Predicting Tube Ovalization in Cold Bending: An Analytical Approach

Abstract

Ovalization (or flattening) of tubes in cold bending operations causes dimensional inaccuracy that may lead to loss of fit-up and function of the formed product. The particular distortion mechanism is governed by radial bending stress components forcing the extremities of the tube section towards the neutral layer of the cross-section. Thus, the magnitude of distortions is limited by the instantaneous stiffness of the tube section upon plastic bending. In order to proactively consider tube ovalization in the product design process, it is necessary to develop a practical methodology that takes into account the impact of governing parameters such as material, tool and section geometries. In the present work, an analytical model of the ovalization problem has been developed using the deformation theory of plasticity. The results show that the diameter of the tube is the most important parameter with respect to tube ovalization, while the thickness of the tube section and the bending radius are of the same relative importance. The developed model indicates that strain hardening is the most important material parameter, whereas tube ovalization is nearly unaffected by the initial yield stress. The present model shows good correlation with a number of experiments.