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.     

Part 2: Analytical modeling of regular planar polygon tube hydroforming as a special case of symmetric multi-nose tube hydroforming

Part 2 of this series of papers presents an analytical model for regular planar polygon tube hydroforming (THF) as a special case of the analytical model for symmetric multi-nose tube hydroforming. The governing equations derived for multi-nose THF in Part 1 were evaluated by taking the limit of die geometric variables, resulting in a new set of governing equations for regular polygon THF. The model was validated using finite element analysis and a THF experiment, where good agreement was obtained. The model is able to predict field variables such as stresses and strain distribution, thinning rate distribution, and deformed shape at a particular pressure.