A Mathematical Model for Force Prediction in Single Point Incremental Sheet Forming with Validation by Experiments and Simulation

Abstract

Incremental sheet forming (ISF) is an emerging technology that has shown great potential in forming customized three-dimensional (3D) parts without the use of product-specific dies. The forming force is reduced in ISF due to the localized nature of deformation and successive forming. Forming force plays an important role in modeling the process accurately, so it needs to be evaluated accurately. Some attempts have been made earlier to calculate the forming force; however, they are mostly limited to empirical formulae for evaluating the average forming force and its different components. The current work presents a mathematical model for force prediction during ISF in a 3D polar coordinate system. The model can be used to predict forces for axis-symmetric cones of different wall angles and also for incremental hole flanging. Axial force component, resultant force in the r-θ plane, and total force have been calculated using the developed mathematical model appearing at different forming depths. The cone with the same geometrical parameters and experimental conditions was modeled and simulated on ABAQUS, and finally, experiments were carried out using a six-axis industrial robot. The mathematical model can be used to calculate forces for any wall angle, but for comparison purposes, a 45° wall angle cone has been used for analytical, numerical, and experimental validation. The total force calculated from the mathematical model had a very high level of accuracy with the force measured experimentally, and the maximum error was 4.25%. The result obtained from the FEA model also had a good level of accuracy for calculating total force, and the maximum error was 4.89%.