Forming characteristics of tube free-bending with small bending radii based on a new spherical connection

In tube free-bending, the connection of the bending die to the guide has a great influence on the stability of mechanical movement and the forming limit of the bent tube. The general connection of the bending die to the guide cannot realize the continuous stable movement of the bending die. Spherical connection of the bending die to the guide can guarantee a continuous changed tipping of the bending die, but has a limited minimal bending ratio (ratio of bending radius to tube outer diameter) of R/D₀ ≥ 3 depending on the geometrical constrains. In this paper, a new spherical connection of the bending die to the guide was designed through geometric derivation, which can lead to a greater deflection of the bending die, to realize the bending ratio of down to R/D₀ = 2.5. Based on the designed spherical connection, the bending ratio of down to R/D₀ = 2.43 and R/D₀ = 2.78 of brass tube were realized in the finite element simulation and bending test respectively. And with the analytical model, simulation model and experimental bending results, the forming characteristics of bent tube with small bending radii based on the spherical connection structure were investigated. The main results show that the equivalent stress, displacement of the strain neutral layer (NL) increase with the decrease of bending radius, and the wall thickness thinning in outer bend shows little differences under tight and big bending radii due to the increased axial thrust.