Abstract: To obtain the optimal process parameters of stamping forming, finite element analysis and optimization technique were integrated via transforming multi-objective issue into a single-objective issue。 A Pareto-based genetic algorithm was applied to optimizing the head stamping forming process。 In the proposed optimal model, fracture, wrinkle and thickness varying are a function of several factors, such as fillet radius, draw-bead position, blank size and blank-holding force。 Hence, it is necessary to investigate the relationship between the objective functions and the variables in order to make objective functions varying minimized simultaneously。 Firstly, the central composite experimental (CCD) with four factors and five levels was applied, and the experimental data based on the central composite experimental were acquired。 Then, the response surface model (RSM) was set up and the results of the analysis of variance (ANOVA) show that it is reliable to predict the fracture, wrinkle and thickness varying functions by the response surface model。 Finally, a Pareto-based genetic algorithm was used to find out a set of Pareto front, which makes fracture, wrinkle and thickness varying minimized integrally。 A head stamping case indicates that the present method has higher precision and practicability compared with the “trial and error” procedure。79936

Key words: stamping forming; heads; finite element analysis; central composite experimental design; response surface methodology; multi-objective genetic algorithm

1Introduction

Head is one of components of the water heater tank。 The research on stamping forming of head in engineering practice has been carried out for a long time。 There are serious defects occurring in the draw forming process of head, such as fracture, wrinkle and serious thinning。 Through the optimization of fillet radius, position of draw-bead, blank size and blank-holding force, the defects can be avoided。 But the traditional optimal design is highly-dependent on the experience and knowledge of the designers through constantly repair and  test  die。 Even with the help of finite element simulation, it was sightless to select the combination of parameters from variable range of various parameters [1]。 The parameters selected are very accidental, and it is doubt whether the combination can obtain an optimal  result。 Meanwhile, the optimal process is time-consuming and needs a lot of computing resource, which cannot meet the needs of modern industry [1−3]。

According to Ref。 [3], different shapes of draw-bead have different effects on the forming quality, and the rectangle  draw-bead  is  more  effective  than  the others。

LIU et al [4] have researched the effect of the main parameters on the forming quality and forming force using the finite element simulation analysis。 SHI et al [5] have researched the effect of blank size and fillet radius on the forming quality。 Although many scholars have studied extensively the head forming technology  and have achieved certain results, the research on head forming still needs to be further studied。 Most of them use single objective optimization, which cannot obtain optimal parameters。 In recent years, with  the development of finite element technique  and optimization theory, using the combination of the finite element analysis and intelligent algorithms to research the improvement of the forming performance becomes a trend [6]。 Many scholars have tried to optimize the sheet metal forming process  of  general  parts。  BREITKOPF et al [7] have constructed sequential response surface model  (RSM)  using  least  squares  method  to  verify the reliability of the models。 SUN et al [1] have combined the sequences of two quadratic programming methods by the response surface method, and found the optimal conditions  of  forming  sheet  drawing。  ZHOU et al [2] have researched the forming process of air conditioner front panel using response surface model   to