An optimization procedure for concave preform design in rectangular tube hydroforming

Preform design is one of the dominant factors affecting the formability of tube hydroforming (THF). It refers to the intermediate geometric design between the initial tube blank and the final product shape in the THF process. An appropriately preformed cross-section configuration can avoid forming defects and improve forming performance. For this purpose, a multi-objective optimization design (MOD) procedure for concave preform of rectangular THF is proposed in this work based on surrogate models of the response functions. In this procedure, the process parameters including the geometric parameters of stamping punches, the stroke length of each punch and hydroforming pressure, are regarded as design variables. The objective is to improve the uniformity of wall thickness and reduce the forming pressure at the same time. Based on the design of experiment technique, the training samples and testing samples are obtained. Then, k-fold cross-validation strategy is used to establish the appropriate surrogate models with high accuracy. Afterward, NSGA-II is employed to search the Pareto front of MOD problem, and the ideal point method is used to determine the best compromise scheme. The application results showed that compared with direct hydroforming, the hydroforming pressure of rectangular tube with target fillet radius of 6 mm and 5 mm can be reduced by 69.4% and 64.0%, respectively. In addition, the thickness uniformity index and maximum thinning ratio can be reduced by up to 33.3% and 28.3%, respectively. Therefore, the proposed procedure is effective and reliable and can be used for the optimal design of concave preforms in rectangular THF.