Dynamic simulation method for crystallization behavior in polymer extrusion processes

Abstract

The application discloses a dynamic simulation method for crystallization behavior of a polymer extrusion process, and particularly relates to the technical field of polymer extrusion molding simulation, wherein viscosity-temperature parameters, crystallization kinetics parameters, pressure relaxation parameters, phase change latent heat parameters and extrusion process parameters of a polymer to be simulated are acquired, a transient flow heat transfer model from a die outlet to a cooling and shaping section is established, a velocity field, a pressure field and a temperature field are obtained, Lagrange material points are set along an extrusion path, temperature variation, shear rate, pressure drop rate and residence time are extracted, thermal mechanical history data are formed, a molecular orientation parameter is calculated through a conformation tensor to correct a nucleation rate, the amount of crystallinity variation is calculated according to the corrected nucleation rate, phase change latent heat is fed back to the temperature field, a crystallinity distribution is obtained, a crystallization hysteresis region is identified and process adjustment parameters are output, and the method improves the prediction accuracy of uneven crystallization and post-crystallization risks of extruded products.

Description

Technical Field

[0001] This invention relates to the field of polymer extrusion molding simulation technology, and more specifically to a dynamic simulation method for the crystallization behavior of polymer extrusion processes. Background Technology

[0002] Polymer extrusion molding is widely used in the continuous production of films, pipes, profiles, and medical microtubules. For semi-crystalline polymers, after the melt enters the cooling and shaping section from the die outlet, it is simultaneously subjected to the combined effects of a sudden drop in temperature, pressure release, traction stretching, and residual shear orientation. Its crystallization behavior is not simply determined by the cooling rate, but is closely related to the thermomechanical history of the melt along the extrusion path.

[0003] In actual production, especially during high-speed extrusion of thin-walled polypropylene microtubes or transparent polyolefin sheets, the rapid release of pressure near the die exit can cause non-uniform relaxation of the melt's internal orientation. The outer layer material crystallizes rapidly due to preferential contact with the cooling medium, while the inner layer material may experience delayed crystallization due to the accumulation of latent heat of phase change and residual orientation memory. This delayed crystallization region continues to increase in crystallinity even after the product leaves the cooling and shaping section, easily leading to inconsistent local shrinkage and defects such as microtube inner diameter drift, haze on the sheet surface, or later warping. These defects usually do not appear immediately at the initial stage of extrusion but rather after placement, sterilization, or secondary heat treatment, making it difficult to trace the process cause in a timely manner. Summary of the Invention

[0004] The purpose of this invention is to provide a dynamic simulation method for the crystallization behavior of polymer extrusion processes, in order to address the shortcomings of the prior art.

[0005] To achieve the above objectives, the present invention provides the following technical solution: a dynamic simulation method for the crystallization behavior of polymer extrusion processes, comprising: The viscosity-temperature parameters, crystallization kinetic parameters, pressure relaxation parameters, latent heat of phase change parameters, and extrusion process parameters of the polymer to be simulated are obtained to obtain a simulation parameter set. A transient flow and heat transfer model from the die outlet to the cooling and shaping section is established using the simulation parameter set, and the velocity field, pressure field, and temperature field on the extrusion path are solved. Multiple Lagrange material points are set along the extrusion path, and the temperature change, shear rate, pressure drop rate and residence time of each Lagrange material point are extracted based on the velocity field, pressure field and temperature field to form thermomechanical history data. Molecular orientation parameters are calculated through the thermomechanical history data, and the molecular orientation parameters are introduced as correction terms into the nucleation rate equation to obtain the corrected nucleation rate. The change in crystallinity is calculated based on the corrected nucleation rate, and the corresponding latent heat of phase change is fed back to the temperature field to obtain the corrected temperature field. The crystallinity distribution is updated based on the corrected temperature field. Regions where the crystallinity is below the threshold after cooling but still has a crystallinity increase are identified as crystallization lag regions, and corresponding process adjustment parameters are output.

[0006] Preferably, a transient flow and heat transfer model is established from the die outlet to the cooling and shaping section using a simulation parameter set, including: Using the die exit section as the calculation inlet and the cooling and shaping section exit section as the calculation outlet, a calculation domain extending along the extrusion direction is established; the calculation domain is divided into an air gap region and a cooling and shaping section region. The average inlet velocity is calculated based on the volumetric flow rate and the cross-sectional area of ​​the die outlet. The average inlet velocity and the melt temperature at the die outlet are used as the inlet velocity and inlet temperature, respectively, and the ambient pressure is used as the outlet pressure. The initial pressure field is determined based on the initial pressure at the die outlet, the ambient pressure, the average inlet velocity, and the pressure relaxation time, so that the initial pressure decreases from the initial pressure at the die outlet to the ambient pressure along the extrusion direction.

[0007] Preferably, the thermomechanical historical data includes: Multiple Lagrange material points are set within the die exit section according to the geometric center of the section element; the position of each Lagrange material point is updated step by step according to the velocity field; at each time step, the temperature, pressure and velocity gradient tensors are extracted from the velocity field, pressure field and temperature field according to the position of the Lagrange material point, and the shear rate is calculated according to the velocity gradient tensor.

[0008] Preferably, the formation of thermomechanical historical data also includes: The pressure drop rate is calculated based on the pressure difference between adjacent time steps at the same Lagrange material point; when the pressure increases or remains constant, the pressure drop rate is zero; the residence time is calculated based on the moment the Lagrange material point enters the die exit section and the current moment; the thermomechanical history data of the corresponding Lagrange material point is composed of the temperature change, shear rate, pressure drop rate, residence time, and velocity gradient tensor.

[0009] Preferably, molecular orientation parameters are calculated using thermomechanical history data, including: The initial conformation tensor of each Lagrange material point is set to a unit tensor; the conformation tensor is updated step by step according to the velocity gradient tensor, orientation relaxation time and pressure drop rate. The partial conformation tensor is calculated based on the updated conformation tensor, and the molecular orientation parameter is calculated based on the partial conformation tensor and the trace value of the conformation tensor; when the conformation tensor is a unity tensor, the molecular orientation parameter is zero.

[0010] Preferably, the molecular orientation parameter is introduced as a correction term into the nucleation rate equation to obtain a corrected nucleation rate, including: The supercooling of crystallization is calculated based on the temperature and equilibrium melting point of the Lagrange material point. When the supercooling of crystallization is greater than zero, the basic nucleation rate is calculated based on the pre-nucleation rate factor and the influence coefficient of nucleation temperature. When the supercooling of crystallization is less than or equal to zero, the basic nucleation rate is zero. The molecular orientation parameter is introduced as an exponential correction term into the basic nucleation rate to obtain the corrected nucleation rate of the corresponding Lagrange material point.

[0011] Preferably, the change in crystallinity is calculated based on the corrected nucleation rate, and the corresponding latent heat of phase transition is fed back to the temperature field to obtain the corrected temperature field, including: The effective crystallization rate constant is determined based on the modified nucleation rate, the reference nucleation rate, the crystal growth rate, and the reference crystal growth rate. The crystallinity change is calculated based on the effective crystallization rate constant, the upper limit of crystallinity, and the current crystallinity. The latent heat release of phase change is calculated based on the crystallinity change, and the latent heat release of phase change is allocated to the calculation unit where the Lagrange material point is located, and added to the energy conservation equation as a volume heat source term to resolve the temperature field of the current time step.

[0012] Preferably, obtaining the corrected temperature field includes: Within the same time step, first calculate the crystallinity change and volumetric heat source term based on the uncorrected temperature field, then solve the corrected temperature field based on the volumetric heat source term, and interpolate the corrected temperature field to each Lagrange material point. The iteration of the time step is stopped when the temperature difference between two adjacent iterations is not greater than the preset temperature difference and the difference in crystallinity change is not greater than the preset crystallinity difference.

[0013] Preferably, the region where the crystallinity is below the threshold after cooling but there is still an increase in crystallinity is defined as the crystallization hysteresis region, including: After all the Lagrange material points reach the outlet of the cooling and shaping section, the crystallinity of each Lagrange material point is mapped to the outlet section grid according to the outlet section coordinates to obtain the crystallinity distribution; the post-crystallization growth is calculated under the preset storage temperature and preset post-crystallization time; the region at the outlet where the crystallinity is lower than the post-cooling crystallinity threshold and the post-crystallization growth is greater than the post-crystallization growth threshold is determined as the crystallization lag region.

[0014] Preferably, the corresponding process adjustment parameters are output, including: calculating the ratio of the area of ​​the crystallization lag region to the total area of ​​the outlet cross section, and applying disturbances to the melt temperature at the die outlet, the traction speed and the cooling medium temperature respectively, and selecting the disturbance condition that reduces the ratio the most as the process adjustment parameter output.

[0015] The technical effects and advantages provided by the present invention in the above technical solution are as follows: This invention differs from existing technologies that estimate crystallization behavior solely based on steady-state temperature fields, average cooling rates, or single shear rates. Instead, it extracts the temperature changes, shear rates, pressure drop rates, and residence times from the die exit to the cooling and shaping section as a continuous thermomechanical history of the same material point. Furthermore, it transforms this thermomechanical history into molecular orientation parameters using a conformational tensor. Consequently, residual orientation caused by rapid pressure release at the die exit, asynchronous orientation relaxation, and orientation differences along the wall thickness direction can be incorporated into the nucleation rate calculation. This core technology directly solves the problem of existing simulation methods' inability to describe the coupling effect of pressure release, residual orientation, and induced nucleation after the melt leaves the die. It ensures that the nucleation rate is no longer solely determined by temperature but reflects the differentiated states of the outer, inner, and core layers along the actual extrusion path, thereby improving the accuracy of predicting the crystallization initiation location, crystal growth region, and uneven crystal distribution.

[0016] This invention, after calculating the change in crystallinity, feeds back the latent heat of phase change released during crystallization as a volumetric heat source term to the temperature field, and continues to update the crystallinity distribution based on the corrected temperature field. This differs from existing technologies that treat the temperature field as a fixed input and ignore the reverse impact of crystallization heat release on the local cooling process. This technique can reflect the true difference between rapid heat dissipation in the outer layer and limited heat dissipation in the inner layer of thin-walled tubes or sheets during the cooling and shaping process, avoiding misjudgment of the degree of crystallization completion due to underestimating the core layer temperature rise or cooling lag. Furthermore, this invention identifies the area at the outlet of the cooling and shaping section where the crystallinity is below the threshold and there is still crystal growth as the crystallization lag area. By perturbing the die outlet temperature, traction speed, and cooling medium temperature, process adjustment parameters are output, thereby directly solving the problem of secondary crystallization, inner diameter drift, warping, or haze after the product is offline, where it is difficult to trace the process cause, providing an executable basis for extrusion process optimization. Attached Figure Description

[0017] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in this invention. For those skilled in the art, other drawings can be obtained based on these drawings.

[0018] Figure 1 This is a flowchart of the method of the present invention.

[0019] Figure 2 This is a schematic diagram of the transient flow and heat transfer model of the polymer extrusion process of the present invention.

[0020] Figure 3 This is a schematic diagram illustrating the extraction of historical thermal mechanical data for Lagrange materials according to the present invention.

[0021] Figure 4This is a schematic diagram of the molecular orientation correction and crystallization dynamic feedback loop based on thermomechanical history of the present invention.

[0022] Figure 5 This is a schematic diagram illustrating the identification of the crystallization lag region and the adjustment of process parameters in this invention. Detailed Implementation

[0023] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0024] Existing polymer extrusion simulation methods are mostly based on steady-state temperature fields, average cooling rates, or empirical crystallization kinetic models. They typically only calculate the overall crystallinity or temperature distribution of the product, lacking continuous tracking of the velocity field, pressure field, temperature field, and material point thermomechanical history from the die exit to the cooling and shaping section. They also do not fully consider the molecular orientation differences caused by the pressure drop rate and the reverse influence of the latent heat of crystallization phase transformation on the local temperature field.

[0025] Therefore, existing methods are unable to accurately identify the hysteresis region where crystallization may continue after cooling, and cannot provide a reliable basis for adjusting the die temperature, traction speed and cooling temperature.

[0026] Example 1, please refer to Figure 1 , Figure 2 , Figure 3 , Figure 4 and Figure 5 As shown in this embodiment, the dynamic simulation method for the crystallization behavior of polymer extrusion processes includes: The viscosity-temperature parameters, crystallization kinetic parameters, pressure relaxation parameters, latent heat of phase change parameters, and extrusion process parameters of the polymer to be simulated are obtained to obtain a simulation parameter set. A transient flow and heat transfer model from the die outlet to the cooling and shaping section is established using the simulation parameter set, and the velocity field, pressure field, and temperature field on the extrusion path are solved.

[0027] In one embodiment, the viscosity-temperature parameters, crystallization kinetic parameters, pressure relaxation parameters, latent heat of phase change parameters, and extrusion process parameters of the polymer to be simulated are obtained, and these parameters are organized into a simulation parameter set according to parameter name, value, and unit. The viscosity-temperature parameters include a reference viscosity. Reference temperature Temperature sensitivity coefficient Characteristic Time and shear-thinning index The crystallization kinetic parameters include the equilibrium melting point. Nucleation rate coefficient Crystal growth rate coefficient and upper limit of crystallinity The pressure relaxation parameters include the pressure relaxation time. and pressure drop influence coefficient The latent heat of phase change parameters include the latent heat of crystallization per unit mass. And simultaneously obtain density Specific heat capacity and thermal conductivity As parameters for heat transfer calculation; the extrusion process parameters include the die outlet cross-sectional area. Volumetric flow rate , melt temperature at the die exit Initial pressure at the die outlet Environmental pressure Length of cooling and shaping section Air gap length air temperature Cooling medium temperature air gap heat transfer coefficient , heat transfer coefficient of the cooling and shaping section and traction speed .

[0028] Based on the simulation parameter set, a calculation inlet is established along the extrusion direction, with the die outlet section as the calculation inlet and the cooling and shaping section outlet section as the calculation outlet. An extended computational domain. The axial length of the computational domain is... ,in The area is an air gap. The area is the cooling and shaping section. Average inlet velocity. Calculate according to the following formula: In the formula, For volumetric flow rate, This represents the cross-sectional area of ​​the die exit. The inlet boundaries are set as a velocity inlet and a temperature inlet, with the inlet velocity taken as... Inlet temperature is taken The export boundary is set as a pressure export, and the export pressure is taken as the environmental pressure. Initial pressure at the die outlet It is not used as the inlet pressure boundary, but rather to determine the initial pressure field so that the velocity boundary and pressure boundary do not overlap.

[0029] The initial pressure field is assigned according to the following formula: In the formula, Indicates the initial time. The axial distance from the die outlet is Pressure at the location; Indicates environmental pressure; Indicates the initial pressure at the die outlet; Indicates the axial distance from the die exit; Indicates the average inlet velocity; Indicates the stress relaxation time; It is a natural constant. The exponential term. It is a dimensionless quantity. This indicates the axial characteristic length of the pressure release.

[0030] The transient flow heat transfer model includes the mass conservation equation, momentum conservation equation, and energy conservation equation. The mass conservation equation is: In the formula, It is a velocity vector. Let be the velocity divergence. The momentum conservation equation is: In the formula, Density; For time; For pressure; Let be the viscous stress tensor. The viscous stress tensor is: ;in, Viscosity; For temperature; Shear rate; Let be the strain rate tensor, and: The shear rate is calculated using the following formula: In the formula, This represents the double dot product of the strain rate tensor and itself.

[0031] viscosity Calculate according to the following formula: In the formula, Reference temperature The reference viscosity is below; This refers to the temperature sensitivity coefficient. Characteristic time; This is the shear-thinning index. From this formula, it can be seen that temperature... and shear rate All of them are used in viscosity calculations, and the resulting viscosity is used to solve the momentum conservation equation.

[0032] The energy conservation equation is: In the formula, Specific heat capacity; Where is the thermal conductivity. The heat transfer boundary on the outer surface is: In the formula, The direction is the normal direction of the outer surface; when hour, , ;when hour, , .

[0033] During the calculation, within each time step, the viscosity is first calculated based on the temperature and shear rate fields of the previous time step. Then, the velocity and pressure fields of the current time step are solved using the mass and momentum conservation equations. Finally, the velocity field of the current time step is substituted into the energy conservation equation to solve for the temperature field of the current time step. Time step size. satisfy: In the formula, To calculate the minimum cell side length within the computational domain. The relative residuals of velocity, pressure, and temperature within the current time step are all no greater than [value missing]. At this point, proceed to the next time step. After the calculation is completed, the velocity field, pressure field, and temperature field along the extrusion path are obtained. The velocity field is used to subsequently determine the positional changes of the Lagrange material points, the pressure field is used to calculate the pressure drop rate, and the temperature field is used to extract the temperature changes of each Lagrange material point and serve as input for subsequent calculations to correct the nucleation rate and crystallinity changes.

[0034] Multiple Lagrange material points are set along the extrusion path, and the temperature change, shear rate, pressure drop rate and residence time of each Lagrange material point are extracted based on the velocity field, pressure field and temperature field to form thermomechanical history data. Molecular orientation parameters are calculated through the thermomechanical history data, and the molecular orientation parameters are introduced as correction terms into the nucleation rate equation to obtain the corrected nucleation rate.

[0035] In one embodiment, after obtaining the velocity, pressure, and temperature fields along the extrusion path, multiple Lagrange material points are set within the die exit section. The die exit section is divided according to the aforementioned computational domain's cross-sectional mesh, with one Lagrange material point set at the geometric center of each cross-sectional element, for a total number of Lagrange material points. , No. The numbering of the Lagrange material points is as follows: ,in . No. The position of the Lagrange material point at the initial moment is: .

[0036] No. The position of each Lagrange material point is updated hourly according to the following formula: In the formula, Indicates the first The Lagrange material point at the th The position of each time step; This represents the velocity vector at that location; Indicates the time step; .when When located within a computational grid cell, velocity, pressure, and temperature are all obtained by interpolating the nodal values ​​using the shape function of that grid cell. When the... The axial coordinate of the Lagrange material point reaches the outlet position of the cooling and shaping section. When that happens, stop updating the location of the Lagrange material point.

[0037] At each time step, extract the first... Temperature of a Lagrange material point ,pressure Velocity gradient tensor and shear rate The velocity gradient tensor is: In the formula, Indicates the first The Lagrange material point at the th The velocity gradient tensor corresponding to each time step; The gradient of the velocity vector with respect to spatial coordinates is represented by the following formula: In the formula, Indicates the first The strain rate tensor corresponding to a Lagrangian material point; This represents the transpose of the velocity gradient tensor. The shear rate is calculated using the following formula: In the formula, Indicates the first The Lagrange material point at the th Shear rate at each time step; This represents the double dot product of the strain rate tensor and itself. The pressure drop rate is calculated using the following formula: In the formula, Indicates the first The Lagrange material point at the th Pressure drop rate at each time step; and These represent the pressure at two adjacent time steps. For the initial time step... ,Pick When the pressure increases or remains constant, the rate of pressure drop is taken as... .

[0038] No. The dwell time of a Lagrange material point is determined by the following formula: In the formula, Indicates the first The Lagrange material point at the th The dwell time of each time step; This indicates the moment when the Lagrange material point enters the die exit section. In this embodiment, each Lagrange material point enters the die exit section from the initial moment, therefore... .

[0039] This forms the first Historical thermomechanical data for Lagrange material points: In the formula, Indicates the first Historical thermomechanical data for a single Lagrange material point; , representing the temperature change between adjacent time steps; Indicates the first The time step number corresponding to when a Lagrange material point reaches the outlet of the cooling and shaping section.

[0040] The conformational tensor is calculated based on the aforementioned thermomechanical history data. The conformation tensor of each Lagrange material point at the initial moment is set as follows: In the formula, Represents the initial conformation tensor; Represents a unit tensor.

[0041] The construct tensor is updated hourly according to the following formula: In the formula, Indicates the first The Lagrange material point at the th The configuration tensor at each time step; Indicates the relaxation time of orientation; Indicates the pressure drop effect coefficient; Represents the unit vector in the extrusion direction; This represents the second-order directional tensor of the extrusion direction. The unit is ,make The unit is .

[0042] Orientation relaxation time is calculated using the following formula: In the formula, Indicates the relaxation time of the reference orientation; Indicates the temperature sensitivity coefficient; Indicates reference temperature; Indicates the first The Lagrange material point at the th Temperature at each time step.

[0043] Calculate the partial conformation tensor based on the updated conformation tensor: In the formula, Represents the partial conformation tensor; Represents the trace of the conformation tensor.

[0044] Molecular orientation parameters are calculated according to the following formula: In the formula, Indicates the first The Lagrange material point at the th Molecular orientation parameters at each time step, with values ​​ranging from [value range missing]. .when hour, .

[0045] The basic nucleation rate is calculated based on temperature. First, the degree of supercooling during crystallization is calculated using the following formula: In the formula, Indicates the first The Lagrange material point at the th Crystallization undercooling at each time step; Indicates the equilibrium melting point.

[0046] when At that time, the basic nucleation rate is calculated according to the following formula: ; when At that time, take: In the formula, Indicates the basic nucleation rate; Indicates the pre-nucleation rate factor; This represents the influence coefficient of nucleation temperature. and These are all parameters related to crystallization kinetics.

[0047] Introducing the molecular orientation parameter as a correction term into the nucleation rate equation yields the corrected nucleation rate: In the formula, Indicates the first The Lagrange material point at the th The corrected nucleation rate at each time step; This represents the influence coefficient of orientation nucleation. Therefore, temperature change, shear rate, pressure drop rate, and residence time are first converted into conformation tensors, then molecular orientation parameters are obtained from the conformation tensor invariants, and finally the basic nucleation rate is corrected using these molecular orientation parameters. The resulting corrected nucleation rate is used for subsequent calculations of crystallinity changes.

[0048] The change in crystallinity is calculated based on the corrected nucleation rate, and the corresponding latent heat of phase change is fed back to the temperature field to obtain the corrected temperature field. The crystallinity distribution is updated based on the corrected temperature field. Regions where the crystallinity is below the threshold after cooling but still has a crystallinity increase are identified as crystallization lag regions, and corresponding process adjustment parameters are output.

[0049] In one embodiment, the extrusion cooling process of a polypropylene thin-walled pipe is used as an example. The thin-walled pipe enters the air gap from the die outlet and then enters the water-cooling shaping section. The aforementioned steps have already obtained the corrected nucleation rate, temperature, pressure, speed, and residence time of each Lagrange point on the extrusion path. This step calculates the crystallinity change based on the above data and corrects the latent heat of phase transition in the temperature field.

[0050] Specifically, no. The initial crystallinity of the Lagrange material point upon entering the die exit is zero. When the temperature at a time step is below the equilibrium melting point, the material point is deemed to have the conditions for crystallization; when the temperature is not lower than the equilibrium melting point, the crystallinity increase is not calculated for that time step. For material points that have the conditions for crystallization, the effective crystallization rate is determined based on their corrected nucleation rate and crystal growth rate. The crystal growth rate is determined by the crystallization kinetic parameters and the current degree of supercooling; the greater the supercooling, the higher the crystal growth rate. When the supercooling is less than the preset lower limit of temperature difference, the calculation is performed according to the preset lower limit of temperature difference to avoid distortion of the calculation results due to the temperature difference being close to zero.

[0051] In this embodiment, the effective crystallization rate constant Determined according to the following formula: In the formula, For the first The Lagrange material point at the th The effective crystallization rate constant for each time step; The crystallization conversion coefficient; To correct the nucleation rate; For reference nucleation rate; This refers to the crystal growth rate; For reference crystal growth rate; This represents the growth rate index. All the above parameters are determined by simulation parameter sets or crystallization kinetic parameters.

[0052] Subsequently, the change in crystallinity at this time step is calculated based on the effective crystallization rate constant. To prevent the crystallinity from exceeding the maximum allowable crystallinity of the material, the change in crystallinity is defined as the difference between the upper limit of crystallinity and the current crystallinity as the potential growth range. The Lagrange material point at the th The change in crystallinity at each time step is: In the formula, This represents the change in crystallinity. This represents the upper limit of crystallinity. This represents the current degree of crystallinity. For time step.

[0053] The latent heat of phase change released during crystallization is calculated based on the change in crystallinity. For each Lagrange point, the heat release rate per unit volume is first obtained based on the change in crystallinity; then, this heat release rate is allocated to the computational unit containing that point. If multiple Lagrange points exist in a computational unit, the average of the heat release rates of these multiple points is taken as the volumetric heat source term for that computational unit; if no Lagrange point exists in that computational unit, the volumetric heat source term for that computational unit is zero.

[0054] After obtaining the volumetric heat source terms for each computational unit, these terms are added to the aforementioned energy equation, and the temperature field at the current time step is re-solved to obtain the corrected temperature field. The corrected temperature field reflects the influence of crystallization exothermics on the local cooling process. For thin-walled pipes, material points near the outer wall cool faster, and the impact of crystallization exothermics on the temperature field is smaller; material points near the inner wall or core layer dissipate heat more slowly, and crystallization exothermics slow down the rate of local temperature decrease, thereby altering the subsequent crystallinity growth process.

[0055] To ensure computational stability, the latent heat feedback of the phase transition is handled through one or more iterations within the same time step. Specifically: first, the change in crystallinity and the volumetric heat source term are calculated based on the uncorrected temperature; then, the corrected temperature field is obtained based on the volumetric heat source term; finally, the corrected temperature field is re-interpolated to each Lagrangian material point, and the change in crystallinity is calculated again. The condition is considered stable when the temperature difference between two adjacent iterations is no greater than 0.05 K, and the difference in the change in crystallinity is no greater than [missing value]. If the condition is not met after five iterations, the iteration for that time step is stopped.

[0056] No. The crystallinity of a Lagrange material point in the next time step is updated by the following formula: Once all the Lagrange material points reach the outlet of the cooling and shaping section, the crystallinity of each material point at the outlet cross-section is recorded, and then mapped onto the outlet cross-section grid according to its outlet cross-section coordinates to obtain the crystallinity distribution of the extruded product cross-section. This crystallinity distribution is used to reflect the degree of crystallization non-uniformity in the outer layer, inner layer, and wall thickness direction of the product.

[0057] To identify regions of delayed crystallization, post-crystallization is assessed at material points after they leave the cooling and setting section. The post-crystallization assessment criteria are set as follows: storage temperature... The post-crystallization calculation time is The shear rate and pressure drop rate are both set to zero. If the crystallinity of a certain region at the outlet of the cooling and shaping section is lower than the crystallinity threshold after cooling... Furthermore, the increase in crystallinity after the post-crystallization calculation period is greater than the post-crystallization growth threshold. Therefore, this region is defined as a crystallization lag region. In this embodiment, Pick , Pick .

[0058] After determining the crystallization lag region, the ratio of the lag region area to the total area of ​​the outlet cross-section is calculated to obtain the lag area ratio. If the lag area ratio is greater than the preset allowable value, disturbance calculations are performed on the melt temperature at the die outlet, the traction speed, and the cooling medium temperature, respectively. The disturbance amount for the melt temperature at the die outlet is ±5 K, the disturbance amount for the traction speed is ±5% of the current traction speed, and the disturbance amount for the cooling medium temperature is ±5 K. Under each disturbance condition, the crystallinity distribution and the lag area ratio are repeatedly calculated, and the disturbance condition that reduces the lag area ratio the most is selected as the process adjustment parameter output.

[0059] The output includes: the location of the hysteresis region in the outlet section, the hysteresis area ratio, the adjustment target, the adjustment direction, and the adjustment amount. For example, when reducing the cooling medium temperature can reduce the hysteresis area ratio from 12% to 5%, the output process adjustment parameter is to reduce the cooling medium temperature by 5 K. Therefore, by correcting the nucleation rate, latent heat feedback of phase change, correcting the temperature field, and determining post-crystallization, regions that may continue to crystallize after cooling can be identified during the extrusion simulation stage, and corresponding process adjustment parameters can be provided.

[0060] This invention first establishes a transient flow and heat transfer calculation process from the die exit to the cooling and shaping section based on polymer material parameters and extrusion process parameters, obtaining the velocity, pressure, and temperature changes of the melt along the extrusion path. Then, it tracks the temperature changes, shear rate, pressure drop rate, and residence time of the melt unit during the movement process using Lagrangian material points, and converts these thermomechanical histories into conformation tensors and molecular orientation parameters, so that the influence of die exit pressure release and residual orientation on nucleation behavior can be quantified. Subsequently, the nucleation rate is corrected using molecular orientation parameters, and the crystallinity change is calculated in combination with the crystal growth rate. At the same time, the latent heat of phase change released by crystallization is fed back to the temperature field to readjust the subsequent cooling and crystallization process. Finally, the crystallinity distribution of the product cross section is obtained, and the region with insufficient crystallinity after cooling but which will continue to grow is identified as the crystallization lag region. Based on this, the adjustment parameters of die temperature, traction speed, or cooling medium temperature are output, thereby improving the prediction accuracy of extrusion crystallization behavior and subsequent dimensional stability.

[0061] To verify the beneficial effects of the method of the present invention, the extrusion process of polypropylene thin-walled pipe was used as the verification object. The pipe has an outer diameter of 2.0 mm, a wall thickness of 0.15 mm, a die exit melt temperature of 220°C, an air gap length of 80 mm, a cooling and shaping section length of 600 mm, and a cooling medium temperature of 25°C. Based on the benchmark traction speed, operating conditions were set with traction speeds increased by 20%, 35%, and 50%, respectively.

[0062] The method of the present invention is compared with two comparative examples. Comparative example 1 is a simulation method that calculates crystallinity based solely on the temperature field; comparative example 2 is a simulation method that calculates crystallinity based on the temperature field and shear rate, but does not consider the pressure drop rate, conformation tensor molecular orientation parameters, and latent heat feedback of phase transition; the method of the present invention is a dynamic simulation method that simultaneously considers temperature change, shear rate, pressure drop rate, conformation tensor molecular orientation parameters, and latent heat feedback of phase transition.

[0063] Under various operating conditions, the crystallinity error, the area ratio error of the crystallization lag region, and the inner diameter drift error caused by the secondary heat treatment after cooling were compared respectively. The results are shown in Table 1.

[0064] Table 1 Comparison of errors of different simulation methods As shown in Table 1, when the traction speed disturbance increases, the crystallinity error, hysteresis area ratio error and inner diameter drift error of Comparative Example 1 and Comparative Example 2 all increase significantly. This indicates that relying solely on the temperature field, or solely combining the temperature field and shear rate, is insufficient to accurately reflect the influence of die outlet pressure release, residual orientation and exothermic crystallization on crystallization behavior after high-speed extrusion.

[0065] In contrast, the method of the present invention maintains a low error under different traction speed disturbances. Taking the condition of a 50% increase in traction speed as an example, the crystallinity MAE of the method of the present invention is 0.015, while that of Comparative Example 1 is 0.063 and that of Comparative Example 2 is 0.043; the hysteresis area ratio error of the method of the present invention is 0.048, while that of Comparative Example 1 is 0.211 and that of Comparative Example 2 is 0.142; the inner diameter drift error of the method of the present invention is 3.46 μm, while that of Comparative Example 1 is 15.92 μm and that of Comparative Example 2 is 10.64 μm.

[0066] The above results show that by introducing pressure drop rate, conformation tensor molecular orientation parameters, and latent heat feedback of phase change into the simulation process of polymer extrusion crystallization behavior, the present invention can improve the prediction accuracy of crystallinity distribution, crystallization hysteresis region, and subsequent size drift, thereby providing a reliable basis for adjusting die temperature, traction speed, and cooling medium temperature.

[0067] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application.

Claims

1. A dynamic simulation method for the crystallization behavior of polymer extrusion processes, characterized in that, include: The viscosity-temperature parameters, crystallization kinetic parameters, pressure relaxation parameters, latent heat of phase change parameters, and extrusion process parameters of the polymer to be simulated are obtained to obtain a simulation parameter set. A transient flow and heat transfer model from the die outlet to the cooling and shaping section is established using the simulation parameter set, and the velocity field, pressure field, and temperature field on the extrusion path are solved. Multiple Lagrange material points are set along the extrusion path, and the temperature change, shear rate, pressure drop rate and residence time of each Lagrange material point are extracted based on the velocity field, pressure field and temperature field to form thermomechanical history data. Molecular orientation parameters are calculated through the thermomechanical history data, and the molecular orientation parameters are introduced as correction terms into the nucleation rate equation to obtain the corrected nucleation rate. The change in crystallinity is calculated based on the corrected nucleation rate, and the corresponding latent heat of phase change is fed back to the temperature field to obtain the corrected temperature field. The crystallinity distribution is updated based on the corrected temperature field. Regions where the crystallinity is below the threshold after cooling but still has a crystallinity increase are identified as crystallization lag regions, and corresponding process adjustment parameters are output.

2. The dynamic simulation method for crystallization behavior in polymer extrusion processes according to claim 1, characterized in that, A transient flow and heat transfer model from the die outlet to the cooling and shaping section is established using a simulation parameter set, including: Using the die exit section as the calculation inlet and the cooling and shaping section exit section as the calculation outlet, a calculation domain extending along the extrusion direction is established; the calculation domain is divided into an air gap region and a cooling and shaping section region. The average inlet velocity is calculated based on the volumetric flow rate and the cross-sectional area of ​​the die outlet. The average inlet velocity and the melt temperature at the die outlet are used as the inlet velocity and inlet temperature, respectively, and the ambient pressure is used as the outlet pressure. The initial pressure field is determined based on the initial pressure at the die outlet, the ambient pressure, the average inlet velocity, and the pressure relaxation time, so that the initial pressure decreases from the initial pressure at the die outlet to the ambient pressure along the extrusion direction.

3. The dynamic simulation method for crystallization behavior in polymer extrusion processes according to claim 1, characterized in that, Generate historical thermomechanical data, including: Multiple Lagrange material points are set within the die exit section according to the geometric center of the section element; the position of each Lagrange material point is updated step by step according to the velocity field; at each time step, the temperature, pressure and velocity gradient tensors are extracted from the velocity field, pressure field and temperature field according to the position of the Lagrange material point, and the shear rate is calculated according to the velocity gradient tensor.

4. The dynamic simulation method for crystallization behavior in polymer extrusion processes according to claim 3, characterized in that, The formation of historical thermomechanical data also includes: The pressure drop rate is calculated based on the pressure difference between adjacent time steps at the same Lagrange material point; when the pressure increases or remains constant, the pressure drop rate is zero; the residence time is calculated based on the moment the Lagrange material point enters the die exit section and the current moment; the thermomechanical history data of the corresponding Lagrange material point is composed of the temperature change, shear rate, pressure drop rate, residence time, and velocity gradient tensor.

5. The dynamic simulation method for crystallization behavior in polymer extrusion processes according to claim 4, characterized in that, Molecular orientation parameters were calculated using thermomechanical history data, including: The initial conformation tensor of each Lagrange material point is set to a unit tensor; the conformation tensor is updated step by step according to the velocity gradient tensor, orientation relaxation time and pressure drop rate. The partial conformation tensor is calculated based on the updated conformation tensor, and the molecular orientation parameter is calculated based on the partial conformation tensor and the trace value of the conformation tensor; when the conformation tensor is a unity tensor, the molecular orientation parameter is zero.

6. The dynamic simulation method for crystallization behavior in polymer extrusion processes according to claim 5, characterized in that, Introducing molecular orientation parameters as correction terms into the nucleation rate equation yields a modified nucleation rate, including: The supercooling of crystallization is calculated based on the temperature and equilibrium melting point of the Lagrange material point; when the supercooling of crystallization is greater than zero, the basic nucleation rate is calculated based on the pre-nucleation rate factor and the influence coefficient of nucleation temperature; when the supercooling of crystallization is less than or equal to zero, the basic nucleation rate is zero; the molecular orientation parameter is introduced as an exponential correction term into the basic nucleation rate to obtain the corrected nucleation rate of the corresponding Lagrange material point.

7. The dynamic simulation method for crystallization behavior in polymer extrusion processes according to claim 6, characterized in that, The change in crystallinity is calculated based on the corrected nucleation rate, and the corresponding latent heat of phase transition is fed back to the temperature field to obtain the corrected temperature field, including: The effective crystallization rate constant is determined based on the modified nucleation rate, the reference nucleation rate, the crystal growth rate, and the reference crystal growth rate. The crystallinity change is calculated based on the effective crystallization rate constant, the upper limit of crystallinity, and the current crystallinity. The latent heat release of phase change is calculated based on the crystallinity change, and the latent heat release of phase change is allocated to the calculation unit where the Lagrange material point is located, and added to the energy conservation equation as a volume heat source term to resolve the temperature field of the current time step.

8. The dynamic simulation method for crystallization behavior in polymer extrusion processes according to claim 7, characterized in that, The corrected temperature field is obtained, including: Within the same time step, first calculate the crystallinity change and volumetric heat source term based on the uncorrected temperature field, then solve the corrected temperature field based on the volumetric heat source term, and interpolate the corrected temperature field to each Lagrange material point. The iteration of the time step is stopped when the temperature difference between two adjacent iterations is not greater than the preset temperature difference and the difference in crystallinity change is not greater than the preset crystallinity difference.

9. The dynamic simulation method for crystallization behavior in polymer extrusion processes according to claim 8, characterized in that, Regions where the crystallinity is below the threshold after cooling but still shows some crystallinity increase are defined as crystallization hysteresis regions, including: After all the Lagrange material points reach the outlet of the cooling and shaping section, the crystallinity of each Lagrange material point is mapped to the outlet section grid according to the outlet section coordinates to obtain the crystallinity distribution; the post-crystallization growth is calculated under the preset storage temperature and preset post-crystallization time; the region at the outlet where the crystallinity is lower than the post-cooling crystallinity threshold and the post-crystallization growth is greater than the post-crystallization growth threshold is determined as the crystallization lag region.

10. The dynamic simulation method for crystallization behavior in polymer extrusion processes according to claim 9, characterized in that, The corresponding process adjustment parameters are output, including: calculating the ratio of the area of ​​the crystallization lag region to the total area of ​​the outlet section, and by applying disturbances to the melt temperature at the die outlet, the traction speed and the cooling medium temperature respectively, selecting the disturbance condition that reduces the ratio the most as the process adjustment parameter output.

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