A method for constructing a rubber vulcanization degree field based on two-dimensional representation and a computing processing system

Abstract

The application discloses a kind of based on two-dimensional representation of rubber vulcanization degree field construction method computing processing system, this method based on Arrhenius vulcanization kinetics temperature field is converted into vulcanization degree field: reading temperature field history;Calculate the vulcanization rate and the increment of vulcanization reaction per unit time and accumulate to obtain total vulcanization reaction equivalent;Equivalent vulcanization performance parameters are obtained by continuous mapping;With the first demarcation threshold as the basis for calculating the final state variable of static mechanical property, the whole process of modulus and hardness from rising, peak to over-sulfur decay is represented;With the second scaling threshold as the basis for calculating the final state variable of thermal history accumulation only increasing without attenuation, representing the irreversible heat accumulation degree;Numerical protection is executed.The application also provides USDFLD and HETVAL subroutine architecture, driven by pure temperature field, no FLUX heat source feedback.The application solves the problems of traditional single-dimensional representation, such as incomplete information, ambiguous physical meaning and poor numerical stability, and can be used for rubber product vulcanization molding simulation.

Description

Technical Field

[0001] This invention belongs to the field of finite element numerical simulation technology, specifically relating to a calculation method for the conversion of temperature field to vulcanization degree field during rubber vulcanization molding, and particularly to a method for constructing a vulcanization degree field with dual physical dimensions, dual final state variables, and dual threshold pairing and independent segmentation, as well as a user subroutine implementation scheme based on the ABAQUS / Standard platform. Background Technology

[0002] Vulcanization is a core process in rubber product manufacturing, directly determining the product's modulus, hardness, fatigue life, and dimensional stability. The industry widely uses finite element method (FEM) simulations to predict vulcanization uniformity and the risk of under- or over-vulcanization, guiding mold design and process parameter optimization.

[0003] Existing vulcanization degree simulation technology has the following obvious drawbacks: Single dimension of representation: Using only a single state variable to represent the degree of sulfidation cannot simultaneously reflect the current mechanical properties and the irreversible cumulative thermal history; The physical meaning is vague: it is impossible to distinguish whether the performance meets the standards or whether the heating is sufficient, and its engineering guidance value is weak; The over-sulfurization stage cannot be fully characterized: the traditional degree of sulfurization is monotonically increased from 0 to 1, which cannot reproduce the true mechanical property evolution law of the modulus first rising to the peak and then decreasing after over-sulfurization; Poor numerical stability: The lack of standardized numerical protection procedures makes it prone to division by zero and negative value oscillations, which can lead to calculation interruptions. Poor material compatibility: It only supports a single material and cannot meet the simulation requirements of multi-material and multi-layer composite rubber structures.

[0004] Currently, there is no publicly available technology, either domestically or internationally, that uses dual final state variables and dual threshold pairs to perform segmented parallel calculations of the vulcanization degree field, making it difficult to achieve high-precision, high-stability, and high-engineering-value rubber vulcanization simulation. Summary of the Invention

[0005] The technical problem to be solved by this invention is to address the issues of incomplete information, ambiguous physical meaning, poor numerical stability, and weak material adaptability in traditional single-dimensional characterization. To solve the above problems, this invention provides a method for constructing a rubber vulcanization degree field based on dual-dimensional characterization and a vulcanization degree field calculation and processing system.

[0006] The object of this invention is achieved in the following manner: A method for constructing a rubber vulcanization degree field based on two-dimensional characterization, the method comprising the following steps; (1) Temperature field reading steps: Obtain the current temperature value of the rubber element integration point at the beginning of each time increment step through finite element analysis; (2) Calculation steps for sulfurization reaction increment: Based on the temperature value read in step (1), convert it into absolute temperature, use the Arrhenius type sulfurization kinetic equation to calculate the sulfurization rate in the current time increment step, and multiply the sulfurization rate by the time increment step size to obtain the sulfurization reaction increment per unit time. (3) Total sulfurization reaction equivalent accumulation step: The sulfurization reaction increment per unit time calculated in step (2) is added to the total sulfurization reaction equivalent at the end of the previous time increment step to obtain the total sulfurization reaction equivalent of the current time increment step; (4) Equivalent vulcanization performance parameter mapping step: Using the pre-established continuous mapping model, the current total vulcanization reaction equivalent obtained in step (3) is mapped to the equivalent vulcanization performance parameter; (5) Parallel calculation steps for two-dimensional state variables: Using the current total sulfurization reaction equivalent as the only input, the following two independent branches are calculated simultaneously: (5a) Static performance state variable calculation branch: Calculate the final static mechanical performance state variables based on the first boundary threshold; where, When the total vulcanization reaction equivalent is less than the first threshold, the final state variable of the static mechanical properties increases linearly with the total vulcanization reaction equivalent. When the total vulcanization reaction equivalent is equal to the first threshold, the final state variable of the static mechanical properties reaches a peak value, which corresponds to the extreme point of the vulcanization mechanical properties. When the total vulcanization reaction equivalent is greater than the first threshold, the final state variable of the static mechanical properties is attenuated and corrected as the total vulcanization reaction equivalent increases. After the calculation is completed, if the value of the state variable is less than 0, it will be forcibly set to 0; (5b) Thermal history state variable calculation branch: Calculate the thermal history cumulative final state variable using the second scaling threshold as the scaling reference; this state variable is completely decoupled from the static mechanical property final state variable of step (5a), and its value is equal to the ratio of the current total sulfurization reaction equivalent to the second scaling threshold; this state variable only increases throughout the process, never decays, and has no upper limit; after the calculation is completed, if the value of this state variable is less than 0, it is forcibly set to 0; (6) Result output steps: Output the final state variables of static mechanical properties obtained in step (5a) and the final state variables of thermal history accumulation obtained in step (5b) as a two-dimensional sulfurization degree field to the finite element result file; Among them, the first boundary threshold and the second scaling threshold are material-specific parameters and must be used in combination; the entire method is driven by a pure temperature field and does not use heat source feedback.

[0007] The Arrhenius-type sulfidation kinetic equation mentioned in step (2) is as follows: , Increment of vulcanization reaction per unit time Where A0 is the pre-exponential factor, E a Δt is the activation energy, R is the gas constant, T is the absolute temperature, and Δt is the time step.

[0008] The normalized range of the final state variable of static mechanical properties mentioned in step (5a) is 0 to 2; the attenuation correction adopts a nonlinear attenuation function based on the degree of sulfurization.

[0009] The thermal history cumulative final state variable mentioned in step (5b) and the static mechanical property final state variable in step (5a) are calculated independently: the value of the thermal history cumulative final state variable is determined only by the ratio of the current total sulfurization reaction equivalent to the second scaling threshold, and does not involve the static mechanical property final state variable; the value of the static mechanical property final state variable is determined only by the relationship between the current total sulfurization reaction equivalent and the first boundary threshold, and does not involve the thermal history cumulative final state variable.

[0010] The continuous mapping model mentioned in step (4) is a rational polynomial model. This model continuously fits the discrete vulcanization test curve to establish a one-way mapping relationship between the total vulcanization reaction equivalent and the equivalent vulcanization performance parameters.

[0011] Numerical protection is performed throughout the calculation process. This numerical protection includes zero-reduction protection and non-negative clamping, and is performed in a fixed order: first zero-reduction protection, then non-negative clamping.

[0012] The zero-prevention protection is specifically as follows: in the equivalent vulcanization performance parameter mapping process of step (4), the denominator of the rational polynomial expression is judged. If the absolute value of the denominator is less than or equal to the preset minimum positive value, the denominator is forcibly assigned the preset minimum positive value. The non-negative clamp is built into the forced zeroing operation of steps (5a) and (5b).

[0013] A sulfurization degree field calculation and processing system for implementing the method comprises the following two processing modules with fixed division of labor: (1) Main calculation and processing module: This module is called at the beginning of each incremental step at each integration point and is responsible for sequentially executing the following functions: Read the temperature value of the current unit integration point; Invoke the aforementioned zero-reduction protection; Call all the sulfurization calculation and state variable update logic in steps (2) to (5b) of claim 1; Automatically match the corresponding vulcanization kinetic parameters, first boundary threshold, second scaling threshold, and experimental fitting coefficients according to the material name; The updated static mechanical properties final state variables and thermal history cumulative final state variables are passed to the ABAQUS main program. (2) Heat source feedback interface module: It is called after the main calculation and processing module. It only performs the operation of setting the heat source item to 0.0, providing zero heat source feedback, and does not participate in any sulfurization reaction equivalent calculation or state variable update logic.

[0014] The main calculation and processing module supports automatic matching of multiple materials: by reading the user-defined material name or material number in the material definition, it calls the pre-stored corresponding material parameter table, so that different rubber materials or multilayer rubbers in the same finite element model can be calculated using their respective dynamic parameters, paired double thresholds and experimental fitting coefficients.

[0015] Both the main calculation processing module and the heat source feedback interface module are written in standard Fortran format, including: explicit declaration of all variables, code written between columns 7 and 72, excessively long statements split after column 72 and continued to be written in column 7 of the next line, and uniformly performing zero protection of the denominator before calculating the sulfurization rate.

[0016] The beneficial effects of the present invention are: (1) complete dual-dimensional characterization. It outputs both static performance field and irreversible thermal history field at the same time, providing more comprehensive simulation information and answering both engineering questions of "insufficient performance" and "insufficient heating".

[0017] (2) Complete reproduction of the entire process of vulcanization-oversulfurization. The static mechanical property state variables can reflect the complete evolution law of modulus from rising, peak to oversulfurization decay, breaking through the traditional characterization limitation of monotonic vulcanization degree from 0 to 1.

[0018] (3) The physical meaning is clear and the engineering guidance value is strong. The two types of state variables are decoupled from each other and each performs its own function, which can be directly used for the evaluation of sulfurization uniformity, the identification of under-sulfurization and over-sulfurization risks and the optimization of sulfurization process parameters.

[0019] (4) High numerical stability. The zero-division protection and non-negative clamping are performed in a fixed sequence, which effectively avoids zero-division interruption and negative value oscillation, and the calculation process is stable and reliable.

[0020] (5) Pure temperature field driven. No fitting error of sulfurization exothermic is introduced, avoiding the uncertainty of temperature field-sulfurization field coupling calculation caused by heat source feedback.

[0021] (6) Versatile for multiple materials. Supports automatic matching of dynamic parameters, paired double thresholds and experimental fitting coefficients by material name, applicable to multi-layer composite rubber structures. Attached Figure Description

[0022] Figure 1 is a flowchart of the overall process for constructing the two-dimensional sulfurization degree field of the present invention; Figure 2 is a block diagram illustrating the principle of independent calculation of dual final state variables in this invention; Figure 3 is a schematic diagram of the dual-threshold independent segmented control strategy of the present invention; Figure 4 is a schematic diagram of the USDFLD+HETVAL subroutine architecture of the present invention. Detailed Implementation

[0023] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0024] It should be noted that the following detailed descriptions are exemplary and intended to provide further explanation of this application. Unless otherwise specified, all technical and scientific terms used herein have the same technical meaning as commonly understood by one of ordinary skill in the art to which this application pertains.

[0025] A method for constructing a rubber vulcanization degree field based on two-dimensional characterization, the method comprising the following steps; (1) Temperature field reading steps: Obtain the current temperature value of the rubber element integration point at the beginning of each time increment step through finite element analysis; (2) Calculation steps for sulfurization reaction increment: Based on the temperature value read in step (1), convert it into absolute temperature, use the Arrhenius type sulfurization kinetic equation to calculate the sulfurization rate in the current time increment step, and multiply the sulfurization rate by the time increment step size to obtain the sulfurization reaction increment per unit time. (3) Total sulfurization reaction equivalent accumulation step: The sulfurization reaction increment per unit time calculated in step (2) is added to the total sulfurization reaction equivalent at the end of the previous time increment step to obtain the total sulfurization reaction equivalent of the current time increment step; (4) Equivalent vulcanization performance parameter mapping step: Using the pre-established continuous mapping model, the current total vulcanization reaction equivalent obtained in step (3) is mapped to the equivalent vulcanization performance parameter; (5) Parallel calculation steps for two-dimensional state variables: Using the current total sulfurization reaction equivalent as the only input, the following two independent branches are calculated simultaneously: (5a) Static performance state variable calculation branch: Calculate the final static mechanical performance state variables based on the first boundary threshold; where, When the total vulcanization reaction equivalent is less than the first threshold, the final state variable of the static mechanical properties increases linearly with the total vulcanization reaction equivalent. When the total vulcanization reaction equivalent is equal to the first threshold, the final state variable of the static mechanical properties reaches a peak value, which corresponds to the extreme point of the vulcanization mechanical properties. When the total vulcanization reaction equivalent is greater than the first threshold, the final state variable of the static mechanical properties is attenuated and corrected as the total vulcanization reaction equivalent increases. After the calculation is completed, if the value of the state variable is less than 0, it will be forcibly set to 0; (5b) Thermal history state variable calculation branch: Calculate the thermal history cumulative final state variable using the second scaling threshold as the scaling reference; this state variable is completely decoupled from the static mechanical property final state variable of step (5a), and its value is equal to the ratio of the current total sulfurization reaction equivalent to the second scaling threshold; this state variable only increases throughout the process, never decays, and has no upper limit; after the calculation is completed, if the value of this state variable is less than 0, it is forcibly set to 0; (6) Result output steps: Output the final state variables of static mechanical properties obtained in step (5a) and the final state variables of thermal history accumulation obtained in step (5b) as a two-dimensional sulfurization degree field to the finite element result file; Among them, the first boundary threshold and the second scaling threshold are material-specific parameters and must be used in combination; the entire method is driven by a pure temperature field and does not use heat source feedback.

[0026] The Arrhenius-type sulfidation kinetic equation mentioned in step (2) is as follows: , Increment of vulcanization reaction per unit time Where A0 is the pre-exponential factor, E a Δt is the activation energy, R is the gas constant, T is the absolute temperature, and Δt is the time step.

[0027] The normalized range of the final state variable of static mechanical properties mentioned in step (5a) is 0 to 2; the attenuation correction adopts a nonlinear attenuation function based on the degree of sulfurization.

[0028] The thermal history cumulative final state variable mentioned in step (5b) and the static mechanical property final state variable in step (5a) are calculated independently: the value of the thermal history cumulative final state variable is determined only by the ratio of the current total sulfurization reaction equivalent to the second scaling threshold, and does not involve the static mechanical property final state variable; the value of the static mechanical property final state variable is determined only by the relationship between the current total sulfurization reaction equivalent and the first boundary threshold, and does not involve the thermal history cumulative final state variable.

[0029] The continuous mapping model mentioned in step (4) is a rational polynomial model. This model continuously fits the discrete vulcanization test curve to establish a one-way mapping relationship between the total vulcanization reaction equivalent and the equivalent vulcanization performance parameters.

[0030] Numerical protection is performed throughout the calculation process. This numerical protection includes zero-reduction protection and non-negative clamping, and is performed in a fixed order: first zero-reduction protection, then non-negative clamping.

[0031] The zero-prevention protection is specifically as follows: in the equivalent vulcanization performance parameter mapping process of step (4), the denominator of the rational polynomial expression is judged. If the absolute value of the denominator is less than or equal to the preset minimum positive value, the denominator is forcibly assigned the preset minimum positive value. The non-negative clamp is built into the forced zeroing operation of steps (5a) and (5b).

[0032] A sulfurization degree field calculation and processing system for implementing the method, the calculation and processing system adopts ABAQUS user subroutines and includes the following two processing modules (subroutine modules) with fixed division of labor: (1) Main processing module: USDFLD subroutine: This subroutine is called at the beginning of each incremental step of each integration point in ABAQUS / Standard analysis and is responsible for sequentially executing the following functions: Read the temperature value of the current unit integration point; Invoke the aforementioned zero-reduction protection; Call all sulfurization calculations and state variable update logic from step (2) to step (5b); Automatically match the corresponding vulcanization kinetic parameters, first boundary threshold, second scaling threshold, and experimental fitting coefficients according to the material name; The updated static mechanical properties final state variables and thermal history cumulative final state variables are passed to the ABAQUS main program. (2) Heat source feedback interface module: HETVAL subroutine: This subroutine is a necessary interface for thermal analysis and is called after the USDFLD subroutine. It only performs the operation of setting the heat source item FLUX to 0.0, providing zero heat source feedback, and does not participate in any sulfurization reaction equivalent calculation or state variable update logic.

[0033] The USDFLD subroutine supports automatic matching of multiple materials: by reading the user-defined material name or material number in the ABAQUS material definition, it calls the pre-stored corresponding material parameter table, so that different rubber materials or multilayer rubbers in the same finite element model can be calculated using their respective dynamic parameters, paired double thresholds and experimental fitting coefficients.

[0034] Both the USDFLD and HETVAL subroutines are written in standard Fortran format, including: explicit declaration of all variables, code written between columns 7 and 72, excessively long statements split after column 72 and continued writing in column 7 of the next line, and uniformly performing zero protection of the denominator before calculating the vulcanization rate.

[0035] runtime environment and subroutine composition This invention is implemented on the ABAQUS / Standard 2016 and later platforms, and uses the Intel Fortran compiler (Intel Fortran Compiler 17.0 and later recommended) to compile user subroutines. The subroutine system consists of the following two parts: The USDFLD subroutine reads the unit integration point temperature in each increment step and sequentially completes zero protection, vulcanization kinetics calculation, total vulcanization reaction equivalent accumulation, equivalent vulcanization performance parameter mapping, dual final state variable update, dual threshold judgment, non-negative clamping, and automatic multi-material matching. It is the main body executing all vulcanization calculation logic.

[0036] HETVAL subroutine: As a necessary user subroutine interface for ABAQUS thermal analysis, it sets the heat source flux FLUX to 0.0 in each incremental step, providing only zero heat source feedback to meet the thermal analysis call specifications, and does not participate in any sulfurization kinetic calculations or state variable updates.

[0037] Example 1: Simulation of Vulcanization of Radial Truck Tire Cartridge This embodiment uses a radial tire blank of a certain specification for passenger cars as an example to illustrate the application of the present invention in tire vulcanization simulation.

[0038] (1) Establishment of finite element model A three-dimensional axisymmetric finite element model of the tire blank was established in ABAQUS / CAE. The model includes seven material regions: tread rubber, bottom layer rubber, pad rubber, tread rubber, sidewall rubber, carcass ply, and inner liner rubber. DC3D4 thermal conductivity elements were used for the rubber elements, resulting in a total of 2860 elements and 3120 nodes. Convection heat transfer boundary conditions were set on the outer surface of the mold cavity, and the heat transfer coefficient was set to [value missing]. The ambient temperature was 25 ℃; the inner surface was set with a constant temperature boundary condition of 175 ℃; the outer surface was set with a constant temperature boundary condition of 151 ℃; and the total vulcanization time was 3600 s.

[0039] (2) Definition of material parameters The tread compound material parameters are as follows: pre-finger factor ,activation energy The first dividing threshold (positive sulfur point reaction equivalent) Second scaling threshold The parameters of the tire sidewall rubber material are as follows: , , = 14.0, = 29.2. The rational polynomial experimental fitting coefficients for each material were obtained by calibration using the vulcanization rheometer (MDR) test data of the corresponding rubber formulation.

[0040] (3) Analysis step settings and subroutine calls Create a heat transfer analysis step (*HEAT TRANSFER) with a time step Δt = 1.0 s and a total analysis time of 3600 s. In the input file, call the USDFLD subroutine using the *USER DEFINED FIELD keyword and the HETVAL subroutine using the *HEATGENERATION keyword. State variables SDV1 store the total sulfurization reaction equivalent, SDV2 store the final state variables of static mechanical properties, and SDV3 store the final state variables of accumulated thermal history.

[0041] (4) Calculation process Within each increment step, USDFLD reads the current temperature T (in K) at each integration point, performs zero-reset protection, and then presses... The vulcanization rate is calculated, yielding the reaction increment per unit time Δα = k(T)•Δt, which is then accumulated to the total vulcanization reaction equivalent α_total. Subsequently, using α_total as the independent variable, equivalent vulcanization performance parameters are obtained through rational polynomial mapping; Calculate SDV2 for the boundary threshold: when α_total < SDV2 grows linearly when α_total ≥ SDV2 performs attenuation correction; parallel computation. (Increment only); Finally, a non-negative clamp is executed, forcing the values ​​less than zero in SDV2 and SDV3 to zero.

[0042] (5) Simulation results and analysis After 3600 s of vulcanization, the SDV2 distribution range in the sidewall rubber area was 0.95~1.2, and the SDV3 distribution range was 1.02~5.02, indicating that the mechanical properties in this area had reached their peak and the accumulated thermal history had been excessive. The SDV2 in the shoulder transition area was the lowest at 0.62, and the SDV3 distribution ranged from 0.62 to 2.05, indicating that the mechanical properties in this area had not yet reached their peak. Uneven vulcanization was observed in various tire components. To alleviate this, the two-dimensional results guided the process engineers to lower the constant temperature setting on the inner surface from 175 ℃ to 165 ℃; and to set a constant temperature boundary condition of 151 ℃ on the inner surface of the outer surface mandrel, with a total vulcanization time of 3900 s. This increased the shoulder SDV2 to above 0.95, while simultaneously reducing the sidewall rubber area SDV3 to below 3.0, making it closer to the tread SDV3, thus optimizing vulcanization uniformity.

[0043] Example 2: Simulation of vulcanization of giant tires This embodiment uses a giant tire as an example to illustrate the application of the present invention in the simulation of seal vulcanization, focusing on demonstrating the complete characterization capability of the over-sulfurization stage.

[0044] (1) Establishment of finite element model A three-dimensional axisymmetric finite element model of the tire blank was established in ABAQUS / CAE. The model includes nine material regions: tread rubber, bottom layer rubber, pad rubber, triangular rubber, sidewall rubber, interlayer rubber, filler rubber, carcass ply, and inner liner rubber. The rubber elements were DC3D4 thermal conductivity elements, with a total of 18,560 elements and 26,540 nodes. Convection heat transfer boundary conditions were set on the outer surface of the mold cavity, with a heat transfer coefficient of 25 W / (m²•K) and an ambient temperature of 25 ℃. A constant temperature boundary condition was set on the inner surface of the mandrel, with a temperature of 165 ℃. A constant temperature boundary condition was also set on the outer surface of the mandrel, with a temperature of 145 ℃. The total vulcanization time was 36,000 s.

[0045] (2) Definition of material parameters To investigate the characterization ability of the over-sulfurization stage, the entire process of the sidewall rubber was analyzed. The material parameters of the sidewall rubber are as follows: , , = 14.0, = 29.2. The rational polynomial experimental fitting coefficients of the sidewall were obtained by calibration based on the vulcanization rheometer (MDR) test data of the corresponding rubber formulation.

[0046] (3) Calculation and Results After simulation, the area in direct contact with the mold on the tire sidewall exhibited the highest temperature and fastest vulcanization. The evolution of SDV2 in this area was as follows: from 0 to 1.0 (peak value of positive vulcanization) within 0 to 28000 s; from 28000 to 36000 s, SDV2 decreased from 1.0 to 0.73, fully replicating the "modulus first increases then decreases" pattern of over-vulcanization. Simultaneously, SDV3 in this area monotonically increased from 0 to 23.8 without any decline, indicating continuous irreversible heat accumulation. Based on this, engineers determined that this part of the tire sidewall had already undergone over-vulcanization and recommended reducing the mold temperature from 165 ℃ to 160 ℃ to mitigate the risk of over-vulcanization. Traditional single-dimensional vulcanization degree (monotonically increasing from 0 to 1) cannot distinguish the over-vulcanization heating state of the tire sidewall where "SDV2 has decreased but SDV3 remains high." This invention's dual-dimensional characterization provides a clear basis for process adjustment.

[0047] Example 3: Simulation of vulcanization of multi-layer composite rubber shock-absorbing pad This embodiment uses a multi-layer composite rubber shock-absorbing pad as an example to illustrate the multi-material automatic matching capability of the present invention.

[0048] (1) Establishment of finite element model The damping pad consists of an upper natural rubber (NR) damping layer, a middle steel plate interlayer, and a lower neoprene (CR) oil-resistant layer. A three-dimensional heat conduction model was established, with C3D8RT elements used for the rubber region. The vulcanization temperature was 150 ℃, and the time was 720 s. The names of the upper and lower rubber materials were defined as "NR_DAMP" and "CR_OIL" respectively. The USDFLD subroutine automatically matched the respective kinetic parameters and paired dual thresholds according to the material names.

[0049] (2) Multiple material parameters NR_DAMP: , , = 7.5, = 10.2; CR_OIL: , , =6.2, = 9.6. The two layers of material are executed independently from step (2) to step (8) in the same model without interfering with each other.

[0050] (3) Calculation and Results Simulation results show that the SDV2 distribution of the NR layer is 0.88~1.12, indicating good vulcanization uniformity; the SDV2 distribution of the CR layer is 0.65~0.94, with a lower SDV2 (0.65) near the steel plate interface, representing a risk zone for under-vulcanization. The SDV3 of the CR layer is generally lower than that of the NR layer because the CR material has a higher activation energy and a slower vulcanization rate at the same temperature. To address the under-vulcanized area of ​​the CR layer near the steel plate interface, engineers added local heating protrusions at corresponding positions in the mold, increasing the SDV2 in this area to above 0.90. This embodiment verifies the practicality of the multi-material automatic matching function in multi-layer composite structures.

[0051] Example 4: Compiling and Calling ABAQUS User Subroutines This example illustrates the specific compilation and calling methods for the USDFLD and HETVAL subroutines.

[0052] (1) Subroutine file Place the two Fortran source files, USDFLD.f and HETVAL.f, in the same working directory. USDFLD.f uses the MATPROP submodule to automatically match by material name (CMNAME). , , , and rational polynomial fitting coefficients; call the EPS zero-prevention function before each division operation, when the absolute value of the denominator is less than Replace it with .

[0053] (2) Compilation command Execute in the ABAQUS command-line environment: abaqus job=tire_cure user=USDFLD.f,HETVAL.f int Where job is the input file name, user specifies the user subroutine source file, and int indicates that the Intel Fortran compiler is used.

[0054] (3) Input file keywords Add the following key fields to the .inp file: *USER DEFINED FIELD *DEPVAR 3 *HEAT GENERATION *DEPVAR 3 declares three solution-related state variables (SDV1: total sulfurization reaction equivalent, SDV2: static mechanical property final state variable, SDV3: thermal history cumulative final state variable).

[0055] (4) Post-processing After the calculation is completed, select SDV2 and SDV3 as cloud map variables in ABAQUS / CAE or Abaqus Viewer to view the spatial distribution of the static performance field and thermal history field respectively, and realize the visualization analysis of the two-dimensional sulfurization degree field.

[0056] Summary of general implementation steps Based on the above embodiments, the general implementation steps of the present invention can be summarized as follows: Step S1: Establish a finite element model of the rubber product and mesh it, and set thermal boundary conditions; Step S2: Assign a unique material name to each rubber material and define the vulcanization kinetic parameters. Paired double threshold and experimental fit coefficients; Step S3: Create a heat conduction analysis step or a thermo-coupling analysis step, and declare the solution-related state variables; Step S4: Compile and call the USDFLD and HETVAL subroutines, and submit them for ABAQUS / Standard calculation; Step S5: In the post-processing, examine the spatial distribution of SDV2 (static performance field) and SDV3 (thermal history field) to evaluate the uniformity of vulcanization and optimize the process.

[0057] Within each incremental step, USDFLD executes in a fixed sequence: "read temperature → prevent zero protection → calculate reaction increment → accumulate total reaction equivalent → map equivalent performance parameters → calculate dual-state variables in segments with dual thresholds → non-negative clamping → update state variables". HETVAL provides zero heat source feedback with FLUX=0.0 simultaneously. The two work together to complete the construction of a two-dimensional sulfurization degree field driven by a pure temperature field.

[0058] The above description is only a preferred embodiment of the present invention. It should be noted that those skilled in the art can make several changes and improvements without departing from the overall concept of the present invention, and these should also be considered within the scope of protection of the present invention.

Claims

1. A method for constructing a rubber vulcanization degree field based on two-dimensional characterization, characterized in that: The method includes the following steps; (1) Temperature field reading steps: Obtain the current temperature value of the rubber element integration point at the beginning of each time increment step through finite element analysis; (2) Calculation steps for sulfurization reaction increment: Based on the temperature value read in step (1), convert it into absolute temperature, use the Arrhenius type sulfurization kinetic equation to calculate the sulfurization rate in the current time increment step, and multiply the sulfurization rate by the time increment step size to obtain the sulfurization reaction increment per unit time. (3) Total sulfurization reaction equivalent accumulation step: The sulfurization reaction increment per unit time calculated in step (2) is added to the total sulfurization reaction equivalent at the end of the previous time increment step to obtain the total sulfurization reaction equivalent of the current time increment step; (4) Equivalent vulcanization performance parameter mapping step: Using the pre-established continuous mapping model, the current total vulcanization reaction equivalent obtained in step (3) is mapped to the equivalent vulcanization performance parameter; (5) Parallel calculation steps for two-dimensional state variables: Using the current total sulfurization reaction equivalent as the only input, the following two independent branches are calculated simultaneously: (5a) Static performance state variable calculation branch: Calculate the final static mechanical performance state variables based on the first boundary threshold; where, When the total vulcanization reaction equivalent is less than the first threshold, the final state variable of the static mechanical properties increases linearly with the total vulcanization reaction equivalent. When the total vulcanization reaction equivalent is equal to the first threshold, the final state variable of the static mechanical properties reaches a peak value, which corresponds to the extreme point of the vulcanization mechanical properties. When the total vulcanization reaction equivalent is greater than the first threshold, the final state variable of the static mechanical properties is attenuated and corrected as the total vulcanization reaction equivalent increases. After the calculation is completed, if the value of the state variable is less than 0, it will be forcibly set to 0; (5b) Thermal history state variable calculation branch: Calculate the thermal history cumulative final state variable using the second scaling threshold as the scaling reference; this state variable is completely decoupled from the static mechanical property final state variable of step (5a), and its value is equal to the ratio of the current total sulfurization reaction equivalent to the second scaling threshold; this state variable only increases throughout the process, never decays, and has no upper limit; after the calculation is completed, if the value of this state variable is less than 0, it is forcibly set to 0; (6) Result output steps: Output the final state variables of static mechanical properties obtained in step (5a) and the final state variables of thermal history accumulation obtained in step (5b) as a two-dimensional sulfurization degree field to the finite element result file; Among them, the first boundary threshold and the second scaling threshold are material-specific parameters and must be used in combination; the entire method is driven by a pure temperature field and does not use heat source feedback.

2. The method for constructing a rubber vulcanization degree field based on dual-dimensional characterization according to claim 1, characterized in that: The Arrhenius-type sulfidation kinetic equation mentioned in step (2) is as follows: , Increment of vulcanization reaction per unit time Where A0 is the pre-exponential factor, E a Δt is the activation energy, R is the gas constant, T is the absolute temperature, and Δt is the time step.

3. The method for constructing a rubber vulcanization degree field based on dual-dimensional characterization according to claim 1, characterized in that: The normalized range of the final state variable of static mechanical properties mentioned in step (5a) is 0 to 2; the attenuation correction adopts a nonlinear attenuation function based on the degree of sulfurization.

4. The method for constructing a rubber vulcanization degree field based on dual-dimensional characterization according to claim 1, characterized in that: The thermal history cumulative final state variable mentioned in step (5b) and the static mechanical property final state variable in step (5a) are calculated independently: the value of the thermal history cumulative final state variable is determined only by the ratio of the current total sulfurization reaction equivalent to the second scaling threshold, and does not involve the static mechanical property final state variable; the value of the static mechanical property final state variable is determined only by the relationship between the current total sulfurization reaction equivalent and the first boundary threshold, and does not involve the thermal history cumulative final state variable.

5. The method for constructing a rubber vulcanization degree field based on dual-dimensional characterization according to claim 1, characterized in that: The continuous mapping model mentioned in step (4) is a rational polynomial model. This model continuously fits the discrete vulcanization test curve to establish a one-way mapping relationship between the total vulcanization reaction equivalent and the equivalent vulcanization performance parameters.

6. The method for constructing a rubber vulcanization degree field based on dual-dimensional characterization according to claim 1, characterized in that: Numerical protection is performed throughout the calculation process. This numerical protection includes zero-reduction protection and non-negative clamping, and is performed in a fixed order: first zero-reduction protection, then non-negative clamping.

7. The method for constructing a rubber vulcanization degree field based on dual-dimensional characterization according to claim 6, characterized in that: The zero-prevention protection is specifically as follows: in the equivalent vulcanization performance parameter mapping process of step (4), the denominator of the rational polynomial expression is judged. If the absolute value of the denominator is less than or equal to the preset minimum positive value, the denominator is forcibly assigned the preset minimum positive value. The non-negative clamp is built into the forced zeroing operation of steps (5a) and (5b).

8. A sulfurization degree field calculation and processing system for implementing the method of any one of claims 1 to 7, characterized in that: It includes the following two processing modules with a fixed division of labor: (1) Main calculation and processing module: This module is called at the beginning of each incremental step at each integration point and is responsible for sequentially executing the following functions: Read the temperature value of the current unit integration point; Invoke the zero-reduction protection as described in claim 6 or 7; Call all the sulfurization calculation and state variable update logic in steps (2) to (5b) of claim 1; Automatically match the corresponding vulcanization kinetic parameters, first boundary threshold, second scaling threshold, and experimental fitting coefficients according to the material name; The updated static mechanical properties final state variables and thermal history cumulative final state variables are passed to the ABAQUS main program. (2) Heat source feedback interface module: It is called after the main calculation and processing module. It only performs the operation of setting the heat source item to 0.0, providing zero heat source feedback, and does not participate in any sulfurization reaction equivalent calculation or state variable update logic.

9. The sulfurization degree field calculation and processing system according to claim 8, characterized in that: The main calculation and processing module supports automatic matching of multiple materials: by reading the user-defined material name or material number in the material definition, it calls the pre-stored corresponding material parameter table, so that different rubber materials or multilayer rubbers in the same finite element model can be calculated using their respective dynamic parameters, paired double thresholds and experimental fitting coefficients.

10. The sulfurization degree field calculation and processing system according to claim 8, characterized in that: Both the main calculation processing module and the heat source feedback interface module are written in standard Fortran format, including: explicit declaration of all variables, code written between columns 7 and 72, excessively long statements split after column 72 and continued to be written in column 7 of the next line, and uniformly performing zero protection of the denominator before calculating the sulfurization rate.

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