Optimization of process parameters for electron beam butt welding of HR-2 hydrogen resistant steel based on response surface method
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摘要: 为解决HR-2抗氢钢电子束插接焊有效熔深不足、焊缝处开裂等问题，采用BBD设计试验方案，基于响应面法建立了HR-2抗氢钢电子束插接焊焊接工艺参数(聚焦电流、焊接速度、束流、倾斜角度)与预测响应值(有效熔深、接头抗剪承载力)之间的统计模型. 根据有效熔深和接头抗剪承载力的要求优化焊接工艺参数，并通过优化电子束焊接工艺参数来预测电子束插接焊的有效熔深和接头抗剪承载力，实现焊缝截面形貌与接头强度的最佳组合. 结果表明，模型拟合度较好，有效熔深预测值比实测值高1.17%，接头抗剪承载力预测值比实测值高2.63%，得到较优的焊接参数为：聚焦电流2.46 A，焊接速度10.00 mm/s，束流8.20 mA，倾斜角度11°. 在该参数下的焊缝有效熔深1 347.82 μm，接头抗剪承载力13.525 kN.Abstract: In order to solve the problems such as insufficient effective penetration and cracking at the weld seam of HR-2 hydrogen resistant steel, a statistical model between the welding process parameters (focusing current, welding speed, beam current, tilt angle) and the predicted response values (effective penetration, joint shear load) of HR-2 hydrogen resistant steel electron beam insertion welding was established based on the response surface method using the BBD design test scheme. It can optimize the welding process parameters according to the requirements of effective penetration and joint shear load, and predict the effective penetration and joint shear load of electron beam plug welding by optimizing the electron beam welding process parameters, so as to achieve the best combination for weld section morphology and joint strength. The results show that the model fits well, the predicted value of effective penetration is 1.17% higher than that of the measured value, and the predicted value of joint shear load is 2.63% higher than the measured value. Better welding parameters are listed as follows: the focusing current is 2.46 A, the welding speed is 10.00 mm/s, the beam current is 8.20 mA, and the tilt angle is 11°. Effective penetration depth of the weld under this parameter is 1 347.82 μm, and shear load of joint is 13.525 kN.
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图 1 HR-2抗氢钢电子束焊接部分接头形貌
Figure 1. Morphology of the electron beam welded joints of some HR-2 hydrogen resistant steel. (a) specimen 7; (b) specimen 21; (c) specimen 22; (d) specimen 25; (e) specimen 6 ; (f) specimen 14; (g) specimen 26; (h) specimen 29
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图 2 电子束插接焊接头结构示意图（mm)
Figure 2. Schematic diagram of the electron beam butt welding joint structure
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图 4 聚焦电流与电子束焦点位置关系示意图
Figure 4. Schematic diagram of the relationship between focusing current and electron beam focal position
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图 5 有效熔深的响应面曲图和等值线图
Figure 5. Response surface 3D graph and contour graph of effective penetration. (a) d = f ( If, v) response surface 3D graph; (b) d = f (If, Ib) response surface 3D graph; (c) d = f ( If, θ ) response surface 3D graph; (d) d = f ( If, v ) contour graph; (e) d = f ( If, Ib) contour graph; (f) d = f ( If, θ ) contour graph
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图 6 各交互作用对接头抗剪承载力的影响
Figure 6. Effect of each interaction on the shear capacity of the joints
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图 7 接头抗剪承载力的响应面曲图和等值线图
Figure 7. Response surface 3D graph and contour graph of of shear capacity of joint. (a) F = f (If, v) response surface 3D graph; (b) F = f (If, Ib) response surface 3D graph; (c) F = f ( If, θ ) response surface 3D graph; (d) F = f ( If, v ) contour graph; (e) F = f ( If, Ib) contour graph; (f) F = f ( If, θ) contour graphe
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图 8 焊缝截面形貌分类
Figure 8. Classification of the cross-sectional morphology of the weld. (a) arc type; (b) wedge type; (c) T-shaped type
表 1 HR-2抗氢钢的化学成分(质量分数，%)
Table 1 Chemical compositions of HR-2 hydrogen resistant steel
C Si Mn P S Ni Cr Fe ≤0.040 ≤1.00 8.00 ~ 10.00 ≤0.025 ≤0.015 5.50 ~ 8.00 19.00 ~ 21.50 余量 
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表 2 工艺参数水平编码及真实值表
Table 2 Process parameter level coding and true value table
水平 聚焦电流
If /A焊接速度
v/(mm·s−1)束流
Ib /mA倾斜角度
θ/(°)1 2.49 11.40 8.65 15 0 2.46 10.00 8.20 11 −1 2.43 8.60 7.75 7
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表 3 试验方案及相对应的响应值
Table 3 Test scheme and corresponding response value
试验序号 聚焦电流If /A 焊接速度v/(mm∙s−1) 束流Ib/mA 倾斜角度θ/(°) 有效熔深d/μm 抗剪承载力F/kN 1 2.49 10.00 8.20 15 360.07 3.856 2 2.43 10.00 8.65 11 1 997.30 16 137 3 2.46 10.00 8.20 11 1 397.18 13.037 4 2.43 10.00 7.75 11 2 117.32 16.352 5 2.43 10.00 8.20 7 2 252.73 16.779 6 2.46 10.00 8.65 15 830.92 8.938 7 2.46 10.00 8.20 11 1 275.58 12.330 8 2.46 11.40 8.20 7 1 840.34 15.907 9 2.46 10.00 7.75 7 1 717.24 16. 096 10 2.46 10.00 8.20 11 1 357.18 13.725 11 2.46 8.60 8.65 11 1 175.61 13.681 12 2.46 11.40 8.20 15 815.54 8.120 13 2.46 10.00 8.65 7 1 975.75 15.935 14 2.49 10.00 8.65 11 787.84 8.388 15 2.49 10.00 7.75 11 575.49 6.710 16 2.49 8.60 8.20 11 775.53 7.844 17 2.43 10.00 8.20 15 1 369.49 13.696 18 2.46 10.00 8.20 11 1 375.64 13.265 19 2.43 11.40 8.20 11 1 796.56 14.908 20 2.46 10.00 8.20 11 1 320.56 13.018 21 2.46 8.60 7.75 11 1 427.96 14.690 22 2.43 8.60 8.20 11 2 203.49 16.368 23 2.49 11.40 8.20 11 827.85 7.564 24 2.46 8.60 8.20 7 2 172.71 16.383 25 2.46 8.60 8.20 15 787.84 8.046 26 2.46 10.00 7.75 15 744.76 7.013 27 2.46 11.40 8.65 11 1 461.81 12.204 28 2.49 10.00 8.20 7 1 089.44 11.404 29 2.46 11.40 7.75 11 1 311.02 11.557
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表 4 有效熔深模型方差分析
Table 4 ANOVA for effective weld penetration reduced cubic model
项目 平方和SS/105 自由度f 均放值MS /105 F值 Prob＞F值 模型 80.22 22 3.646 60.48 < 0.000 1 If 11.80 1 11.80 195.74 < 0.000 1 θ 11.21 1 11.21 185.88 < 0.000 1 vIf 0.527 276 4 1 0.527 276 4 8.75 0.025 4 vIb 0.406 304 6 1 0.406 304 6 6.74 0.040 9 IfIb2 0.418 443 5 1 0.418 443 5 6.94 0.038 8 残差 0.361 760 2 6 0.060 293 4 失拟项 0.269 499 2 2 0.134 749 6 5.84 0.065 0 绝对误差 0.092 261 0 4 0.023 065 3 总离差 80.58 28
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表 5 接头抗剪承载力模型方差分析
Table 5 ANOVA for the shear capacity of welded joins reduced quadratic model
项目 平方和SS /107 自由度f 均方值MS /106 F值 Prob > F值 模型 37.13 14 26.52 36.23 < 0.000 1 If 19.58 1 195.8 267.50 < 0.000 1 v 0.379 9 1 3.799 5.19 0.038 9 θ 15.29 1 152.9 208.88 < 0.000 1 θIf 0.498 4 1 4.984 6.81 0.020 6 If2 0.729 9 1 7.299 9.97 0.007 0 θ2 0.404 7 1 4.047 5.53 0.033 9 残差 1.025 14 0.732 0 失拟项 0.923 0 10 0.923 0 3.63 0.113 0 绝对误差 0.101 8 4 0.254 6 总离差 38.15 28
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表 6 响应面法分析优化验证结果
Table 6 Optimization and verification results of response surface analysis method
类别 聚焦电流If /A 焊接速度v/(mm∙s−1) 束流Ib /mA 倾斜角度θ/(°) 有效熔深d/μm 接头抗剪承载力F/kN 试验值 2.46 10.00 8.20 11 1 347.82 13.525 预测值 2.463 10.21 8.12 11.26 1 363.63 13.881 相对误差e(%) 0.12 2.1 −0.98 2.36 1.17 2.63
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