JPH10244575A - Screw planning method in twin-screw extruder - Google Patents

Abstract

PROBLEM TO BE SOLVED: To plan a screw shape in consideration of tress relaxation. SOLUTION: A mesh data of the meshing phase of a screw flight is corrected at every time step (Δt) and convergence calculation considering the time increment item of each fundamental equation related to heat and flow is performed to calculate a cyclical non-steady solution (step S1 - step S12). Next, the history of particles of a resin flow mark line is quantified and, at every flow mark line, on the basis of the stress value of each flow mark line position at every Δt from an inflow port, the temp. history from the position to an outflow port and a relax time of time characteristics, the relax quantity of the stress 1 calculated (steps S13, S14) and the residual stress value a t the outflow port of the stress at each flow mark line position is integrated as the whole of the flow mark line. The residual stress values are calculated with respect to all of imaginary particles and the standard deviation value is set to the surface property index APE to a final product (steps S15, S16). The surface property index APE is used to plan the optimum screw shape.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a screw designing method for a twin screw extruder.

[0002]

2. Description of the Related Art The screw performance of a conventional twin-screw extruder was examined by quantifying the resin flow and pressure distribution in a screw portion of a twin-screw co-rotating extruder (ANTEC: 90).
P. 135-138) A three-dimensional analysis of the resin flow path in the twin-screw co-rotating extruder to quantify the resin flow, operating characteristics, and screw shape characteristics in the screw part (A
NTEC: 90P. 139-142) The kneading performance of a screw element of a twin-screw co-rotating extruder was experimentally performed (ANTEC: 91P.149-152). The resin flow rate in a resin flow path in a twin-screw co-rotating extruder , Pressure and shear rate (ANTEC: 92P.131)
1-1316).

[0003] The applicant of the present invention performs a three-dimensional numerical analysis based on mesh data obtained by dividing a resin flow path in an extruder into three-dimensional microelements (JP-A-3-288620, JP-A-4-364921). Japanese Patent Application Laid-Open No. Hei 3-288819, and a method for determining a screw shape that matches the required quality by using the results of these numerical analysis.

[0004] Among them, a screw designing method in a twin screw extruder disclosed in Japanese Patent Application Laid-Open No. Hei 3-288819 discloses a method in which a twin screw is provided in a barrel and the resin in the barrel is extruded by the rotation of the screw. Done 2
In a screw extruder, the resin flow path in the barrel is divided into small elements, and based on the mesh data obtained by this division, numerical analysis is performed using input data such as resin temperature and extrusion pressure, and the analysis results are analyzed. Based on this, the optimum screw size in the resin flow path and the input data is determined.

[0005]

That is, the conventional screw designing method in a twin-screw extruder simply uses a physical quantity distribution or a physical quantity history distribution based on a trajectory calculated by heat and flow analysis in the twin-screw extruder. Is used as an index to design screws.

[0006] However, the stress applied in the process of determining the surface properties of a product is relaxed depending on the temperature and time. Therefore, if this stress relaxation is not taken into account, the correlation between the actual product surface properties and the stress distribution and stress history distribution is low, and the appropriate screw shape to obtain an extruded product with good surface properties for each raw material mix There was a problem that conversion could not be performed.

SUMMARY OF THE INVENTION The present invention has been made to solve such a problem, and an object of the present invention is to provide an optimum extruded product having good surface properties for each raw material mixture by considering stress relaxation. It is an object of the present invention to provide a screw designing method for a twin-screw extruder capable of designing various screw shapes.

[0008]

Means for Solving the Problems To solve the above problems, a screw designing method for a twin screw extruder according to the present invention comprises:
In a twin-screw extruder in which a two-axis screw is provided in a barrel and the resin in the barrel is extruded by the rotation of the screw, the resin flow path in the barrel is spatially converted into three-dimensional microelements. Based on the divided mesh data, all the basic equations governing heat and flow are treated in three dimensions, including the time increment term, and unsteady based on various boundary conditions and resin characteristics according to the actual phenomena. When performing numerical analysis and discretizing, the area where the two-axis screw flight meshes is divided into two blocks for each screw axis, and the resin flow path is divided into three-dimensional microelements. The block is rotated for each time step by the time increment term while performing the transfer process of the boundary condition with each other, and one block surface in the area is set to the other block. The mesh data is deformed so as not to enter the screw part of the screw, and the resin flow trajectory of the molten resin in the extruder due to the rotation of the screw based on the flow velocity vector discretized at each time step in this way is Based on the stress value at each position of the trajectory, the stress relaxation characteristics of the resin, and the temperature history from each flow position to the outlet, the amount of stress to be relaxed to the outlet is calculated based on the trajectory. Calculate for each position, calculate the residual stress value integrated over the entire trajectory, calculate this residual stress value for all the virtual particles injected into the uniform distribution from the inlet, and minimize the variation In this way, the optimum screw dimensions are designed.

Numerical analysis means that resin flow path data (mesh data) is converted into various conditions (screw rotation peripheral speed, wall temperature,
The flow field and the temperature field based on the inflow, etc.) until the cyclic unsteady solution is finally obtained. The analysis scheme is the finite element method, finite difference method, finite volume method However, the finite difference method is preferable in terms of calculation time and calculation capacity. The solution by the finite difference method may be either the MAC method or the SIMPLE method, and the convergence method includes the SOR method, the Jacobi method, and the Gaussian method.
The Seidel method may be used. The mesh may be a triangular element or the like in addition to the hexahedral cell element.

As described above, based on the resin history of the molten resin in the twin-screw extruder, the residual stress is considered in consideration of the stress value applied to the resin and the amount of relaxation caused by the temperature and time until the stress reaches the outlet. By calculating the distribution of the amount of relaxation, it is possible to design an optimal screw shape for obtaining an extruded product having good surface properties.

Here, the filled portion of the molten resin may be a completely filled state occupying 100% of the resin flow path in a molten flow state in the resin flow path between the barrel and the screw in the twin-screw extruder. % May be unfilled.

[0012]

Embodiments of the present invention will be described below with reference to the drawings. In the following example, a completely filled portion is described, but a flow analysis can be performed in a similar manner by using a VOF method (Volume of Fluid method) even in an unfilled portion.

The screw design method of the present invention is applied 2
In the screw extruder, the screw rotation direction may be opposite for each axis, or any of the same, but in this embodiment,
A case in which the direction of screw rotation is opposite, that is, a case where the present invention is applied to a biaxially different direction rotary extruder will be described.

The resin to be filled in the twin-screw extruder to which the screw designing method of the present invention is applied is a thermoplastic resin which exhibits meltability and fluidity by heat and energy by shearing. Examples include polypropylene, polystyrene, polycarbonate, hard vinyl chloride resin, soft vinyl chloride resin, nylon resin, polyvinyl acetal resin, acrylic resin, acetal resin, and polyester resin. A plasticizer, a filler, and the like may be added to these thermoplastic resins. In addition, it is a thermosetting resin that is insolubilized (hard reaction) by energy due to heat or shearing and does not melt even when reheated. Epoxy resin, alkyd resin, silicon resin, polyimide resin, polyurethane resin and the like may be used.

FIG. 1 shows a system configuration diagram for executing a screw designing method in a twin-screw extruder according to the present invention. This system includes a preprocessor (mesh generator) 11 having an extruder mesh generation program for creating mesh data for performing heat flow analysis by dividing a resin flow path in an extruder three-dimensionally by hexahedral cell elements,
A solver processor 12 having an analysis program for repeatedly calculating a flow field and a temperature field using mesh data created by the preprocessor 11 and various boundary conditions defined by actual phenomena, and an analysis program of the solver processor 12 Postprocessor 13 equipped with a trajectory display program for plotting the three-dimensionally discretized physical quantities on mesh data and displaying the trajectory of the resin using the flow velocity of each element, and graphing the analysis results It is constituted by a graph processor 14 which converts the data into a graph.

The preprocessor 11 defines the main parameters characterizing the screw shape in the extruder and the number of divisions in each of the three-dimensional directions, creates mesh data, and operates, for example, operating conditions (such as boundary conditions) and resin characteristics. And setting parameters for controlling the convergence conditions of the analysis program.

The input parameters for the trapezoidal screw of the twin screw counter-rotating extruder are shown below. That is, first, the resin flow path of the biaxially different-direction rotary extruder is divided into minute elements to form a set of hexahedral solid model elements. This division determines the number of divisions in the screw axial direction, the number of divisions in the radial direction, and the number of divisions in the circumferential direction. As shown in FIGS. 2 and 3, the screw inner radius (RI), screw outer radius (RO), barrel This is performed by setting the inner radius (RB), the distance between screw shafts (RL), the flight pitch (PICH), the flight top width (A), the flight pressure angle (ALF), and the number of flights (ISN). In this case, since the shape becomes complicated, the analysis target is divided into two blocks for each screw axis, and mesh data is created.

FIG. 4 is a cross-sectional view perpendicular to the axis of the mesh data of the biaxially different-direction rotary extruder generated by the preprocessor 11. Solver processor 12
The analysis program comprises a flow analysis unit and a temperature analysis unit, and uses a data file created by the preprocessor 11 to mutually connect physical blocks between blocks using a multi-block method so as to smoothly connect physical quantities between the blocks. The calculation is advanced by passing the boundary conditions. Also,
By the convergence calculation of the flow analysis unit and the temperature analysis unit, the time step is updated until the entire analysis area reaches the periodic unsteady state, and the convergence calculation is repeatedly performed within the time step.

FIG. 5 shows a basic flowchart of the analysis program. First, the data file created by the preprocessor 11 is read, and constants are set (step S1). Next, the time is advanced by a time increment Δt from the time t _n (time t _{n + 1} ), and each block is rotated around the screw axis by Δt (steps S2 and S3). The mesh data is deformed so as not to overlap and so that one block surface does not enter the screw portion in the other block (step S4), and the boundary condition is set (step S5).

Next, the viscosity at each grid point of the mesh data at the time t _{n + 1} is determined from the temperature and the shear rate (step S6), and the flow velocity field is determined by solving the equation of motion (step S7). . Next, the pressure increase on each grid point of the mesh data is determined by solving the Poisson equation relating to the pressure using, for example, the SOR method (step S8), and the flow velocity is corrected with this pressure increase (step S9). Also,
The temperature field is obtained by solving an energy equation (step S10).

Next, the particle position coordinates within the analysis area defined by the data file created by the preprocessor 11 are detected, and the particle containing the particle position coordinates and the flow velocity of the surrounding elements are used to determine the particle position coordinates. Is calculated by interpolation (step S11). Thereafter, the particles are moved at the flow velocity, and the time is advanced by the time increment Δt again (step S).
The processing of the loop such as 2) is continued until all physical quantities in the two blocks reach the periodic unsteady state (step S12).

In this way, the mesh data of the mesh phase of the screw flight is corrected for each time step (time increment Δt), and the convergence calculation is performed in consideration of the time increment term of each basic equation relating to heat and flow. This enables periodic unsteady analysis. Therefore, the original flow state in the twin-screw extruder can be strictly expressed.
The resin history (temperature, shear rate, viscosity, stress, pressure, etc.) of the molten resin in the screw extruder can be accurately quantified.

The post-processor 13 displays a distribution map of each physical quantity and a trajectory based on the flow velocity of each element on the mesh data, using the mesh data created by the pre-processor 11 and the calculation results by the analysis program. The convergence state of the convergence calculation and the history of each physical quantity are graphically output by switching the analysis control data.

FIGS. 6 to 8 show the graphical output of the analysis results of the flow velocity and the temperature in the biaxially different direction rotary extruder. FIG. 6 shows the flow velocity in the cross section perpendicular to the axis based on the calculation result of the analysis program. FIG. 7 is a vector contour diagram, FIG. 7 is a temperature contour diagram in a section perpendicular to the axis according to the calculation result of the analysis program, and FIG.
FIG. 3 is a resin trajectory diagram in a three-dimensional bird's-eye view based on a calculation result of an analysis program.

Next, in the solver processor 12, the history of particles of the resin trajectory over the entire full filling portion of the molten resin in the twin-screw extruder based on the calculation result of the analysis program is calculated.
Quantification is performed on, for example, 1000 pieces at the analysis area entrance (step S13). Then, for each of the trajectories, the stress value at each position of the trajectory, for example, every 0.1 seconds (Δt) from the inlet, and the temperature history from that position to the outlet (resin temperature and residence time) Then, based on the relaxation time of the resin characteristic, the relaxation amount of the stress is calculated (step S14).

Next, the residual stress value at the outlet of each stress at each position of the trajectory is integrated over the entire trajectory. The residual stress value is calculated for all the 1000 particles described above (step S15), and the standard deviation value is used as the surface property index APE for the final product (step S16).

Hereinafter, Steps S13 to S16 will be specifically described using mathematical expressions. The physical quantity at each position shown in FIG. 9 of a certain trajectory is defined below.

That is, resin temperature: T _k , stress value:
σ _k , relaxation constant (function of temperature): τ (T), time step interval of trajectory: Δt Therefore, the outlet of the stress value received by the resin at the position of k = n (k ≦ k _max−2 ) Is represented by the following equation (1).

[0029]

(Equation 1) The value of the above equation (1) is calculated for each position of the trajectory, and a value (σ _{res (i)} ) obtained by integrating the calculated value over the entire trajectory is
The residual stress value at the outlet is represented by the following equation (2).

[0030]

(Equation 2) This σ _{res (i)} is calculated for all of the virtual particles of the n _max value (1000 particles in the above embodiment ₎ which are input into the uniform distribution from the inlet, and the standard deviation value is used as the surface property index APE.

[0031]

(Equation 3) Then, the optimum screw size is designed using the surface property index APE thus obtained.

FIG. 10 is a flowchart showing the operation for designing the optimum screw size. That is, based on input data such as screw shape, extrusion operation conditions, and resin data (step S21), the heat and flow state of the molten resin inside the extruder are analyzed according to the analysis program shown in FIG. 5 (step S22). The surface property index APE obtained from the analysis result is compared with the required quality (steps S23 and S24). Then, the input data of the screw shape is changed (Step S25), and Step S22 is performed.
By repeating the analysis in (1), the design is completed with the screw size when the surface property index APE becomes a value satisfying the required quality as the optimum screw size (step S2).
6).

The chart shown in FIG. 11 was formed by extrusion using a screw-shaped twin-screw extruder newly designed using the surface property index APE and an existing screw-shaped twin-screw extruder according to the flowchart shown in FIG. The comparison result of a product is shown.

Newly Designed Screw (Examples 1-4)
And the conditions of the twin-screw extruder using the existing screws (Comparative Examples 1 to 4) are as follows. Extruder used: Two-axis different-direction rotating parallel type extruder (external diameter of screw tip: 91.2 mm) Resin used: Hard PVC (degree of polymerization 1400, manufactured by Tokuyama Sekisui TS-1400 K) Die used: product thickness 3 mm, width 300 mm sheet mold Extrusion molding condition: 200 kg / h of extrusion rate, 190 ° C. barrel temperature Measurement of surface defect phenomenon: Measurement of arithmetic average roughness (Ra) of extruded product using contact surface roughness meter, measurement conditions Is a cut-off value of 25 mm and an evaluation length of 100 mm (extrusion direction). As can be seen from the comparison results shown in FIG. 11, the newly designed screw designed using the screw design method of the present invention has a surface property of the extruded sheet. However, under any of the extrusion conditions, it was confirmed that the surface properties of the sheet extruded with the existing screw were better.

[0035]

The screw designing method in the twin screw extruder according to the present invention relates to an extruder in which a twin screw is provided in a barrel, and the resin in the barrel is extruded by rotation of the screw. Based on mesh data obtained by spatially dividing the resin flow path in the barrel into three-dimensional microelements, all basic equations governing heat and flow are handled in three dimensions, including time increment terms, and are based on actual phenomena. Based on the various boundary conditions and resin characteristics that have been determined, when performing unsteady numerical analysis and discretization, the area where the two-axis screw flight meshes is divided into two blocks for each screw shaft, and the resin flow path is three-dimensionally divided. While dividing into small elements and performing a process of transferring boundary conditions to each other at a boundary surface between the regions, the block is rotated at each time step by a time increment term, Then, the mesh data is deformed so that one block surface does not enter the screw part in the other block. In this way, based on the flow velocity vector discretized for each time step, Calculate the resin trajectory of the molten resin in the extruder,
Based on the stress value at each position of this trajectory, the stress relaxation characteristics of the resin, and the temperature history from each flow position to the outlet,
The amount of stress to be relaxed to the outlet is calculated for each position of the trajectory line, the residual stress value integrated over the entire trajectory line is calculated, and this residual stress value is input from the inlet to the uniform distribution. The calculation is performed for all of the particles, and the optimum screw size is designed so as to minimize the variation. That is, 2
Based on the stress value applied to the molten resin in the screw extruder and the stress relaxation characteristics of the resin, the amount of relaxation of the stress up to the outlet is calculated, and the stress in consideration of the stress relaxation of the polymer melt is calculated. The amount of distribution can be quantified, and the screw shape and operating conditions that ensure good surface properties of the actual extruded product can be determined. In addition, since optimization for each extruded raw material and each product can be performed on a desk, an optimal screw can be designed in a very short time. In addition, since the design guidelines are clear and quantitative, it is possible to construct a database for various screws.

[Brief description of the drawings]

FIG. 1 is a system configuration diagram for executing a screw designing method in a twin-screw extruder of the present invention.

FIG. 2 is an explanatory diagram of input parameter variables of a preprocessor.

FIG. 3 is an explanatory diagram of input parameter variables of a preprocessor.

FIG. 4 is a cross-sectional view at right angles to the mesh data of a two-axis different-direction rotary extruder generated by a preprocessor.

FIG. 5 is a basic flowchart of an analysis program.

FIG. 6 is a flow velocity vector diagram in a cross section perpendicular to the axis based on the calculation result of the analysis program.

FIG. 7 is a temperature contour diagram in a section perpendicular to the axis according to a calculation result of an analysis program.

FIG. 8 is a resin trajectory diagram in a three-dimensional bird's-eye view based on a calculation result of an analysis program.

FIG. 9 is a diagram showing an example of a trajectory from an inlet to an outlet.

FIG. 10 is a flowchart showing an operation for designing an optimal screw size.

FIG. 11 is a table showing a comparison result between a newly designed screw designed by the screw designing method of the present invention and a product extruded and formed using an existing screw shape.

[Explanation of symbols]

 11 Preprocessor 12 Solver processor 13 Postprocessor

Claims (1)

[Claims] 1. A two-axis screw is provided in a barrel,
In a twin-screw extruder formed such that the resin in the barrel is extruded by the rotation of these screws, heat and flow are generated based on mesh data obtained by spatially dividing the resin flow path in the barrel into three-dimensional minute elements. Each of the governing basic equations, including the time increment term, is all handled in three dimensions, and when performing unsteady numerical analysis and discretization based on various boundary conditions and resin characteristics according to actual phenomena, The area where the shaft screw flight meshes is divided into two blocks for each screw shaft, the resin flow path is divided into three-dimensional microelements, and the boundary conditions between the areas are transferred to each other at the boundary surface. The block is rotated at each time step according to the time increment term so that one block surface does not enter the screw portion in the other block in the area. The mesh data is deformed, and the resin trajectory of the molten resin in the extruder accompanying the rotation of the screw is calculated based on the flow velocity vector discretized for each time step in this manner. Based on the stress value at each position, the stress relaxation characteristics of the resin, and the temperature history from each flow position to the outlet, the amount of stress to be relaxed to the outlet is calculated for each position of the trajectory, The residual stress value integrated over the entire trajectory is calculated, and this residual stress value is calculated as
A screw designing method for a twin-screw extruder, characterized in that the calculation is performed for all virtual particles injected into an equal distribution from an inlet and an optimum screw dimension is designed so as to minimize the variation.