Physics of large radius air bending

Abstract

Abstract Conventional or small radius air bending has been modeled and analytically described by many authors. This process is traditionally called 3-point bending. When using a large radius punch for design reasons or because it is necessary when bending high strength steels, a new phenomenon arises.The contact area between the punch and the plate, which is located at the tip of the punch at the outset of the forming operation, splits into two areas during the bending process by sliding away from the tip of the punch. This phenomenon is the so-called multi-breakage effect. It follows that the process is better described by a 4-point bending scheme in which the contact points of applied forces are continuously changing during the bending operation. The different phenomena of importance for this type of air bending process are addressed in the current contribution. First, the theoretical characteristic equation, required for determining the plate profile and the punch force, is established. Further, this initial model is enhanced by the effects of the tool indentation, the plate thinning and the friction coefficient variations. The introduction of these effects allows to develop an analytical model of the large radius air bending based on physical considerations. Although the developed model is not the ultimate one, it is an important step towards the complete understanding and the robust prediction of large radius air bending.