Rheological design method of variable radius straight manifold hanger mold and its balanced flow channel

Abstract

The present invention discloses a design method of a clothes hanger type mold with a variable radius straight manifold and a balanced flow channel thereof. Without changing the cross-sectional shapes of the inlet area, the relaxation area and the forming area in the clothes hanger type mold flow channel, the manifold is designed as a straight manifold whose cross-sectional size decreases toward both sides along the flow channel width direction, and the flow blocking area is designed as a flow blocking area I and a flow blocking area II with different thicknesses along the flow channel length direction. By analyzing the melt flow in the flow channel of the clothes hanger type mold with a variable radius straight manifold, based on the condition that the melt outlet flow rate is uniform along the flow channel width direction, the differential equation of the boundary curve between the flow blocking area I and the flow blocking area II is deduced using rheological theory. Combined with the given boundary conditions under the processing conditions, the differential equation of the boundary curve is solved by a numerical method and the boundary curve between the flow blocking area I and the flow blocking area II is obtained by fitting, and a flow channel geometric model is established. The flow channel has the advantages of uniform melt outlet flow rate along the flow channel width direction, short flow blocking area length and short melt residence time.

Description

Technical Field

[0001] The invention relates to the technical field of mold design, and in particular to a variable-radius straight manifold hanger-type mold and a rheological design method for a balanced flow channel thereof. Background Art

[0002] Hanger-type molds are widely used in the extrusion molding of plastic sheets and cast films. The runner design requires that the melt outlet flow rate is uniform along the width of the runner, the extrusion pressure is moderate, the melt residence time is as short as possible, and the runner length is short. The existing runner design method of hanger-type molds adopts a single-thickness choke zone, and designs the manifold radius and manifold trajectory based on the principle of uniform melt outlet flow rate in the width direction of the runner and equal melt residence time in the manifold and the choke zone. The designed runner choke zone length is relatively large and is not suitable for the extrusion molding of wide sheets and cast films. The above method is improved by increasing the melt residence time in the manifold to several times the melt residence time in the choke zone, which can shorten the choke zone length, but leads to an increase in the manifold radius, which significantly increases the residence time of the melt in the runner. In addition, the change of the manifold radius along the width of the runner and the trajectory of the manifold designed by this method are relatively complex, which increases the difficulty of mold processing and limits the application of this method.

[0003] The manifold structure of the straight manifold hanger mold is relatively simple and is widely used in production. However, when a single thickness choke zone is used, the uniformity of the melt outlet flow rate along the width of the flow channel is poor. In engineering, empirical design is usually adopted and a choke bar is added to the mold. The uniformity of the melt outlet flow rate is improved by trial and mold repair and adjustment of the choke bar. The addition of a choke bar to the mold makes the mold structure complicated and increases the manufacturing cost of the mold. When the flow channel structure is poorly designed, it is difficult to achieve the ideal uniformity of the melt outlet flow rate even if the choke bar is adjusted. Summary of the invention

[0004] The purpose of the present invention is to overcome the shortcomings of the prior art and provide a variable radius straight manifold hanger type mold with uniform melt outlet flow rate along the flow channel width direction, small flow resistance zone length and short melt residence time.

[0005] Another object of the present invention is to provide a rheological design method for a balanced flow channel of a hanger-type mold with a variable radius straight manifold. The design method designs the manifold of the hanger-type mold flow channel as a straight manifold whose cross-sectional dimensions gradually decrease along the flow channel width direction, and designs the flow blocking area as two flow blocking areas (i.e., flow blocking area I and flow blocking area II) with different thicknesses along the flow channel length direction (i.e., the extrusion direction). Under the condition that the melt outlet flow rate is uniform along the flow channel width direction, the rheological theory is used to deduce the differential equation of the boundary curve of the two flow blocking areas along the flow channel width direction, and combined with the boundary conditions, the numerical method is used to solve the boundary curve differential equation and fit it to obtain the boundary curve of the two flow blocking areas.

[0006] The technical solution of the present invention is: a variable radius straight manifold hanger-type mold, the flow channel of the variable radius straight manifold hanger-type mold includes an inlet area, a manifold, a flow blocking area, a relaxation area and a molding area arranged in sequence along the flow direction, the manifold is a straight manifold whose cross-sectional size decreases to both sides along the width direction of the flow channel, and the flow blocking area includes a flow blocking area I and a flow blocking area II with different thicknesses designed along the length direction of the flow channel.

[0007] The area adjacent to the manifold is the choke zone I, and the area adjacent to the relaxation zone is the choke zone II. The outlet cross section of the choke zone II is perpendicular to the extrusion direction, and the thickness of the choke zone I and the thickness of the choke zone II remain unchanged along the width direction of the flow channel. The manifold cross section is circular, and the radius of the manifold decreases toward both sides along the width direction of the flow channel.

[0008] A rheological design method for a balanced flow channel of a variable radius straight manifold hanger-type mold is applicable to the flow channel design of a mold that is symmetrical along the width direction, comprising the following steps:

[0009] Constructing a physical model: Assumptions a. The melt is an incompressible fluid; b. The melt flow is a steady laminar flow, ignoring inertial force and volume force; c. The melt flows only along the axial direction of the manifold in the manifold, and only flows along the extrusion direction in the flow resistance zone I, flow resistance zone II, relaxation zone and molding zone, and the flow of the melt in the manifold and the flow in the flow resistance zone I do not interfere with each other; d. Ignore the effect of stretching caused by the change of manifold radius on the melt flow in the manifold; e. Ignore the effect of the two side walls at the end of the flow channel on the melt flow; f. The temperature of the melt remains unchanged during the flow process;

[0010] Constructing the flow channel geometry model: the mold flow channel includes the inlet area, manifold, flow blocking area, relaxation area and molding area arranged in sequence along the melt flow direction; the manifold is designed as a straight manifold with a cross-sectional size gradually decreasing toward both sides along the flow channel width direction; the flow blocking area is designed as flow blocking area I and flow blocking area II along the flow channel length direction (extrusion direction), and the thickness of flow blocking area I and flow blocking area II are different;

[0011] The differential equation of the boundary curve between the choke zone I and the choke zone II is deduced by using rheological theory: a coordinate system is constructed, and based on the uniform outlet flow rate of the melt along the width direction of the flow channel, the pressure gradient of the melt along the width direction of the flow channel in the manifold is calculated, and the pressure drop from the entrance of the choke zone I to the exit of the choke zone II when the melt flows along the extrusion direction is calculated; based on the fact that the melt pressure at the entrance of the choke zone I is equal to the pressure of the melt in the manifold and the melt pressure at the exit of the choke zone II is constant along the width direction of the flow channel, the differential equation of the boundary curve between the choke zone I and the choke zone II in the coordinate system along the width direction of the flow channel is obtained; the differential equation is numerically solved and fitted in combination with the boundary conditions of the boundary curve between the choke zone I and the choke zone II, and the boundary curve between the choke zone I and the choke zone II is obtained.

[0012] As a preferred embodiment, in constructing the flow channel geometric model, the manifold cross section is circular, and the manifold radius decreases toward both sides along the flow channel width direction.

[0013] As a preferred embodiment, in constructing the flow channel geometric model, the area adjacent to the manifold is the flow blocking area I, and the area adjacent to the relaxation area is the flow blocking area II.

[0014] As a preferred embodiment, in constructing the flow channel geometric model, the outlet cross section of the flow resistance II zone is perpendicular to the extrusion direction.

[0015] As a preferred embodiment, in constructing the flow channel geometric model, the thickness of the flow blocking area I and the flow blocking area II remains unchanged along the flow channel width direction.

[0016] As a preferred embodiment, in constructing the flow channel geometric model, the thickness of the flow blocking area I is less than the thickness of the flow blocking area II.

[0017] As a preferred embodiment, in constructing the flow channel geometric model, the thickness of the flow blocking area I is greater than the thickness of the flow blocking area II.

[0018] Preferably, the flow blocking area I is provided with a spacing between the position of the symmetric plane of the flow channel and the end of the flow channel and the manifold, and the flow blocking area II is provided with a spacing between the position of the symmetric plane of the flow channel and the end of the flow channel and the relaxation area.

[0019] As a preferred embodiment, in constructing the flow channel geometric model, the thickness and length of the relaxation zone and the forming zone remain unchanged along the flow channel width direction, and the inlet cross section and the outlet cross section of the relaxation zone and the forming zone are perpendicular to the extrusion direction.

[0020] As a preference, at any position in the flow channel width direction, the melt pressure at the inlet of the choke zone I is equal to the melt pressure in the manifold, and the melt pressure at the outlet of the choke zone II remains unchanged along the flow channel width direction.

[0021] As a preferred embodiment, the deduction process of rheological theory is:

[0022] The temperature of the melt remains unchanged during the flow process, and the viscosity of the melt is described by the power law model, that is,

[0023]

[0024] Where η is the melt viscosity; K is the consistency coefficient; is the shear rate; n is the power law exponent;

[0025] According to the symmetry of the flow channel width, half of the flow channel is taken for analysis. Ignoring the influence of the inlet area, the manifold cross section is selected as a circle and the size decreases along the flow channel width. Other shapes can be converted through the shape factor. The coordinate system is constructed with the flow channel width direction as the x-axis, the flow channel length direction as the y-axis, and the boundary line between the manifold and the flow blocking area I as the z-axis.

[0026] The pressure gradient of the melt flowing along the manifold is

[0027]

[0028] Where p(z) is the pressure of the melt at z in the manifold; Q(z) is the volume flow rate of the melt at z in the manifold; r(z) is the radius of the manifold at z;

[0029] Assuming that the volume flow rate of the melt at the flow channel inlet is 2Q0, and the melt outlet flow rate is required to be uniform along the flow channel width, the volume flow rate of the melt in the manifold along the manifold direction is

[0030] Q(z)=Q0(1-zsinθ / W) (3)

[0031] Where W is half of the channel width; θ is half of the expansion angle of the choke area;

[0032] According to the coordinate system, we have

[0033] x=zsinθ (4)

[0034] dx=sinθdz (5)

[0035] p(x)=p(z) (6)

[0036] r(x)=r(z) (7)

[0037] Where p(x) is the pressure of the melt in the manifold at position x; r(x) is the radius of the manifold at position x.

[0038] On the other hand, the pressure gradient of the melt in the manifold along the manifold direction and the pressure gradient along the flow channel width direction satisfy

[0039]

[0040] Substituting equations (3) to (8) into equation (2), we have

[0041]

[0042] Since the thickness and length of the relaxation zone and the forming zone are constant along the flow channel width, the melt pressure at the outlet of the blocking zone II is constant along the flow channel width when the melt outlet flow rate is required to be uniform along the flow channel width. The length of the blocking zone at the symmetry plane of the flow channel is L, and the melt pressure at the outlet of the blocking zone II (i.e. y = L) is p L At any position x in the flow channel width direction, when the melt flows in the obstruction zone along the extrusion direction, the pressure drop between the inlet of the obstruction zone I and the outlet of the obstruction zone II is

[0043]

[0044] Wherein, h1 and h2 are the thickness of the blocking area I and the blocking area II respectively; y is the boundary curve between the blocking area I and the blocking area II, which is a function of the coordinate x;

[0045] Taking the derivative of formula (10) with respect to x, we have

[0046]

[0047] From equation (9) and equation (11), we can get

[0048]

[0049] Formula (12) means the boundary curve between the flow blocking area I and the flow blocking area II is Figure 2 Differential equation in the coordinate system shown.

[0050] As a preferred embodiment, the boundary condition of the differential equation (12) of the boundary curve between the blocking zone I and the blocking zone II is

[0051] x=W,y=y E (13)

[0052] In the formula, y E It is the coordinate of the boundary curve between choke zone I and choke zone II at the end of the flow channel.

[0053] As a preferred embodiment, the boundary condition of the differential equation (12) of the boundary curve between the blocking zone I and the blocking zone II is

[0054] x=0, y=y C (14)

[0055] In the formula, y C It is the coordinate of the boundary curve between the choke zone I and the choke zone II at the symmetry plane of the flow channel.

[0056] As a preferred embodiment, when the radius of the manifold decreases along the width direction of the flow channel and the end size is not 0, a numerical method is required to solve the differential equation of the boundary curve between the choke zone I and the choke zone II and perform fitting to obtain the boundary curve between the choke zone I and the choke zone II.

[0057] As a preferred embodiment, the pressure drop of the melt flowing from the manifold inlet through the manifold and the choke zone along any path is equal, which can be calculated by the pressure drop of the melt at the symmetric plane of the flow channel in the choke zone, that is,

[0058]

[0059] As a preferred embodiment, when the melt flows in the manifold, the residence time t from the manifold inlet to any position x can be expressed as

[0060]

[0061] When the manifold radius decreases along the flow channel width and the end size is not 0, equation (16) needs to be solved by numerical methods.

[0062] x=0,t=0 (17)

[0063] As a preferred embodiment, numerical simulation software is used to perform numerical simulation on the flow field of the melt in the flow channel, and the ratio of the volume flow rate per unit width at a certain position in the flow channel width direction at the melt outlet to the average volume flow rate per unit width is defined as the dimensionless flow rate of the melt outlet, which is used to reflect the uniformity of the melt outlet flow rate, and further verify the reliability of the differential equation of the dividing curve and its numerical solution.

[0064] The principle of the present invention is as follows: in the flow channel of the hanger-type mold, after the melt enters the manifold from the inlet area and flows along the manifold, a part of the melt enters the flow blocking area and flows into the relaxation area and the molding area along the extrusion direction. The melt pressure in the manifold decreases nonlinearly along the flow direction, that is, the melt pressure at the inlet of the flow blocking area decreases nonlinearly along the flow channel width direction. Under the condition that the cross-sectional shapes of the inlet area, the relaxation area and the molding area are not changed, the present invention designs the manifold as a straight manifold whose cross-sectional dimensions decrease toward both sides along the flow channel width direction, and designs the flow blocking area into two regions with different thicknesses (i.e., flow blocking area I and flow blocking area II) along the flow channel length direction (extrusion direction). Based on the condition that the melt outlet flow rate is uniform along the flow channel width direction, the pressure gradient of the melt in the manifold along the flow channel width direction is calculated, and the pressure drop from the entrance of the choke zone I to the exit of the choke zone II when the melt flows along the extrusion direction is calculated; according to the fact that the melt pressure at the entrance of the choke zone I is equal to the melt pressure in the manifold and the melt pressure at the exit of the choke zone II is constant along the flow channel width direction, or in other words, the pressure drop of the melt flowing from the manifold inlet through the manifold and the choke zone along any path is equal, or in other words, the pressure gradient of the melt in the manifold along the flow channel width direction is the same as the gradient of the pressure drop of the melt in the choke zone (choke zone I and choke zone II) along the flow channel width direction, the differential equation of the boundary curve between the choke zone I and the choke zone II is deduced; combined with the boundary conditions of the boundary curve, the numerical method is used to solve the differential equation of the boundary curve and the numerical solution is fitted to obtain the boundary curve between the choke zone I and the choke zone II.

[0065] Compared with the prior art, the present invention has the following beneficial effects:

[0066] The present invention designs the manifold of the hanger-type mold flow channel as a straight manifold whose cross-sectional dimensions decrease toward both sides along the flow channel width direction, and designs the flow blocking area along the flow channel length direction into a flow blocking area I and a flow blocking area II with different thicknesses. By analyzing the melt flow in the flow channel, the flow channel structure and dimensions are theoretically designed based on the rheological theory on the premise that the melt outlet flow rate is uniform along the flow channel width direction, and the differential equation of the boundary curve between the flow blocking area I and the flow blocking area II is deduced.

[0067] The present invention uses a numerical method to solve the differential equation of the boundary curve between the choke I zone and the choke II zone and fits its numerical solution, thereby establishing a runner geometry model of a coat-hanger type mold, numerically simulating the flow behavior of the melt in the runner, and verifying the deduced differential equation of the boundary curve between the choke I zone and the choke II zone and the solution method thereof, indicating that the deduced differential equation of the boundary curve is reliable and can be used to guide the design of the runner of the coat-hanger type mold.

[0068] Compared with the existing hanger-type mold runner design method, the runner design method proposed in the present invention can effectively reduce the length of the flow resistance zone and thus reduce the runner length, significantly reduce the residence time of the melt in the manifold and thus reduce the residence time of the melt in the runner, while meeting the condition of uniform melt outlet volume flow rate.

[0069] Compared with the existing hanger-type mold runner design method, the runner design method proposed in the present invention can design the manifold radius and its change law along the runner width direction, the length and expansion angle of the flow blocking area, the thickness of the flow blocking area I and the flow blocking area II, and the boundary shape curve according to the molding requirements. BRIEF DESCRIPTION OF THE DRAWINGS

[0070] Figure 1 Schematic diagram of the flow channel structure of the variable radius straight manifold hanger type mold designed for this patent.

[0071] Figure 2 Schematic diagram of the rheological design model of the variable radius straight manifold hanger-type mold flow channel in the embodiment.

[0072] Figure 3 It is the dimensionless flow rate per unit width along the width direction of one side of the flow channel obtained by numerical simulation of the melt flow field in flow channel scheme 1 in the embodiment.

[0073] Figure 4 It is the dimensionless flow rate per unit width along the width direction of one side of the flow channel obtained by numerical simulation of the melt flow field in flow channel scheme 2 in the embodiment.

[0074] Figure 5 It is the dimensionless flow rate per unit width along the width direction of one side of the flow channel obtained by numerical simulation of the melt flow field in flow channel scheme 3 in the embodiment.

[0075] Figure 6 It is the melt pressure contour line obtained by numerical simulation of melt flow field in flow channel scheme 1 in the embodiment.

[0076] Figure 7 It is the melt pressure contour line obtained by numerical simulation of melt flow field in flow channel scheme 2 in the embodiment.

[0077] Figure 8It is the melt pressure contour line obtained by numerical simulation of melt flow field in flow channel scheme 3 in the embodiment.

[0078] As shown in the figure, 1 is the inlet area, 2 is the manifold, 31 is the flow blocking area I, 32 is the flow blocking area II, 4 is the relaxation area, and 5 is the forming area. DETAILED DESCRIPTION

[0079] The present invention will be further described in detail below in conjunction with examples, but the embodiments of the present invention are not limited thereto.

[0080] The present embodiment provides a rheological design method for a balanced flow channel of a variable radius straight manifold hanger-type mold, which is applicable to the flow channel design of a mold that is symmetrical along the width direction, and includes the following steps:

[0081] S1. Construct a physical model: Assumptions a. The melt is an incompressible fluid; b. The melt flows in a steady laminar flow, and the inertial force and volume force are ignored; c. The melt flows only along the axial direction of the manifold in the manifold, and only flows along the extrusion direction in the flow resistance zone I, flow resistance zone II, relaxation zone and molding zone, and the melt flow in the manifold and the flow in the flow resistance zone I do not interfere with each other; d. The effect of stretching caused by the change of the manifold radius on the melt flow is ignored; e. The effect of the two side walls at the end of the flow channel on the melt flow is ignored; f. The temperature of the melt remains unchanged during the flow process.

[0082] S2. Construct the flow channel geometry model: Figure 1 As shown, the mold flow channel includes an inlet area 1, a manifold 2, a blocking area, a relaxation area 4 and a molding area 4 which are arranged in sequence along the melt flow direction; the manifold is designed to be a straight manifold with a circular cross-section and a manifold radius that decreases toward both sides along the flow channel width direction; the blocking area is designed to be a blocking area I 31 and a blocking area II 32 along the flow channel length direction, the thickness of the blocking area I and the blocking area II are different, the area adjacent to the manifold is the blocking area I, and the area adjacent to the relaxation area is the blocking area II, and the thickness of the blocking area I and the blocking area II is constant along the flow channel width direction; the blocking area I is provided with a spacing at the flow channel symmetry plane position and between the flow channel end and the manifold, and the blocking area II is provided with a spacing at the flow channel symmetry plane position and between the flow channel end and the relaxation area; the thickness and length of the relaxation area and the molding area are constant along the flow channel width direction.

[0083] S3. Use rheological theory to deduce the differential equation of the boundary curve between the flow-blocking zone I and the flow-blocking zone II: Construct a coordinate system, such as Figure 2As shown, based on the uniform outlet flow rate of the melt along the width direction of the flow channel, the pressure gradient of the melt in the manifold along the width direction of the flow channel is calculated, and the pressure drop from the inlet of the choke zone I to the outlet of the choke zone II when the melt flows along the extrusion direction is calculated; according to the melt pressure at the inlet of the choke zone I being equal to the melt pressure in the manifold and the melt pressure at the outlet of the choke zone II being constant along the width direction of the flow channel, the differential equation of the boundary curve between the choke zone I and the choke zone II in the coordinate system is obtained.

[0084] The deduction process of rheological theory is:

[0085] According to the symmetry of the flow channel in the width direction, half of the flow channel is taken for analysis. Ignoring the influence of the inlet area, the manifold cross section is selected as a circle and the manifold radius decreases along the width direction of the flow channel. The coordinate system is constructed with the flow channel width direction as the x-axis, the flow channel length direction as the y-axis, and the boundary line between the manifold and the flow blocking area I as the z-axis, as shown in Figure 2 shown.

[0086] The pressure gradient of the melt flowing along the manifold is

[0087]

[0088] Where p(z) is the pressure of the melt at z in the manifold; Q(z) is the volume flow rate of the melt at z in the manifold; r(z) is the radius of the manifold at z;

[0089] Assuming that the volume flow rate of the melt at the flow channel inlet is 2Q0, and the melt outlet flow rate is required to be uniform along the flow channel width, the volume flow rate of the melt in the manifold along the manifold direction is

[0090] Q(z)=Q0(1-zsinθ / W) (3)

[0091] Where W is half of the channel width; θ is half of the expansion angle of the choke area;

[0092] According to the coordinate system, we have

[0093] x=zsinθ (4)

[0094] dx=sinθdz (5)

[0095] p(x)=p(z) (6)

[0096] r(x)=r(z) (7)

[0097] Where p(x) is the pressure of the melt in the manifold at position x; r(x) is the radius of the manifold at position x.

[0098] On the other hand, the pressure gradient of the melt in the manifold along the manifold direction and the pressure gradient along the flow channel width direction satisfy

[0099]

[0100] Substituting equations (3) to (8) into equation (2), we have

[0101]

[0102] Since the thickness and length of the relaxation zone and the forming zone are constant along the flow channel width, the melt outlet flow rate is required to be uniform along the flow channel width, and the melt pressure at the outlet of the blocking zone II is constant along the flow channel width. The length of the blocking zone at the symmetry plane of the flow channel is L, and the melt pressure at the outlet of the blocking zone II (i.e. y = L) is p L At any position x in the flow channel width direction, when the melt flows in the obstruction zone along the extrusion direction, the pressure drop between the inlet of the obstruction zone I and the outlet of the obstruction zone II is

[0103]

[0104] Wherein, h1 and h2 are the thickness of the blocking area I and the blocking area II respectively; y is the boundary curve between the blocking area I and the blocking area II, which is a function of the coordinate x;

[0105] Taking the derivative of formula (10) with respect to x, we have

[0106]

[0107] From equation (9) and equation (11), we can get

[0108]

[0109] Formula (12) means the boundary curve between the flow blocking area I and the flow blocking area II is Figure 2 Differential equation in the coordinate system shown.

[0110] It can be seen from formula (12) that the differential equation of the boundary curve between the choke zone I and the choke zone II is related to the flow channel width, the manifold radius and its variation along the flow channel width, the thickness of the choke zone I and the choke zone II, the choke zone expansion angle, and the power law index n of the melt, but has nothing to do with the consistency and output of the melt. The flow channel width is determined by the product specifications, the power law index is the material parameter of the melt, and the manifold radius and its variation along the flow channel width, the thickness of the choke zone I and the choke zone II, and the choke zone expansion angle can all be used as flow channel design parameters. The boundary curve between the choke zone I and the choke zone II is designed according to formula (12).

[0111] When the radius of the manifold decreases along the width of the flow channel and the end size is not 0, equation (12) needs to be solved by numerical methods and fitted to obtain the boundary curve between the flow-blocking zone I and the flow-blocking zone II.

[0112] The boundary conditions are

[0113] x=W,y=y E (13)

[0114] In the formula, y E It is the coordinate of the boundary curve between choke zone I and choke zone II at the end of the flow channel.

[0115] The choke I area has an appropriate spacing between the manifold and the choke II area at the end of the flow channel to facilitate mold manufacturing, which is determined according to the processing conditions. The dimensions of each part of the flow channel need to be considered comprehensively during design to ensure that the length y of the choke I area at the symmetry plane of the flow channel calculated by formula (12) is C It is smaller than the length L of the flow-blocking area, and the flow-blocking area II has a suitable length at the symmetry plane of the flow channel to facilitate flow channel processing.

[0116] The pressure drop of the melt flowing from the manifold inlet through the manifold and the choke area along any path is equal, which can be calculated using the pressure drop at the symmetric surface of the flow channel, that is,

[0117]

[0118] The residence time of the melt in the runner is also one of the important aspects of the runner design of the hanger mold. The residence time t of the melt in the manifold from the inlet to any position x can be expressed as

[0119]

[0120] When the radius of the manifold decreases along the width of the flow channel and the end size is not 0, equation (15) needs to be solved by numerical methods.

[0121] x=0,t=0 (16)

[0122] S4. Verification: In order to verify the reliability of the differential equation of the boundary curve between the choke zone I and the choke zone II in the design of the variable radius straight manifold hanger-type mold flow channel derived in the present invention, taking an ABS sheet extrusion as an example, the differential equation of the boundary curve between the choke zone I and the choke zone II is solved and the flow channel is designed, the flow of the melt in the flow channel is analyzed using numerical simulation software, and the verification is carried out by calculating the melt outlet flow rate.

[0123] The power law model is used to describe the rheological properties of ABS. When the extrusion temperature is 220°C, the power law index n = 0.486 and the consistency K = 7496.8 Pa·s -0.514 The flow channel width (2W) is 2000mm, the length and thickness of the relaxation zone are 40mm and 4mm respectively, the length and thickness of the forming zone are 20mm and 1.5mm respectively, the expansion angle of the choke zone is 177°, the length of the choke zone at the symmetry plane of the flow channel width is 40mm, and the boundary curve between the choke zone I and the choke zone II is at the end of the flow channel y E Take 34mm.

[0124] The radius of the manifold decreases exponentially along the width of the flow channel, that is,

[0125] r(x)=R E +(R C -R E )(1-x / W) m (17)

[0126] In the formula, R C R is the radius of the manifold at the symmetry plane of the flow channel; E is the radius of the manifold at the end of the flow channel; m is an exponent.

[0127] Three manifold sizes and their variation patterns were selected, and the fourth-order explicit Runge-Kutta method was used to solve the differential equation (12) of the boundary curve between the choke zone I and the choke zone II. The thickness of the choke zone I and the choke zone II and their boundary curves were designed taking into account the manufacturability of the flow channel, as shown in Table 1. Spline curves were used to fit the boundary curves between the choke zone I and the choke zone II, and the flow channel was modeled using 3D design software. According to the symmetry of the flow channel in the width direction, half of the melt flow field in the flow channel was taken for numerical simulation. The flow channel was divided into hexahedral units, and smaller meshes were used for the flow channel wall boundary and the location of size mutation. Quadratic interpolation was used for velocity and linear interpolation was used for pressure when solving the flow field to improve the accuracy of the numerical simulation results.

[0128] Table 1 Manifold and choke dimensions

[0129]

[0130]

[0131] The ratio of the volume flow rate per unit width at a certain position in the flow channel width direction at the melt outlet to the volume flow rate per unit width at the average unit width is defined as the dimensionless flow rate at the melt outlet. Figure 3 to Figure 5As shown in the figure, the dimensionless flow rate of the melt outlet along the width direction of one side of the flow channel obtained by numerical simulation for flow channel schemes 1 to 3 when the extrusion speed is 25 mm / s. The dimensionless flow rate of the melt outlet gradually increases along the width direction of the flow channel, and then gradually decreases after reaching the maximum value. The dimensionless flow rates of the melt outlet at the symmetric plane in the width direction of the flow channel for schemes 1 to 3 are 0.995, 0.996 and 0.996, respectively, and the maximum dimensionless flow rates of the melt outlet are 1.012, 1.008 and 1.009, respectively. The melt outlet flow rate has good uniformity and can meet engineering requirements. On the other hand, within a range of about 10 mm at the end of the flow channel, the dimensionless flow rate of the melt outlet is less than 1. This is because the influence of the side wall at the end of the flow channel on the melt flow is ignored in the theoretical derivation. When the melt flow is numerically simulated, considering that there is a no-slip boundary between the melt and the side wall of the flow channel in actual production, the dimensionless flow rate of the melt outlet in the boundary layer is less than 1.

[0132] like Figure 6 to Figure 8 As shown in the figure, the melt pressure contours in the flow channel of flow channel schemes 1 to 3 obtained by numerical simulation when the extrusion speed is 25 mm / s. It can be seen that when the melt leaves the choke zone, the melt pressure contour is parallel to the flow channel outlet, the pressure drop of the melt in the manifold obtained by simulation is consistent with the pressure drop obtained by solving the differential equation (9) using the fourth-order explicit Runge-Kutta method, and the pressure drop of the melt in the choke zone at the end of the flow channel is consistent with the pressure drop calculated using formula (10).

[0133] In flow channel schemes 1 to 3, the pressure drop of the melt flowing from the manifold inlet along any path to the outlet of the flow blocking II zone is 7.74MPa, 4.75MPa and 7.41MPa respectively. The manifolds of flow channel schemes 1 and 2 have the same radius at the flow channel symmetry plane and the flow channel end, but the change law of the manifold radius along the flow channel width direction is different. At any position in the flow channel width direction, the manifold radius of scheme 1 is smaller than the manifold radius of scheme 2. Therefore, the melt pressure gradient in the manifold of scheme 1 is large, and the pressure drop of the melt flowing from the manifold inlet along any path to the outlet of the flow blocking II zone is large. The manifold radius of schemes 2 and 3 has the same change law along the flow channel width direction, but the manifold radii at the flow channel symmetry plane and the flow channel end are different. At any position in the flow channel width direction, the manifold radius of scheme 3 is smaller than the manifold radius of scheme 2. Therefore, the melt pressure gradient in the manifold of scheme 3 is large, and the pressure drop of the melt flowing from the manifold inlet along any path to the outlet of the flow blocking II zone is large.

[0134] Generally, the residence time of the melt in the manifold is much longer than the residence time of the melt after leaving the manifold. For the sake of comparison, the residence time of the melt at 0.98W from the manifold inlet is selected for calculation. The fourth-order explicit Runge-Kutta method is used to solve equation (15). The residence time of the melt at 0.98W from the manifold inlet in flow channel schemes 1 to 3 is 29.7s, 43.3s, and 30.8s, respectively. When the distance from the symmetry plane in the flow channel width direction is constant, the manifold radius of schemes 1 and 3 is smaller than that of scheme 2. Therefore, the melt flow rate in the manifold of schemes 1 and 3 is large, and the residence time of the melt in the manifold is short.

[0135] This embodiment is a variable radius straight manifold hanger type mold, such as Figure 1 As shown, the flow channel of the variable radius straight manifold hanger-type mold includes an inlet area 1, a manifold 2, a flow blocking area, a relaxation area 4 and a molding area 5 arranged in sequence along the flow direction. The manifold is a straight manifold whose cross-sectional dimensions decrease toward both sides along the width direction of the flow channel. The flow blocking area includes a flow blocking area 31 and a flow blocking area 32 of different thicknesses designed along the length direction of the flow channel. The area adjacent to the manifold is the flow blocking area I, and the area adjacent to the relaxation area is the flow blocking area II. The outlet cross section of the flow blocking area II is perpendicular to the extrusion direction, and the thickness of the flow blocking area I and the thickness of the flow blocking area II remain unchanged along the width direction of the flow channel. The cross section of the manifold is circular, and the radius of the manifold decreases along the width direction of the flow channel.

[0136] In addition to the methods mentioned in the above embodiments, for manifolds with other cross-sectional shapes, the melt pressure gradient in the manifold can be converted by the shape factor, and then the differential equations of the boundary curves of the flow channel resistance zone I and the flow channel resistance zone II corresponding to the manifolds with different cross-sectional shapes and their changing rules in the flow channel width direction and their numerical solution results are obtained. These transformation methods are all within the protection scope of the present invention.

[0137] In addition to the above-mentioned embodiments, the radius of the manifold may be changed in other ways along the width of the flow channel, thereby obtaining the boundary curves of the flow channel flow resistance zone I and flow resistance zone II corresponding to manifolds of different shapes. These changes are all within the protection scope of the present invention.

[0138] In addition to the methods mentioned in the above embodiments, other numerical methods can be used to solve the differential equation of the boundary curve between the flow passage obstruction zone I and the flow obstruction zone II and other reasonable methods can be used for fitting. These transformation methods are all within the protection scope of the present invention.

[0139] In addition to the methods mentioned in the above embodiments, the boundary curve between the blocking zone I and the blocking zone II calculated by the above design method essentially determines the length of the blocking zone I and the blocking zone II at any position in the flow channel width direction. Therefore, the positions of the blocking zone I and the blocking zone II are swapped in the extrusion direction or decomposed into a combination of multiple regions to ensure uniform melt outlet volume flow rate. These changes are all within the scope of protection of the present invention.

[0140] In addition to the above-mentioned embodiments, the chamfering or rounding transition between the flow blocking area I and the flow blocking area II does not affect the melt outlet volume flow rate. These changes are all within the scope of protection of the present invention.

[0141] As described above, the present invention can be better implemented. The above embodiments are only preferred embodiments of the present invention and are not intended to limit the scope of implementation of the present invention; that is, all equivalent changes and modifications made according to the content of the present invention are covered by the scope of protection required by the claims of the present invention.

Claims

1. A rheological design method for a variable radius straight manifold hanger-type mold balanced flow channel, characterized in that: The flow channel of the variable radius straight manifold hanger-type mold includes an inlet area, a manifold, a flow blocking area, a relaxation area and a molding area arranged in sequence along the flow direction, the manifold is a straight manifold whose cross-sectional size decreases toward both sides along the width direction of the flow channel, and the flow blocking area includes a flow blocking area I and a flow blocking area II with different thicknesses designed along the length direction of the flow channel; The design method comprises the following steps: Constructing the physical model: Assumptions a. The melt is an incompressible fluid; b. The melt flow is a steady laminar flow, ignoring the inertial force and volume force; c. The melt flows only along the axial direction of the manifold in the manifold, and only flows along the extrusion direction in the flow resistance zone I, flow resistance zone II, relaxation zone and molding zone, and the flow of the melt in the manifold and the flow in the flow resistance zone I do not interfere with each other; d. Ignore the effect of stretching caused by the change of the manifold radius on the melt flow; e. Ignore the effect of the two side walls at the end of the flow channel on the melt flow; f. The temperature of the melt remains unchanged during the flow process; Constructing the flow channel geometric model: the mold flow channel includes the inlet area, manifold, flow blocking area, relaxation area and molding area arranged in sequence along the flow direction; the manifold is designed as a straight manifold with the cross-sectional size decreasing toward both sides along the flow channel width direction; the flow blocking area is designed as flow blocking area I and flow blocking area II with different thicknesses along the flow channel length direction; Derive the differential equation of the boundary curve between the choke zone I and the choke zone II: construct a coordinate system, calculate the pressure gradient of the melt in the manifold along the width direction of the flow channel based on the uniform outlet flow rate of the melt along the width direction of the flow channel, and calculate the pressure drop from the entrance of the choke zone I to the exit of the choke zone II when the melt flows along the extrusion direction; obtain the differential equation of the boundary curve between the choke zone I and the choke zone II in the coordinate system based on the fact that the melt pressure at the entrance of the choke zone I is equal to the melt pressure in the manifold and the melt pressure at the exit of the choke zone II is constant along the width direction of the flow channel; The process of deriving the differential equation of the boundary curve between the choke zone I and the choke zone II is as follows: According to the symmetry of the flow channel in the width direction, half of the flow channel is taken for analysis, the influence of the inlet area is ignored, the manifold cross section is selected as a circle, and the manifold radius decreases to both sides along the width direction of the flow channel. Other shapes are converted by shape factors; The pressure gradient of the melt flowing along the manifold is Where p(z) is the pressure of the melt at z in the manifold; Q(z) is the volume flow rate of the melt at z in the manifold; r(z) is the radius of the manifold at z; Assuming that the volume flow rate of the melt at the flow channel inlet is 2Q0, and the melt outlet flow rate is required to be uniform along the flow channel width, the volume flow rate of the melt in the manifold along the manifold direction is Q(z)=Q0(1-zsinθ / W) (3) Where W is half of the channel width; θ is half of the expansion angle of the choke area; According to the coordinate system, we have x=zsinθ (4) dx=sinθdz (5) P(x)=P(z) (6) r(x)=r(z) (7) Where p(x) is the pressure of the melt in the manifold at x; r(x) is the radius of the manifold at x; On the other hand, the pressure gradient of the melt in the manifold along the manifold direction and the pressure gradient along the flow channel width direction satisfy Substituting equations (3) to (8) into equation (2), we have Since the thickness and length of the relaxation zone and the forming zone are constant along the flow channel width, the melt outlet flow rate is required to be uniform along the flow channel width, and the melt pressure at the outlet of the blocking zone II is constant along the flow channel width; the length of the blocking zone at the symmetric plane of the flow channel is L, and the melt pressure at the outlet of the blocking zone II when y=L is p L At any position x in the flow channel width direction, when the melt flows in the obstruction zone along the extrusion direction, the pressure drop between the inlet of the obstruction zone I and the outlet of the obstruction zone II is Wherein, h1 and h2 are the thickness of the blocking area I and the blocking area II respectively; y is the boundary curve between the blocking area I and the blocking area II, which is a function of the coordinate x; Taking the derivative of formula (10) with respect to x, we have From equation (9) and equation (11), we can get Formula (12) is the differential equation of the boundary curve between the choke zone I and the choke zone II in the coordinate system.

2. The rheological design method of a variable radius straight manifold hanger type mold balanced flow channel according to claim 1, characterized in that: The area adjacent to the manifold is the choke zone I, and the area adjacent to the relaxation zone is the choke zone II. The outlet cross section of the choke zone II is perpendicular to the extrusion direction, and the thickness of the choke zone I and the thickness of the choke zone II remain unchanged along the width direction of the flow channel. The manifold cross section is circular, and the radius of the manifold decreases toward both sides along the width direction of the flow channel.

3. The rheological design method of a variable radius straight manifold hanger type mold balanced flow channel according to claim 1, characterized in that: The area adjacent to the manifold is the choke zone I, and the area adjacent to the relaxation zone is the choke zone II. The outlet cross section of the choke zone II is perpendicular to the extrusion direction, and the thickness of the choke zone I and the thickness of the choke zone II remain unchanged along the width direction of the flow channel.

4. The rheological design method for a variable radius straight manifold hanger type mold balanced flow channel according to claim 1, characterized in that: The blocking zone I is provided with a distance between the symmetric plane of the flow channel and the end of the flow channel and the manifold, and the blocking zone II is provided with a distance between the symmetric plane of the flow channel and the end of the flow channel and the relaxation zone.

5. The rheological design method of a variable radius straight manifold hanger type mold balanced flow channel according to claim 1, characterized in that: In constructing the flow channel geometry model, the thickness and length of the relaxation zone and the forming zone remain unchanged along the flow channel width direction, and the inlet and outlet cross sections of the relaxation zone and the forming zone are perpendicular to the extrusion direction.

6. The rheological design method for a variable radius straight manifold hanger type mold balanced flow channel according to claim 1, characterized in that: At any position along the width direction of the flow channel, the melt pressure at the entrance of the choke zone I is equal to the melt pressure in the manifold, and the melt pressure at the exit of the choke zone II remains unchanged along the width direction of the flow channel; the pressure drop of the melt flowing from the manifold inlet through the manifold and the choke zone along any path is equal; at any position along the width direction of the flow channel, the pressure gradient of the melt in the manifold along the width direction of the flow channel is equal to the gradient of the pressure drop along the width direction of the flow channel when the melt in the choke zone flows along the extrusion direction.

7. The rheological design method for a variable radius straight manifold hanger type mold balanced flow channel according to claim 1, characterized in that: When the radius of the manifold decreases along the width of the flow channel and the end size is not 0, the numerical method is used to solve the differential equation of the boundary curve between the choke zone I and the choke zone II and fit it to obtain the boundary curve between the choke zone I and the choke zone II, which is used as the location of the interface between the choke zone I and the choke zone II for flow channel geometric modeling.

8. The rheological design method for a variable radius straight manifold hanger type mold balanced flow channel according to claim 1, characterized in that: Numerical simulation software is used to simulate the flow field of the melt in the runner. The ratio of the volume flow rate per unit width at a certain position along the width direction of the runner at the melt outlet to the average volume flow rate per unit width is defined as the dimensionless flow rate of the melt outlet. It is used to reflect the uniformity of the melt outlet flow rate, and then verify the reliability of the boundary shape curve.

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