Generalized model of strains during bending of metal tubes in bending machines

Abstract

According to the postulate concerning a local change of the "actual active radius" with a bending angle in the bent zone, a generalized model of strain during bending of ametal tube has been derived. The considered tubes should be subjected to bending in tube bending machines by the method of wrapping on a rotating template and with the use of a lubricated steel mandrel. The model is represented by three components of strain in the analytical form, including displacement of the neutral axis. Generalization of the model of metal tubes in the existing papers consists in including the displacement of the neutral axis and the possibility of determination of strains at each point along the thickness of the wall of the bent tube in the bending zone. The derived scheme of strain satisfies initial and boundary kinematic conditions of the bending process, conditions of continuity and inseparability of strains. The obtained analytical expressions can be classified as acceptable from the kinematic point of view.