A tire repair rubber strip vulcanization process optimization method based on digital twinning

Abstract

The application discloses a kind of based on digital twinning tire repair rubber strip vulcanization process optimization method, it is related to rubber vulcanization process optimization technical field, it includes steps S1 constructs the digital twin model of tire repair rubber strip vulcanization process, step S2 real-time data acquisition, step S3 digital twin state synchronization, step S4 process parameter rolling optimization and step S5 process execution.This application calculates rubber strip internal temperature field and vulcanization degree field by digital twin model online real-time, solves the difficult problem of " invisible, inaccurate " in the internal state of tire repair rubber strip vulcanization process, realizes the change from " black box operation " to " transparent production ";Using ensemble Kalman filter algorithm, the limited mold temperature observation data is assimilated with high-dimensional physical model, and the simulation deviation caused by model simplification and unknown disturbance is corrected in time, to ensure the high-fidelity mapping between digital twin and physical entity.

Description

Technical Field

[0001] This invention relates to the field of rubber vulcanization process optimization technology, and in particular to a method for optimizing the vulcanization process of tire repair strips based on digital twins. Background Technology

[0002] Tire repair strips are widely used strip-shaped repair materials in automotive tire repair. They are usually made of uncured or partially cured rubber, and their cross-section is mostly trapezoidal or rectangular. During use, they are inserted into the puncture hole and then cured under heat and pressure, forming a strong bond with the tire. The uniformity of the curing degree of the tire repair strip directly determines its repair strength and durability. If there are under-cured areas inside the strip, the tensile strength is insufficient, and the patch is prone to detachment; if it is over-cured, the strip becomes brittle and its elasticity decreases.

[0003] Currently, the vulcanization of tire repair strips mostly employs a flatbed vulcanizing machine molding process, with process control primarily relying on open-loop control based on constant temperature and time. Operators set fixed heating plate temperatures and vulcanization times according to the rubber compound formula. However, due to factors such as ambient temperature fluctuations, differences in mold heat dissipation, and variations in thermal parameters between batches of rubber compounds, the actual temperature field and vulcanization degree field inside the strip vary significantly, easily leading to uneven cross-sectional vulcanization. Furthermore, the uneven thickness of the strip exacerbates the dispersion of temperature gradients and vulcanization degree.

[0004] Existing technologies include vulcanization process optimization methods based on offline finite element simulation. However, these methods require pre-setting boundary conditions and cannot perceive changes in actual operating conditions during the process, making them a static open-loop optimization. Once the actual operating conditions deviate from the assumptions, the offline optimization parameters lose their guiding significance. Therefore, there is an urgent need for a method that can perceive the internal vulcanization state in real time, dynamically compensate for disturbances, and optimize the process online. Summary of the Invention

[0005] The technical problem to be solved by this invention is to address the difficulties of unpredictable internal state and uneven vulcanization caused by working condition disturbances during the vulcanization process of tire repair rubber strips. This invention provides a method for optimizing the vulcanization process of tire repair rubber strips based on digital twins, thereby achieving online closed-loop control of the vulcanization quality of the rubber strips.

[0006] To achieve the above objectives, the present invention adopts the following technical solution: A method for optimizing the vulcanization process of tire repair strips based on digital twins includes the following steps: Step S1: Construct a digital twin model of the tire repair strip vulcanization process: Based on the geometry of the actual vulcanization equipment and the cross-sectional shape of the tire repair strip, establish a three-dimensional geometric model including the mold and the strip, and assign thermal property parameters of the strip material as a function of temperature. Couple the transient heat conduction equation and the vulcanization reaction kinetic equation to form a multi-physics coupled model. Use intrinsic orthogonal decomposition combined with discrete empirical interpolation to reduce the order of the multi-physics coupled model to obtain a reduced-order model. The reduced-order model serves as the digital twin model, and its single-step simulation time does not exceed 1 second to meet the timeliness requirements of online real-time simulation. Step S2, Real-time data acquisition: During the vulcanization process, temperature and pressure sensors arranged inside the mold near the cavity are used to collect mold temperature and cavity pressure at a preset frequency and transmit them to the host computer. The cavity pressure is used for pressure closed-loop feedback and overpressure safety interlock. Step S3, Digital Twin State Synchronization: The real-time mold temperature data collected in step S2 is used as the observation vector and input into the digital twin model. Using ensemble Kalman filtering, the temperature and vulcanization degree of each grid node inside the rubber strip are used as the state vector. The state vector is optimally recursively estimated through the observation values. The state variables of the temperature field and vulcanization degree field inside the model are corrected online to keep the digital twin model synchronized with the current vulcanization state of the physical entity. Step S4, rolling optimization of process parameters: Based on the synchronized digital twin model, a multi-objective optimization model is constructed with minimizing the standard deviation of the vulcanization degree of the rubber strip cross section as the primary objective, while also taking into account the shortest vulcanization time and the lowest energy consumption. The model uses at least one of vulcanization temperature, vulcanization time and vulcanization pressure as decision variables, adopts a rolling time-domain optimization strategy, and solves the problem with a preset optimization algorithm to obtain the optimal process parameter sequence in the future time domain. Step S5, Process Execution: The first control command in the optimal process parameter sequence obtained in step S4 is sent to the programmable controller of the vulcanizing equipment to adjust the heating power or pressure valve, thus completing the optimization closed loop of one control cycle.

[0007] As a preferred technical solution of the present invention, the kinetic equation for the sulfidation reaction in step S1 adopts the Kamal-Sourour model: ; in, The degree of sulfidation, For time, , To be the temperature-dependent rate constant that follows the Arrhenius equation, , denoted as the reaction order.

[0008] As a preferred technical solution of the present invention, the transient heat conduction equation in step S1 includes a term for the exothermic source of the sulfidation reaction: ; in, For density, For specific heat capacity, For temperature, Thermal conductivity, This represents the total heat released during the sulfidation reaction.

[0009] As a preferred technical solution of the present invention, the model reduction method in step S1 is specifically as follows: by performing transient simulation on the full-order model under different process conditions, collecting transient simulation snapshots of the temperature field and the degree of sulfidation field, and constructing a snapshot matrix; performing eigenorthogonal decomposition on the snapshot matrix, extracting the first N dominant modes as the reduction basis, where the value of N is such that the cumulative energy percentage is not less than 99%; for nonlinear terms such as the exothermic source term of the sulfidation reaction, the discrete empirical interpolation method is used for processing, and the nonlinear terms are projected onto the low-dimensional space spanned by the reduction basis for approximate calculation, thereby realizing the conversion from the full-order model to the reduced-order model.

[0010] As a preferred technical solution of the present invention, the state vector of the Kalman filter in step S3 is... Temperature of all finite element mesh nodes inside the adhesive strip and degree of sulfidation ,Right now Where M is the total number of grid nodes; observation vector The measured values ​​from the mold temperature sensor collected in step S2; ensemble Kalman filtering is used to construct... The set of states consists of 50-80 members. The set members are updated recursively using the observed values. The mean of the set is taken as the optimal estimate of the state variables.

[0011] As a preferred embodiment of the present invention, the objective function of the multi-objective optimization model in step S4 is: ; in, The standard deviation of the degree of vulcanization at all nodes on the cross-section of the rubber strip. This is the currently predicted vulcanization completion time. As the baseline vulcanization time, To predict energy consumption, As the reference energy, , , Here are the weighting coefficients; The value is greater than and The primary optimization objective is to reflect the uniformity of the cross-sectional vulcanization degree.

[0012] As a preferred technical solution of the present invention, the specific implementation of the rolling optimization strategy in step S4 is as follows: In each control cycle, the multi-objective optimization problem is solved in the preset prediction time domain with the current synchronized digital twin model state as the initial condition, and the optimal control sequence in the time domain is obtained; only the first control quantity in the control sequence is issued and executed; in the next control cycle, the optimization solution is re-performed with the updated model state to realize the forward rolling of the control time domain.

[0013] As a preferred technical solution of the present invention, in step S2, the temperature sensor is a plurality of thermocouples, which are arranged at equal intervals along the length of the mold and 2-5mm away from the surface of the cavity.

[0014] As a preferred technical solution of the present invention, the preset optimization algorithm in step S4 is an improved particle swarm optimization algorithm, whose inertial weights adaptively decrease with the number of iterations, and introduces chaotic perturbations in the velocity update to avoid getting trapped in local optima.

[0015] As a preferred technical solution of the present invention, the rolling optimization cycle in step S4 is 5-30 seconds, and the time domain for each optimization prediction is from the current moment to the expected end of vulcanization.

[0016] The beneficial effects of this invention are as follows: 1. The present invention enables transparency of the internal state driven by digital twins: Specifically, by using a digital twin model to calculate the internal temperature field and vulcanization degree field of the rubber strip in real time online, the problem of "invisible and inaccurate measurement" of the internal state of the tire repair rubber strip during vulcanization process is solved, realizing the transformation from "black box operation" to "transparent production".

[0017] 2. The model reduction method of this invention ensures the feasibility of real-time simulation: Specifically, the POD+DEIM model reduction method is adopted to compress the full-order model with tens of millions of degrees of freedom to a state space of tens of dimensions. The single-step simulation time is reduced from minutes to sub-seconds (0.2 seconds), making online real-time simulation possible instead of impossible, and providing a real-time computing basis for rolling optimization.

[0018] 3. The present invention uses ensemble Kalman filtering to ensure high-fidelity mapping: Specifically, the ensemble Kalman filtering algorithm is used to assimilate the limited mold temperature observation data with the high-dimensional physical model, and to correct the simulation deviation caused by model simplification and unknown disturbances in a timely manner, so as to ensure high-fidelity mapping between the digital twin and the physical entity.

[0019] 4. The present invention achieves adaptive closed-loop control through rolling time-domain optimization: Specifically, with minimizing the standard deviation of cross-sectional vulcanization as the primary objective, a rolling time-domain optimization strategy is adopted. Each control cycle is re-optimized based on the latest synchronization state, which can adaptively compensate for fluctuations in operating conditions, significantly reduce the risk of under-vulcanization and over-vulcanization of rubber strips, and improve product qualification rate and consistency.

[0020] 5. This invention achieves multi-objective optimization that balances quality, efficiency, and energy consumption: Specifically, while ensuring vulcanization quality (cross-sectional uniformity), it simultaneously optimizes vulcanization time and energy consumption to achieve the comprehensive optimal balance of quality, efficiency, and energy consumption. Attached Figure Description

[0021] Figure 1 This is an overall flowchart of the method of the present invention. Detailed Implementation

[0022] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments.

[0023] Example 1, referring to Figure 1 A method for optimizing the vulcanization process of tire repair strips based on digital twins includes the following steps: S1. Constructing a digital twin model: Based on the geometric dimensions of the mold cavity of the flat vulcanizing machine and the tire repair strip, a three-dimensional geometric model is established. Parameters such as the thermal conductivity and specific heat capacity of the rubber strip material are experimentally determined and fitted as functions of temperature.

[0024] By coupling the transient heat conduction equation with the Kamal-Sourour sulfidation reaction kinetic equation, a multiphysics full-order model is generated.

[0025] To meet the requirements of real-time simulation, intrinsic orthogonal decomposition (POD) combined with discrete empirical interpolation (DEIM) was used to reduce the order of the full-order model. Specifically, transient simulations of the full-order model were first performed under various process conditions (heating plate temperature 150-170℃, vulcanization time 300-600 seconds), and snapshot matrix data of temperature field and vulcanization degree field were collected at each time step. POD decomposition was performed on the snapshot matrix, and the top 20 dominant modes were extracted as the reduction basis (cumulative energy percentage > 99%). For nonlinear terms such as the exothermic source term of the vulcanization reaction, DEIM was used to select interpolation points for approximate calculation. Testing showed that the reduced-order model's single-step simulation time was 0.2 seconds, meeting the requirements for online real-time simulation.

[0026] S2. Real-time Data Acquisition: Multiple armored thermocouples are evenly distributed along the length of the mold at a distance of 3mm from the cavity surface. A pressure sensor is also installed in the cavity. During vulcanization, the temperature of characteristic points on the mold and the cavity pressure are collected at a frequency of 1Hz and uploaded to the host computer via a data acquisition card.

[0027] S3. Digital Twin State Synchronization: Using a reduced-order model running in the host computer as the prediction model, and taking the collected mold temperature data from six measurement points as the observation vector. The temperature of all finite element mesh nodes inside the adhesive strip and degree of sulfidation (The total number of states is approximately 2000 dimensions) forming the state vector. An ensemble Kalman filter algorithm is used, with 60 members in the ensemble, to correct the state vector in real time, eliminate accumulated model errors, and make the digital twin model consistent with the physical vulcanization process.

[0028] S4. Rolling Optimization of Process Parameters: In each control cycle (e.g., 10 seconds), using the synchronized digital twin model and the current synchronized model state as the initial condition, predict the distribution of the vulcanization degree of the rubber strip under different process parameter inputs (e.g., heating plate temperature setpoint, vulcanization time) within the prediction time domain (from the current moment to the preset maximum vulcanization time). The primary objective is to minimize the standard deviation of the vulcanization degree across the entire cross-section of the rubber strip, while secondary objectives are short vulcanization time and low energy consumption. A multi-objective optimization function is constructed as follows: ; in, The standard deviation of the degree of vulcanization at all nodes on the cross-section of the rubber strip. This is the currently predicted vulcanization completion time. As the baseline vulcanization time, To predict energy consumption, As the reference energy, , , Here are the weighting coefficients; The value is greater than and The primary optimization objective is to reflect the uniformity of the cross-sectional vulcanization degree.

[0029] in The maximum weight is 0.6. An improved particle swarm optimization algorithm with adaptive inertial weights and chaotic perturbation is used for multi-objective rolling optimization. Only the heating plate temperature or pressure command at the current moment in the optimization result is used as the control output.

[0030] S5. Process Sending: Send the current heating plate temperature or pressure command from the optimization results to the PLC of the vulcanizing machine, adjust the heating power or hydraulic valve to achieve closed-loop control, and repeat S2-S5 in the next cycle until the vulcanization is completed.

[0031] As a preferred method, the parameters of the sulfurization reaction kinetic model were obtained by differential scanning calorimetry at different heating rates and then fitted.

[0032] As a preferred approach, the ensemble Kalman filter used for state synchronization has a set of 50-80 members, which effectively fuses sensor data and model predictions.

[0033] As a preferred approach, the prediction time domain for rolling optimization is from the current moment to the expected completion time of vulcanization, and the standard deviation has the highest weight among the optimization objectives.

[0034] Example 2: This example uses a trapezoidal cross-section tire repair strip as an example. The rubber matrix is ​​a blend of natural rubber and styrene-butadiene rubber, and the vulcanization system is a sulfur accelerator system. The mold is a multi-cavity flat mold, and the heating plate power is controllable.

[0035] Step S1: Using 3D modeling software, establish a geometric model based on the actual mold and rubber strip dimensions. The rubber strip cross-section is a trapezoid with an upper base of 4mm, a lower base of 6mm, a height of 5mm, and a length of 200mm. The rubber density, specific heat capacity, and thermal conductivity are fitted as functions of temperature. Using the Kamal-Sourour model, the equation parameters are determined through DSC experiments. , , , , After establishing a full-order transient finite element model, snapshot matrices were generated under various operating conditions. A 20th-order modal basis was extracted using POD, and nonlinear terms were processed using DEIM to construct a reduced-order model. Testing showed that the single-step simulation time for the reduced-order model was 0.2 seconds.

[0036] Step S2: Arrange a K-type thermocouple every 40mm along the length of the rubber strip at a position 3mm from the bottom surface of the cavity on the lower mold plate, for a total of 6 temperature measuring points. A pressure sensor monitors the cavity pressure. The signal is transmitted to the industrial control computer at a frequency of 1Hz via an AD module.

[0037] Step S3: Deploy the reduced-order model and ensemble Kalman filter algorithm in the industrial control computer. The state vector consists of the temperature and vulcanization degree of the finite element nodes of the rubber strip (approximately 2000 dimensions), and the observation vector consists of the temperature values ​​of 6 thermocouples; the observation noise covariance is set according to the sensor accuracy. The ensemble number is set to 60. For each set of real-time temperatures received, the filtering algorithm updates the entire state field to achieve synchronization.

[0038] Step S4: Set the control cycle to 15 seconds. In each cycle, using the synchronized state as the initial field, the optimization variables are the heating plate temperature setpoint (constrained at 150-170℃) and the remaining vulcanization time. The multi-objective function is: , The standard deviation of the cross-sectional sulfidation degree is denoted as 0.03, with a target value less than 0.03. An improved particle swarm optimization algorithm is used, with a population size of 30 and 40 iterations, to solve for the optimal temperature curve in the prediction time domain. The first control variable is then executed.

[0039] Step S5: Send the temperature command to the temperature controller, adjust the heater output, and repeat S2-S5 in the next cycle until vulcanization is complete.

[0040] After actual operation, the standard deviation of the vulcanization degree of the tire repair strip cross section decreased from 0.07 to below 0.02, the average vulcanization time was shortened by 8%, energy consumption was reduced by 6%, and the product batch qualification rate increased from 92% to 99.5%.

[0041] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A method for optimizing the vulcanization process of tire repair strips based on digital twins, characterized in that, Includes the following steps: Step S1: Construct a digital twin model of the tire repair strip vulcanization process: Based on the geometry of the actual vulcanization equipment and the cross-sectional shape of the tire repair strip, establish a three-dimensional geometric model including the mold and the strip, and assign thermal property parameters of the strip material as a function of temperature. Couple the transient heat conduction equation and the vulcanization reaction kinetic equation to form a multi-physics coupled model. Use intrinsic orthogonal decomposition combined with discrete empirical interpolation to reduce the order of the multi-physics coupled model to obtain a reduced-order model. The reduced-order model serves as the digital twin model, and its single-step simulation time does not exceed 1 second to meet the timeliness requirements of online real-time simulation. Step S2, Real-time data acquisition: During the vulcanization process, temperature and pressure sensors arranged inside the mold near the cavity are used to collect mold temperature and cavity pressure at a preset frequency and transmit them to the host computer. Step S3, Digital Twin State Synchronization: The real-time mold temperature data collected in step S2 is used as the observation vector and input into the digital twin model. Using ensemble Kalman filtering, the temperature and vulcanization degree of each grid node inside the rubber strip are used as the state vector. The state vector is optimally recursively estimated through the observation values. The state variables of the temperature field and vulcanization degree field inside the model are corrected online to keep the digital twin model synchronized with the current vulcanization state of the physical entity. Step S4, rolling optimization of process parameters: Based on the synchronized digital twin model, a multi-objective optimization model is constructed with minimizing the standard deviation of the vulcanization degree of the rubber strip cross section as the primary objective, while also taking into account the shortest vulcanization time and the lowest energy consumption. The model uses at least one of vulcanization temperature, vulcanization time and vulcanization pressure as decision variables, adopts a rolling time-domain optimization strategy, and solves the problem with a preset optimization algorithm to obtain the optimal process parameter sequence in the future time domain. Step S5, Process Execution: The first control command in the optimal process parameter sequence obtained in step S4 is sent to the programmable controller of the vulcanizing equipment to adjust the heating power or pressure valve, thus completing the optimization closed loop of one control cycle.

2. The method for optimizing the vulcanization process of tire repair strips based on digital twins according to claim 1, characterized in that, The kinetic equation for the sulfidation reaction in step S1 adopts the Kamal-Sourour model: ； in, The degree of sulfidation, For time, , To be the temperature-dependent rate constant that follows the Arrhenius equation, , denoted as the reaction order.

3. The method for optimizing the vulcanization process of tire repair strips based on digital twins according to claim 1, characterized in that, The transient heat conduction equation in step S1 includes a term representing the exothermic source of the sulfidation reaction: ； in, For density, For specific heat capacity, For temperature, Thermal conductivity, This represents the total heat released during the sulfidation reaction.

4. The method for optimizing the vulcanization process of tire repair strips based on digital twins according to claim 1, characterized in that, The model reduction method in step S1 is as follows: by performing transient simulation on the full-order model under different process conditions, transient simulation snapshots of the temperature field and the degree of sulfidation field are collected, and a snapshot matrix is ​​constructed. The snapshot matrix is ​​subjected to eigenorthogonal decomposition, and the top N dominant modes are extracted as the reduced-order basis. The value of N is such that the cumulative energy percentage is not less than 99%. For nonlinear terms such as the exothermic source term of the sulfurization reaction, the discrete empirical interpolation method is used to process them. The nonlinear terms are projected onto the low-dimensional space spanned by the reduced-order basis for approximate calculation, thereby realizing the conversion from the full-order model to the reduced-order model.

5. The method for optimizing the vulcanization process of tire repair strips based on digital twins according to claim 1, characterized in that, In step S3, the state vector of the Kalman filter is set. Temperature of all finite element mesh nodes inside the adhesive strip and degree of sulfidation ,Right now Where M is the total number of grid nodes; observation vector The measured values ​​from the mold temperature sensor collected in step S2; ensemble Kalman filtering is used to construct... The set of states consists of 50-80 members. The set members are updated recursively using the observed values. The mean of the set is taken as the optimal estimate of the state variables.

6. The method for optimizing the vulcanization process of tire repair strips based on digital twins according to claim 1, characterized in that, The objective function of the multi-objective optimization model in step S4 is: ； in, The standard deviation of the degree of vulcanization at all nodes on the cross-section of the rubber strip. This is the currently predicted vulcanization completion time. As the baseline vulcanization time, To predict energy consumption, As the reference energy, , , Here are the weighting coefficients; The value is greater than and The primary optimization objective is to reflect the uniformity of the cross-sectional vulcanization degree.

7. The method for optimizing the vulcanization process of tire repair strips based on digital twins according to claim 1, characterized in that, The specific implementation of the rolling optimization strategy in step S4 is as follows: In each control cycle, the multi-objective optimization problem is solved within the preset prediction time domain, using the current synchronized digital twin model state as the initial condition, to obtain the optimal control sequence within that time domain; only the first control quantity in the control sequence is issued and executed; in the next control cycle, the optimization solution is re-performed with the updated model state, thereby realizing the forward rolling of the control time domain.

8. The method for optimizing the vulcanization process of tire repair strips based on digital twins according to claim 1, characterized in that, In step S2, the temperature sensor consists of multiple thermocouples, which are arranged at equal intervals along the length of the mold and 2-5 mm away from the surface of the cavity.

9. The method for optimizing the vulcanization process of tire repair strips based on digital twins according to claim 1, characterized in that, In step S4, the preset optimization algorithm is an improved particle swarm optimization algorithm, in which the inertial weights adaptively decrease with the number of iterations, and chaotic perturbations are introduced in the velocity update to avoid getting trapped in local optima.

10. The method for optimizing the vulcanization process of tire repair strips based on digital twins according to claim 1, characterized in that, The rolling optimization cycle in step S4 is 5-30 seconds, and the time domain for each optimization prediction is from the current moment to the expected end of vulcanization.

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