Loading path optimization of a hydroformed part using multilevel response surface method

In tube hydroforming, the loading path that is the relationship between axial feeding and internal fluid pressure is of important significance. Researchers have employed various optimization approaches to find an optimum loading path. In this research, a statistical method based on finite element analysis has been developed. An accurate FEA has been used to simulate the process and to find the response of the process to the loading. By performing an experimental test, the model is verified in comparison with the actual T part. The multilevel response surface method (MLRSM) has been used to model the responses from the finite element analysis. The behavior of the process can be predicted using the response surface methodology (RSM) model, and then, the obtained model is used to optimize the process. The optimum point in the RSM highly depends on the initial range of design variables. Thus, after finding the optimum point in each level, the ranges of variables are adjusted around the last optimum point. Then, the optimization process can be continued as a multilevel process. In the performed optimizations, the thickness variance has been considered as the objective function and the protrusion height as the constraint. The thickness variation based on the optimum loading path is highly improved, and it shows that multilevel RSM is very effective in improving the results.