Multi-Objective Optimization of Loading Paths for Double-Layered Tube Hydroforming using Finite Element Analysis

Abstract

One of the most important studies in tube hydroforming process is optimization of loading paths. The primary purpose of this research is to maximize formability by detecting the optimal forming parameters. The most significant settings in the prosperity of tube hydroforming process, are internal pressure and end axial feed (i.e., load path). In this paper, a finite element analysis was performed for a double-layered tube hydroforming process using the ABAQUS/Explicit software. Then, the finite element model has been verified with published experimental data. Using design of experiments (DOE) working with the Taguchi method, 32 loading paths are designed for optimization. All 32 loading paths are modelled using the finite element method in ABAQUS/Explicit and the magnitudes of bulge height and the total thickness of tubes at the branch tip are obtained in each loading path. The regression analysis is carried out to estimate the tubes formability and obtain objective functions that are bulge height and the total thickness of tubes at the protrusion peak as functions of loading parameters (internal pressure and axial feed). For solving the multi-objective optimization problem, the non-dominated sorting genetic algorithm II (NSGA-II) is utilized and the optimum results were obtained from the Pareto optimal front. Finally, the optimized loading path was applied to the finite element model and better formability (3.4% increase in the bulge height) has been achieved in the results.