Forming tubes with various bending radii without changing the bending dies is much easier for the 3D free bending forming (FBF) process. In the 3D-FBF process, different bending radii were realized by adapting the eccentricities of the bending dies. The accuracy of the U-R curve is crucial for the precision forming of complex bending components. In this study, the U-R relation curve of the Al alloy tube with a specific friction coefficient, fixed geometry size, clearance between tubes, and bending die was fitted first based on the forming results of AA6061-T6 tubes under different eccentricities. Second, the U-R relationship curve based on the experiment is used to propose the U-R relationship's mathematical formula based on many hypotheses. Finally, the modified U-R mathematical formula was applied in the finite element (FE) simulation and the actual FBF experiments for the AA6061-T6 Al alloy complex shape space bending members. The U-R relationship curve's reliability was verified by comparing the simulation and experimental results. The results obtained from the modified U-R relationship align well with the FE modeling results and can be directly applied to the bending process for the intended components.
Keywords: 3D free bending forming; U-R relation curve; aluminum alloy tube; finite element simulation; forming experiment.