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摘要: 采用实验设计田口法及响应面法，对镍基高温合金选择性激光熔化过程中的三个工艺参数（激光功率、扫描速度和扫描间距）进行优化，以成形样品的相对密度作为评价标准，研究工艺参数对最终试样相对密度的影响。基于方差分析、信噪比、主效应图、响应曲线图等，分析各因素及其之间的相互作用对样品相对密度的影响。研究结果表明，不同工艺参数对试样相对密度的影响效果差别很大，其中扫描间距的影响效果最大，其次是激光功率和扫描速度，此外扫描速度与扫描间距的交互作用对于试样相对密度的影响也比较显著。两种不同优化方法获得的最佳工艺参数组合相同，均为激光功率280 W、扫描速度1000 mm·s−1以及扫描间距0.12 mm。Abstract: The experimental design Taguchi method and response surface methodology were used to optimize the process parameters of the selective laser melting for Ni-based superalloy (laser power, scanning speed and scanning spacing). The effect of the process parameters on the relative density of the final samples was determined by using the relative density as the evaluation standard. Based on the analysis of variance, signal-to-noise ratio, main effect diagram, and response curve, the effects of the process parameters and the parameter interactions on the relative density of samples were evaluated. In the results, the effects of the process parameters on the relative density of the final samples vary greatly, the scanning spacing shows the largest effect, followed by laser power and scanning speed. In addition, the interaction between scanning speed and scanning spacing is also significant for the effect on the sample relative density. The best process parameters obtained by two different optimization methods are the same as the laser power is 280 W, the scanning speed is 1000 mm·s−1, and the scanning spacing is 0.12 mm.
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图 2 扫描策略在选择性激光熔化实验中的应用
Figure 2. Application of the scanning strategy in the selective laser melting experiment
图 3 各因素的相对密度信噪比对比图
Figure 3. Signal-to-noise ratio of relative density for various factors
图 4 相对密度的残差正态概率分布图
Figure 4. Residual normal probability distribution of the relative density
图 5 相对密度的残差与预测值分布图
Figure 5. Residual and predicted distribution of the relative density
图 6 与相对密度对应的响应优化曲线图：（a）激光功率；（b）扫描速度；（c）扫描间距
Figure 6. Response optimization curve corresponding to the relative density: (a) laser power; (b) scanning speed; (c) scanning spacing
表 1 镍基粉末高温合金化学成分（质量分数）
Table 1. Chemical composition of the nickel-based powder superalloys
% Al Cr Fe Ti Y Cu Si C Ni 0.25 21.00 0.85 0.57 0.68 0.009 0.002 0.059 余量 
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表 2 田口法分析的输入参数及其水平
Table 2. Input parameters and the levels of Taguchi method
水平 激光功率 / W 扫描速度 / (mm·s−1) 扫描间距 / mm 水平1 240 600 0.09 水平2 280 800 0.12 水平3 320 1000 0.15 水平4 360 — — 水平5 400 — —
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表 3 响应面中Box-Behnken分析的输入参数及其水平
Table 3. Input parameters and the levels of Box-Behnken analysis in response surface
水平 因素 激光功率 / W 扫描速度 / (mm·s−1) 扫描间距 / mm −1 280 600 0.09 0 320 800 0.12 1 360 1000 0.15
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表 4 田口法实验记录的相对密度及其信噪比
Table 4. Relative density and signal-to-noise ratio recorded by Taguchi method
序号 因素 响应 激光功率 /
W扫描速度 /
(mm·s−1)扫描间距 /
mm相对密度 /
%信噪比 /
dB1 320 800 0.09 95.97 39.64 2 400 600 0.12 95.42 39.59 3 400 800 0.15 94.74 39.53 4 400 1000 0.09 95.76 39.62 5 360 1000 0.09 96.61 39.70 6 360 800 0.15 94.96 39.55 7 320 600 0.15 94.29 39.49 8 280 600 0.09 96.19 39.66 9 280 1000 0.12 96.85 39.72 10 400 600 0.09 95.38 39.59 11 240 1000 0.15 93.70 39.43 12 240 600 0.09 95.83 39.63 13 320 800 0.09 95.97 39.64 14 280 600 0.15 96.29 39.67 15 360 800 0.09 95.35 39.59 16 240 800 0.12 95.96 39.64 17 400 800 0.12 95.36 39.59 18 240 600 0.09 95.83 39.63 19 240 800 0.12 95.96 39.64 20 360 600 0.12 95.40 39.59 21 280 800 0.12 95.49 39.60 22 320 600 0.12 96.44 39.69 23 280 800 0.09 95.40 39.59 24 360 600 0.12 95.40 39.59 25 320 1000 0.12 96.54 39.69
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表 5 相对密度的方差分析
Table 5. Variance analysis of the relative density
来源 激光功率 / W 扫描速度 / (mm·s−1) 扫描间距 / mm 残差误差 合计 自由度 4 2 2 12 20 平方和 0.017280 0.006672 0.033382 0.043051 0.100385 平方均值 0.003780 0.002618 0.016691 0.003588 — F值 1.05 0.73 4.65 — — P值 0.421 0.502 0.032 — — 贡献 / % 17.21 6.65 33.25 42.89 —
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表 6 各因素的平均信噪比及极差范围
Table 6. Average signal-to-noise ratio and the range of each factor
dB 水平 因素 激光功率 扫描速度 扫描间距 水平1 39.57 39.61 39.63 水平2 39.65 39.59 39.64 水平3 39.63 39.64 39.54 水平4 39.61 — — 水平5 39.58 — — 极差范围 0.08 0.04 0.10 排序 2 3 1
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表 7 基于Box-Behnken设计的响应面法工艺参数及其相对密度
Table 7. Process parameters and the relative density of RSM based on Box-Behnken design
序号 因素 相对密度 / % 激光功率 / W 扫描速度 / (mm·s−1) 扫描间距 / mm 1 360 800 0.15 94.96 2 280 600 0.12 96.13 3 320 800 0.12 95.82 4 360 600 0.12 95.40 5 320 800 0.12 95.82 6 280 800 0.09 95.40 7 320 800 0.12 95.82 8 320 800 0.12 95.82 9 320 600 0.15 94.29 10 280 1000 0.12 96.85 11 320 1000 0.09 96.06 12 360 800 0.09 95.35 13 320 1000 0.15 96.37 14 320 800 0.12 95.82 15 360 1000 0.12 96.41 16 280 800 0.15 95.89 17 320 600 0.09 95.43
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表 8 各模型的统计信息
Table 8. Statistics for each model
类型 均方差 相关系数，R2 调整决定系数 预测决定系数 预测误差平方和 选择建议 一阶线性模型 0.44 0.5558 0.4533 0.0755 5.860 — 2FI 0.42 0.6879 0.5006 −0.5815 8.410 — 二阶模型 0.23 0.9582 0.9004 0.3311 15.588 建议
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表 9 响应面二次模型的方差分析
Table 9. Variance analysis of response surface quadratic model
类型 平方和 自由度 均方差 F值 P值 Prob > F 模型 5.340 9 0.590 17.86 0.0005 显著 A 0.580 1 0.580 17.38 0.0042 — B 2.460 1 2.450 74.14 <0.0001 — C 0.067 1 0.065 2.00 0.1998 — AB 0.021 1 0.020 0.63 0.4525 AC 0.190 1 0.190 5.82 0.0465 — BC 0.530 1 0.530 15.81 0.0053 — A2 0.061 1 0.060 1.82 0.2189 — B2 0.280 1 0.280 8.40 0.0230 — C2 1.230 1 1.240 36.94 0.0005 — 残差 0.230 7 0.033 — — — 失拟项 0.230 3 0.078 — — — 纯误差 0 4 0 — — — 总离差 5.560 16 — — — — 标准差 0.180 — 相关系数R2 0.9583 — — 平均值 95.740 — 调整决定系数 0.9046 — — 变化系数 /
%0.190 — 预测决定系数 0.3325 — — 预测误差平方和 3.720 — 精确度 17.307 — —
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表 10 田口法和响应面法的预测值与实验验证值
Table 10. Predicted and confirmatory values in experiment of TM and RSM
方法 因素 相对密度 / % 误差 / % 激光功率 / W 扫描速度 / (mm·s−1) 扫描间距 / mm 预测值 验证值 田口法 280 1000 0.12 96. 61 96.87 0.27 响应面法 280 1000 0.12 96.95 96.87 0.07
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表 11 田口法预测值和验证性实验值
Table 11. Predicted and confirmatory values in experiment by TM
方法 因素 相对密度 / % 激光功率 / W 扫描速度 / (mm·s−1) 扫描间距 / mm 测量值 预测值 CI值及其范围 差值百分数 / % 田口法 280 1000 0.12 96.87 96.61 ±4.24[92.37, 100.85] 0.26 240 1000 0.15 93.98 94.95 ±4.24[90.71, 99.19] 0.97
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