Analytical prediction of strains and forming forces in incremental forming

The process of incremental forming involves moving a stylus tool gradually over sheet of metal. It is a promising way to manufacture spare parts, but is physically a slow process, and simulation of the process by finite element modelling is also very slow. It is of interest to obtain an analytical method to predict changes in strain caused by a tool pass, and consequently to predict forming forces quickly. The dominant strains must be estimated realistically. A number of analyses exist that make restrictive assumptions to reduce the problem to two dimensions (eg Mirnia 2012). The component of force in the forming direction does plastic work, and can be estimated from the increment in plastic work that occurs during a tool pass. Estimated strain increments can also be added to find the total due to all tool passes in a stage of forming. This enables prediction of thinning of the sheet, which can lead to tearing if it becomes excessive. Previous strain estimates have assumed a material point moves either vertically (eg Li 2014) or moves normal to the surface of the tool (Bambach 2010). The present work combines both types of estimate to minimize equivalent plastic strain, estimating the angle to the vertical of material movement below the tool. Results are compared to finite element analysis and to experimental measurements of forming forces and of thinning