Prediction and optimization of tensile strength of 7A52 aluminum alloy friction stir welding joints based on response surface methodology
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摘要: 为了研究7A52铝合金搅拌摩擦焊的焊接速度、搅拌头转速及轴肩压深对接头抗拉强度的影响，采用响应面法的中心复合试验设计法设计20组试验，并建立抗拉强度响应函数关系式. 为了验证响应函数关系式的精确性，通过方差分析和回归分析确定该回归模型为显性，相关性系数R2的偏差为3.17%. 通过单一焊接参数因素和双因素焊接参数对抗拉强度的影响分析，进一步验证了模型的准确性，最后通过拉伸试验验证. 结果表明，基于响应面法拟合的搅拌摩擦焊焊接速度、搅拌头转速及轴肩压深与接头抗拉强度响应函数关系式能精确的预算不同焊接参数组合所对应的接头抗拉强度，并获得接头最佳参数组合为焊接速度110 mm/min、搅拌头转速1 436 r/min和轴肩压深0.55 mm，得到最大预测抗拉强度为380 MPa.Abstract: In order to study the effects of welding speed, stirring head rotation speed and pressure deep of shaft shoulder on tensile strength of 7A52 aluminum alloy friction stir welding. 20 groups of tests were designed by response surface methodology based on central composite test design, and response function relationship were established. In order to verify the accuracy of the response function relationship, variance analysis and regression analysis were used to determine the dominance of the regression model, and the deviation of correlation coefficient R2 was only 3.17%. The accuracy of the model was verified by analyzing the influence of single welding parameter and double welding parameter on tensile strength. Finally, the model was verified by tensile test. The results show that the joint tensile strength can be predicated based on response function relationship of response surface methodology fitting, and the best combination of welding parameter (welding speed 110 mm/min, stirring head rotation speed 1 436 r/min, pressure deep of shaft shoulder 0.55 mm) was gained. The maximum predication tensile strength was 380 MPa.
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图 1 各因素对抗拉强度的直接影响
Figure 1. Direct effect of each factor on the tensile strength. (a) welding speed; (b) stirring head rotation speed; (c) pressure deep of shaft
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图 2 两因素交互对接头抗拉强度的响应面图
Figure 2. Response surface of the tensile strength. (a) weld speed and stirring head rotationg speed; (b) welding speed and pressure deep of shaft shoulder; (c) stirring head rotation speed and pressure deep of shaft shoulder
表 1 7A52铝合金的化学成分(质量分数，%)
Table 1 Chemical compositions of 7A52 aluminum alloy
Zr Zn Mg Fe Mn Si Cr Cu Al 0.12 4.2 2.3 0.33 0.31 0.24 0.23 0.13 余量 
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表 2 焊接工艺参数
Table 2 Welding parameter
焊接速度
v/(mm·min−1)转速
n/(r·min−1)轴肩压深
h/mm60 ~ 200 600 ~ 2 500 0.3 ~ 0.8
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表 3 基于CCD试验设计的FSW接头抗拉强度
Table 3 Results of tensile strength of FSW joints based on CCD
因素 实际焊接参数 标准化焊接参数 抗拉强度
Rm/MPa焊接速度v/(mm·min−1) 转速n/(r·min−1) 轴肩压深h/mm 焊接速度X1 转速X2 轴肩压深X3 1 70 700 0.3 −1 −1 −1 275.10 2 70 700 0.8 −1 −1 1 328.92 3 70 1500 0.3 −1 1 −1 251.61 4 70 1500 0.8 −1 1 1 305.43 5 150 700 0.3 1 −1 −1 167.58 6 150 700 0.8 1 −1 1 221.40 7 150 1500 0.3 1 1 −1 247.96 8 150 1 500 0.8 1 1 1 301.77 9 42.73 1 100 0.55 −1.68 0 0 267.45 10 177.27 1 100 0.55 1.68 0 0 266.72 11 110 427.28 0.55 0 −1.68 0 260.62 12 110 1 772.72 0.55 0 1.68 0 371.91 13 110 1 100 0.13 0 0 −1.68 141.16 14 110 1 100 0.97 0 0 1.68 231.66 15 110 1 100 0.55 0 0 0 368.89 16 110 1 100 0.55 0 0 0 378.68 17 110 1 100 0.55 0 0 0 348.72 18 110 1 100 0.55 0 0 0 388.89 19 110 1 100 0.55 0 0 0 375.59 20 110 1 100 0.55 0 0 0 386.58
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表 4 标准条件下回归系数及P值
Table 4 Coefficients and their P values in coded condition
项目 预测系数 误差e F值 Prob > F值 X1 −16.371 1 6.236 805 6.890 166 0.025 4 X2 22.035 61 6.236 805 12.483 19 0.005 4 X3 26.907 62 6.236 805 18.613 42 0.001 5 X12 −35.301 9 6.071 366 33.808 2 0.000 2 X1 X2 25.966 25 8.148 775 10.153 92 0.009 7 X1 X3 −0.001 25 8.148 775 2.356 53 0.999 9 X22 −17.914 1 6.071 366 8.705 962 0.014 5 X2X3 −0.001 25 8.148 775 2.354 33 0.999 9 X32 −63.824 9 6.071 366 110.511 3 < 0.000 1
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表 5 模型的方差分析结果
Table 5 Results of ANOVA test
项目 自由度 f 平方和 SS 均方值 MS F值 Prob > F值 X1 1 3 660.20 3660.20 8.268 0.014 X2 1 6 631.33 6631.33 14.980 0.002 X3 1 9 887.83 9887.83 22.336 0.001 X12 1 17 959.60 17959.60 40.570 <0 X1X2 1 5 393.97 5393.97 12.185 0.005 X22 1 4 624.78 4624.78 10.447 0.007 X32 1 58 705.87 58705.87 132.614 <0 模型 7 97 667.90 13952.56 31.518 <0
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表 6 模型预测值与试验值比较
Table 6 Comparison of model predicted value and experimental value
因素 转速
n/(r·min−1)焊接速度
v/(mm·min−1)轴肩压深
h/mm抗拉强度Rm/MPa 误差e(%) 预测值 试验值 预测值 1100 110 0.55 374 369 1.33 优化值 1436 110 0.55 380 377 0.79
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