Real-time and data-efficient springback prediction in tube bending using force measurement and physics-informed machine learning

Tube bending is widely used in manufacturing structural components with complex curvatures and angles. However, springback is a major issue affecting the dimensional accuracy of components and production efficiency. Accurately predicting and controlling springback in tube bending is a critical challenge, as traditional analytical models, while useful, struggle with deformation complexities and manufacturing uncertainties, limiting their prediction accuracy. Meanwhile, machine learning models show great potential for addressing these limitations but often require large datasets, posing a challenge in data-limited industrial applications. In this research, we develop a physics-informed neural network (PINN) that integrates an analytical force-springback relationship into a convolutional neural network (CNN) framework. Firstly, a validated force-monitoring system is used to capture real-time force data during tube bending, while springback is measured using a soft sensor that combines displacement measurements with analytical calculation. Furthermore, an attention-based mechanism is applied to enhance the model's explainability, identifying the most influential forces and time steps in predicting springback. The PINN model is evaluated from three aspects, i.e., the overall predictive performance and explainability, the ability to learn effectively with limited training data, and the feasibility for real-time springback prediction utilizing truncated force sequences. The results demonstrate that PINN successfully predicts springback and adapts to variations in material properties, achieving comparable accuracy to CNN. Additionally, when trained with fewer samples, PINN benefits from the embedded physical constraints, thus exhibiting faster convergence, improved stability and more consistent predictions. These findings indicates that PINN provides a data-efficient and reliable approach for springback prediction, with promising applications in real-time monitoring, explainable AI, and closed-loop process control for tube bending. • Real-time springback prediction using physics-informed neural networks. • In-process monitoring system integrates real-time force data and soft sensor measurement. • Embedding analytical constraints enhance model stability and accuracy. • Channel-wise attention identifies critical forces, improving interpretability. • Early-stage prediction supports inline correction in tube bending.