Part 1: Analytical modeling of symmetric multi-nose tube hydroforming

Part 1 of this series of papers presents an analytical model for a multi-nose tube hydroforming process based on a mechanistic approach. In this process, the tube is surrounded by a number of evenly distributed circular dies. The model was established based on equilibrium conditions, yielding criteria, geometrical relationships, and a volume constancy condition. The system of equations was derived and solved for various process parameters. The model validation was performed using finite element analysis and experiments. The model has the ability to predict process parameters such as stresses, strains, internal pressure, geometry variables, and thinning rate distribution. The model could be applied to regular planar tube hydroforming of polygonal shapes such as square, pentagon, or octagon. Details for establishing governing relationships for polygonal shape hydroforming from the multi-nose analytical model are given in Part 2 of this series of papers.