Selection of punch radius for air bending of sheet metal to prevent contact surface crushing

Abstract

Air bending is widely used in the low-volume or custom manufacturing of thin-walled enclosures for small devices. This process involves maintaining an air gap between the sheet metal and the walls of a V-shaped die. In the process of V‑bending, the technological tooling can leave marks on the surface of the deformed part, such as dents, scratches, and other defects. In order to avoid damage to the surface of the metal sheet by the technological tooling during V‑bending, the maximum contact stresses (σ_con) generated by the punch acting on the sheet material should not exceed the permissible crushing stress (σ_cr). In this study, the permissible crushing stress (σ_cr) was calculated using a formula based on the material’s yield strength and ultimate strength during deformation. To determine the maximum contact stresses (σ_con) during the elastic contact between a cylinder and a plane, which is characteristic of the initial stage of air bending, the Hertz-Belyaev approach was used, while the deformation force was calculated using a standard formula from the sheet metal forming theory. An expression was derived to determine the permissible punch radius, i.e., the minimum radius required to prevent the surface of the deformed metal from crushing. As a result of performed calculations, the relationships between the permissible punch radius (R_p), thickness of the sheet material, and distance between the working edges (groove width) of the die were obtained. The proposed methodology was successfully applied to develop technologies for step bending of thin sheet metal made of low-carbon and corrosion-resistant steels.