Effect of die fillet radius on tube thinning in free bending

During the operation of a free-bending die, its fillets inevitably wear out, thereby reducing their "sharpness" and decreasing the forming accuracy of tubes. To clarify the influence law of fillet radius on the wall thickness of freely bent pipes, this study employs a combined approach of finite element simulation and experimental testing to systematically analyze the strain characteristics and wall thickness distribution of the pipes. The results indicate that the outer surface of the pipe exhibits the maximum thinning rate when the mold ceases upward movement. During the mold movement stage, increasing the fillet radius can mitigate tube wall thinning by expanding the contact area between the mold and the pipe. The thinnest region of the bent pipe is located at the end of the radius formation section, with a maximum thinning rate of 5.4%. Furthermore, an increase in mold offset distance, a rise in friction coefficient, and the adoption of thin-walled pipe structures all exacerbate the thinning phenomenon in this vulnerable region, which warrants special attention in engineering practice. With the increase of fillet radius, the maximum thinning rate presents a variation pattern of "first decreasing rapidly and then decreasing extremely slowly". Within the range where the fillet radius-to-tube radius ratio (R_B/r) is less than 0.33, the rate of decrease is significantly faster than that in the range where R_B/r > 0.33. When R_B/r = 0.33, a sudden enhancement of the thinning-inhibiting effect is observed. Subsequently, further increasing the fillet radius exerts no significant inhibitory effect on the maximum thinning rate. The findings of this study provide a theoretical basis and engineering guidance for the optimization of fillet parameters of free bending dies and the control of pipe forming accuracy.