The Robust Optimization Of The Loading Path For T-shape Tube Hydroforming

Tube hydroforming(THF) is a novel meta-forming technique which uses the combination of the internal pressure and axial force to deform the tubular blank to a desired shape of the die cavity. THF technique has been widely used in the sanitation, automotive and aerospace industry due to its advantages compared to traditional stamping and welding process, such as high strength, high stiffness and weight reduction, etc. The optimization design and method of the loading path for THF is a challenge for many researchers. In the traditional optimization design for THF, the accuracy and efficiency of the optimization design are difficult to be guaranteed, and the uncertainties including material properties, geometrical dimensions and process parameters, etc. are not taken into consideration, so the optimum may violate the constraints when considering the uncertainties.In this study, the recent developments of the optimization of the loading path for THF are summarized and some shortcomings are pointed out, then taking the T-shape THF as an example and the following studies are carried out:(1) The optimization of the loading path for T-shape THF using adaptive RBF model: Firstly, the basic concept of the adaptive RBF model for global optimization is introduced and a numerical example is carried out to illustrate the effecttiveness of the adaptive RBF. Secondly, the finite element model used for simulating T-shape THF is validated against the experimental results and the design variables, objective functions and constraints are difined. Thirdly, the Taguchi method is used to screen the important factors which have significant effects on the forming quality. Finally the adaptive RBF model is applied for optimizing the loading path for T-shape THF.(2) A Kriging-based non-probability interval optimization of the loading path for T-shape THF: Firstly, the basic concept of interval optimization method is introduced. Secondly, the Kriging-based interval optimization method is developed and a numerical example is used to show the effectiveness of the proposed method. Thirdly, the Taguchi method is used to screen the important uncertain factors that have significant effects on the forming quality. Finally, the Kriging-based interval optimization method is applied to optimize the loading path for T-shape THF, and the results obtained from interval optimization are compared with those obtained from the deterministic optimization method.(3) The multi-objective optimization of the loading path for T-shape THF using adaptive LSSVR model: Firstly, the basic concept of multi-objective optimization and the strategy of adaptive LSSVR for multi-objective optimization are introduced. Secondly, a numerical example is carried out to show the effectiveness of the adaptive LSSVR for multi-objective optimization. Thirdly, the multi-objective optimization of the loading path for T-shape THF is studied using adaptive LSSVR model. Finally, the ideal point method is employed to select a compromise solution for the engineers.(4) The multi-objective non-probability interval optimization of the loading path for Tshape THF using LSSVR model: Firstly, the basic concept of multi-objective interval optimization and the strategy of LSSVR-based multi-objective non-probability interval optimization are introduced. Then the multi-objective interval optimization of the loading path for T-shape THF using LSSVR model is carried out, and the Pareto set and Pareto front are obtained. Finally the ideal point method is employed to select a compromise solution for the engineers and the results are compared with those obtainded from the multi-objective deterministic optimization.