Determination of the punch tip radius in air bending of sheet metal

The issue of manufacturing thin-walled enclosures of small devices of small-scale or single production using air bending, in which there is an air gap between the sheet and the walls of a V-shaped matrix, is considered. During the operation of various mechanisms, the load is often transferred from one part to another through a common contact surface (bolted, riveted, keyed, splined joints, coupling parts, etc.). In such cases, it is necessary to assess the strength of the parts for crumpling. To avoid damage to the surface of the deformable sheet, it is necessary that the maximum contact stresses σcon from the impact of the punch do not exceed the permissible crumpling stress [σcm], the values of which can be determined from reference data or, as in this work, according to the formula in which the permissible crumpling stresses for plastic materials under static loading conditions are determined through the yield strength and time the resistance of the deformable material. The value of the maximum contact stresses σcon is determined by the Hertz-Belyaev method, for which the punch is presented in the form of a cylinder, the radius of which is equal to the radius of the tip of the punch Rp. Formulas are given for determining the maximum contact stresses σcon in the case of elastic cylinder-plane contact, which is characteristic of the initial stage of air bending, and the deformation force (punch) during free bending. An expression is obtained for determining the radius of the punch tip, which does not lead to crumpling of the contact surface of the workpiece, which is used to determine the parameters of stepwise bending of sheet metal.