material model on the cell surface of each flow path model 11a to 11c (shown in FIG. 6) is obtained (step S203). “Mass flow rate before correction” is the mass flow rate that is first used in the loop of the SIMPLE algorithm. Here, since the error is large, it is expressed as “before correction”. Next, the velocity field and the pressure field are coupled using the SIMPLE algorithm, and the following pressure correction equation for correcting the pressure field is constructed (step S204).
▽ [k ▽ φ] = src

Next, the pressure correction equation obtained in the above step is calculated by an iterative method such as AMG solver, CG or Bi-CG, for example, and a pressure correction amount p ′ is calculated (step S205). Next, the pressure field is corrected based on the calculated solution (step S206). The correction of the pressure field is performed as follows.
p ^{n + 1} = p ⁿ + ωp ′
In the above formula, the symbols are as follows.
p: pressure n: current number of steps ω: relaxation coefficient (0.3 in this embodiment)

Next, the boundary condition of the wall surface 11e (shown in FIG. 7) is corrected (updated). That is, a pressure gradient is obtained from the corrected pressure field, and the pressure gradient is given as a boundary condition (step S207). Next, the mass flow rate on the cell surface is corrected (step S208). The correction is performed as follows.
mf ^{n + 1} = mf * + m'f
In the above formula, the symbols are as follows.
mf ^{n + 1} : mass flow rate on the cell surface after correction mf *: mass flow rate on the cell surface before correction m'f: correction value of the mass flow rate

Next, the speed field is corrected (step S209). The speed field is corrected as follows, for example.
v ^{n + 1} = v * − (V ▽ p ′ / α _p ^V )
In the above formula, the symbols are as follows.
▽ p ': slope of pressure correction amount α _p ^V : diagonal component of velocity in equation of motion

  Next, the temperature of the material model is calculated by solving the energy equation (step S210).

  In the motion calculation of the material model, when the shear rate γ ′ of the material model is small and the shear viscosity η is large, the shear heat generation Hs of the material model is calculated to be larger than that of the actual rubber material. There is a fear. Such an increase in the shear heat generation Hs may cause divergence of the flow calculation. In an actual rubber material, if the shear rate γ ′ is small, the shear heat generation Hs does not increase even if the shear viscosity η is large. For this reason, when the shear rate γ ′ of the material model is small, it is desirable that the shear heat generation Hs is corrected to be small regardless of the shear viscosity η. Thereby, the divergence of the flow calculation can be suppressed.

In this embodiment, first, the weighting coefficient W of the shear heat generation Hs is obtained by the following equation. The weight coefficient W decreases as the shear rate γ ′ decreases. In the present embodiment, when the value of the weight coefficient is less than “1”, it is determined that the shear rate γ ′ is sufficiently small. The coefficients A and B are appropriately set based on the experimental results of the rubber material.
W = A × ln (γ ′ ² ) + B
γ ′: shear rate A, B: coefficient

Next, based on the weight coefficient W, the shear heat generation Hs is corrected.
・ If 0.05 <W <1, Hs = 1
・ W ≦ 0.05 Hs = W × Hs

  As described above, in this embodiment, when the shear rate γ ′ is small (the weight coefficient W is less than 1) based on the weight coefficient W, the shear heat generation Hs is corrected to be small as described above. Can be suppressed. When the weight coefficient W is 1 or more, the shear heat generation Hs does not increase excessively, so the shear heat generation Hs is not corrected.

Next, it is determined whether or not the flow of each material model has become stable (calculation has converged) (step S211). In the present embodiment, the stable state of each material model is the difference between the amount of the material model at the supply port 11i (shown in FIG. 7) and the amount of the material model at the discharge port 11o (shown in FIG. 7) (hereinafter referred to as the material model). , Simply referred to as “extrusion error of material model.”) A state where r is within a predetermined range. Note that, when calculated for a plurality of material models as in this embodiment, all the material models are calculated based on the root mean square R _rms obtained from the extrusion error r _i of each material model. It is desirable to determine a stable state. Since the root mean square R _rms is an extrusion error considering all material models, the stable state of all material models can be easily determined. The root mean square R _rms can be obtained based on the following formula (7).

In the above formula, the symbols are as follows.
n: the total number of material models r _i: extrusion error of each material model

The root mean square R _rms may vary easily due to the extrusion error of each material model. For this reason, it is desirable to make a determination based on a value obtained by standardizing the root mean square R _rms (hereinafter, simply referred to as “standard value”) R _pres . Thereby, the stable state of each material model can be easily determined. The standard value R _pres can be obtained based on the following formula (8).

In the above formula, the symbols are as follows.
R _norm : Maximum value of the absolute value of each extrusion error in all material models

In step S211, when it is determined that the flow of each material model is in a stable state ("Y" in step S211), the process returns to the flowchart of FIG. On the other hand, when it is determined that the flow of each material model is not in a stable state (“N” in step S211), step S201 and subsequent steps are repeated. Thereby, in 1st calculation step S41 of this embodiment, the flow of each material model by which shear viscosity (eta) was set constant can be made into a stable state. In the present embodiment, when the standard value R _pres converges to a certain value, it is determined that the stable state has been reached. If the standard value R _pres is larger than the initial standard value R _pres , the extrusion error r _i of each material model is large, so even if the standard value R _pres converges to a constant value, It is desirable to determine that the calculation result is abnormal. In this case, the calculation conditions are reset and the calculation is performed again.

  Next, as shown in FIG. 8, the flow of each material model in which the shear viscosity η having only one of shear rate dependency and temperature dependency is set is calculated (second calculation step S42). In the second calculation step S42 of this embodiment, only the shear rate dependency is set in the shear viscosity η, and the temperature dependency is not set. FIG. 11 is a flowchart showing an example of the processing procedure of the second calculation step S42.

  In the second calculation step S42, first, the calculation result of each material model obtained in the first calculation step S41 is set as the initial value of the second calculation step S42 (step S301). In step S301 of the present embodiment, the speed (three components) and pressure of each element 13 (shown in FIG. 7) of each flow path model 11a to 11c are determined based on the movement (flow) of each material model in step S304 described later. Set as the initial velocity field when starting the calculation.

  Next, an initial shear viscosity η having shear rate dependency is defined for each material model (step S302), and these material models are supplied to the flow path models 11a to 11c (step S303). The initial shear viscosity η is a shear viscosity η that has a shear rate dependency smaller than the shear rate dependency (finally set) based on each rubber material and has no temperature dependency. In addition, the shear rate dependence based on each rubber material is specified based on the experimental result of each rubber material (not shown).

  In the present embodiment, as shown in FIG. 4, the shear rate parameter n of the above formula (1) that defines the shear viscosity η is the initial value (for example, 1 (shear rate dependent) set in the first calculation step S41. The value is set in a range smaller than the value “0” which is smaller than the value “0” and has the largest shear rate dependency, for example, “0.9” is set. Thereby, in step S302, a shear viscosity η having a small shear rate dependency can be defined for each material model.

  Next, based on the first material model to the third material model in which the shear viscosity η having the shear rate dependency is defined, and each flow path model 11a to 11c (shown in FIG. 6), each material The motion (flow) of the model is calculated (motion calculation step S304). In addition, this exercise | movement calculation step S304 is performed by the process procedure similar to the exercise | movement calculation step shown in FIG. 10 similarly to 1st calculation step S41. Thereby, in the motion calculation step S304, the flow of each material model in which the shear viscosity η having shear rate dependency is defined can be stabilized.

  Usually, in each of the flow path models 11a to 11c (shown in FIG. 6), the shear rate γ ′ is different for each element 13 (shown in FIG. 7). In step S304, the shear viscosity η based on the shear rate γ ′ of the element 13 is calculated. The uneven distribution of the shear viscosity η affects the velocity field of each of the flow path models 11a to 11c and causes a pressure change. In step S304, convergence calculation is performed until they are balanced.

  Next, it is determined whether the shear rate dependency of the shear viscosity η of each material model is the same as the shear rate dependency based on each rubber material (step S305). When it is determined that the shear rate dependency is the same as the shear rate dependency based on each rubber material ("Y" in step S305), the process returns to the flowchart of FIG. On the other hand, when it is determined that the shear rate dependency is not the same as the shear rate dependency based on each rubber material (“N” in step S305), the shear rate dependency is increased (step S306). The motion (flow) of the model is calculated again (step S304).

  In step S306, as shown in FIG. 4, the shear rate parameter n of the above equation (1) is changed to define a greater shear rate dependency than the previously set shear rate dependency. For example, when “0.9” is set in the shear rate parameter n in the previous step S302 (or step S306), the shear rate parameter n is decreased by “0.1” and “0.8”. Is set. Thereby, it is possible to define a greater shear rate dependency on the shear viscosity η of each material model than the previously set shear rate dependency.

  Step S306 is repeated until the shear rate dependency of the shear viscosity η of each material model becomes the same as the shear rate dependency based on each rubber material, so that the influence of the shear rate dependency on each material model gradually increases. As shown, the definition of the shear viscosity η can be changed in multiple stages. In addition, in step S304, calculation is performed until the material model becomes stable at each stage where the shear viscosity η is changed.

  For example, if the shear viscosity dependence η based on each rubber material is suddenly given to the shear viscosity η of each material model (the shear rate parameter n is changed from “1.0” to “0.1”, for example), the shear In many cases, the viscosity η varies greatly and the calculation does not converge. In the present invention, by gradually decreasing the shear rate parameter n from “1.0”, the shear rate dependency is gradually increased from the state without the shear rate dependency, thereby increasing the shear viscosity η. Since the change can be suppressed, it is possible to suppress the flow calculation from diverging in step S304. Therefore, in this embodiment, the flow of the material model in which the shear viscosity η having shear rate dependency (shear rate dependency based on each rubber material) is set can be reliably calculated.

  The number of times step S306 for increasing the shear rate dependency can be set as appropriate. If the number of executions of step S306 is small (that is, the amount of decrease in the shear rate parameter n is large), the influence of the shear rate dependency on each material model can be expressed early, but the change in the shear viscosity η is large ( For example, the calculation may not be converged. On the other hand, if the number of executions of step S306 is small (that is, the amount of decrease in the shear rate parameter n is small), the calculation can be converged stably, but the effect of the shear rate dependency on the material model is expressed early. The calculation time may increase. From such a viewpoint, the number of times that step S306 is performed is preferably 5 times or more, and preferably 20 times or less.

  Next, as shown in FIG. 8, the flow of each material model in which the shear viscosity η having shear rate dependency and temperature dependency is set is calculated (third calculation step S43). In the third calculation step S43 of the present embodiment, a shear viscosity η is further defined in which the temperature dependency is further set to the shear rate dependency set in the second calculation step S42. FIG. 12 is a flowchart illustrating an example of a processing procedure of the third calculation step S43.

  In the third calculation step S43, first, the calculation result of each material model obtained in the second calculation step S42 is set as the initial value of the third calculation step S43 (step S401). Thereby, temperature dependence can be set to shear viscosity (eta) which has shear rate dependence after step S402 mentioned later.

  Next, initial shear viscosity η having shear rate dependence and temperature dependence is defined for each material model (step S402), and these material models are defined in each flow path model 11a to 11c (shown in FIG. 6). Is supplied (step S403). The initial shear viscosity η has the shear rate dependency set in the second calculation step S42, and has a temperature dependency smaller than the temperature dependency (finally set) based on each rubber material. Shear viscosity η. The temperature dependence based on each rubber material is specifically set based on the experimental result of each rubber material (not shown).

  In the present embodiment, as shown in FIG. 5, the temperature parameter O of the above equation (1) that defines the shear viscosity η is the initial value (for example, 0.00001 (temperature-dependent) set in the first calculation step S41. For example, “0.1” is set. Thereby, in step S402, a shear viscosity η having a small temperature dependency can be defined in each material model. The temperature parameter O is preferably set based on the logistics curve of the above equation (2).

  Next, based on the first material model to the third material model in which the shear viscosity η having the shear rate dependency and the temperature dependency is defined, and the flow path models 11a to 11c (shown in FIG. 6). The motion (flow) of each material model is calculated (motion calculation step S404). In addition, this exercise | movement calculation step S404 is performed by the same processing procedure as the exercise | movement calculation step shown in FIG. 10 similarly to 1st calculation step S41 and 2nd calculation step S42. Thereby, in step S404, the flow of each material model in which the shear viscosity η having the shear rate dependency and the temperature dependency is defined can be stabilized.

  Next, it is determined whether the temperature dependence of the shear viscosity η of each material model is the same as the temperature dependence based on each rubber material (step S405). When it is determined that the temperature dependency is the same as the temperature dependency based on each rubber material (“Y” in step S405), the process returns to the flowchart of FIG. On the other hand, when it is determined that the temperature dependency is not the same as the temperature dependency based on each rubber material (“N” in step S405), the temperature dependency is increased (step S406), and the motion of each material model is increased. (Flow) is calculated again (step S404).

  In step S406, as shown in FIG. 5, the temperature parameter O of the above equation (1) is changed to define a temperature dependency that is greater than the temperature dependency set previously. For example, when “0.1” is set to the temperature parameter O in the previous step S402 (or step S406), the temperature parameter O is increased by “0.1” and set to “0.2”. Is done. As a result, it is possible to define a greater temperature dependency than the previously set temperature dependency in the shear viscosity η of each material model.

  Step S406 is repeated until the temperature dependence of the shear viscosity η of each material model becomes the same as the temperature dependence based on each rubber material, so that the influence of the temperature dependence on each material model gradually appears. The definition of the shear viscosity η can be changed in multiple stages. Moreover, in step S404, calculation is performed until the material model becomes stable at each stage where the shear viscosity η is changed.

  For example, when the temperature dependence based on each rubber material is suddenly given to the shear viscosity η of each material model (for example, the temperature parameter O is changed from “0.1” to “1.0”), the shear viscosity In many cases, η changes greatly and the calculation does not converge. In the present invention, since a large change in the shear viscosity η can be suppressed, it is possible to suppress the flow calculation from diverging in step S404. Therefore, in this embodiment, the flow of the material model having the shear rate dependency and the temperature dependency based on each rubber material can be reliably calculated. The number of executions of step S406 for increasing the temperature dependence is preferably 5 or more, and preferably 20 or less, from the same viewpoint as the number of executions of step S306 for increasing the shear rate dependence. is there.

  Thus, in the flow calculation of the present embodiment, after the flow of the material model with a constant shear viscosity η is calculated (first calculation step S41), the calculation result is used as an initial value to obtain the shear viscosity η. The flow of the material model giving only the shear rate dependency is calculated (second calculation step S42). Further, using the calculation result of the second calculation step S42 as an initial value, the flow of the material model in which the shear viscosity η is given the shear rate dependency and the temperature dependency is calculated (third calculation step S43). In 1st calculation step S41-3rd calculation step S43, it calculates until the flow of a material model will be in a stable state. Therefore, in the flow calculation of the present embodiment, since the flow of the material model is calculated by gradually setting the shear rate dependency and the temperature dependency, stable flow calculation can be realized.

  Moreover, in the flow calculation of the present embodiment, in the second calculation step S42 and the third calculation step S43, the definition of the shear viscosity η is defined so that the influence of the shear rate dependency or the temperature dependency on the material model gradually appears. It can be changed in multiple stages. For this reason, in the flow calculation of this embodiment, a large change in the shear viscosity η of the material model can be suppressed, and the flow calculation of the material model can be converged stably.

  In the present embodiment, for the shear viscosity η of the material model, the temperature dependence is set after the shear rate dependence is set first, but after the temperature dependence is set first, Needless to say, the shear rate dependency may be set. Further, in the second calculation step S42 and the third calculation step S43, the definition of the shear viscosity η is changed in multiple stages so that the influence of the shear rate dependency and the temperature dependency on the material model gradually appears. However, the present invention is not limited to this. A large change in the shear viscosity η is likely to occur when the shear rate dependency or temperature dependency is large. For this reason, the definition of the shear viscosity η may be changed in multiple stages so that the influence on the material model gradually appears only for one of the shear rate dependence and temperature dependence that is large. Thereby, the calculation cost can be suppressed while the flow calculation of the material model is converged stably.

  Whether the shear rate dependency is large or not is determined in the above formula (1) as the absolute value of n-1 is larger (for example, | n-1 |> 0.5). It can be judged that it is large. In addition, the determination as to whether or not the temperature dependency is large can be determined as the temperature dependency is larger as the absolute value of m in the above equation (1) is larger (for example, | m |> 0.04).

  Next, as shown in FIG. 3, the computer 1 obtains a physical quantity from each material model having a stable flow (step S5). The physical quantity includes the speed, pressure and temperature of each material model obtained by the flow calculation, and in particular, the physical quantity at each position of the discharge port 11o (shown in FIG. 7) of each flow path model 11a to 11c. It is desirable to obtain.

Next, based on the physical quantity of the extrudate (material model) extruded from the discharge port 11o (shown in FIG. 7), it is determined whether or not the extrudate is in a good state (step S6). As a judgment of the quality of the extrudate,
a) Flow velocity distribution at the discharge port is small (uniform speed) b) A plurality of rubber materials with different shear viscosities are distributed as designed c) Temperature distribution is uniform (No local fever)
Etc.

  Next, when the evaluation of the extrudate is good (“Y” in step S6), a rubber material (not shown) is added based on the three-dimensional shape of each flow path model 11a to 11c (shown in FIG. 6). The extrusion flow path 3 at the time of extrusion is designed (step S7). On the other hand, when the evaluation of the extrudate is not good (“N” in step S6), the shape of each of the flow path models 11a to 11c is reset (step S8), and step S3 and subsequent steps are repeated. Thereby, the extrusion flow path 3 with a favorable extrudate can be designed reliably.

  As mentioned above, although especially preferable embodiment of this invention was explained in full detail, this invention is not limited to embodiment of illustration, It can deform | transform and implement in a various aspect.

  According to the processing procedures shown in FIG. 3 and FIGS. 8 to 12, the flow viscosity calculation is performed by changing the definition of the shear viscosity η in multiple stages so that the influence of the shear rate dependency and the temperature dependency gradually appears. (Example 1 and Example 2). In Example 1, according to the procedure described in the specification, when the shear rate γ ′ of the material model is low, the shear heat generation Hs is corrected to be small. On the other hand, in Example 2, the shear heat generation Hs is not corrected.

For comparison, flow calculation was performed by sequentially setting the shear rate dependency and the temperature dependency without changing the definition of the shear viscosity η in multiple stages according to the procedure of Patent Document 1 ( Comparative example). The common specifications are as described in the specification except for the specifications described below.
Number of channel models: 5
The above formula (1) defining the shear viscosity η:
Range of shear rate parameter n: 0 to 1
Range of temperature parameter O: 0 to 1
Shear rate parameter c: 9.39 × 10 ⁵
Temperature parameter m: 0.209
The above formula (2) defining the temperature parameter O:
Range of parameter M: 0 to 1
Maximum value a: 1
Coefficient b: 1
Coefficient d: 1
Weight coefficient W:
Coefficient A: 0.3469
Coefficient B: -0.6135
Number of executions of step S306 for increasing shear rate dependency: 10 times Number of executions of step S406 for increasing temperature dependency: 10 times

  As a result of the test, in Example 1 and Example 2, the flow calculation diverges less than in the comparative example, and the flow calculation of the material model can be converged stably. Moreover, in Example 1, since the shear heat generation Hs was corrected to be small, the flow calculation of the material model could be stably converged as compared with Example 2.

3 Extrusion channel 11 Channel model

Claims (5)

The computer calculates how the plastic material passes through an extrusion passage having a supply port through which the plastic material is supplied at one end and a discharge port through which the plastic material is extruded at the other end and the cross-sectional area changes. A method for simulating extrusion of a plastic material,
Inputting a material model modeling the plastic material into the computer;
Discretizing the extrusion flow path with finite elements into the computer and inputting a flow path model;
The computer performs the flow calculation of arranging the material model in the flow channel model and flowing from the supply port to the discharge port based on a predetermined condition;
The computer includes obtaining a physical quantity from the material model;
The material model defines shear viscosity,
The shear viscosity has a shear rate dependency in which the shear viscosity changes according to the shear rate,
In the flow calculation, the method includes the step of changing the definition of the shear viscosity in multiple stages so that the influence of the shear rate dependency on the material model gradually appears. . The computer calculates how the plastic material passes through an extrusion passage having a supply port through which the plastic material is supplied at one end and a discharge port through which the plastic material is extruded at the other end and the cross-sectional area changes. A method for simulating extrusion of a plastic material,
Inputting a material model modeling the plastic material into the computer;
Discretizing the extrusion flow path with finite elements into the computer and inputting a flow path model;
The computer performs the flow calculation of arranging the material model in the flow channel model and flowing from the supply port to the discharge port based on a predetermined condition;
The computer includes obtaining a physical quantity from the material model;
The material model defines shear viscosity,
The shear viscosity has a temperature dependency in which the shear viscosity changes according to temperature,
In the flow calculation, the plastic material extrusion simulation method includes a step of changing the definition of the shear viscosity in multiple stages so that the influence of the temperature dependency on the material model gradually appears. The shear viscosity has the shear rate dependency and the temperature dependency in which the shear viscosity changes according to the temperature,
In the flow calculation, the calculation result of the material model in which the influence of the shear rate dependence appears as an initial value, and the influence of the temperature dependence on the material model gradually appears, 2. The method for simulating extrusion of a plastic material according to claim 1, further comprising a step of changing the definition in multiple stages.   The method for simulation of extruding a plastic material according to any one of claims 1 to 3, wherein the flow calculation is performed until the material model becomes stable at each stage where the shear viscosity is changed.   The plasticity according to claim 4, wherein the stable state is a state in which a difference between the amount of the material model at the supply port and the amount of the material model at the discharge port is within a predetermined range. Material extrusion simulation method.