Pure error 0。000 5 0

Cor total 487。32 29

R2=0。8691; Adjusted  R 2 =0。7469; Predicted R2=0。2458; Adequate precision=9。848

Table 4 gives the regression analysis results of the Dw。 It shows that the P-value of model is less than significance level α (α=0。05)。 The results suggest that there is a significant difference between the dependent

variable (Dw) and the polynomial terms。 The model value of the coefficient of multiple determination (R2=0。8669) implies that the fitted model adequately represents the

experimental results。 Both the model F-test value (F=6。21>F0。05(14,29)=2。76)  and  the  P-values  (P<0。05)

indicate the significance of the regression model。

Table 5 lists the ANOVA results of the polynomial model of Dt。 The ANOVA results show that the associated model with a large value of the coefficient of multiple determination (R2=0。8525) is adequate to represent the experimental results。 Meanwhile, both the model F-test value (F=7。45>F0。05(14,29)=2。31) and the P-value of model (P=0。0003<0。05) indicates the significance of the regression model。

In summary, these mathematical expressions can successfully pass the F statistics and the  R2-test, implying that the current data fitting is excellent。 The independent variables are significantly correlative to Df , Dw and Dt。

4。3Response surface analysis

It shows that the conspicuous interactive influence factors of Df, Dw  and Dt  are x2×x3, x1×x3  and x1×x2  in the

Tables 3−5, respectively。 To visualize the effect of the variables on the required responses, the 3-D response surface plots are applied to describing the regression equations。 For the three required responses including the Df, Dw and Dt, the corresponding 3-D response surfaces and contour maps are shown in Figs。 5−7, respectively。

Figure 5 shows the status of response surface and contour plot for Df, under the condition that the fillet radius is 3 mm and the blank-holding force is 0。8×105  N。

The region where the value of Df  is between 0。02 and

0。03 is defined as the optimum region。 As the figure shown, the optimum region for the Df is in the blank size of  431−440  mm  and  the  draw-bead  position  of 382−

390 mm。 In this region, the Df  increases significantly with decreasing of blank size。 By increasing draw-bead position, the Df decreases firstly to a peak and then increases。

Figure 6 shows the status of response surface and contour plot for Dw, under the condition that the position of draw-bead is 385 mm and the blank-holding force is 0。8×105 N。 The region where the value of Dw is less than 26 is defined as the optimum region。 The figure shows that there are several optimum regions for the Dw in the blank size of 430−442 mm and the fillet radius of 2。5−3。65 mm。 In this region, Dw decreases with the increasing of fillet radius at certain blank size。 The Dw increases firstly with the increasing of blank size,  and为了获得冲压成形的最优工艺参数，有限元分析和优化技术通过将多目标问题转化为单目标问题进行了整合。基于帕累托的遗传算法被应用于优化箱盖的冲压成形过程。在所提出的最佳模型中，断裂，褶皱和厚度变化是几个因素的函数，例如圆角半径，拉珠位置，坯料尺寸和坯料夹持力。因此，有必要调查目标函数和变量之间的关系，以使目标函数同时最小化。首先应用四因素五级的中心复合实验（CCD），并获得基于中心复合实验的实验数据。然后建立响应表面模型（RSM），方差分析（ANOVA）的结果表明，通过响应表面模型预测断裂，皱纹和厚度变化函数是可靠的。最后基于帕累托的遗传算法来找出一组帕累托前沿，这使得断裂，皱纹和厚度变化整体最小化。箱盖的冲压情况表明，与“试错法”相比，本方法具有更高的精度和实用性。论文网