JP6848754B2 - Kneading simulation method for thermoplastic materials - Google Patents

Description

The present invention relates to a method for investigating the kneading performance of a Banbury mixer for kneading a thermoplastic material.

The following Non-Patent Document 1 proposes, for example, a method for evaluating the kneading performance (for example, the dispersion performance of a polymer) of a Banbury mixer for kneading a polymer. In Non-Patent Document 1 below, first, the shear rate γ and the vorticity ω are measured from the polymer being kneaded, and the parameter (shear stress λ) relating to the dispersed state of the polymer is calculated using the following equation.
λ = | γ | / (| γ | + | ω |)

Ica Manas-Zloczower, "Mixing and Compounding of Polymers", 2nd Edition, Hanser Gardner Pubns, 2009

By the way, the Banbury mixer has a rotor that rotates in the chamber. The rotor is provided with a tip portion that protrudes so as to approach the outer peripheral surface of the chamber. In the Banbury mixer, the polymer is effectively compressed and sheared in the gap (chip clearance) between the chip portion and the outer peripheral surface of the chamber. Therefore, it is important to consider the influence of the chip portion when calculating the parameters related to the dispersed state of the polymer.

However, the method of Non-Patent Document 1 has a problem that it is not sufficient for evaluating the kneading performance of the Banbury mixer because the influence of the chip portion is not taken into consideration.

The present invention has been devised in view of the above circumstances, and an object of the present invention is to provide a method capable of evaluating the kneading performance of a Banbury mixer in consideration of the influence of the tip portion of the rotor.

ここで、
Ｖ：可塑性材料モデルの体積
Ｒ：フィラーの半径
ｔ：単位時間
Ｔ：可塑性材料モデルがチップ部を通過するのに要する時間
Ｑ：チップ部を通過する可塑性材料モデルの単位時間当たりの流量
τ：可塑性材料モデルのせん断応力
γ：可塑性材料モデルのせん断速度
α、τ_ｃ：定数 The present invention has a chamber that is a space for kneading a plastic material, and at least one rotor that rotates in the chamber, and a tip portion that protrudes so that the rotor approaches the outer peripheral surface of the chamber. This is a simulation method for investigating the kneading performance of a chambery mixer in which the plastic material contains a filler, wherein the rotor is divided into a finite number of elements and a rotor model is input to the computer. The chamber is divided into a finite number of elements and a chamber model is input to the computer, and a plastic material model that models the plastic material is input to the computer. The calculation step includes a calculation step of simulating a state in which the plastic material is kneaded in the chamber by arranging the plastic material model in the chamber model and rotating the rotor model. A method for simulating kneading of a plastic material, which comprises a step of calculating a parameter D regarding a dispersed state of the plastic material according to 1).

here,
V: Volume of the thermoplastic material model R: Radius of the filler t: Unit time T: Time required for the thermoplastic material model to pass through the chip part Q: Flow rate per unit time of the plastic material model passing through the chip part τ: Plasticity Shear stress of material model γ: Shear rate of thermoplastic material model α, τ _c : Constant

In the method for simulating kneading of plastic materials according to the present invention, the calculation step may further include a step of calculating the time average of the parameter D during a period in which the rotor model makes one or more rotations.

In the method for simulating kneading of a plastic material of the present invention, the plastic material in the chamber is kneaded by arranging the plastic material model in the chamber model and rotating the rotor model based on predetermined conditions. Includes computational steps to simulate the resulting state. The calculation step includes a step of calculating the parameter D regarding the dispersed state of the plastic material by the following formula (1).

ここで、
Ｖ：可塑性材料モデルの体積
Ｒ：フィラーの半径
ｔ：単位時間
Ｔ：可塑性材料モデルがチップ部を通過するのに要する時間
Ｑ：チップ部を通過する可塑性材料モデルの単位時間当たりの流量
τ：可塑性材料モデルのせん断応力
γ：可塑性材料モデルのせん断速度
α、τ_ｃ：定数

here,
V: Volume of the thermoplastic material model R: Radius of the filler t: Unit time T: Time required for the thermoplastic material model to pass through the chip part Q: Flow rate per unit time of the plastic material model passing through the chip part τ: Plasticity Shear stress of material model γ: Shear rate of thermoplastic material model α, τ _c : Constant

In the above equation (1), the shear stress τ of the plastic material model and the shear velocity γ, as well as the parameters (time T, flow rate Q) related to the chip portion are included. Therefore, the kneading simulation method for the plastic material of the present invention can evaluate the kneading performance of the Banbury mixer in consideration of the influence of the tip portion of the rotor.

It is a partial cross-sectional view which shows an example of a Bunbury mixer. It is a partial cross-sectional view which shows an example of the Bunbury mixer 1 which kneads a plastic material. It is a perspective view which shows an example of the computer for executing the kneading simulation method of a plastic material. It is a flowchart which shows an example of the processing procedure of the kneading simulation method of a plastic material. It is a flowchart which shows an example of the processing procedure of a mixer model input step. It is sectional drawing which shows an example of the Bunbury mixer model. It is a partially enlarged view of FIG. It is a perspective view of a chamber model and a rotor model. It is sectional drawing of the chamber model. It is sectional drawing which shows the chamber model disassembled. It is a flowchart which shows an example of the processing procedure of a calculation step. It is sectional drawing which shows the chamber model in which a plastic material model and a gas phase model are arranged in a mixed manner. It is a graph which shows the relationship between the parameter D and the time t regarding the dispersion state of a plastic material for the 1st rotor and the 2nd rotor which have different land widths. It is a flowchart which shows an example of the processing procedure of the calculation step of another embodiment of this invention. It is a graph which shows the relationship between the time average and the time t of the parameter D regarding the dispersion state of a plastic material for the 1st rotor and the 2nd rotor which have different land widths. It is a graph which shows the relationship between the parameter D and the time t regarding the dispersion state of the plastic material of an Example. It is a graph which shows the relationship between the shear stress of a comparative example, and time t.

Hereinafter, embodiments of the present invention will be described with reference to the drawings.
In the method for simulating the kneading of a plastic material of the present embodiment (hereinafter, may be simply referred to as a “simulation method”), the kneading performance of a Banbury mixer for kneading the plastic material is evaluated using a computer. Further, in the present embodiment, the shape of the rotor capable of exhibiting high kneading performance and the like are designed based on the kneading performance of the evaluated Bunbury mixer.

Here, "kneading" means, for example, as a pretreatment at the time of molding a plastic material including a rubber material or a resin material, the chemicals, powders, etc. of the raw materials and the liquid binder are dispersed and wetted with each other to homogenize them. It is defined as an action or operation. A typical kneading process is performed using a Banbury mixer (kneader). FIG. 1 is a partial cross-sectional view showing an example of a Banbury mixer. FIG. 2 is a partial cross-sectional view showing an example of the Banbury mixer 1 in which the thermoplastic material 5 is kneaded.

As shown in FIG. 1, the Banbury mixer 1 has a chamber 4 which is a space for kneading the thermoplastic material 5 (shown in FIG. 2) and at least one rotor 3 rotating in the chamber 4 (the present embodiment). , Is configured to include a pair of rotors 3, 3). Further, the Banbury mixer 1 of the present embodiment includes a casing 2 provided with an inner wall surface 9 defining the chamber 4. The casing 2 of the present embodiment is formed in a tubular shape.

Each rotor 3 includes a cylindrical base portion 3a and a wing portion 3b extending from the base portion 3a toward the inner wall surface 9 of the casing 2 formed in a cylindrical shape. As shown in FIG. 2, the wing portion 3b includes a tip portion 8 projecting so as to approach the outer peripheral surface 4o (inner wall surface 9 of the casing 2) of the chamber 4. The plastic material 5 is effectively compressed and sheared in the gap (chip clearance) 10 between the chip portion 8 and the outer peripheral surface 4o of the chamber 4.

The land width L1, which is the length of the chip portion 8 in the rotor circumferential direction, is appropriately set according to, for example, the blending of the plastic material 5 to be kneaded. If the land width L1 is large, the plastic material 5 can be kneaded in a short time, but the plastic material 5 tends to be easily heated. On the contrary, when the land width L1 is small, the heating of the plastic material 5 can be suppressed, but the kneading time of the plastic material 5 tends to increase. Therefore, it is important to consider the influence of the chip portion 8 (land width L1) in the evaluation of the kneading performance of the Banbury mixer 1.

As shown in FIG. 1, the chamber 4 is partitioned between the rotors 3 and 3 and the casing 2. The chamber 4 of the present embodiment is formed in a substantially 8-shaped cross section. The chamber 4 is not limited to such a shape and is not interpreted.

As shown in FIG. 2, the thermoplastic material 5 of the present embodiment is a rubber material before cross-linking. However, in addition to such a rubber material, a material having fluidity such as a resin material or an elastomer can be adopted as the plastic material 5. Further, it is assumed that the thermoplastic material 5 is in a state where it is sufficiently kneaded and can be regarded as a stable flow state (fluid). In the case of rubber before cross-linking, such a state corresponds to a state in which the rubber is sufficiently kneaded and the temperature is raised to about 80 ° C.

The plastic material 5 contains a filler (not shown). As the filler, for example, silica, carbon black, alumina or the like is adopted. Such a filler is finely ground by kneading with the Banbury mixer 1 and is evenly dispersed in the plastic material 5.

FIG. 3 is a perspective view showing an example of a computer for executing a method of simulating a kneading of a plastic material. The computer 6 includes a main body 6a, a keyboard 6b, a mouse 6c, and a display device 6d. The main body 6a is provided with, for example, a storage device such as an arithmetic processing unit (CPU), a ROM, a work memory, and a magnetic disk, and disk drive devices 6a1 and 6a2. Further, the storage device stores in advance software or the like for executing the simulation method of the present embodiment. FIG. 4 is a flowchart showing an example of the processing procedure of the kneading simulation method for the plastic material.

In the simulation method of the present embodiment, first, the Banbury mixer model 11 that models the Banbury mixer 1 shown in FIG. 1 is input to the computer 6 (model input step S1). FIG. 5 is a flowchart showing an example of the processing procedure of the model input step S1. FIG. 6 is a cross-sectional view showing an example of the Bunbury mixer model 11. In FIG. 6, the elements H (i) (shown in FIG. 9) of the chamber model 14 are omitted.

In the model input step S1 of the present embodiment, first, the casing model 12 in which the casing 2 (shown in FIG. 1) is divided by a finite number of elements F (i) (i = 1, 2, ...) Is input to the computer 6. (Step S11). In step S11, based on the design data (for example, CAD data) of the casing 2 (shown in FIG. 1), at least a part of the contour of the casing 2 is a finite number of elements F (i) that can be handled by the numerical analysis method. Is discretized (modeled) by. This defines the casing model 12. The casing model 12 has an inner wall surface model 19 in which an inner wall surface 9 (shown in FIG. 1) of the casing 2 is defined.

As the element F (i) of the present embodiment, for example, a three-dimensional solid element is adopted. The solid element is preferably a hexahedral element having high accuracy and easy to set the contact surface, but may be a tetrahedral element or a polyhedral element suitable for expressing a complicated shape. In addition to these elements, there is no particular limitation as long as it is a three-dimensional solid element or a two-dimensional shell element that can be used by software. In each element F (i), an element number, a node number (not shown), numerical data such as a node coordinate value, and thermal conditions are defined. Further, each element F (i) is defined as a rigid body that cannot be deformed even when an external force acts on it. As a result, the stress calculation in the casing model 12 can be omitted, so that the calculation cost can be reduced. The casing model 12 is stored in the computer 6 (shown in FIG. 3).

Since the simulation method of the present embodiment is specialized in calculating the kneaded state of the plastic material 5 kneaded by the Banbury mixer 1, the casing model 12 may be defined only by the inner wall surface model 19. In this case, it is desirable that a two-dimensional shell element is adopted as the element F (i).

Next, in the model input step S1 of the present embodiment, the rotor 3 is input to the computer 6 by dividing the rotor 3 by a finite number of elements G (i) (i = 1, 2, ...) (Step). S12). In step S12, the contours of the base portion 3a and the wing portion 3b shown in FIG. 1 are formed by a finite number of elements G (for example, CAD data) based on the design data (for example, CAD data) of the rotors 3 and 3 (shown in FIG. 1). It is discretized (modeled) in i). As a result, a pair of rotor models 13 and 13 including a base model 13a and a wing model 13b are defined. The pair of rotor models 13 and 13 are arranged inside the casing model 12. Further, the pair of rotor models 13 and 13 are defined as rotation regions that can rotate around their centers Oa and Ob.

FIG. 7 is a partially enlarged view of FIG. In FIG. 7, the element G (i) shown in FIG. 6 is omitted. At the tip of the wing model 13b, a tip portion 18 projecting so as to approach the inner wall surface model 19 (outer peripheral surface 14o of the chamber model 14) of the casing model 12 is provided. The land width L2 of the tip portion 18 is set based on the land width L1 (shown in FIG. 2) of the tip portion 8 of the rotor 3.

As shown in FIG. 6, as the element G (i) of the present embodiment, a three-dimensional solid element can be adopted as in the element F (i), and the rigidity that cannot be deformed is defined. As with the casing model 12, the rotor model 13 may be modeled only on the surface of the rotor 3. The pair of rotor models 13, 13 are stored in the computer 6 (shown in FIG. 3).

Next, in the model input step S1 of the present embodiment, the chamber 4 (shown in FIG. 1) is divided by a finite number of elements H (i) (i = 1, 2, ...) In the computer 6, and the chamber model 14 Is input (step S13). FIG. 8 is a perspective view of the chamber model 14 and the rotor model 13. FIG. 9 is a cross-sectional view of the chamber model 14. FIG. 10 is a cross-sectional view showing the chamber model 14 in an exploded manner. In FIG. 10, the shape of the element H (i) is simplified and displayed.

In step S13 of the present embodiment, based on the design data (for example, contour, etc.) of the casing 2 and the pair of rotors 3 and 3 shown in FIG. 1, the inner wall surface 9 of the casing 2 and the pair of rotors 3 and 3 The three-dimensional space (contour) closed by the outer peripheral surface 3o is discretized (modeled) by the finite number of elements H (i) shown in FIG. As a result, the closed chamber model 14 is input. As shown in FIGS. 6 and 8, the chamber model 14 has an outer peripheral surface 14o partitioned by the inner wall surface model 19 of the casing model 12 and an inner peripheral surface 13o partitioned by the outer peripheral surfaces 13o of the pair of rotor models 13 and 13. It has a surface 14i.

As shown in FIGS. 9 and 10, for example, the Euler element is adopted as the element H (i). Element division (discretization) is performed by, for example, a tetrahedron, a hexahedron, or a polyhedron cell. In addition to these elements, there is no particular limitation as long as it is a three-dimensional grid-like element that can be used by software. Further, for each element H (i), physical quantities such as pressure, temperature, and velocity are calculated for the thermoplastic material model 16 and the gas phase model 17, which will be described later.

As shown separately in FIG. 10, the chamber model 14 of the present embodiment connects the pair of rotatable rotating portions 14A and 14B and the pair of rotating portions 14A and 14B, and also connects the pair of rotating portions 14A and 14A. , 14C and an outer frame portion 14C in which 14B is housed are included. Therefore, the chamber model 14 is configured to include three portions (that is, a pair of rotating portions 14A, 14B, and an outer frame portion 14C).

The rotating portions 14A and 14B have circular outer circumferences 14Ao and 14Bo, respectively, and inner circumferences 14Ai and 14Bi equal to the outer peripheral surface 13o (shown in FIG. 6) of the rotor model 13. The rotating portions 14A and 14B are respectively fitted inside the outer frame portion 14C. Further, the rotating portions 14A and 14B are defined so as to be rotatable around the centers (rotational axes) Oa and Ob together with the rotor models 13 and 13. The element H (i) in the rotating portions 14A and 14B can express the change in the volumetric shape of the chamber 4 accompanying the rotation of the rotors 3 and 3 shown in FIG.

The outer frame portion 14C is formed in a tubular shape surrounding the rotating portions 14A and 14B. Both ends of the outer frame portion 14C in the axial direction are closed by both end faces 14t (shown in FIG. 8). The outer frame portion 14C has a concave arc surface 14Co that comes into contact with the rotating portions 14A and 14B. Boundary conditions such as a sliding surface are defined for the concave arc surface 14Co of the outer frame portion 14C and the outer circumferences 14Ao and 14Bo of the rotating portions 14A and 14B. As a result, in the calculation step S2 described later for rotating the rotor models 13 and 13, the physical action (force, heat, etc.) generated in the rotating portions 14A and 14B of the chamber model 14 is transmitted through the concave arc surface 14Co. It is transmitted to the outer frame portion 14C. The chamber model 14 is stored in computer 6 (shown in FIG. 3).

Next, in the simulation method of the present embodiment, the computer 6 calculates (simulates) the state in which the plastic material 5 is kneaded in the chamber 4 (calculation step S2). In the calculation step S2 of the present embodiment, the thermoplastic material model 16 is arranged in the chamber model 14 and the rotor model 13 is rotated based on predetermined conditions (boundary conditions in the present embodiment). As a result, in the calculation step S2, the state in which the thermoplastic material 5 is kneaded in the chamber 4 (shown in FIG. 2) is simulated. FIG. 11 is a flowchart showing an example of the processing procedure of the calculation step S2.

In the calculation step S2 of the present embodiment, first, the plastic material model 16 that models the plastic material 5 (shown in FIG. 2) is input to the computer 6 (step S21). FIG. 12 is a cross-sectional view showing a chamber model 14 in which the thermoplastic material model 16 and the gas phase model 17 are arranged in a mixed manner. In addition, in FIG. 12, the plastic material model 16 is colored and displayed.

The thermoplastic material model 16 of the present embodiment is defined by the element H (i) of the chamber model 14 in which the Euler element shown in FIG. 10 is adopted. The physical properties (for example, shear viscosity, specific heat, thermal conductivity, etc.) of the plastic material 5 (shown in FIG. 2) are defined in the element H (i) of the chamber model 14. In step S21 of the present embodiment, the physical characteristics of the plastic material 5 containing the filler (not shown) are defined. Therefore, different physical properties are defined depending on the type of filler contained in the thermoplastic material 5. As a result, in step S21, the thermoplastic material model 16 arranged in the chamber model 14 is set. The thermoplastic material model 16 of this embodiment is defined as an incompressible fluid whose density does not change with pressure. Further, in the chamber model 14, the filling rate of the plastic material model 16 is set in step S23, which will be described later, in which the boundary conditions are set.

For the shear viscosity, for example, the viscoelastic properties (G'and G ") are measured from the thermoplastic material 5 (shown in FIG. 2) to be analyzed under a plurality of temperature conditions, and the shear viscosity is determined by using the Cox-Merz law or the like. It is obtained by conversion. The shear viscosity η thus obtained is approximated by the power law, for example, in the same manner as in the formula (1) described in Patent Document (Japanese Patent Laid-Open No. 5514236).

The specific heat is measured from the thermoplastic material 5 (shown in FIG. 2) to be analyzed by, for example, an adiabatic continuous method (@ 25 ° C.). The thermal conductivity is measured from the viscous fluid to be analyzed by, for example, the hot wire method (@ 25 ° C.). The thermoplastic material model 16 is input to the computer 6 (shown in FIG. 3).

Next, in the calculation step S2 of the present embodiment, the air (not shown) existing in the chamber 4 (shown in FIG. 1) is modeled by a finite number of elements in the computer 6 (shown in FIG. 3). The phase model 17 is input (step S22). The gas phase model 17 of the present embodiment is defined by the element H (i) of the chamber model 14 in which the Euler element shown in FIG. 10 is adopted, similarly to the thermoplastic material model 16. Physical properties such as viscosity and specific gravity of air are defined in the element H (i) of the chamber model 14. As a result, in step S22, the gas phase model 17 arranged in the chamber model 14 is set.

The gas phase model 17 of the present embodiment is defined as an incompressible fluid whose density does not change with pressure, similar to the thermoplastic material model 16. In the chamber model 14, the filling rate of the gas phase model 17 is set in step S23, which will be described later, in which the boundary conditions are set. The gas phase model 17 is input to the computer 6 (shown in FIG. 3).

Next, in the calculation step S2 of the present embodiment, various conditions such as boundary conditions necessary for the flow calculation of the plastic material model 16 are defined in the computer 6 (shown in FIG. 3) (step S23). As shown in FIG. 6, the boundary conditions of the present embodiment include a flow velocity boundary condition defined on the outer peripheral surface 14o of the chamber model 14 and a temperature boundary condition.

As the flow velocity boundary condition of the present embodiment, the wall surface slip condition is adopted. Under the wall surface slip condition, the plastic material model 16 (shown in FIG. 12) of the chamber model 14 has a flow velocity in the inner wall surface model 19 (outer peripheral surface 14o between the chamber models 14) of the casing model 12. In this case, the slip phenomenon of the contact surface between the plastic material model 16 and the chamber model 14 is simulated by using Navier's Law or the like, as in the simulation method described in Patent Document (Patent No. 5514236), for example. Can be patented.

As the temperature boundary condition, either a condition in which the outer surface temperature of all the chamber models 14 is set to a temperature control temperature (for example, 50 ° C.) or a heat insulation condition is adopted. The heat insulating condition is a condition in which heat does not escape to the outside on each outer surface of the chamber model 14. In the present embodiment, the heat insulating condition is adopted as the temperature boundary condition of the chamber model 14 from the viewpoint of reducing the calculation load.

Other conditions include the initial state of the flow calculation, the size of the unit time (minute time) of the simulation, the number of iterations of the iteration in the internal processing, the calculation end time, the radius R of the filler, and the like. The radius R of the filler is set based on the filler blended in the thermoplastic material 5 (shown in FIG. 2).

Further, other conditions include the rotation speed of the rotor model 13 (rotational speeds of the rotating portions 14A and 14B of the chamber model 14 shown in FIG. 10), the slip ratio of the outer peripheral surface 14o of the chamber model 14, and the volume of the chamber model 14. The filling rate of the plastic material model 16 and the gas phase model 17 with respect to the above is included. By setting such a filling rate, the flow calculation can be performed when the filling rate of the viscous fluid is 100% or less (for example, 50% to 90%).

As shown in FIG. 12, the chamber model 14 in the initial state has the region A of the gas phase model 17 above the horizontal boundary surface S across the chamber model 14 as a reference, and the plasticity below it. It is arranged in a mixed manner as the region M of the material model 16. The boundary surface S is set based on the filling rates of the thermoplastic material model 16 and the gas phase model 17. Further, the filling rate of the thermoplastic material model 16 may be adjusted by changing the level of the boundary surface S. These conditions are arbitrarily determined according to the purpose of the simulation and the like.

Next, in the calculation step S2 of the present embodiment, the rotor models 13 and 13 are rotated to simulate the state in which the plastic material model 16 in the chamber model 14 is kneaded (step S24). In step S24, the flow calculation of the plastic material model 16 is performed based on the rotations of the rotor models 13 and 13. In the flow calculation, for example, similarly to the simulation method described in Patent Document (Patent No. 5514236), the velocity components in three directions (x, y, z) for specifying the motion state of the fluid and the internal state of the fluid are calculated. The pressure p and the temperature T, which are unknown quantities to be specified, are calculated. The pressure p of the present embodiment includes the pressure of at least the portion of the inner wall surface model 19 in contact with the thermoplastic material model 16. Further, in the present embodiment, the Navier-Stokes equation is used in the case of incompressible flow, and the densities of the plastic material model 16 and the gas phase model 17 are constant.

In this embodiment, the thermoplastic material model 16 is treated as a fluid in the entire temperature range. Therefore, the fluid equations (Navier-Stokes equations, mass conservation equations, and energy equations) will be solved. Further, in the present embodiment, since it is necessary to handle two fluids of the thermoplastic material 5 (shown in FIG. 2) and air (not shown) at the same time, the VOF (Volume of Fluid) used in the calculation of the flow at the free interface is used. ) Method is used. The VOF method does not directly calculate the movement of the interface between the two fluids (ie, the thermoplastic material 5 and the air), but rather the filling rate (volume) of the fluid in the volume of each element (sometimes referred to as a "cell"). It defines the fraction) and expresses the free interface. The governing equations (equation of motion, conservation of mass, energy equation, and volume fraction transport equation) are as described in, for example, Patent Document (Patent No. 5514236). The flow calculation can be easily calculated by using, for example, FLUNET or CFX of ANSYS or STAR-CCM + general-purpose fluid analysis software of Siemens PLM Software.

Further, in the present embodiment, the governing equation is solved by a pressure-based separated solution method. For the coupling of the pressure equation and the equation of motion, for example, it is desirable to use the SIMPLE (Semi-Implicit Method for Pressure-Linked Equations) algorithm.

As a result, in step S24, the state in which the plastic material 5 is kneaded in the chamber 4 shown in FIG. 2 can be simulated for each unit time (time t). In step S24 of the present embodiment, the shear stress τ and the shear velocity γ are calculated for each unit time (time t) for each element H (i) constituting the plastic material model 16 in the chamber model 14. The calculation results of the shear stress τ and the shear velocity γ are stored in the computer 6 (shown in FIG. 3).

Next, in the calculation step S2 of the present embodiment, the parameter D regarding the dispersion state of the plastic material 5 (shown in FIG. 2) is calculated by the following formula (1) (step S25). The parameter D regarding the dispersed state of the plastic material of the present embodiment indicates that the larger the numerical value, the better the dispersed state of the plastic material 5 (shown in FIG. 2).

ここで、
Ｖ：可塑性材料モデルの体積
Ｒ：フィラーの半径
ｔ：時刻
Ｔ：可塑性材料モデルがチップ部を通過するのに要する時間
Ｑ：チップ部を通過する可塑性材料モデルの単位時間当たりの流量
τ：可塑性材料モデルのせん断応力
γ：可塑性材料モデルのせん断速度
α、τ_ｃ：定数

here,
V: Volume of the thermoplastic material model R: Radius of the filler t: Time T: Time required for the thermoplastic material model to pass through the chip part Q: Flow rate per unit time of the plastic material model passing through the chip part τ: Plastic material Model shear stress γ: Thermoplastic material model shear rate α, τ _c : Constant

The volume V of the plastic material model of the above formula (1) is the volume of the plastic material model 16 (shown in FIG. 12) defined in the chamber model 14. The radius R of the filler of the above formula (1) is a parameter input in step S23 for inputting the above-mentioned boundary condition. The time t in the above equation (1) is the simulation time carved for each unit time.

The time T in the above formula (1) indicates the time required for the thermoplastic material model 16 (shown in FIG. 10) to pass through the chip portion 18 (shown in FIG. 7) of the rotor model 13. The time T is the velocity v of the plastic material model 16 passing through the land width L2 of the chip portion 18 through the gap (chip clearance) 20 (shown in FIG. 7) between the chip portion 18 and the outer peripheral surface 14o of the chamber model 14. It can be obtained by dividing by. The velocity v is a plastic material parallel to the tangent line at the center portion 18c in the width direction (rotor circumferential direction) of the tip portion 18 of the rotor model 13 (in the present embodiment, in the direction along the tip portion 18) at time t. It is defined as the velocity component of model 16. The larger the value of such time T, the longer it takes for the thermoplastic material model 16 to pass through the chip portion 18, and the thermoplastic material model 16 is effectively compressed and sheared. This means that the dispersed state of the plastic material 5 (shown in FIG. 2) is good.

The flow rate Q of the above formula (1) indicates the flow rate per unit time of the plastic material model 16 (shown in FIG. 10) passing through the chip portion 18 (shown in FIG. 7). The flow rate Q is one of the elements H (i) (shown in FIG. 10) of the plastic material model 16 arranged in the gap (chip clearance) 20 at the time t-1 one before the current time t. At the current time t, it is obtained as the total volume of the elements H (i) discharged from the gap 20. Such a flow rate Q means that the larger the value is, the more the plastic material model 16 is compressed and sheared, so that the dispersed state of the plastic material is better.

In the present embodiment, the elements H (i) (shown in FIG. 10) of the plastic material model 16 arranged in the gap 20 are, as shown in FIG. 7, each end of the chip portion 18 in the rotor circumferential direction. It is an element arranged in the region 22 surrounded by the boundary surfaces 21 and 21 extending from the 18t and 18t to the outer peripheral surface 14o of the chamber model 14. The boundary surfaces 21 and 21 of the present embodiment are oriented in a direction orthogonal to the tangent line at the center portion 18c in the width direction (rotor circumferential direction) of the chip portion 18 (in the present embodiment, a direction orthogonal to the chip portion 18). It extends in parallel.

The shear stress τ of the plastic material model of the above formula (1) is, at time t, between the chip portion 18 and the outer peripheral surface 14o of the chamber model 14 among the elements H (i) constituting the plastic material model 16. It is an average value of the shear stress calculated by the element H (i) arranged in the gap (chip clearance) 20. The shear rate γ of the plastic material model of the above formula (1) is also an average value of the shear rates calculated by the element H (i) arranged in the gap (chip clearance) 20 like the shear stress τ.

The constant α in the above formula (1) is a material constant of the thermoplastic material 5 (shown in FIG. 2). _{Further, the constant τ c} in the above equation (1) is a critical shear stress indicating a boundary of whether or not the plastic material 5 is plastically deformed. These constants alpha, the tau _c, for example, can be appropriately set based on experiments and results and the like using a plastic material 5. In the calculation step S2 of the present embodiment, for example, based on a paper (Ica Manas-Zloczower, "Mixing and Compounding of Polymers", (Denmark), UNIVERSITE CATHOLIQUE DE LOUVAIN, 2nd edition, Hanser Gardner Pubns, 2009). , Is defined as follows.
α = 1.3 × 10 ^-5 [μm / Pa]
τ _c = 72000 [Pa]

In the above formula (1), dR / dt obtained by differentiating the radius R of the filler at time t indicates the amount of decrease in the radius R of the filler at time t.

In the above formula (1), when the shear stress τ of the plastic material model 16 is a constant (critical shear stress) τ _c or less, the plastic material 5 arranged in the gap 10 in the Banbury mixer 1 shown in FIG. Is not plastically deformed, and it is judged that the size of the filler (not shown) does not change. In this case, 0 is defined for the reduction amount dR / dt of the radius of the filler.

On the other hand, in the above equation (1), when the shear stress τ of the plastic material model 16 _{is larger than the constant (critical shear stress) τ c} , it is arranged in the gap 10 in the Banbury mixer 1 shown in FIG. It is determined that the plastic material 5 is plastically deformed and the size of the filler (not shown) becomes smaller. _{In this case, − (α (τ−τ c} ) γ) / 3R ² is defined as the amount of decrease in the radius of the filler, dR / dt.

-(Α (τ-τ _c ) γ) / 3R ² of the above equation (1) is proportional to the material constant α, the difference between the shear stress and the critical shear stress τ-τ _c , and the shear rate γ. The amount of decrease in the radius R of the filler is increased (that is, the negative number dR / dt is decreased). Details of the calculation formula are as described in the above paper. As described above, the decrease amount dR / dt of the radius of the filler means that the smaller the value (the larger the absolute value), the finer the filler is pulverized and the better the dispersed state of the plastic material is.

The parameter D relating to the dispersion state of the thermoplastic material in the above formula (1) is −dR / dt obtained by multiplying the amount of decrease in the radius of the filler by -1, the time T required for the thermoplastic material model to pass through the chip portion, and It is obtained by multiplying the flow rate Q per unit time of the plastic material model passing through the chip portion and further dividing by the volume V of the plastic material model.

As described above, the larger the value of the time T required for the thermoplastic material model to pass through the chip portion and the flow rate Q per unit time of the plastic material model passing through the chip portion, the more the thermoplastic material 5 (FIG. FIG. It shows that the dispersed state (shown in 2) is good.

On the other hand, the amount of decrease in the size of the filler, dR / dt, indicates that the smaller the value, the larger the amount of decrease in the radius R of the filler, and the better the dispersed state of the thermoplastic material 5 (shown in FIG. 2). It is a thing. Therefore, the magnitude relationship between the amount of decrease in the size of the filler, dR / dt, and the time T and the flow rate Q is different from each other. Therefore, in the above equation (1), the amount of decrease in the size of the filler, dR / dt, is multiplied by -1 to be converted into a positive number, so that the time T and the flow rate Q have a magnitude relationship with each other. ..

In the above formula (1), the amount of decrease in the radius of the filler converted to a positive value −dR / dt, the time T required for the thermoplastic material model to pass through the chip portion, and the plastic material passing through the chip portion. As for the parameter −dR / dt · T · Q multiplied by the flow rate Q per unit time of the model, the larger the value, the better the dispersed state of the thermoplastic material 5 (shown in FIG. 2) at time t. Shown. However, when the parameters −dR / dt · T · Q are used for comparison of the kneading performance (dispersed state of the plastic material 5) of a plurality of Banbury mixers 1, for example, they are arranged in the chamber model 14 shown in FIG. It is assumed that the volume V of the thermoplastic material model 16 is the same.

In order to eliminate such a premise, in the present embodiment, the parameter −dR / dt · T · Q is divided by the volume V of the plastic material model, so that the dispersed state per unit volume of the plastic material model 16 is obtained. Parameter D is required. The larger the value of the parameter D, the better the dispersion efficiency of the thermoplastic material model 16 at time t, and the better the kneading performance of the Banbury mixer 1.

As described above, in the above equation (1), along with the shear stress τ and the shear rate γ of the plastic material model, the parameters (time T,) relating to the chip portion 8 (chip portion 18 shown in FIG. 7) shown in FIG. 2 are shown. Flow rate Q) is included. Therefore, in the kneading simulation method of the present embodiment, the kneading performance of the Banbury mixer 1 (dispersed state of the plastic material 5) can be evaluated in consideration of the influence of the tip portion 8 of the rotor 3. The parameter D regarding the dispersed state of the plastic material is stored in the computer 6.

Next, in the calculation step S2, it is determined whether or not the current time t has reached the calculation end time (step S26). The calculation end time is appropriately set in step S23 for defining the boundary conditions and the like.

If it is determined in step S26 that the current time t has reached the calculation end time (“Y” in step S26), the series of processes in calculation step S2 ends. On the other hand, if it is determined in step S26 that the current time t has not reached the calculation end time (“N” in step S26), the unit time (time t) is advanced by one (step S27), and step S24. ~ Step S26 is carried out again. As a result, in the calculation step S2, the rotor models 13 and 13 shown in FIG. 6 were rotated every unit time from the start of the calculation to the end time of the calculation, and the thermoplastic material 5 in the chamber 4 was kneaded. The state can be simulated. Further, in the calculation step S2, the parameter D regarding the dispersion state of the thermoplastic material 5 (shown in FIG. 2) can be calculated every time t.

Next, in the simulation method of the present embodiment, it is determined whether or not the kneading performance of the Banbury mixer 1 (shown in FIG. 1) is good (step S3). Whether or not the kneading performance of the Banbury mixer 1 is good can be determined as appropriate. In the present embodiment, it is determined that the kneading performance of the Banbury mixer 1 is good when the parameter D regarding the dispersion state of the plastic material 5 calculated at each time t is equal to or higher than a predetermined threshold value. The threshold value can be appropriately set according to the kneading performance required for the Banbury mixer 1.

As described above, the influence of the chip portion 8 of the rotor 3 shown in FIG. 2 is taken into consideration in the parameter D regarding the dispersed state of the plastic material. Therefore, the performance of the Banbury mixer 1 can be evaluated more accurately than the method of Non-Patent Document 1.

When it is determined in step S3 that the kneading performance of the Banbury mixer 1 is good (“Y” in step S3), the Banbury mixer 1 is manufactured based on the Banbury mixer model 11 (shown in FIG. 6). (Step S4). On the other hand, when it is determined in step S3 that the kneading performance of the Banbury mixer 1 is not good (“N” in step S3), the design factor of the Banbury mixer 1 (rotor 3) shown in FIGS. 1 and 2 (for example). , The land width L1 of the chip portion 8 and the like) are changed (step S5), and steps S1 to S3 are executed again. Thereby, in the simulation method of the present embodiment, the Banbury mixer 1 (including the rotor 3) capable of exhibiting high kneading performance can be reliably designed.

In the simulation method of the present embodiment, as shown in FIG. 12, the thermoplastic material model 16 and the gas phase model 17 are defined in the chamber model 14, but the simulation method is not limited to such an embodiment. For example, only the thermoplastic material model 16 may be defined within the chamber model 14. As a result, the calculation target of the chamber model 14 is limited to the thermoplastic material model 16, so that the calculation load can be reduced. Further, when only the thermoplastic material model 16 is filled in the chamber model 14, the calculation can be performed only by the finite volume method by omitting the VOF method, so that the calculation load can be reduced.

FIG. 13 is a graph showing the relationship between the parameter D and the time t regarding the dispersion state of the plastic material for the first rotor model and the second rotor model having different land widths L2 (shown in FIG. 7). The land width L1 of the second rotor model is set to 1.1 times the land width L1 of the first rotor model.

By the way, based on the parameter D regarding the dispersion state of the plastic material calculated every time t, for example, the kneading performance of the Banbury mixer model (not shown) having a pair of first rotor models and the pair of second rotor models Comparing the kneading performance of the Banbury mixer model (not shown), as shown in FIG. 13, the magnitude relationship between the parameter D of the first rotor model and the parameter D of the second rotor model is exchanged, and the kneading performance is improved. It can be difficult to assess superiority or inferiority. The change in the magnitude relation of the parameter D is due to the difference in the land width L1 and the flow of the plastic material model 16 around each chip portion 8 of the first rotor model and the second rotor model (that is, the plastic material model 16 is the chip). It is considered that this is because the time when the model passes through the part 8 and the time when the shear acts on the plastic material model 16 and the shear rate are different from each other.

In order to clarify the magnitude relationship of the parameter D regarding the dispersed state of the plastic material, the calculation step S2 further includes a step S28 for calculating the time average of the parameter D during the period in which the rotor model 13 makes one or more rotations. desirable. FIG. 14 is a flowchart showing an example of the processing procedure of the calculation step S2 of another embodiment of the present invention. In this embodiment, the same configurations as those in the previous embodiments are designated by the same reference numerals, and the description thereof may be omitted.

In step S28 of the present embodiment, the time average of the parameter D is calculated during the period in which the rotor model 13 (shown in FIG. 6) makes one rotation. For example, when the period for one rotation of the rotor model 13 is 1.0 second and the unit time is 0.1 second, the time average of the parameter D at the time t (1.0 second) for one rotation is , It is obtained as the average value of 11 parameters D calculated for each unit time (0.1 seconds) from the time t (0 seconds) to the time t (1.0 seconds).

Further, the time average of the parameter D at the time t (1.1 seconds) when the unit time 0.1 seconds has elapsed from the time t (1.0 seconds) of one rotation is the time from the time t (0.1 seconds). It is obtained as the average value of 11 parameters D calculated every unit time (0.1 seconds) up to t (1.1 seconds). The time average of such a parameter D is calculated every unit time (0.1 seconds) from the time t (1.0 seconds) required for one rotation of the rotor model to the calculation end time.

FIG. 15 is a graph showing the relationship between the time average and the time t of the parameter D regarding the dispersed state of the plastic material for the first rotor model and the second rotor model having different land widths L1. As shown in FIG. 15, in step S28, the time average of the parameter D of the second rotor model is calculated to be larger than the time average of the parameter D of the first rotor model at all time t. Therefore, in this embodiment, the kneading performance of the Banbury mixer 1 can be reliably evaluated by obtaining the time average of the parameter D.

The time average of the parameter D of this embodiment was calculated for each period in which the rotor model 13 makes one rotation, but if the period in which the rotor model 13 makes one rotation or more, the parameter D is calculated for each appropriately set period. Time averages may be calculated. If the period is long, the number of samples on the time average of parameter D may decrease. From this point of view, it is desirable that the period during which the time average of the parameter D is calculated is shorter than the period during which the rotor model 13 makes three rotations.

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

[Example A]
According to the processing procedure shown in FIGS. 4 and 5, a Banbury mixer model having a pair of second rotor models and a Banbury mixer model having a pair of third rotor models having different chip land widths from the second rotor model. Was input to the computer (Example 1, comparative example). In Example 1 and Comparative Example, a calculation step was carried out in which a thermoplastic material model was placed in each Bunbury mixer to simulate the state in which the thermoplastic material was kneaded in the chamber.

In the calculation step of the first embodiment, according to the processing procedure shown in FIG. 11, the variance mixer model having a pair of second rotor models and the variance mixer model having a pair of third rotor models are of the above equation (1). Parameter D with respect to the dispersed state of the plastic material was calculated. FIG. 16 is a graph showing the relationship between the parameter D and the time t regarding the dispersion state of the plastic material of Example 1.

In the calculation step of the comparative example, the dispersion state of the polymer is related to the Banbury mixer model having a pair of second rotor models and the Banbury mixer model having a pair of third rotor models according to the same procedure as in Non-Patent Document 1. The parameter (shear stress λ) was calculated. FIG. 17 is a graph showing the relationship between the shear stress of the comparative example and the time t.

Then, in Examples and Comparative Examples, the kneading performance of the Bunbury mixer model having a pair of second rotor models and the Bunbury mixer model having a pair of third rotor models was evaluated. The common specifications are as follows.
Bunbury Mixer (Bunbury Mixer model):
Number of rotors (rotor model): 2
Rotation speed of one rotor (rotor model): 42 rpm
Rotation speed of the other rotor (rotor model): 38 rpm
Filling rate of viscous fluid (viscous fluid model): 70%
Land width of the tip of the 3rd rotor model: 1/3 times the land width of the tip of the 2nd rotor model

As a result of the test, in Example 1, as shown in FIG. 16, the parameter D of the second rotor model was calculated to be larger than the parameter D of the third rotor model at all times. As a result, it was possible to evaluate that the Banbury mixer model having a pair of second rotor models has better kneading performance than the Banbury mixer model having a pair of third rotor models.

On the other hand, in the comparative example, as shown in FIG. 17, the shear stress of the second rotor model and the shear stress of the third rotor model are close to each other, and the superiority or inferiority cannot be evaluated.

As described above, in Example 1, the kneading performance of the Banbury mixer could be evaluated in consideration of the influence of the tip portion of the rotor as compared with the comparative example.

[Example B]
According to the processing procedure shown in FIGS. 4 and 5, a Banbury mixer model having a pair of first rotor models and a Banbury mixer model having a pair of second rotor model models were input to the computer (Example 2). In Example 2, a calculation step was performed in which a thermoplastic material model was placed in each Bunbury mixer to simulate the state in which the thermoplastic material was kneaded in the chamber.

In the calculation step of the second embodiment, the rotor model makes one rotation for the variance mixer model having a pair of first rotor models and the variance mixer model having a pair of second rotor models according to the processing procedure shown in FIG. During the period, the time average of the parameter D regarding the dispersed state of the plastic material of the above formula (1) was calculated.

Then, the kneading performance of the Banbury mixer having a pair of first rotor models and the Banbury mixer having a pair of second rotor models was evaluated. The common specifications are the same as in Example A except for the land width of the chip portion of the second rotor model.
Land width of the tip of the 2nd rotor model: 1.1 times the land width of the tip of the 1st rotor model

As shown in FIG. 15, in the second embodiment, the time average of the parameter D of the second rotor model was calculated to be larger than the time average of the parameter D of the first rotor model at all time t. Therefore, in Example 2, the kneading performance of the Banbury mixer having the first rotor model and the second rotor model in which the land widths of the chip portions are close to each other could be reliably evaluated.

S2 calculation step

Claims (2)

It has a chamber that is a space for kneading a plastic material, and at least one rotor that rotates in the chamber, and has a tip portion that projects so that the rotor approaches the outer peripheral surface of the chamber. A simulation method for investigating the kneading performance of a chambery mixer in which the plastic material contains a filler.
A step of inputting a rotor model into a computer by dividing the rotor into a finite number of elements,
A step of inputting a chamber model into the computer by dividing the chamber into a finite number of elements,
A step of inputting a thermoplastic material model modeling the plastic material into the computer,
Including a calculation step of simulating a state in which the thermoplastic material is kneaded in the chamber by arranging the thermoplastic material model in the chamber model and rotating the rotor model based on predetermined conditions. ,
The calculation step includes a step of calculating parameter D regarding the dispersed state of the plastic material by the following formula (1).
Kneading simulation method for thermoplastic materials.

here,
V: Volume of the thermoplastic material model R: Radius of the filler t: Unit time T: Time required for the thermoplastic material model to pass through the chip part Q: Flow rate per unit time of the plastic material model passing through the chip part τ: Plasticity Shear stress of material model γ: Shear rate of thermoplastic material model α, τ _c : Constant The kneading simulation method for a plastic material according to claim 1, wherein the calculation step further includes a step of calculating the time average of the parameter D during a period in which the rotor model makes one or more rotations.

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