Optimization and Sensitivity Analysis of Numerical Simulation of Tubular Hydroforming

Optimization and sensitivity analysis is important although difficult to obtain for tubular hydroforming, because of the implicit relationship between the load path variables (internal pressure and tube end displacement) and the dependent variables (such as stress, strain and final tube thickness). In this paper, the Taguchi method was used in conjunction with virtual hydroforming experiments using LS-DYNA® to carry out the sensitivity analysis and optimization of straight-tube hydroforming. This method employs an orthogonal array to study a large parameter space using only a small number of numerical simulations. Since the tube wall undergoes bending as it fills the corner of the die during the final stage of hydroforming, the strain path becomes non-linear. In this situation, the traditional strain forming limit diagram (FLD) is not a reliable criterion for necking/fracture. In contrast, the forming limit stress diagram (FLSD) is practically strain path-independent. Therefore, the FLSD was adopted for the necking/fracture criterion of the process. Multi-objective functions that consider necking/fracture, wrinkling and severe thinning were taken to evaluate the performance of each simulation. The Pareto optimum was obtained with a minimum failure value using the minimum distance method. Furthermore, the analysis of variance (ANOVA) statistical method was used to determine the effects of the forming parameters on the quality of the final hydroformed part. The factor response was completed using the Signal-to-Noise (S/N) ratio and ANOVA results. The ANOVA indicates the degree of sensitivity for the hydroforming parameters, and expansion pressure, calibration pressure, and tube end displacement were shown to be the three most important factors. This combination of numerical analyses and an optimization technique has helped to define a load path that leads to a robust manufacturing process and good part quality. Keywords: Tube hydroforming, FLSD, Taguchi method, Sensitivity analysis, Pareto optimization