A method for optimizing the design of rubber and plastic extrusion dies

Abstract

The present invention discloses a method for optimizing the design of a rubber and plastic extrusion die, which sequentially completes the flow balance optimization design and geometric precision optimization design of the extrusion die, and calculates the optimal solution for the geometric precision of the extrusion die; first, the material rheological model and its parameters are determined by fitting experimental data; then, a finite element model of in-die flow is established, and a flow balance optimization design method is adopted to obtain the optimal solution for flow balance and the flow balance design space; then, in-die and out-die flow finite element models are established with the optimal solution for flow balance, and the validity of the finite element model is verified by experiments; finally, based on the finite element models of in-die and out-die flow verified by experiments, a geometric precision optimization design method is adopted to obtain the optimal solution for geometric precision. The present invention fully combines the high efficiency of the flow balance optimization design method and the high precision of the geometric precision optimization design method, and significantly improves the geometric precision of the extruded product on the basis of achieving die outlet flow balance.

Description

Technical Field

[0001] The invention relates to the field of rubber and plastic material processing, and in particular to a method for optimizing the design of a rubber and plastic extrusion die. Background Art

[0002] With the development of precision extrusion molding and micro extrusion molding, higher and higher requirements are placed on the precision of polymer extrusion molding. For example, in the fields of medical treatment and communications, the dimensional accuracy of extruded products has approached the micron level. The influence of extrusion swell and the extrusion deformation caused by it on the geometric accuracy of extruded products is further highlighted, which poses new challenges to the design and manufacture of extrusion dies. A well-designed extrusion die can produce extruded products with high precision and good performance, among which the dimensional accuracy of the cross section of the extruded product is particularly important. Traditional extrusion die design adopts the trial and error method. If the geometric accuracy of the extruded product does not meet the design requirements, it is necessary to repeatedly test and repair the mold to obtain the desired geometric accuracy of the extruded product.

[0003] The existing optimization design methods for rubber and plastic extrusion dies are mainly based on the principle of flow balance, with the uniformity of the outlet velocity of the extrusion die as the optimization design target. The design variables for the optimization design of extrusion dies mainly include the geometric parameters of the extrusion die flow channel, especially the geometric parameters of the preforming section and the forming section. The objective function has various forms, such as the research on the optimization design method of plastic extrusion dies based on numerical analysis (Liu Bin, Wang Minjie, Liu Yaozhong, Song Mancang. Research on the optimization design method of plastic extrusion dies based on numerical analysis [J]. Journal of Mechanical Engineering, 2003 (05): 139-144.) The optimization target is to make the average flow velocity of each sub-area on the profile cross section at the die outlet equal. Another example is "A method for optimizing the flow channel of a tire rubber extruder head" (application number 201711309716.X; application date 2017.12.11), which takes the skewness value of the rubber flow velocity as the optimization design objective function. In the optimal design of the extrusion die, the flow supply in the low-speed area is increased, the flow supply in the high-speed area is reduced or baffles are added so that different sub-areas have the same average speed.

[0004] For the design of complex plastic profile extrusion dies, flow balance at the die outlet is a necessary condition, but it is not sufficient. The extruded product still has extrusion deformation caused by extrusion swell anisotropy. In other words, even if the flow at the die outlet is fully balanced, it still belongs to Poiseuille flow. After leaving the die, the polymer melt will turn into parallel flow, resulting in velocity redistribution and uneven extrusion deformation, which makes the geometric accuracy of the extruded product low. Summary of the invention

[0005] The present invention proposes an extrusion die optimization design method with the flow balance at the die outlet and the geometric accuracy of the cross section of the extruded product as optimization targets, so as to solve the problem of low geometric accuracy of the extruded product obtained by the existing optimization design method.

[0006] In order to solve the above technical problems, the technical solution adopted by the present invention is:

[0007] A method for optimizing the design of a rubber and plastic extrusion die comprises the following steps:

[0008] Step 1: Determination of the rheological model of rubber and plastic materials and its parameter fitting; Use a rheometer to test and obtain the rheological experimental data of the rubber and plastic materials, use data analysis software to perform least squares regression fitting on the rheological experimental data, and find the rheological model and its rheological parameters with the largest fitting determination coefficient;

[0009] Step 2: Establishment of the in-mold flow finite element model; according to the cross-sectional geometry and target size of the extruded product, a parametric geometric model of the extrusion mold flow channel is established in the 3D modeling software; the parametric geometric model of the mold flow channel is imported into the meshing software for parametric mesh discretization to obtain a parametric mesh model; based on the parametric mesh model, the rheological model and its rheological parameters obtained in step 1 are used in the CFD software to define the material parameters, and the calculation domain and boundary conditions are defined to generate the in-mold flow finite element model; CFD solution of the in-mold flow finite element model can obtain the velocity distribution at the extrusion die outlet, the pressure loss of the extrusion die (die pressure drop) and the residence time of the polymer melt in the die;

[0010] Step 3: Flow balance optimization design; The extrusion die optimization design with flow balance as the goal is based on the CFD solution of the in-die flow finite element model in step 2, and the geometric parameters of the die flow channel are modified to obtain a uniform velocity distribution at the die outlet of the extrusion die; the objective function of the flow balance optimization design is the flow balance coefficient, which is used to evaluate the uniformity of the flow at the die outlet; the design variables are the geometric parameters of the parametric geometric model of the extrusion die flow channel, and further the geometric parameters of the inlet section of the extrusion die molding section, the molding section and the length of the pre-molding section; the constraint condition is the pressure loss of the extrusion die (die pressure drop), or the residence time of the melt in the extrusion die, or no constraint condition is imposed; with flow balance as the optimization goal, the optimization design method is used to obtain the optimal solution of flow balance for the extrusion die design; the flow balance design space is constructed with the optimal solution of flow balance, that is, the range of design variable values ​​with good flow balance;

[0011] Step 4: Establishment of in-mold and out-mold flow finite element models; Based on the optimal solution of flow balance for extrusion mold design obtained in step 3, establish a parametric geometric model of mold flow channel and free jet area in 3D modeling software; Import the parametric geometric model into meshing software for parametric mesh discretization to obtain a parametric mesh model; Based on the parametric mesh model, use the rheological model and its rheological parameters obtained in step 1 in CFD software to define material parameters, define the calculation domain and boundary conditions, and generate in-mold and out-mold flow finite element models; Perform CFD solution on the in-mold and out-mold flow finite element models to obtain the simulation value of the target cross-sectional size of the extruded product;

[0012] Step 5: Experimental verification of the in-mold and out-mold flow finite element models; Based on the CFD solution of the in-mold and out-mold flow finite element models in step 4, the simulation value of the cross-sectional target size of the extruded product is compared with the measured value of the actual extrusion molding experiment to verify the accuracy of the in-mold and out-mold flow finite element models in step 4; If the deviation between the simulation value and the measured value of all target sizes of the extruded product is less than the deviation criterion, it is deemed to be qualified and enters the sixth step; If the deviation is greater than the deviation criterion, return to the fourth step, encrypt the parameterized grid in the finite element model, or modify the boundary conditions or process parameters until the deviation is less than the deviation criterion;

[0013] Step 6: Geometric accuracy optimization design; Geometric accuracy optimization design is based on the CFD solution of the in-mold and out-mold flow finite element models verified experimentally in step 5, with the maximization of the geometric accuracy of the target size on the cross section of the extruded product (minimization of geometric deviation) as the optimization goal, and the optimization design method is used to obtain the optimal solution for the geometric accuracy of the extrusion die; the objective function of geometric accuracy optimization design is the geometric accuracy coefficient; the design variables are the flow channel geometric parameters of the extrusion die, and the value range is the flow balance design space in step 3; the constraint condition is that the simulation values ​​of all target sizes of the cross section of the extruded product should be within the tolerance range of the design target value.

[0014] As a further preferred embodiment, the rheometer in step one is preferably a rotational rheometer or a capillary rheometer; the data analysis software is preferably Origin or ANSYS Polymat; and the rheological model is preferably a Bird-Carreau model, a PTT model or a KBKZ model.

[0015] As a further preferred embodiment, the extruded product in step 2 should include the definition of basic dimensions and tolerances of cross-sectional geometry and target dimensions.

[0016] As a further preferred solution, the 3D modeling software in step 2 is preferably ANSYS Designmodeler and ANSYS Spaceclaim, the meshing software is preferably ANSYS Meshing, Gambit, and Hypermesh; the CFD software is preferably ANSYS Polyflow and STAR-CCM+; the calculation domain only includes the mold domain, and the boundary conditions include inlet boundary conditions, outlet boundary conditions, wall boundary conditions, and symmetry surface boundary conditions.

[0017] As a further preferred solution, the calculation domain in step 4 includes the mold domain and the free jet domain, and the boundary conditions include inlet boundary conditions, outlet boundary conditions, wall boundary conditions, symmetry surface boundary conditions, and free surface boundary conditions.

[0018] As a further preferred solution, the deviation criterion in step five is between 1% and 10%.

[0019] As a further preferred solution, the geometric accuracy coefficient in step 6 is constructed based on minimizing the actual deviation between the simulation value of the target size on the cross section of the extruded product and the design target value; the tolerance of the target size and the upper limit, lower limit and deviation band of the actual deviation are comprehensively considered, and its expected value is zero, which can be expressed as:

[0020]

[0021] Where i is the serial number of the target size, n is the number of target sizes, and A i is the weight, is the deviation band size of the actual deviation of the simulated value of the i-th target size, is the tolerance of the i-th target dimension; is the upper limit of the actual deviation of the simulated value of the i-th target size, is the upper deviation of the i-th target size; is the lower limit of the actual deviation of the simulated value of the i-th target size, is the lower deviation of the i-th target dimension. If the upper or lower deviation of the target dimension is zero, it needs to be converted to a symmetric tolerance.

[0022] As a further preferred solution, the design variables for optimization design in step six include geometric parameters of the inlet cross section of the preforming section, and the value range thereof is the flow balance design space described in step four; the design variables also include geometric parameters of the cross section of the forming section.

[0023] As a further preferred solution, in step 6, the constraints of the geometric accuracy optimization design are set as follows:

[0024] (1) The deviation band of the actual deviation of the simulated value of the i-th target size should be smaller than the tolerance of the target size, that is,

[0025] (2) The upper limit of the actual deviation of the simulated value of the i-th target size should be between the upper and lower deviations of the target size, that is,

[0026] (3) The lower limit of the actual deviation of the simulated value of the i-th target size should be between the upper and lower deviations of the target size, that is,

[0027] As a further preferred solution, the weight of the target size in the geometric accuracy coefficient represents the importance of the target size among all sizes; the larger the weight, the higher the priority of the target size should be in the optimization design process.

[0028] As a further preferred solution, the optimization design methods in step three and step six are selected as response surface optimization method, gradient optimization method, and multi-objective optimization design method.

[0029] In summary, the present invention fully combines the high efficiency of the flow balance optimization design method and the high precision of the geometric accuracy optimization design method. On the basis of achieving the flow balance at the die outlet, it significantly improves the geometric accuracy of the extruded product and realizes the unification of the optimization design method and the traditional trial and error design idea.

[0030] The invention is suitable for occasions such as precision extrusion and micro extrusion molding, which require high extrusion molding accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 Optimize the design process of the rubber and plastic extrusion die of the present invention;

[0032] Figure 2 is the cross-sectional geometry of the rubber and plastic extrusion product;

[0033] Figure 3 Definition of the geometric model and boundary conditions of the mold runner;

[0034] Figure 4 It is the finite element model of in-mold flow;

[0035] Figure 5 Definition of design variables at the entrance of the preforming section;

[0036] Figure 6 Velocity distribution at the die exit before and after optimization for flow balance;

[0037] Figure 7 Definition of the geometric model and boundary conditions inside and outside the mold;

[0038] Figure 8 Finite element model for in-mold and out-mold flow;

[0039] Fig. 9 Definition of actual deviation of simulated value of target size of extruded product;

[0040] Fig.10 Extrusion deformation for the optimal solution of geometric accuracy. DETAILED DESCRIPTION

[0041] The present invention is further described below in conjunction with the accompanying drawings and specific embodiments, but the protection scope of the present invention is not limited thereto.

[0042] The present invention mainly optimizes the design of an extrusion die for a rubber and plastic extrusion product. The design process is as follows: Figure 1 shown.

[0043] The cross-sectional geometry of rubber and plastic extrusion products, such as Figure 2 The coordinate values ​​of the points on the cross section of the extruded product (represented by code P) are shown in Table 1. The basic dimensions (length dimension represented by code D, thickness dimension represented by code T) and tolerances of the target dimensions on the cross section of the extruded product are shown in Table 2. The tolerances of the target dimensions on the cross section of the extruded product are determined according to the German standard DIN 16941-2012 (General dimensional and positional tolerances for thermoplastic extruded profiles).

[0044] Table 1 Coordinate values ​​of points on the cross section of extruded products (unit: mm)

[0045]

[0046] Table 2 Basic dimensions and tolerances of target dimensions (unit: mm)

[0047]

[0048] Table 3 Parameters of the Bird-Carreau model

[0049]

[0050] The method for optimizing the flow channel of a rubber and plastic extrusion die according to the present invention comprises the following steps:

[0051] Step 1: Determination of the rheological model of rubber and plastic materials and its parameter fitting. The rheological experimental data of rubber and plastic materials were obtained by testing with the HR10DISCOVERY hybrid rheometer. The rheological experimental data were fitted with the least squares regression method using ANSYS Polymat software, and the rheological model with the largest fitting determination coefficient was found to be the pure viscous Bird-Carreau model. The parameters of the Bird-Carreau model are shown in Table 3.

[0052] Step 2: Establishment of the finite element model of in-mold flow. Figure 2 The cross-sectional geometry of the extruded product shown in Figure 1 was used to establish a parametric geometric model of the extrusion die flow channel in ANSYS DesignModeler. Figure 3 As shown. The extrusion die flow channel usually consists of a machine neck (inlet section), a transition section, a preforming section and a forming section. For simplicity, the influence of the upstream of the preforming section is ignored here, and the extrusion die flow channel only includes the preforming section and the forming section. The forming section is also called a straight section, and its inlet and outlet cross-sections are geometrically consistent. The total length of the die flow channel is 8 mm, of which the initial length of the preforming section (subdomain 1, SD1) is 6 mm, and the initial length of the forming section (subdomain 2, SD2) is 2 mm.

[0053] The parametric geometry model of the mold runner is imported into ANSYS Meshing for parametric mesh discretization to obtain a parametric mesh model, such as Figure 4 Based on the parameterized mesh model, the Bird-Carreau model shown in Table 3 is used in the CFD software to define the material parameters and define Figure 3 The calculation domain and boundary conditions shown are used to generate the in-mold flow finite element model;

[0054] The boundary set of the finite element model includes the inlet boundary (BS1), the outlet boundary (BS2), the symmetry surface boundary (BS3), and the no-slip wall boundary (BS4).

[0055] The boundary conditions are defined as follows:

[0056] 1) Inlet boundary: constant normal force is applied, and the inlet flow rate is 3000mm 3 / s;

[0057] 2) Exit boundary: There is no traction at the exit, that is, the normal force and tangential force at the exit are both zero;

[0058] 3) Symmetry plane boundary: the normal velocity on the symmetry plane is zero and the surface force (tangential force) is zero;

[0059] 5) No-slip wall boundary: The normal velocity and tangential velocity of the fluid at the wall are both zero.

[0060] The CFD solution of the in-mold flow finite element model can obtain the velocity distribution at the die outlet of the extrusion die, the pressure loss of the extrusion die (die pressure drop) and the residence time of the polymer melt in the die;

[0061] Step three: flow balance optimization design; the extrusion die optimization design with flow balance as the goal is based on the CFD solution of the in-mold flow finite element model in step two, and the geometric parameters of the mold flow channel are modified to obtain a uniform velocity distribution at the outlet of the extrusion die. The objective function of the flow balance optimization design is the flow balance coefficient, which is used to evaluate the uniformity of the flow at the outlet of the die; the design variables are the geometric parameters of the parametric geometric model of the extrusion die flow channel described in step two, which are the geometric parameters of the inlet cross-section of the molding section of the extrusion die, and the length of the molding section and pre-molding section; no constraints are imposed; with flow balance as the optimization goal, the optimization design method is used to obtain the optimal solution for flow balance in the design of the extrusion die; the flow balance design space is constructed with the optimal solution for flow balance, that is, the range of design variable values ​​with good flow balance;

[0062] The objective function of the flow balance optimization design, i.e., the flow balance coefficient, is used to evaluate the uniformity of the flow at the die outlet. It is defined here as the variance of the normal velocity at the die outlet relative to the average velocity, as shown in Formula 1. Ideally, if a uniform velocity distribution is obtained at the die outlet, the value of the flow balance coefficient should be zero.

[0063]

[0064] Where υ is the flow velocity at the mold outlet, Q is the volume flow rate at the mold outlet, n is the direction along the outer normal at the mold outlet, and S is the cross-sectional area at the mold outlet.

[0065] The design variables for flow balance optimization design include the geometric parameters of the inlet cross section of the preforming section (SD1), the length of the preforming section (SD1), and the length of the forming section (SD2), such as Figure 3 shown.

[0066] By modifying the geometry of the entrance section of the preform section, a low-velocity area (thin-wall area, such as Figure 2 The feeding of the inlet of T1, T3, T4) is reduced, and the high-speed area (thick wall area, such as Figure 2 The feed of the inlet (T8, T9) in the middle is used to achieve diversion and flow control, so that each area of ​​the die outlet has the same average velocity. The length of the preforming section and the forming section is also modified, but the overall length of the die remains unchanged. During the optimization design process, the outlet cross-section of the extrusion die forming section remains unchanged.

[0067] The modification of the inlet cross section of the preforming section of the extrusion die is achieved by modifying the size of the inlet geometry to drive the displacement of points and lines to achieve the opening and closing of the area, such as Figure 5As shown. The positions of the dotted lines (E1, E2, E3, E4, E5) and points (A, B) are determined by the optimization solver, the positions of the thick solid line (E6) and point (C) are fixed, and the shape and position of the dotted line adapt to the movement of the adjacent lines or points. (In order to adapt to the changes in geometric parameters during the optimization design process, all arcs in the cross-sectional geometry are defined as 1 / 4 ellipse). The geometry of the preform section outlet is consistent with the geometry of the die forming section (i.e., the geometry of the extruded product). The design variables and their value ranges are described in Table 4:

[0068] Table 4 Design variables and their value ranges (unit: mm)

[0069]

[0070]

[0071] DV3, DV4, DV7, DV8, DV11 (dimensionless) are continuous independent variables, DV5 and DV10 are constants, and other variables are defined as follows: DV1 = DV10*DV11, DV2 = DV10*(DV11-1). In order to reduce the number of design variables, it is reasonable to assume that point A and arc E2 move synchronously, and straight lines E4 and E5 move synchronously toward the center line, that is, DV6 = DV4-0.3, DV9 = 51-DV8.

[0072] With the goal of flow balance, the response surface method is used to optimize the geometric variables of the extrusion die flow channel. It is necessary to complete the three steps of experimental design, response surface construction and response surface optimization in sequence. In the experimental design stage, since the calculation domain does not contain free surfaces, the solution speed is fast, and the solution time is about 3 minutes. Therefore, the Latin hypercube sampling method is used here, and the number of experimental samples is 200; in the response surface construction stage, the Kriging genetic algorithm is used here; in the response surface optimization stage, the continuous quadratic programming method (NLPQL) algorithm is used. The convergence criterion of the optimization design is 1e-6.

[0073] Table 5 Design variables and objective function (initial values ​​and optimal values)

[0074]

[0075] From the results of the flow balance optimization design based on the response surface method, as shown in Table 4, the flow balance optimization design increases the inlet wall thickness (DV3, DV4) of the thin-walled area (T1, T3, T4) and reduces the inlet wall thickness (DV7, DV8) of the thick-walled area (T8, T9), forcing the fluid to flow to the thin-walled area, so that the flow velocity of each area at the mold outlet tends to be consistent. The flow balance coefficient at the mold outlet is reduced from the initial 143054 to 34145.2, a decrease of 76.1%.

[0076] Compared with the initial design, the flow uniformity at the die exit of the optimized extrusion die has been significantly improved, such as Figure 6 As shown. Before optimization (OF = 143054), the maximum speeds of each area (T1, T3, T8, T9) at the mold outlet were 54.5 mm / s, 8.5 mm / s, 88.1 mm / s, and 231.1 mm / s, respectively, and the average speed at the outlet was 72.4 mm / s, showing a significant flow imbalance. After optimization (OF = 34145.2), the maximum speeds of each area (T1, T3, T8, T9) at the mold outlet were 99.0 mm / s, 28.1 mm / s, 92.0 mm / s, and 128.0 mm / s, respectively, and the average speed at the outlet was 72.0 mm / s. Except for the T3 area, the flow balance at the outlet was significantly improved.

[0077] Through the flow balance optimization design based on the response surface method, the range of the design variables is further narrowed, thereby limiting the design space to the flow balance design space, that is, the area with good flow balance. The flow balance design space is constructed with the optimal value 1 shown in Table 5, and the value interval size of the design variables DV3, DV4, DV7, and DV8 is 0.1mm. The design variable DV11 is the ratio of the molding section length to the total length of the mold (8mm), so the value interval size of the variable is 0.01, and the value interval size of the molding section length is 0.08mm. The design variables and their value ranges are shown in Table 6.

[0078] Table 6 Design variables and their value ranges in flow balance design space (unit: mm)

[0079]

[0080] Step 4: Establishment of in-mold and out-mold flow finite element models. Figure 2 The cross-sectional geometry of the extruded product shown in Table 5 and the values ​​of the design variables in the optimal solution of flow balance obtained were used to establish the parametric geometric model of the die flow channel and free jet area in ANSYS DesignModeler, as shown in Figure 7 As shown. The total length of the mold runner is 8mm, of which the length of the preforming section (subdomain 1, SD1) is 6.975mm, and the initial length of the forming section (subdomain 2, SD2) is 1.025mm. The length of the free jet section (subdomain 3, SD3) is 20mm. The junction of subdomain 1 and subdomain 2 is defined as I1-2, and the junction of subdomain 2 and subdomain 3 is defined as I2-3, which is the interface between the mold runner area and the free jet area, also known as the die lip.

[0081] Import the parametric geometry model into ANSYS Meshing software, perform parametric mesh discretization on the geometry model, and obtain a parametric mesh model, such as Figure 8 shown.

[0082] The Bird-Carreau model shown in Table 3 is used in the CFD software to define the material parameters and define Figure 7 The calculation domain and boundary conditions shown are used to generate the finite element model of the in-mold and out-mold flows required for Polyflow simulation analysis;

[0083] The boundary set of the finite element model includes the inlet boundary (BS1), the outlet boundary (BS2), the symmetry surface boundary (BS3), the free surface boundary (BS4), and the fixed wall boundary (BS5).

[0084] The boundary conditions are defined as follows:

[0085] 1) Inlet boundary: A constant normal force is applied at the inlet, and the inlet flow rate is 3000mm 3 / s;

[0086] 2) Exit boundary: There is no traction at the exit of the free jet section, that is, the normal force and tangential force at the exit are both zero;

[0087] 3) Symmetry plane boundary: the normal velocity on the symmetry plane is zero and the surface force (tangential force) is zero;

[0088] 4) Free surface boundary: The position of the free surface is unknown (the inlet is I2-3, the outlet is BS2, and the windward term is added to the equation of motion);

[0089] 5) Wall boundary: The wall no-slip assumption is adopted, that is, the normal velocity and tangential velocity of the fluid at the wall are both zero.

[0090] Step 5: Experimental verification of the in-mold and out-mold flow finite element model; Using ANSYS Polyflow to perform CFD solution on the in-mold and out-mold flow finite element model can obtain the simulation value of the target cross-sectional dimensions of the extruded product; According to the target dimensions shown in Table 2, the simulation value of the cross-sectional target dimensions of the extruded product is compared with the measured value of the actual extrusion molding experiment to verify the accuracy of the in-mold and out-mold flow finite element model in step 4. If the deviation between the simulation value and the measured value of all target dimensions shown in Table 2 is within 5%, it is deemed qualified and enters the sixth step. On the contrary, if the deviation is greater than 5%, return to the fourth step, encrypt the parameterized grid in the finite element model, or modify the boundary conditions or process parameters until the deviation is less than 5%.

[0091] Step 6: Geometric precision optimization design; Geometric precision optimization design is based on the CFD solution of the in-mold and out-mold flow finite element model verified by the experiment in step 5, with the maximization of the geometric precision of the target size on the cross section of the extruded product (minimization of geometric deviation) as the optimization goal, and the optimization design method is used to obtain the optimal solution for the geometric precision of the extrusion die. The objective function of the geometric precision optimization design is the geometric precision coefficient; the design variables are the flow channel geometric parameters of the extrusion die, including the geometric parameters of the inlet section of the preforming section and the geometric parameters of the forming section, and the value range is the flow balance range; the constraint condition is that the simulation value of the cross-sectional target size of the extruded product should be within the tolerance range of the design target value.

[0092] The actual deviation of the simulated value of the target size on the cross section of the extruded product is used to characterize the differences in the extrusion swell behavior in different directions, such as Fig. 9 As shown. The upper limit of actual deviation indicates the maximum deviation of actual dimension, the lower limit of actual deviation indicates the minimum deviation of actual dimension, and the size of deviation band is the difference between the upper limit and the lower limit. For the distance dimension between two straight lines, the smaller the deviation band, the higher the measured geometric parallelism. For the distance dimension or positioning dimension between two points, there is no deviation band for actual deviation.

[0093] The geometric accuracy coefficient is constructed based on minimizing the actual deviation of the simulated value of the target size on the cross section of the extruded product, taking into account the tolerance of the target size and the upper and lower limits and deviation band of the actual deviation. Its expected value is zero and can be expressed as:

[0094]

[0095] Where i is the serial number of the target size, n is the number of target sizes, and A i is the weight, which represents the importance of the target size among all the sizes. The larger the weight, the higher the priority of the target size should be in the optimization design process. is the deviation band size of the actual deviation of the simulated value of the i-th target size, is the tolerance of the i-th target dimension; is the upper limit of the actual deviation of the simulated value of the i-th target size, is the upper deviation of the i-th target size; is the lower limit of the actual deviation of the simulated value of the i-th target size, is the lower deviation of the i-th target size. In practical applications, if the upper or lower deviation of the target size is zero, it needs to be converted to a symmetric tolerance.

[0096] From formula (2), it can be seen that the geometric accuracy coefficient includes three items, and the divisors are the tolerance, upper deviation and lower deviation of the target size, which are given by the initial design and reflect the molding accuracy requirements of the extruded product. The smaller its value, the higher the molding accuracy requirements, and the more sensitive the response of the geometric accuracy coefficient.

[0097] The first term of the geometric accuracy coefficient is the ratio of the deviation band size of the actual deviation of the target size simulation value to the tolerance. If the deviation band size of the actual deviation is zero, that is, Then the upper and lower limits of the actual deviation are equal, that is like Fig. 9 The actual deviation is shown as 2 and 3. At this time, the actual deviation is not zero, but the first item of the geometric accuracy coefficient is zero. At this time, the second and third items of the geometric accuracy coefficient are not zero, which can still reflect the molding accuracy of the extruded product.

[0098] In the target size, the distance between two parallel lines and the distance from a point to a line, the geometric accuracy coefficient can include all items or the last two items, but it needs to be consistent throughout the optimization design process. There is no deviation band for the actual deviation of the distance between two points and the positioning size, so the geometric accuracy coefficient only includes the first item. The weights of the target size of the extruded product are shown in Table 7.

[0099] Table 7 Weights of target dimensions of extruded products (unit: mm)

[0100]

[0101] The design variables of the optimization design are basically the same as the flow balance optimization design space, but in order to obtain higher geometric accuracy, the D2 dimension on the cross section of the extrusion die molding section is added as the design variable DV12.

[0102] Table 8 Design variables and value ranges for geometric accuracy optimization design

[0103]

[0104]

[0105] In order to ensure that all target dimensions meet the design requirements, the constraints of the geometric accuracy optimization design are set as follows:

[0106] 1. The deviation band of the actual deviation of the simulated value of the i-th target size should be smaller than the tolerance of the target size, that is,

[0107] 2. The upper limit of the actual deviation of the simulated value of the i-th target size should be between the upper and lower deviations of the target size, that is,

[0108] 3. The lower limit of the actual deviation of the simulated value of the i-th target size should be between the upper and lower deviations of the target size, that is,

[0109] The basic process of dimensional accuracy optimization design based on response surface method is similar to that of flow balance optimization design, which requires the completion of experimental design, response surface construction and response surface optimization in sequence. In the experimental design stage, since the calculation domain contains free surfaces, the solution speed is slow, about 10 minutes when the die outlet flow balance is good, so the Latin hypercube sampling method is used here, and the number of experimental samples is 100; in the construction stage of the response surface, the Kriging genetic algorithm is used here; in the response surface optimization stage, the continuous quadratic programming method (NLPQL) algorithm is used. The convergence criterion of the optimization design is 1e-6.

[0110] From the results of the geometric precision optimization design based on the response surface method, as shown in Table 9, the geometric precision coefficient of the optimal solution of the initial flow balance is 18258. The optimal value obtained by the geometric precision optimization design method, that is, the optimal solution of geometric precision, has small anisotropy of extrusion swell and extrusion deformation, and the geometric precision coefficient is 62.929, which is 99.7% lower than the optimal solution of the flow balance optimization design.

[0111] Table 9 Design variables and objective function (initial values ​​and optimal values)

[0112]

[0113]

[0114] The dimensional accuracy optimization design method significantly reduces the extrusion deformation, and the cross-sectional profile of the extruded product is basically consistent with the expectation, such as Fig.10 In the figure, the thick solid line with a square frame represents the outlet of the extrusion die, and the thin solid line with dots represents the outlet of the extruded product.

[0115] The tolerance and actual deviation of the target size on the extruded product obtained by the geometric precision optimization design are shown in Table 10. The * in the table indicates that the target size is the distance size or positioning size between two points, and the geometric precision coefficient (Formula 2) only includes the first item, that is, the actual deviation of the target size does not exist. Fig. 9 The actual upper and lower deviation limits are stated.

[0116] Table 10 Tolerance and actual deviation of target size (unit: mm)

[0117]

[0118] It can be seen from Table 10 that the accuracy of all target dimensions has been greatly improved. At the same time, since the weight of the wall thickness dimension T3 is increased in the geometric accuracy optimization design objective function (geometric accuracy coefficient), and the design variable increases the molding section size, the accuracy of the wall thickness target dimension T3 is improved most significantly, which also shows that the weight of the target dimension in the geometric accuracy coefficient represents the priority of the target dimension.

[0119] The preferred embodiments of the present invention are described in detail above; however, the present invention is not limited to the specific details in the above embodiments. Within the technical concept of the present invention, various equivalent transformations can be made to the technical solutions of the present invention, and these equivalent transformations all belong to the protection scope of the present invention.

[0120] The specific implementation methods described above further illustrate the objectives, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above description is only a specific implementation method of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for optimizing the design of a rubber and plastic extrusion die, characterized in that: The following steps are involved: Step 1: Determination of the rheological model of rubber and plastic materials and its parameter fitting; Use a rheometer to test and obtain the rheological experimental data of the rubber and plastic materials, use data analysis software to perform least squares regression fitting on the rheological experimental data, and find the rheological model and its rheological parameters with the largest fitting determination coefficient; Step 2: Establishment of the in-mold flow finite element model; according to the cross-sectional geometry and target size of the extruded product, establish the parametric geometric model of the extrusion mold flow channel in the 3D modeling software; import the parametric geometric model of the mold flow channel into the meshing software for parametric mesh discretization to obtain a parametric mesh model; based on the parametric mesh model, use the rheological model and its rheological parameters obtained in step 1 in the CFD software to define material parameters, define the calculation domain and boundary conditions, and generate the in-mold flow finite element model; perform CFD solution on the in-mold flow finite element model to obtain the velocity distribution at the extrusion die outlet, the pressure loss of the extrusion die, and the residence time of the polymer melt in the die; Step 3: Flow balance optimization design; The extrusion die optimization design with flow balance as the goal is based on the CFD solution of the in-die flow finite element model in step 2, and the geometric parameters of the die flow channel are modified to obtain a uniform velocity distribution at the die outlet of the extrusion die; the objective function of the flow balance optimization design is the flow balance coefficient, which is used to evaluate the uniformity of the flow at the die outlet; the design variables are the geometric parameters of the parametric geometric model of the extrusion die flow channel, and further the geometric parameters of the inlet section of the extrusion die molding section, the molding section and the length of the pre-molding section; the constraint condition is the pressure loss of the extrusion die, or the residence time of the melt in the extrusion die, or no constraint condition is imposed; Taking flow balance as the optimization goal, the optimal solution of flow balance in extrusion die design is obtained by using the optimization design method. The flow balance design space is constructed with the optimal solution of flow balance, that is, the range of design variable values ​​with good flow balance; Step 4: Establishment of in-mold and out-mold flow finite element models; Based on the optimal solution of flow balance for extrusion die design obtained in step 3, establish a parametric geometric model of the mold flow channel and free jet area in the 3D modeling software; Import the parametric geometric model into the meshing software for parametric mesh discretization to obtain a parametric mesh model; Based on the parametric mesh model, use the rheological model and its rheological parameters obtained in step 1 in the CFD software to define material parameters, define the calculation domain and boundary conditions, and generate in-mold and out-mold flow finite element models; Perform CFD solution on the in-mold and out-mold flow finite element models to obtain the simulation value of the target cross-sectional size of the extruded product; Step 5: Experimental verification of the in-mold and out-mold flow finite element models; Based on the CFD solution of the in-mold and out-mold flow finite element models in step 4, the simulation value of the cross-sectional target size of the extruded product is compared with the measured value of the actual extrusion molding experiment to verify the accuracy of the in-mold and out-mold flow finite element models in step 4; If the deviation between the simulated value and the measured value of all target dimensions of the extruded product is less than the deviation criterion, it is considered qualified and proceeds to the sixth step; If the deviation is greater than the deviation criterion, return to step 4 to encrypt the parameterized mesh in the finite element model, or modify the boundary conditions or process parameters until the deviation is less than the deviation criterion; Step 6: Geometric precision optimization design; Geometric precision optimization design is based on the CFD solution of the in-mold and out-mold flow finite element models verified experimentally in step 5, with maximizing the geometric precision of the target size on the cross section of the extruded product as the optimization goal, and using the optimization design method to obtain the optimal solution for the geometric precision of the extrusion die; the objective function of geometric precision optimization design is the geometric precision coefficient, which is constructed based on minimizing the actual deviation between the simulation value of the target size on the cross section of the extruded product and the design target value; the design variables are the flow channel geometric parameters of the extrusion die, and the value range is the flow balance design space in step 3; The constraint condition is that the simulation values ​​of all target dimensions of the cross section of the extruded product should be within the tolerance range of the design target value.

2. The method for optimizing the design of a rubber and plastic extrusion die according to claim 1, characterized in that: The rheometer in the step 1 is a rotational rheometer or a capillary rheometer; the data analysis software is Origin or ANSYS Polymat; and the rheological model is a Bird-Carr eau model, a PTT model, or a KBKZ model.

3. The method for optimizing the design of a rubber and plastic extrusion die according to claim 1, characterized in that: The extruded product in step 2 should include the definition of the basic dimensions and tolerances of the cross-sectional geometry and target dimensions.

4. The method for optimizing the design of a rubber and plastic extrusion die according to claim 1, characterized in that: The 3D modeling software in the step 2 is ANSYS Design modeler and ANSYS Spaceclaim, the meshing software is ANSYS Meshing, Gambit, and Hypermesh; the CFD software is ANSYS Polyflow and STAR-CCM+; the calculation domain in step 2 only includes the mold domain, and the boundary conditions include inlet boundary conditions, outlet boundary conditions, wall boundary conditions, and symmetry surface boundary conditions.

5. The method for optimizing the design of a rubber and plastic extrusion die according to claim 1, characterized in that: The calculation domain in step 4 includes the mold domain and the free jet domain, and the boundary conditions include inlet boundary conditions, outlet boundary conditions, wall boundary conditions, symmetry surface boundary conditions, and free surface boundary conditions.

6. The method for optimizing the design of a rubber and plastic extrusion die according to claim 1, characterized in that: The deviation criterion in step 5 is between 1% and 10%.

7. The method for optimizing the design of a rubber and plastic extrusion die according to claim 1, characterized in that: In step 6, the tolerance of the target size and the upper limit, lower limit and deviation band of the actual deviation are comprehensively considered, and the expected value is zero. The geometric accuracy coefficient is expressed as: Where i is the serial number of the target size, n is the number of target sizes, and A i is the weight, is the deviation band size of the actual deviation of the simulated value of the i-th target size, is the tolerance of the i-th target dimension; is the upper limit of the actual deviation of the simulated value of the i-th target size, is the upper deviation of the i-th target size; is the lower limit of the actual deviation of the simulated value of the i-th target size, is the lower deviation of the i-th target dimension. If the upper or lower deviation of the target dimension is zero, it needs to be converted to a symmetric tolerance.

8. The method for optimizing the design of a rubber and plastic extrusion die according to claim 1, characterized in that: The design variables optimized in step six include geometric parameters of the inlet cross section of the preforming section, and the value range thereof is the flow balance design space described in step four; the design variables also include geometric parameters of the cross section of the forming section.

9. The method for optimizing the design of a rubber and plastic extrusion die according to claim 1, characterized in that: In step 6, the constraints for geometric accuracy optimization design are set as follows: (1) The deviation band of the actual deviation of the simulated value of the i-th target size should be smaller than the tolerance of the target size, that is, is the deviation band size of the actual deviation of the simulated value of the i-th target size, is the tolerance of the i-th target dimension; (2) The upper limit of the actual deviation of the simulated value of the i-th target size should be between the upper and lower deviations of the target size, that is, is the lower deviation of the i-th target size, is the upper limit of the actual deviation of the simulated value of the i-th target size, is the upper deviation of the i-th target size; (3) The lower limit of the actual deviation of the simulated value of the i-th target size should be between the upper and lower deviations of the target size, that is, is the lower limit of the actual deviation of the simulated value of the i-th target size.

10. The method for optimizing the design of a rubber and plastic extrusion die according to claim 7, characterized in that: The weight of the target size of the geometric accuracy coefficient represents the importance of the target size among all sizes; the larger the weight, the higher the priority of the target size should be in the optimization design process.

11. The method for optimizing the design of a rubber and plastic extrusion die according to claim 1, characterized in that: The optimization design methods in step three and step six are selected from response surface optimization method, gradient optimization method and multi-objective optimization design method.

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