A derivation of the generalized model of strains during bending of metal tubes at bending machines

According to the postulate concerning a local change of the “actual active radius” with a bending angle in the bend zone, a generalized model of strain during metal tube bending was derived. The tubes should be subjected to bending at tube bending machines by the method of wrapping at the rotating template and with the use of a lubricated steel mandrel. The model is represented by three components of strain in the analytic form, including displacement of the neutral axis. Generalization of the model during bending metal tubes at the tube bending machines as compared with the existing papers (Śloderbach, 1999; Śloderbach and Rechul, 2000) consists in including the neutral axis displacement and possibility of determination of strains at each point along the thickness of the wall of the bent tube in the bending and bend 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 analytic expressions can be classified as acceptable from the kinematic point of view.