Theoretical analysis, finite element modeling and experimental investigation of the impact of friction between tube and bending die on the formability of the tube during the free-bending process

In the free-bending process, the tube undergoes bending and deformation due to the action of a guide mechanism and bending die. The plastic deformation zone of the bent tube is less constrained by the die, and the quality of the formed tube is significantly affected by the friction between the tube and the die. To assess the impact of friction between tube and die on the formability of the bent tube, the theoretical modeling that considers the friction coefficient is conducted. Afterward, the free-bending experiments and finite element simulations are performed using Cr12MoV and ceramic bushing. The theoretical and experimental results are compared with those obtained from finite element simulation under different friction conditions to confirm the validity of finite element simulation. The influence of friction on the arc radius, wall thickness variation, and cross-section deformation of the curved tube is explored and discussed. With the increase of friction coefficient, the arc radius decreases gradually, the wall thickness thickens more obviously, and the cross-sectional distortion becomes more serious. Furthermore, the effect of different bushing materials on the surface quality of aluminum alloy and stainless-steel bent tubes is experimentally investigated. Those findings expand our understanding of the influence of tube-die friction on deformation behavior and it is necessary to first determine the friction condition during the actual free-bending forming process.