A flexible and incremental sheet metal bulging machine using a path-controlled spherical roller performed a wide range of sheet metal shaping of complex shapes, e.g., pyramidal shells, shells of the frustum of a pyramid, shallow pans and embossed panels. The deformation analysis on the incremental forming of sheet metal becomes a very useful method for the planning of shell products, the choice of material, the design of the forming process and the planning of the non-traditional machine tool.

In this article, firstly, an approximate deformation analysis for the bulging height, the strain distributions and the forming load of the shell is proposed, using a plane-strain deformation model and a forming-limit diagram. Secondly, the FEM based on the shell theory is applied to the calculation of the bulging height, the strain and the stress distributions and to an explanation of the plane-strain deformation, which is a unique phenomenon in incremental forming.

The predictions by the approximate deformation analysis and the FEM analysis for the shell of the frustum of a quadrangular pyramid were in reasonably good agreement with experimental values for annealed aluminum sheet.