Conceptual Design of a Novel Four-Axis Free-Bending Equipment with Smooth Processing Trajectories for Spatial Tube High-Precision Manufacturing

Spatial bent tubes with variable curvature and torsion are widely used in high-end manufacturing. Traditional free-bending (FB) equipment with discrete processing trajectories has limited processing capabilities, which restricts the forming quality of spatial bent tubes. This paper first proposes a novel four-axis FB equipment with smooth processing trajectories. The design of this equipment is inspired by the six-axis FB equipment, with the C-axis repositioned to the front and redundant translational and rotational axes eliminated. On this basis, a springback behavior-guided process parameter optimization method is introduced. This method consists of two components: springback behavior prediction using Parallel FNO (P-FNO) and process parameter optimization using Robustness-Enhanced AGE-MOEA2 (RE-AGE-MOEA2). P-FNO is considered as the fitness function during parameter optimization. RE-AGE-MOEA2 employs Monte Carlo sampling and multiple predictions to eliminate the effects of uncertainty in P-FNO. The proposed FB equipment and parameter optimization method are validated through numerical simulations. The results indicate that bent tubes processed by the four-axis FB equipment exhibit higher geometric stability compared to those processed by the six-axis FB equipment. The process parameter optimization method can provide FB parameters that effectively compensate for springback. Integrating the novel four-axis FB equipment with the process parameter optimization method enables high-precision FB forming of spatially complex tubes.