Data-Driven Approach for Minimizing Springback in Roll Forming: An Adaptive Process Parameter Control Strategy

Springback is the most common quality defect in roll forming. It is difficult to control springback efficiently because the forming process is very complex and difficult to analyze. This paper proposes a data-driven springback control method that can adaptively adjust process parameters to minimize springback. Firstly, a digital twin model was established for efficiently collecting equipment data, formed part data, and remote equipment control. Then, based on gathered springback data considering different sheet widths, materials, uphill volumes, and roll gaps, a high-precision springback prediction model was constructed using the SAPSO-SVR algorithm. Lastly, building upon the prediction model, optimization models were developed using bat algorithm, enabling the system to automatically adjust process parameters based on optimization results when forming different sheets.The experimental results show that after optimization, the springback at the two corners of the hat-shaped part is reduced by 36.8% and 14.3% respectively. Experimental findings initially demonstrate the efficacy of this approach in controlling springback across sheets of diverse materials and varying widths. The proposed adaptive springback control method significantly enhances production efficiency and forming quality, driving the intelligent advancement of sheet metal roll forming technology.


Introduction
Roll forming is a process that uses multi-pass forming rolls to gradually bend the sheet to make a metal profile with a specific cross-section (Figure 1).Roll forming has the characteristics of high efficiency, low cost and flexibility, and is widely used in new energy vehicles, aerospace and other industries.Springback is the most common and difficultly solved quality defect in roll forming.How to efficiently control springback has become a difficult problem.
The parameters affecting springback have been extensively studied.Based on previous theoretical and experimental analysis [2][3][4][5], the process parameters related to springback selected in this article include the uphill volume and the roll gap.The uphill volume is the vertical height difference between the centres of the upper (lower) rolls of two adjacent passes (Figure 2).
The common control methods for the springback in roll forming include theoretical analysis [7] and finite element simulation [8][9][10][11][12].However, due to the complexity of the roll forming process, there are limitations in the accuracy and reliability of theoretical analysis results.Simulating complex cross-sections also incurs significant time costs.Both of these methods have constraints.
In other fields, some studies have explored the use of optimization algorithms to seek an optimal process.For instance, Gauntt [13] employed genetic algorithms in lightweighting  research on gears to search for the optimal gear structure.However, the optimization function relies on simulations for calculation.Each search iteration necessitates running a large number of simulations to obtain a single iteration result, leading to a final result that is relatively reliable but with low time efficiency.
Aiming at solving the limitations of previous methods, this paper proposes an adaptive springback intelligent control method for roll forming.First, a digital twin model is built for real-time monitoring and regulation.Then, a SAPSO (simulated annealing particle swarm optimization)-SVR (support vector regression) springback prediction model was constructed based on 32 sets of springback data obtained from actual experiments.In previous study [6], the SAPSO-SVR predictive model exhibited high accuracy in predicting springback.However, the focus of this study is on a part with a more intricate cross-sectional geometry, namely a hat-shaped component, introducing increased complexity to the forming process.Moreover, the model is constructed based on actual orthogonal experimental data, with a relatively limited quantity, potentially leading to some deviation in the results compared to previous studies.Based on the springback prediction model, the method takes the prediction function as the optimization function and the process parameters as the optimization parameters.And it obtains the optimal springback scheme in real time when different sheets are input.This method achieves higher accuracy and reliability than traditional theoretical analysis methods and demonstrates greater timeliness than FEA method.It promotes the intelligent upgrading of roll forming technology.

The adaptive springback optimization method 2.1. Data acquisition, control and visualization
To achieve real-time optimization, it is necessary to provide an optimization plan in advance before the sheet metal forming process.This requires a closed-loop method consisting of data acquisition, springback prediction, springback optimization, and remote equipment control.The overall framework is shown in Figure 3. Firstly, a prediction model is constructed based on previous experimental data.This prediction model serves as the optimization function for the optimization module.The optimization algorithm utilizes this function to search for the optimal process parameters under different material conditions.The results are then fed back to the digital twin system for real-time control of the equipment and recording of the final outcomes.The optimal solution and results can be re-inputted into the prediction model to expand its dataset, continuously improving the prediction accuracy.Real-time reading and adjustment of key parameters, including roll gap and uphill volume, is crucial for achieving springback prediction and optimization.The roll gap can be calculated based on the positions of the upper and lower rolls for each pass, as well as the lateral positions of the passes.Therefore, the elemental parameters include the positions of the upper and lower rolls for each pass, the lateral positions of the passes, and the rotational speed of the motors.
In the digital twin system, the principle of real-time reading and adjustment of key parameters involves the following steps, as shown in Figure 4: Analyzing the code of the PLC control unit to determine the memory addresses and data types of the key parameters.Establishing a communication connection and using a suitable communication protocol such as Modbus TCP for data exchange with the PLC.By reading the real-time parameter data stored in the PLC memory, we can obtain the current values of the parameters.These parameter values are typically stored in memory as binary representations of floating-point numbers.To achieve precise control, appropriate conversions and processing may be required to obtain the actual values of roll gap, roll crown, and rotational speed.
Once the parameter values are obtained, adjustments can be made as needed, for example, setting target positions or adjusting the rotational speed.The adjusted parameter values are transmitted to the servo motors to achieve precise motion control.Servo motors provide higher accuracy and stability for controlling the motion of the upper and lower rolls and passes in the roll-forming equipment.The currently implemented digital twin system is shown in figure 5.
Real-time monitoring and adjustment of key parameters enable the optimization of roll-forming equipment operation, facilitating springback prediction and optimization.This provides crucial technical support for improving process accuracy and production efficiency.

Springback prediction model
This article uses the SAPSO-SVR algorithm to predict springback.SVR is a common machine learning model used to solve regression problems.SVR is very suitable for solving small sample, high-dimensional, non-linear problems.These characteristics make it feasible to build highprecision regression models at low cost and in a short time.In order to ensure the scalability of the model and avoid the unreliability of results and time costs caused by manual parameter adjustment, SAPSO is used to optimize the model.The improved SAPSO-SVR can perform adaptive parameter adjustment after the model database is expanded, so that the versatility and accuracy of the new prediction model are automatically improved.This facilitates the continuous addition of new data to the model during the roll forming process and taking into account the forming of new sections.
In previous study [6], the SVR kernel function used adopts RBF (radial basis function) kernel.The three key parameters to be determined are the insensitive loss coefficient ε, the penalty coefficient C, and the width coefficient γ.Optimization of the SVR model must optimize all three parameters simultaneously.Inappropriate parameters can make the accuracy of the trained model degrade and make it difficult to fit the real situation.And the algorithm parameters of the optimal prediction model corresponding to data sets with different data volumes are also different.Therefore, it is necessary to use SAPSO to optimize SVR.The SAPSO-SVR algorithm flow chart is shown in Figure 6.The temperature in the algorithm diagram is associated with the annealing process in the simulated annealing algorithm.The optimized algorithm no longer needs manual parameter adjustment.Whenever the data set is expanded with a part of the data, the algorithm is automatically adjusted to improve the prediction accuracy and applicability.

Springback optimization model
On the basis of realizing high-precision springback prediction model, bat algorithm is used to seek optimal process parameters.The prediction model with the highest accuracy is saved as the optimization function.Before the optimization algorithm runs, the digital twin system needs to be given the current sheet data, and the optimization algorithm searches for the corresponding optimal process parameters.This optimization method realizes real-time optimization, and its significance i s t hat w hen a p art w ith d ifferent sh eet wi dths an d di fferent mat erials nee ds to be 6 formed, this method can automatically obtain the optimal process parameters and transfer them to the digital twin model for adjustment without human intervention.
At the same time, it should be noted that the reliability of the optimization results depends on the accuracy of the prediction model.If the accuracy of the prediction model is low, the obtained optimization results may not achieve the expected results.It is therefore necessary to continuously record molding data and augment predictive model datasets.In order to train the springback prediction model and optimization model in the shortest time and at the lowest cost, we designed an orthogonal experiment to accumulate the relatively most comprehensive hat-shaped part forming data.The data set contains 32 sets of experiments.In each experiment, due to the symmetrical characteristics of the hat-shaped part, the springback of the two corners on the left side of the hat-shaped part was taken as the forming evaluation index.The measurement method is to measure the two bending angles of the cross-section at 1/4, 1/2, and 3/4 of the molded part.These three cross-sections can be seen in Figure 8.The advantage of this is that the forming situation of the entire sheet is comprehensively considered.The deformation at both ends of the sheet is not stable, so the two sections at the starting point and end point of the length direction of the sheet are not taken.

Results and analysis
The prediction accuracy test was carried out based on the forming data of hat-shaped parts.All experiments were conducted using the Shensi Lab roll forming equipment.The dataset is available upon request from the authors.In each experiment, the data was shuffled and 70% of it was selected as the training set, while 30% was used as the testing set.And the optimal SVR parameter pairs obtained by SAPSO-SVR and the corresponding resultant metrics are shown in Table 1.
The results show that the optimized parameters are not stable.Common reasons for this phenomenon are too little data volume and some noisy data.The difference in R2 between  This also shows that some experimental results may be distorted and require further processing.
The optimal model obtained in 5 experiments has the R2 of 0.94, the mean absolute error of 0.223, and the median absolute error of 0.172.The accuracy of this model initially meets the needs of the optimization model.At the same time, further expansion of the data set can be considered to improve the accuracy of the prediction model.It takes about 0.04s to use the trained prediction model to predict 500 pieces of data.The prediction speed of SAPSO-SVR prediction model is very fast and can meet the need of real-time prediction.
Based on the highest-precision springback prediction model obtained in Experiment No. 3 as the optimization function, the springback optimization model was obtained using the BA algorithm.An experiment was conducted on a sheet with a material model of Al6061 and a sheet width of 100.The initial unadjusted process and the optimized process were compared.The experimental results are shown in the Table 2. he results show that the average springback of the two bending corners of the hat-shaped part obtained by the optimized process is reduced by 0.7°and 0.3°respectively.With the current small sample set, this result is considered to initially demonstrate the effectiveness of the model.The reason why the optimization results are not closer to 90°may be that the insufficient amount of data results in insufficient accuracy of the prediction model.It may also be caused by some noisy data.In the future, it is necessary to further expand the experimental collection data to obtain a better molding result.

Conclusion
This research is dedicated to solving the complex cross-section and springback defects in the sheet metal roll forming process through an adaptive springback intelligent control method.Through the collaboration of the digital twin module, springback prediction module and springback optimization module, this method realizes the fully automatic adjustment of process parameters, thereby significantly improving production efficiency and forming quality.Experimental results show that the cross-section after the optimized process has a springback reduction of 36.8% and 14.3% respectively at the two bend corners compared to the default process.The effectiveness of the springback optimization model proposed in this paper has been initially verified.
In the future, it is necessary to further expand the data set, enhance the reliability of the model, and consider more process parameters and more complex cross-sections to enhance the versatility of the model.

Figure 3 .
Figure 3.The framework of the intelligent optimization method.

Figure 5 .
Figure 5. Virtual scene in the digital twin system of roll forming equipment.
part The hat-shaped parts are used for verification.Its section is shown in the Figure 7.The flange part changes with the width of the original sheet.

3. 2 .
Experimental design The process parameters studied include uphill volume and roll gap.The values of the uphill volume are 0 mm, 2.5 mm, 5 mm, 7.5 mm, and 10 mm.The values of the roll gap are 1.48 mm, 1.49 mm, 1.5 mm, 1.51 mm, and 1.52 mm.Three materials, Al3003, Al5052, and Al6061, were used for research.There are 4 different sheet widths: 85 mm, 90 mm, 95 mm, and 100 mm.

Table 1 .
Optimal parameters and results found by SAPSO-SVR in 5 experiments.

Table 2 .
The comparison of the springback result of unadjusted process (the first row) and the optimized process (the second row).