Mathematical approach to design preform for multi stage robot assisted incremental forming

Robo-forming is a flexible version of Incremental Sheet Forming (ISF) that utilizes industrial robots to guide the forming tool along a desired trajectory on a blank surface. ISF is particularly suitable for rapid prototyping and low-volume production; however, the process is limited by a critical wall angle, beyond which the material fails by necking. Geometric shapes that exceed this critical wall angle have to be formed in multiple stages, adhering to the maximum limit of wall angle in each of the intermediate stages. Since the final outcome depends upon the intermediate shapes formed, it is essential to optimize the design of pre-form shape(s). The existing methods for multi-stage forming rely heavily on intuition and other heuristics for preform design. The current work proposes a frequency decomposition based approach using Fourier transform to generate preforms. The proposed multi-stage methodology presents a more standardized, algorithmic approach, ensuring an effective and reliable methodology that can be applied to any new complex shape. Experimental results demonstrate that the forming depth of the target geometries has improved significantly up to \(235\%\) for the human cranial implant shape (a freeform shape) and by \(155\%\) and \(173\%\), respectively, for hemispherical and elliptical components compared to the case without preform, ensuring successful forming of the components without fracture.