阅读说明：本技术 T型挤出模具及其设计方法 (T-shaped extrusion die and design method thereof ) 是由 麻向军 于 2019-11-29 设计创作，主要内容包括：涉及一种T型挤出模具,其流道包括沿熔体的流动方向依次设置的入口区、歧管、阻流区、松弛区和成型区；歧管的管径沿熔体的流动方向逐渐减小；阻流区包括厚度不等的阻流I区和阻流II区,靠近歧管的区域为阻流I区,靠近松弛区的区域为阻流II区,阻流I区和阻流II区的分界面是沿阻流区厚度方向的曲面。该挤出模具能够使得熔体沿流道宽度方向的出口流率均匀一致,熔体流经整个流道的压力降适中,熔体在流道中的停留时间更短。还涉及该挤出模具的设计方法,针对该挤出模具的流道设计,使熔体沿模具宽度方向的出口流率均匀,利用流变学理论基于变化的歧管管径推演阻流I区和阻流II区的分界形状曲线的微分方程。(Relates to a T-shaped extrusion die, wherein a runner of the T-shaped extrusion die comprises an inlet area, a manifold, a flow blocking area, a relaxation area and a forming area which are sequentially arranged along the flow direction of a melt; the pipe diameter of the manifold is gradually reduced along the flow direction of the melt; the flow resisting area comprises a flow resisting area I and a flow resisting area II which are different in thickness, the area close to the manifold is the flow resisting area I, the area close to the relaxation area is the flow resisting area II, and the interface of the flow resisting area I and the flow resisting area II is a curved surface along the thickness direction of the flow resisting area. The extrusion die can enable the flow rate of the melt to be uniform along the width direction of the runner, the pressure drop of the melt flowing through the whole runner is moderate, and the residence time of the melt in the runner is shorter. Aiming at the flow channel design of the extrusion die, the outlet flow rate of the melt along the width direction of the die is uniform, and a differential equation of a boundary shape curve of a flow blocking I area and a flow blocking II area is deduced by utilizing a rheological theory based on a changed manifold pipe diameter.)

T type extrusion tooling, its characterized in that: the runner of the extrusion die comprises an inlet area, a manifold, a flow blocking area, a relaxation area and a forming area which are sequentially arranged along the flow direction of the melt; the pipe diameter of the manifold is gradually reduced along the flow direction of the melt; the flow resisting area comprises a flow resisting area I and a flow resisting area II which are different in thickness, the area close to the manifold is the flow resisting area I, the area close to the relaxation area is the flow resisting area II, and the interface of the flow resisting area I and the flow resisting area II is a curved surface along the thickness direction of the flow resisting area.

2. A T-shaped extrusion die as set forth in claim 1, wherein: the separation distance exists between the position of the symmetrical surface of the interface in the width direction of the flow channel and the manifold, and between the tail end of the interface in the width direction of the flow channel and the relaxation area.

3. A T-shaped extrusion die as set forth in claim 2, wherein: when the thickness of the flow resisting I area is larger than that of the flow resisting II area, the length of the flow resisting I area is gradually increased along the width direction of the flow channel by taking the symmetrical plane in the width direction of the flow channel as the center, and the length of the flow resisting II area is gradually decreased along the width direction of the flow channel.

4. A T-shaped extrusion die as set forth in claim 2, wherein: when the thickness of the flow resisting I area is smaller than that of the flow resisting II area, the length of the flow resisting I area is gradually reduced along the width direction of the flow channel by taking the symmetrical plane in the width direction of the flow channel as the center, and the length of the flow resisting II area is gradually increased along the width direction of the flow channel.

The design method of the T-shaped extrusion die is characterized by comprising the following steps: aiming at the flow channel design of the extrusion die, the outlet flow rate of the melt along the width direction of the die is uniform;

(1) gradually reducing the cross-sectional dimension of the manifold in the flow direction of the melt in the manifold to increase the flow rate of the melt, thereby reducing the residence time of the melt in the manifold;

(2) the flow-resisting area is set to be a flow-resisting area I and a flow-resisting area II with different thicknesses, the total length of the flow-resisting area is kept unchanged, and the pressure drop of the melt flowing through the flow-resisting area is reduced along the two sides of the width of the flow channel by changing the change of the relative lengths of the flow-resisting area I and the flow-resisting area II along the two sides of the width of the flow channel, so that the uniformity of the flow rate of the melt outlet is improved;

(3) differential equations of the boundary shape curves of the choked flow I and II regions are derived using rheology theory based on varying manifold cross-sectional dimensions.

6. A method of designing a T-shaped extrusion die as set forth in claim 5, wherein the derivation process of the rheology theory is:

the temperature of the melt is not changed in the flowing process, and the viscosity of the melt is described by adopting a power law model, namely

Wherein η is the melt viscosity, K is the consistency coefficient;

constructing a rectangular coordinate system by taking the boundary line of the manifold and the flow resisting region I as an x axis and the symmetrical plane of the mold as a y axis;

the pressure gradient as the melt flows along the manifold is expressed as

Wherein P is the pressure of the melt in the manifold at x; q is the volumetric flow rate of the melt in the manifold at x; r is the manifold radius at x;

assuming a volume flow rate of 2Q for the melt at the die entrance₀When the outlet volume flow rate of the melt in the width direction of the die is required to be uniform, the melt is subjected to

Q＝Q₀(1-x/W) (3)

In the formula, W is half of the width of the flow channel;

substituting formula (3) for formula (2) with

The pressure drop of the melt flowing in the extrusion direction in the zones I and II at any point x can be expressed as the pressure drop

In the formula,. DELTA.P_DTo block the pressure drop in the flow area, h₁And h₂The thickness of the flow-resisting region I and the flow-resisting region II respectively; l is_DThe total length of the flow-resisting area is y, and the y is the coordinate of a shape curve which is defined by the flow-resisting area I and the flow-resisting area II;

the thickness and length of the relaxation area and the forming area of the runner are not changed along the width direction of the runner, the flow rate of the melt outlet is required to be uniform along the width direction of the runner, the pressure of the melt at the outlet of the flow-resisting area II is not changed along the width direction of the runner, namely, the pressure gradient of the melt in the flow direction in the manifold is equal to the pressure gradient of the melt in the flow-resisting area along the width direction of the runner, and the flow-resisting area has the advantages that

From the formulae (4) to (6)

The formula (7) is a differential equation of the boundary shape curve of the choked flow I area and the choked flow II area in the coordinate system shown in figure 3, and the boundary condition is

x＝0，y＝L_C(8)

In the formula, L_CThe distance between the position of the symmetrical plane of the flow passage and the boundary line between the flow-resisting region I and the manifold is the boundary shape curve;

when the thickness of the flow-resisting I area and the flow-resisting II area is not changed along the width direction of the flow channel, the radius of the manifold is reduced along the width direction of the flow channel, and the size of the tail end of the manifold is not 0, the formula (7) is difficult to obtain an analytic formula, and a numerical method is adopted to solve and fit to obtain a boundary shape curve of the flow-resisting I area and the flow-resisting II area.

7. The method of designing a T-shaped extrusion die according to claim 6, wherein: the boundary shape curve has a distance between the tail end of the mold and the boundary line of the relaxation area and the flow resisting area II; the boundary profile has a spacing between the mold symmetry plane and the boundary between the flow-impeding region I and the manifold.

8. A method of designing a T-shaped extrusion die as set forth in claim 7, wherein: in the derivation of the theory of rheology, the effect of draw in the manifold due to changes in the manifold radius on the melt flow and the effect of the two side walls of the runner on the melt flow were neglected.

9. A method of designing a T-shaped extrusion die as set forth in claim 8, wherein: the flow of the melt in the runner is numerically simulated by adopting ANSYS Polyflow software, and the reliability of the boundary shape curve is verified by calculating the outlet flow rate of the melt.

Technical Field

The invention relates to the field of die design, in particular to a T-shaped extrusion die and a design method thereof.

Background

The extrusion molding of thermoplastic plastic sheets and cast films adopts a flat seam type extrusion die, and the key problems of the flow channel design comprise that the outlet flow rate of the melt along the width direction of the flow channel is uniform and consistent, the pressure drop of the melt flowing through the whole flow channel is moderate, and the residence time of the melt in the flow channel is as short as possible. When a T-shaped extrusion die is used to form a thermoplastic article, in order to improve the uniformity of the transverse thickness of the article, when a conventional design method is used, the cross-sectional dimension of the manifold is usually increased or the thickness of the choked flow region is reduced to improve the uniformity of the melt outlet flow rate, i.e., the uniformity of the transverse thickness of the article, due to the limitation of the length of the die. Increasing the manifold radius, while beneficial in reducing extrusion pressure, significantly increases melt residence time (particularly in the manifold near the end of the die width), which tends to cause thermal degradation of the melt; while reducing the thickness of the flow-resistant zone significantly increases the extrusion pressure, generally increases the difficulty of extrusion and decreases the extrusion throughput. Auxiliary measures such as a flow blocking rod and a flexible die lip are usually required, but the structure of the die is complicated, and the manufacturing cost is increased. The engineering also adopts two areas with different thicknesses to design the flow resisting area to reduce the melt residence time and the extrusion pressure, but because of lacking the guidance of design theory, the flow resisting rod is required to be additionally arranged or/and the flexible die lip is adopted, and the uniformity of the melt outlet flow rate is improved by local adjustment during the die test. Even if the flow channel with poor design is adjusted by the flow blocking rod and the flexible die lip, the uniformity of the melt outlet flow rate along the width direction of the flow channel is difficult to reach the ideal state, and the melt is easy to be detained.

Disclosure of Invention

Aiming at the technical problems in the prior art, the invention aims to: provided is a T-shaped extrusion die which can remarkably reduce extrusion pressure and melt retention time.

The invention also aims to provide a design method of the T-shaped extrusion die.

In order to achieve the purpose, the invention adopts the following technical scheme:

the flow channel of the extrusion die comprises an inlet area, a manifold, a flow blocking area, a relaxation area and a forming area which are sequentially arranged along the flow direction of the melt; the pipe diameter of the manifold is gradually reduced along the flow direction of the melt; the flow resisting area comprises a flow resisting area I and a flow resisting area II which are different in thickness, the area close to the manifold is the flow resisting area I, the area close to the relaxation area is the flow resisting area II, and the interface of the flow resisting area I and the flow resisting area II is a curved surface along the thickness direction of the flow resisting area.

Preferably, the boundary surface is spaced between the position of the symmetry plane of the width of the flow channel and the manifold, and the boundary surface is spaced between the end of the width of the flow channel and the relaxation region.

Preferably, when the thickness of the flow blocking I region is greater than that of the flow blocking II region, the length of the flow blocking I region is gradually increased along the width direction of the flow channel and the length of the flow blocking II region is gradually decreased along the width direction of the flow channel, with the symmetrical plane in the width direction of the flow channel as the center.

Preferably, when the thickness of the flow blocking I region is smaller than that of the flow blocking II region, the length of the flow blocking I region is gradually reduced along the width direction of the flow channel and the length of the flow blocking II region is gradually increased along the width direction of the flow channel by taking the symmetrical plane in the width direction of the flow channel as the center.

The design method of the T-shaped extrusion die aims at the flow channel design of the extrusion die to ensure that the outlet flow rate of a melt along the width direction of the die is uniform; (1) gradually reducing the cross-sectional dimension of the manifold in the flow direction of the melt in the manifold to increase the flow rate of the melt, thereby reducing the residence time of the melt in the manifold; (2) the flow-resisting area is set to be a flow-resisting area I and a flow-resisting area II with different thicknesses, the total length of the flow-resisting area is kept unchanged, and the pressure drop of the melt flowing through the flow-resisting area is reduced along the two sides of the width of the flow channel by changing the change of the relative lengths of the flow-resisting area I and the flow-resisting area II along the two sides of the width of the flow channel, so that the uniformity of the flow rate of the melt outlet is improved; (3) differential equations of the boundary shape curves of the choked flow I and II regions are derived using rheology theory based on varying manifold cross-sectional dimensions.

The deduction process of the rheology theory is as follows:

the temperature of the melt is not changed in the flowing process, and the viscosity of the melt is described by adopting a power law model, namely

Wherein η is the melt viscosity, K is the consistency coefficient;

is the shear rate; n is a power law index;

a rectangular coordinate system is constructed by taking the boundary line of the manifold and the flow-resisting region I as an x axis and the symmetrical plane of the die as a y axis, and the pressure gradient of the melt flowing along the manifold is expressed as

Wherein P is the pressure of the melt in the manifold at x; q is the volumetric flow rate of the melt in the manifold at x; r is the manifold radius at x;

assuming a volume flow rate of 2Q for the melt at the die entrance₀When the outlet volume flow rate of the melt in the width direction of the die is required to be uniform, the melt is subjected to

Q＝Q₀(1-x/W) (3)

In the formula, W is half of the width of the flow channel;

substituting formula (3) for formula (2) with

The pressure drop of the melt flowing in the extrusion direction in the zones I and II at any point x can be expressed as the pressure drop

In the formula,. DELTA.P_DTo block the pressure drop in the flow area, h₁And h₂The thickness of the flow-resisting region I and the flow-resisting region II respectively; l is_DThe total length of the flow-resisting area is y, and the y is the coordinate of a shape curve which is defined by the flow-resisting area I and the flow-resisting area II;

the thickness and length of the relaxation area and the forming area of the runner are not changed along the width direction of the runner, the flow rate of the melt outlet is required to be uniform along the width direction of the runner, the pressure of the melt at the outlet of the flow-resisting area II is not changed along the width direction of the runner, namely, the pressure gradient of the melt in the flow direction in the manifold is equal to the pressure gradient of the melt in the flow-resisting area along the width direction of the runner, and the flow-resisting area has the advantages that

From the formulae (4) to (6)

Equation (7) is a differential equation of the boundary shape curve of the choked flow I region and the choked flow II region in the coordinate system shown in FIG. 3, and the boundary conditions are as follows:

x＝0，y＝L_C(8)

in the formula, L_CThe distance between the position of the symmetrical plane of the flow passage and the boundary line between the flow-resisting region I and the manifold is the boundary shape curve;

when the thickness of the flow-resisting I area and the flow-resisting II area is not changed along the width direction of the flow channel, the radius of the manifold is reduced along the width direction of the flow channel, and the size of the tail end of the manifold is not 0, the formula (7) is difficult to obtain an analytic formula, and a numerical method is adopted to solve and fit to obtain a boundary shape curve of the flow-resisting I area and the flow-resisting II area.

Preferably, the radius of the manifold decreases linearly when the cross-section of the manifold is circular.

As a preference, in the derivation of the theory of rheology, the influence of the stretching in the manifold due to the change in the manifold radius on the melt flow and the influence of the two side walls of the runner on the melt flow were neglected.

Preferably, the flow of the melt in the flow channel is numerically simulated using ANSYS teflon software, and the reliability of the boundary shape curve is verified by calculating the outlet volume flow rate of the melt.

The principle of the invention is as follows: based on analysis of flow characteristics of a melt in a flow channel, the total length of a flow blocking area is kept unchanged, the flow blocking area is designed into a flow blocking I area and a flow blocking II area which are different in thickness, the relative length of the flow blocking I area and the flow blocking II area is changed along the width direction of the flow channel to reduce extrusion pressure, a manifold with the pipe diameter gradually reduced along the flow direction of the melt is adopted to reduce the residence time of the melt, a differential equation of a boundary shape curve of the flow blocking I area and the flow blocking II area is deduced by using a rheology theory under the condition that the outlet flow rate of the melt along the width direction of the flow channel is uniform, and then a numerical method is. Compared with the traditional design method, the manifold with the pipe diameter gradually reduced along the flow direction of the melt and the runners of the flow resisting I area and the flow resisting II area with different thicknesses are adopted, so that the residence time of the melt can be obviously reduced, and the extrusion pressure can be obviously reduced.

In summary, the present invention has the following advantages:

1. the flow passage of the T-shaped extrusion die adopts a manifold with the pipe diameter gradually reduced along the flow direction of a melt, a flow blocking area is designed into two areas with different thicknesses, a differential equation of a boundary shape curve of a flow blocking area I and a flow blocking area II is deduced based on the condition of uniform flow rate of a melt outlet, and the boundary of the flow blocking area I and the flow blocking area II is manufactured according to the boundary shape curve. The differential equation is solved numerically and can be used for designing the radius of the runner manifold, the thickness of the flow-resisting region I and the flow-resisting region II and the boundary shape curve of the flow-resisting region II.

2. The differential equation of the boundary shape curve of the flow resisting region I and the flow resisting region II is solved by adopting a numerical method, a flow channel geometric model is established, and the designed flow channel is verified by utilizing numerical simulation, so that the deduced boundary shape curve differential equation is reliable and can guide the flow channel design of the T-shaped extrusion die.

3. Compared with the runner with the radius of the manifold and the thickness of the flow-resisting area unchanged, the runner with the manifold with the changed pipe diameter and the flow-resisting areas with the two different thicknesses can obviously reduce the residence time of the melt in the runner and the extrusion pressure of the die under the condition that the flow rate of the melt outlet is uniform along the width direction of the runner.

4. The extrusion die can ensure that the flow rate of the melt is uniform along the outlet of the width direction of the runner, namely, products with uniform transverse thickness can be obtained, the pressure drop of the melt flowing through the whole runner is moderate, and the residence time of the melt in the runner is shorter.

Drawings

Fig. 1 is a schematic view of a flow channel structure of a T-shaped extrusion die in an embodiment.

Fig. 2 is a cross-sectional view of B-B in fig. 1.

FIG. 3 is a schematic view of a geometric model of a flow channel of the T-shaped extrusion die in the example.

FIG. 4 is a pressure contour of the melt in the runner.

FIG. 5 is a graph of the variation of the melt outlet dimensionless flow rate across the width of the flow channel.

The reference numbers and corresponding part names in the figures are: 1-inlet zone, 2-manifold, 3-choked flow I zone, 4-choked flow II zone, 5-relaxation zone, 6-forming zone.

Detailed Description

The present invention will be described in further detail with reference to examples and drawings, but the present invention is not limited to these examples.

The design method of the T-shaped die is suitable for producing products symmetrical along the width direction, and comprises the following steps:

s1: and constructing a physical model. In this example, the cross-section of the manifold is circular, and when analyzing the flow of the melt in the runner, the following assumptions are made: (1) the melt is an incompressible fluid; (2) the melt flow is fully developed steady laminar flow, and inertia force and volume force are ignored; (3) the melt flows in the manifold only along the axial direction of the manifold, and flows in the flow-resisting I area, the flow-resisting II area, the relaxation area and the molding area only along the extrusion direction, and the flow of the melt in the manifold and the flow in the flow-resisting I area are not interfered with each other; (4) neglecting the influence of stretching caused by the change of the pipe diameter of the manifold on the melt flow in the manifold and the influence of two side walls of the runner on the melt flow; (5) the temperature of the melt is not changed in the flowing process, and the viscosity of the melt is described by adopting a power law model, namely

Wherein η is the melt viscosity, K is the consistency coefficient;

is the shear rate; n is a power law exponent.

S2: and (5) constructing a geometric model. As shown in fig. 1 and 2, the widths and lengths of the flow-obstructing region, the relaxing region, and the molding region are constant in the mold width direction. Designing a boundary shape curve of a flow resisting region I and a flow resisting region II by designing the size of a manifold and the thickness of two flow resisting regions on the premise of uniform outlet volume flow rate of the melt along the width direction of the die, and processing and manufacturing an interface of the flow resisting region I and the flow resisting region II by the boundary shape curve; the interface divides the flow-resisting area into a flow-resisting area I and a flow-resisting area II along the extrusion direction, wherein the area close to the manifold is the flow-resisting area I, and the area close to the relaxation area is the flow-resisting area II; the thickness of the flow-resisting I area and the thickness of the flow-resisting II area are different, and in the embodiment, the thickness of the flow-resisting I area is larger than that of the flow-resisting II area.

After the melt enters the manifold, a part of the melt enters the flow-resisting region I and flows along the extrusion direction while flowing to the two sides of the runner along the manifold, so that the volume flow rate of the melt in the manifold is gradually reduced. If equal radius manifolds are used, the flow rate of the melt in the manifold decreases more rapidly across the width of the channel and the residence time increases rapidly. To this end, the cross-sectional dimension of the manifold is gradually reduced in the direction of flow of the melt in the manifold to slow the decrease in the melt flow rate in the direction of the width of the flow path, thereby reducing the residence time of the melt in the manifold. On the other hand, when the melt flows to the two sides of the runner along the manifold, the pressure is gradually reduced, namely the pressure of the melt at the inlet of the flow-resisting area I is gradually reduced along the two sides of the runner, particularly when the pipe diameter of the manifold is reduced along the width direction of the runner, the pressure reduction of the melt at the inlet of the flow-resisting area I is larger, if the flow-resisting area with the same thickness is adopted, the flow rate of the melt outlet is reduced more along the two sides of the runner, in order to improve the uniformity of the flow rate of the melt outlet, the pressure reduction of the melt flowing through the. Therefore, the flow resisting area is designed into two areas with different thicknesses, and the pressure drop of the melt flowing through the flow resisting area is reduced along the two sides of the width of the flow channel by changing the change of the relative lengths of the two flow resisting areas along the two sides of the width of the flow channel, so that the uniformity of the flow rate of the melt outlet is improved. Fig. 1 is a schematic view of a flow channel structure with a large flow-resisting region I and a small flow-resisting region II, wherein a proper distance is left between the flow channel symmetry plane position of the flow channel region I and the manifold, and between the flow channel end of the flow-resisting region II and the relaxation region, so as to facilitate the mold manufacturing. Under the condition that the flow rate of a melt outlet is uniform along two sides of a flow passage, the boundary shape curve of a flow-resisting I area and a flow-resisting II area can be designed by designing the size of a manifold and the thicknesses of two flow-resisting areas.

S3: and solving an expression of the boundary shape curve. As shown in fig. 3, neglecting the influence of the inlet region, considering the symmetry of the runner in the width direction, one half of the inlet region is taken for theoretical calculation, and a rectangular coordinate system is constructed with the boundary line of the manifold and the flow-blocking I region as the x-axis and the symmetry plane of the mold as the y-axis.

The pressure gradient as the melt flows along the manifold is expressed as

Wherein P is the pressure of the melt in the manifold at x; q is the volumetric flow rate of the melt in the manifold at x; r is the manifold radius at x.

Assuming a volume flow rate of 2Q for the melt at the die entrance₀. When the melt is required to have a uniform outlet volume flow rate in the width direction of the die

Q＝Q₀(1-x/W) (3)

Wherein W is half the width of the flow channel.

Substituting formula (3) for formula (2) with

The pressure drop of the melt flowing in the extrusion direction in the zones I and II at any point x can be expressed as the pressure drop

In the formula,. DELTA.P_DTo block the pressure drop in the flow area, h₁And h₂The thickness of the flow-resisting region I and the flow-resisting region II respectively; l is_DAnd y is the coordinate of the shape curve of the boundary of the flow resisting region I and the flow resisting region II.

The thickness and length of the relaxation area and the forming area of the runner are not changed along the width direction of the runner, the flow rate of the melt outlet is required to be uniform along the width direction of the runner, the pressure of the melt at the outlet of the flow-resisting area II is not changed along the width direction of the runner, namely, the pressure gradient of the melt in the flow direction in the manifold is equal to the pressure gradient of the melt in the flow-resisting area along the width direction of the runner, and the flow-resisting area has the advantages that

From the formulae (4) to (6)

Equation (7) is a differential equation of the boundary shape curve of the choked flow I area and the choked flow II area in the coordinate system shown in FIG. 3.

From the formula (7), it can be seen that the shape curve of the boundary between the flow-resisting region I and the flow-resisting region II is related to the change of the manifold radius along the width direction of the flow channel, the thickness of the flow-resisting region I and the flow-resisting region II, the flow channel width and the power law index of the melt, and is not related to the consistency coefficient and the yield of the melt. The width of the runner is determined by the product specification, the power law index is a material parameter of the melt, the radius of the manifold, the thickness of the flow-resisting I area and the thickness of the flow-resisting II area can be used as design parameters of the runner, and the boundary shape curve of the flow-resisting I area and the flow-resisting II area is designed according to the formula (7).

When the thickness of the flow blocking I area and the flow blocking II area is not changed along the width direction of the flow channel, the radius of the manifold is reduced along the width direction of the flow channel, and the size of the tail end of the manifold is not 0, the formula (7) is difficult to obtain an analytic formula, a numerical method is adopted to solve and fit to obtain a boundary shape curve of the flow blocking I area and the flow blocking II area, and the boundary condition is as follows:

x＝0，y＝L_C(8)

L_Ci.e. the distance between the position of the boundary profile on the flow path symmetry plane and the boundary between the flow-impeding I-zone and the manifold. Leaving appropriate spacing to facilitate mold fabrication, depending on processing conditions.

As can be seen from the formula (7), y is a monotonically increasing function of x, i.e., the thickness of the choked flow I region is greater than that of the choked flow I region while the length of the flow channel in the choked flow region is kept constantAnd when the thickness of the area II is larger, the length of the flow resisting area I is gradually increased along the width direction of the flow channel, and the length of the flow resisting area II is gradually reduced along the width direction of the die. The design needs to comprehensively consider the sizes of all parts of the flow passage to ensure the L calculated by the formula (7)_ELess than the length L of the choke zone_DAnd the flow-resisting zone II is spaced from the end of the flow channel by a proper distance (i.e. L in FIG. 3)_D-L_E) So as to facilitate the processing of the flow channel.

At any position x in the width direction of the runner, the pressure drop of the melt flowing from the manifold inlet to the outlet of the flow-resisting area II through the manifold and the flow-resisting area is equal. Thus, the pressure drop of the melt from the manifold inlet to the flow-obstructing zone II outlet can be calculated from the pressure drop at the symmetry plane of the flow channel, i.e.

The residence time of the melt in the manifold at any position x can be expressed as

When the radius of the manifold decreases along the width direction of the flow channel and the size of the tail end of the manifold is not 0, the equation (10) needs to be solved by a numerical method, and the boundary conditions are as follows:

x＝0，t＝0 (11)

step S4: and (6) verifying. In order to verify the reliability of the differential equation of the boundary shape curve of the flow-resisting region I and the flow-resisting region II when the radius of the manifold changes, taking LDPE sheet extrusion as an example, ANSYS Polyflow software is adopted to carry out numerical simulation on the flow of melt in a runner, and the verification is carried out through the dimensionless flow rate of a melt outlet, namely the ratio of the volume flow rate of a unit width at a certain position along the width direction of the runner to the volume flow rate of the average unit width.

Describing the rheological property of LDPE by adopting a power law model, wherein when the extrusion temperature is 170 ℃, the power law index n is 0.496, and the consistency K is 7083Pa s^-0.504. The width (2W) of the sheet was 2000mm, the thickness and length of the relaxation zone were 4mm and 45mm, respectively, and the molding zoneThe thickness and length of (2) were 1.5mm and 25mm, respectively, and the extrusion speed was 15 mm/s. Assuming that the radius of the manifold is linearly reduced, the radius of the symmetrical surface and the radius of the tail end of the flow channel are respectively 15mm and 6mm, the thickness of the flow blocking I area and the thickness of the flow blocking II area are respectively 1.9mm and 0.9mm, the total length of the flow blocking area is 40mm, the length of the flow blocking I area at the symmetrical surface of the flow channel is 6mm, a differential equation of a boundary shape curve is solved by adopting a four-order explicit Runge-Kutta method, and the length of the flow blocking I area at the tail end of the flow channel is 34.4mm through calculation.

And fitting the boundary shape curve by adopting a spline curve, modeling the flow channel, and calculating by taking half of the flow channel in the width direction. In order to improve the calculation accuracy, a hexahedral unit is adopted to divide a flow channel, a grid with a smaller size is adopted at the boundary of the wall surface of the flow channel and the position of size mutation, quadratic interpolation is adopted for the speed during flow field solution, and linear interpolation is adopted for the pressure.

The simulation results show the variation of the melt pressure field and the outlet dimensionless flow rate in the width direction of the flow channel for half of the width direction of the flow channel as shown in fig. 4 and 5. It can be seen that when the melt leaves the choked flow region, the pressure contour line of the melt is parallel to the outlet of the flow channel, and the pressure drop of the melt in the choked flow region at the symmetrical plane of the flow channel is consistent with the theoretical calculation. The melt outlet flow rate is uniform along the width direction of the runner, and the melt dimensionless outlet flow rate is less than 0.99 only within about 10mm of the tail end of the runner, because the influence of the side wall of the runner on the melt flow is ignored in theoretical derivation, and a non-slip boundary is formed between the melt and the side wall in simulation calculation and is consistent with actual production.

Aiming at the sheet specification, the extrusion speed and the material, under the condition of keeping the length of the flow-blocking area unchanged, the manifold and the flow-blocking area are designed by different methods, and the pressure drop of the melt in the damping area at the symmetrical plane of the flow channel is compared with the residence time of the melt in the manifold. The residence time of the melt in the manifold increases along the width of the runner, and near the two sides of the runner, the residence time of the melt in the manifold is much longer than that of the melt after leaving the manifold, and for comparison, the residence time of the melt in the manifold at a distance of 0.95W from the inlet is selected. The pressure drop of the melt from the manifold inlet to the flow-resisting zone II outlet is constant along the width direction of the flow channel, and has important influence on the extrusion pressure.

When the traditional design method is adopted, namely the length and thickness of the flow-blocking area and the radius of the manifold are all unchanged along the width direction of the flow channel, the melt outlet volume flow rate uniformity index UI is usually used as the basis for designing the flow channel.

Wherein R is the manifold radius; l is the length of the flow blocking area; h is the thickness of the flow-resisting area; half the width of the W die. In the traditional flow channel design, the thickness and the length of the flow blocking area are not changed along the width direction of the flow channel.

When the thickness of the choked flow region is 0.9mm and 0.7mm respectively, according to the formula (12), in order to ensure that the UI is more than or equal to 0.95, the radius R of the manifold is required to be more than 37mm and 30mm, the pressure drop of the melt in the choked flow region at the symmetrical plane of the flow channel is respectively 9.20MPa and 15.18MPa, and the residence time of the melt in the manifold at the position 0.95W is respectively 572.6s and 376.5 s. Because the thickness and length of the choke zone are constant along the width of the channel and the melt pressure at the entrance of the choke zone is reduced along the width of the channel, the pressure drop of the melt flowing through the manifold must be much less than the pressure drop of the melt flowing through the choke zone to improve the uniformity of the melt exit flow rate, the pressure drop of the melt flowing through the choke zone must be increased when the radius of the manifold is reduced, resulting in increased extrusion pressure, and the radius of the manifold must be increased when the thickness of the choke zone is increased, resulting in increased melt residence time.

By adopting two flow-blocking areas with different thicknesses, when the radius of the manifold is not changed along the width direction of the flow channel, the equations (7) and (10) can be resolved. Still taking the sheet as an example, taking the radius R of the manifold as 15mm, the thicknesses of the flow-resisting region I and the flow-resisting region II as 1.8mm and 1.2mm respectively, and the length of the flow-resisting region I at the symmetrical plane of the runner as 6mm, the length of the flow-resisting region I at the tail end of the runner is calculated to be 34.4mm, the pressure drop of the melt at the flow-resisting region at the symmetrical plane of the runner is 4.76MPa, and the residence time of the melt in the manifold at a position 0.95W away from the inlet is 94.1 s. The pressure drop of the melt flowing through the choked flow region at the symmetry plane was reduced by 48.2% and 68.6%, respectively, and the melt residence time in the manifold at 0.95W from the inlet was reduced by 83.6% and 75.0%, respectively, as compared to the 37mm and 27mm manifold runners using conventional design methods. It can be seen that when two choked flow zones of different thickness are used, the pressure drop of the melt flowing through the choked flow zones at the symmetry plane of the flow channel is significantly reduced, regardless of the melt residence time.

To further reduce the residence time of the melt in the manifold, the manifold radius is selected to decrease in a power law along the runner width, i.e. the radius of the manifold decreases in a power law manner

R＝R_C-(R_C-R_E)(x/W)^m(13)

In the formula, R_CRadius of manifold at the symmetry plane of the flow channel, R_EThe manifold radius at the ends of the flow channels.

Get R_C＝15mm，R_E＝6mm，L_CAnd (3) selecting the thicknesses of the two flow blocking areas according to 6mm, considering the manufacturability of the flow channel, solving the formula (7) by adopting a four-step explicit Runge-Kutta method to obtain the boundary shape curve coordinates of the flow blocking I area and the flow blocking II area, calculating the pressure drop of the melt at the flow blocking area at the symmetrical plane according to the formula (9), and solving the formula (10) by adopting the four-step explicit Runge-Kutta method to obtain the melt residence time of 0.95W away from the inlet in the manifold, as shown in the table 1.

TABLE 1 influence of manifold radius variation law on melt residence time and pressure drop

As can be seen from Table 1, the residence time of the melt increases as the index m of the manifold radius along the width of the channel increases, while the pressure drop of the melt at the choke zone at the symmetry plane of the channel decreases. From equation (13), 0< x/W <1, and when the distance between the width direction of the runner and the symmetric plane is fixed, i.e. x is fixed, the radius of the manifold increases with the increase of the index m, and the volume flow rate of the melt in the manifold is the same, therefore, the flow rate and the pressure gradient of the melt both decrease with the increase of the index m, the residence time of the melt in the manifold increases with the increase of the index m, and the pressure drop of the melt flowing through the choke area at the symmetric plane of the runner decreases with the increase of the index m.

Compared with a runner with a constant manifold radius, when the manifold radius is reduced along the width direction of the runner, the flow speed and the pressure gradient of the melt in the manifold are increased at the same position from the symmetrical plane, so that the residence time of the melt is reduced, and the pressure drop of the melt flowing through the flow-blocking area at the symmetrical plane is increased. When the index m is 1, 2 and 3, respectively, the pressure drop of the melt flowing through the choked zone at the symmetry plane is reduced by 41.1%, 55.7% and 63.4%, respectively, and the melt residence time in the manifold at 0.95W from the inlet is reduced by 90.7%, 87.6 and 85.6%, respectively, as compared to a channel with a manifold radius of 27mm designed by the conventional method. It can be seen that the conventional runner design method can cause a significant increase in extrusion pressure or/and a significant increase in melt residence time while improving the uniformity of the melt outlet flow rate, whereas the runner design method provided by the present invention can significantly reduce the residence time of the melt at a lower extrusion pressure.

The design method has the beneficial effects that:

(1) the flow passage of the T-shaped extrusion die adopts a manifold with the pipe diameter gradually reduced along the flow direction of a melt, a flow blocking area is designed into two areas with different thicknesses, a differential equation of a boundary shape curve of a flow blocking area I and a flow blocking area II is deduced based on the condition of uniform flow rate of a melt outlet, and the boundary of the flow blocking area I and the flow blocking area II is manufactured according to the boundary shape curve. The differential equation is solved numerically and can be used for designing the radius of the runner manifold, the thickness of the flow-resisting region I and the flow-resisting region II and the boundary shape curve of the flow-resisting region II.

(2) A differential equation of a boundary shape curve of a flow resisting region I and a flow resisting region II is solved by adopting a four-order explicit Runge-Kutta method, a flow channel geometric model is established, and a designed flow channel is verified by utilizing numerical simulation, so that the derived differential equation of the boundary shape curve is reliable and can guide the flow channel design of the T-shaped extrusion die.

(3) Compared with the runner with the radius of the manifold and the thickness of the flow-resisting area unchanged, the runner with the manifold with the changed pipe diameter and the flow-resisting areas with two different thicknesses can obviously reduce the residence time of the melt in the runner and the extrusion pressure of the die under the condition that the flow rate of the melt outlet is uniform along the width direction of the runner.

A T-shaped extrusion die is characterized in that a runner of the T-shaped extrusion die comprises an inlet area, a manifold, a flow blocking area, a relaxation area and a forming area which are sequentially arranged along the flow direction of a melt; the pipe diameter of the manifold is gradually reduced along the flow direction of the melt; the flow resisting area comprises a flow resisting area I and a flow resisting area II which are different in thickness, the area close to the manifold is the flow resisting area I, the area close to the relaxation area is the flow resisting area II, and the interface of the flow resisting area I and the flow resisting area II is a curved surface along the thickness direction of the flow resisting area.

The extrusion die determines the pipe diameter change of the manifold and the boundary shape curve of the choked flow I area and the choked flow II area by the design method of the extrusion die according to the specification, the extrusion speed and the material of the required product under the condition of keeping the total length of the choked flow area unchanged, then the interface is manufactured according to the boundary shape curve, and the manifold is manufactured according to the determined size of the manifold at each position. In the embodiment, the thickness of the flow blocking I area of the T-shaped extrusion die is larger than that of the flow blocking II area, the cross section of the manifold is circular, and the radius of the manifold is linearly reduced. The flow-resisting I area is arranged between the position of the symmetrical plane of the flow channel and the manifold, and the flow-resisting II area is arranged between the tail end of the flow channel and the relaxation area.

In addition to the above-mentioned manner, for manifolds of other shapes, the melt pressure drop in the manifold can be converted by a shape factor, so as to obtain a boundary shape curve of the flow-resisting region I and the flow-resisting region II corresponding to the mold runners of the manifolds of different shapes. These variations are all within the scope of the present invention.

Except for the above mentioned mode of the embodiment, the radius of the manifold changes in other forms along the width direction of the flow channel, so as to obtain the boundary shape curve of the flow blocking I area and the flow blocking II area corresponding to the mold flow channel when the pipe diameters of different manifolds change along the width direction of the flow channel. These variations are all within the scope of the present invention.

In addition to the above-mentioned manner of the embodiment, the lengths of the flow-resisting region I and the flow-resisting region II at any position in the width direction of the die are substantially determined for the boundary shape curves of the flow-resisting region I and the flow-resisting region II calculated by the above-mentioned design method, and therefore, the melt outlet flow rate can be ensured to be uniform by changing or decomposing the positions of the flow-resisting region I and the flow-resisting region II in the extrusion direction. These variations are all within the scope of the present invention.

In addition to the above-mentioned manner of the embodiment, after the boundary shape curves of the flow-resisting region I and the flow-resisting region II are calculated by the above-mentioned design method, the region with the larger thickness in the flow-resisting region I and the flow-resisting region II is arranged on both sides of the region with the smaller thickness in the thickness direction, and the boundary shape curves of the flow-resisting region I and the flow-resisting region II are not affected by adopting the chamfer or fillet transition between the regions with different thicknesses. These variations are all within the scope of the present invention.

In addition to the above-mentioned manner, other numerical methods may be used to solve the differential equation of the boundary shape curve for the choked flow I region and the choked flow II region, and other reasonable methods may be used to fit. These variations are all within the scope of the present invention.

The above embodiments are preferred embodiments of the present invention, but the present invention is not limited to the above embodiments, and any other changes, modifications, substitutions, combinations, and simplifications which do not depart from the spirit and principle of the present invention should be construed as equivalents thereof, and all such changes, modifications, substitutions, combinations, and simplifications are intended to be included in the scope of the present invention.