Optimizing process parameters of ultrasonic vibration assisted grinding CFRP based on response surface method
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摘要: 针对CFRP加工表面高质量和高效率相矛盾的问题，利用响应曲面法建立三维表面粗糙度Sa和表面损伤层深度Dd的二阶回归模型，并采用遗传算法进行多目标优化，获得小的Sa、Dd和最大的材料去除率VMRR。结果表明：Sa和Dd的回归模型显著、可靠性好，其中进给速度vf对Sa和Dd的影响最显著，磨削深度ap、主轴转速n和超声振幅A的影响次之。响应曲面分析结果显示：n−A、vf−ap以及vf−A之间的交互作用对Sa影响显著；n−A、vf−A、vf−ap以及ap−A之间的交互作用对Dd影响显著。在Sa、Dd和VMRR权重占比分别为1/5、1/5和3/5的条件下，与中心点结果相比，优化后的Sa降低了11.01%，Dd降低了10.08%，VMRR提高了62.02%。且在优化工艺参数下的Sa和Dd的试验值与预测值的相对误差绝对值分别为8.25%和9.41%，表明预测模型准确性较高，可用于CRFP超声振动磨削的工艺参数优化和预测。Abstract: To solve the contradiction between high quality and high efficiency of CFRP machining surface, the quadratic regression models of 3D surface roughness Sa and surface damage layer depth Dd were established by using the response surface method, and the genetic algorithm was used for multi-objective optimization to obtain small Sa, Dd and maximum material removal rate VMRR. The results show that the regression models of Sa and Dd are explicit and reliable, and the feed speed vf has the most significant influence on Sa and Dd, followed by the grinding depth ap, the spindle speed n and the ultrasonic amplitude A. The results of response surface analysis show that the interactions of n and A, vf and ap, vf and A have significant effects on Sa. The interactions of n and A, vf and A, vf and ap, ap and A have significant effects on Dd. When the weight ratios of Sa, Dd and VMRR are 1/5, 1/5 and 3/5 respectively, compared with the central point results, the optimized Sa decreases by 11.01%, Dd decreases by 10.08%, and VMRR increases by 62.02%. The absolute values of the relative errors between the experimental and the predicted values of Sa and Dd under the optimized process parameters are 8.25% and 9.41% respectively, indicating that the prediction model has high accuracy and can be used for the optimization and prediction of the process parameters of CRFP ultrasonic vibration grinding.
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图 5 磨削表面三维轮廓形貌（Sa=7.29 μm）
Figure 5. Three-dimensional topography of grinding surface（Sa=7.29 μm）
图 6 Sa 和 Dd的模型预测值与实际值对比
Figure 6. Comparison between model predicted value and actual value of Sa and Dd
图 7 Sa 和 Dd 模型的标准残差概率分布图
Figure 7. Probability distribution of standard residuals of Sa and Dd models
表 1 试验因素水平
Table 1. Experiment factors and levels
编码水平 因素 主轴转速
n / (r·min−1)进给速度
vf / (mm·min−1)磨削深度
ap / mm超声振幅
A / μm−2 8 000 200.00 0.50 4.00 −1 12 000 400.00 0.75 5.00 0 16 000 600.00 1.00 6.00 1 20 000 800.00 1.25 7.00 2 24 000 1 000.00 1.50 8.00 
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表 2 因素设计及测试结果
Table 2. Factor design and test results
序号
m磨削参数 响应结果 n vf ap A Sa / μm σSa / μm Dd / μm σDd / μm 1 0 0 −2 0 4.66 0.25 55.96 11.38 2 1 −1 −1 −1 3.87 0.20 45.63 8.81 3 1 −1 1 −1 3.79 0.15 73.36 12.46 4 0 0 0 −2 6.60 0.29 138.66 22.58 5 0 0 0 0 5.28 0.26 108.70 8.42 6 1 1 1 −1 7.06 0.33 156.59 18.68 7 −1 1 −1 −1 7.29 0.31 161.52 21.05 8 0 0 2 0 6.95 0.26 145.89 13.02 9 0 0 0 0 5.58 0.26 117.15 8.42 10 −1 −1 1 1 4.68 0.18 94.18 15.88 11 −1 1 −1 1 5.42 0.35 113.89 12.05 12 −1 1 1 1 7.36 0.29 154.54 19.43 13 −1 1 1 −1 8.30 0.41 218.65 23.68 14 −1 −1 −1 −1 4.93 0.19 103.44 9.17 15 0 0 0 0 5.81 0.26 122.11 8.42 16 0 0 0 0 5.75 0.26 120.65 8.42 17 0 −2 0 0 3.90 0.25 88.28 10.28 18 −1 −1 1 −1 5.85 0.18 122.77 14.93 19 −1 −1 −1 1 5.39 0.27 113.24 21.26 20 0 0 0 0 6.19 0.26 129.91 8.42 21 0 0 0 2 7.16 0.31 150.27 15.91 22 0 2 0 0 5.98 0.23 205.31 21.82 23 −2 0 0 0 6.40 0.21 134.49 20.19 24 0 0 0 0 5.56 0.26 116.85 8.42 25 1 −1 1 1 6.18 0.34 129.84 23.63 26 1 1 1 1 7.00 0.33 147.00 15.71 27 1 1 −1 −1 3.97 0.17 83.42 9.08 28 2 0 0 0 3.98 0.22 70.96 12.72 29 0 0 0 0 5.86 0.26 102.11 8.42 30 1 1 −1 1 5.52 0.18 120.22 14.63 31 1 −1 −1 1 5.23 0.28 109.73 17.03
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表 3 Sa的方差分析
Table 3. Variance analysis of Sa
项目 平方和 自由度 均方值 F值 P值 备注 模型 37.89 14 2.71 15.78 < 0.000 1 非常显著 n 5.46 1 5.46 31.83 < 0.000 1 3 vf 10.87 1 10.87 63.38 < 0.000 1 1 ap 7.21 1 7.21 42.07 < 0.000 1 2 A 0.34 1 0.34 1.96 0.180 6 4 n−vf 0.58 1 0.58 3.38 0.084 6 n−ap 0.32 1 0.32 1.90 0.187 6 n−A 4.78 1 4.78 27.85 < 0.000 1 vf−ap 2.57 1 2.57 14.99 0.001 4 vf−A 1.19 1 1.19 6.93 0.018 1 ap−A 0.10 1 0.10 0.59 0.453 3 n2 0.45 1 0.45 2.63 0.124 5 vf2 1.02 1 1.02 5.92 0.027 1 ap2 0.02 1 0.02 0.13 0.722 7 A2 2.51 1 2.51 14.64 0.001 5 残差 2.74 16 0.17 失拟项 2.26 10 0.23 2.77 0.112 3 不显著 纯误差 0.49 6 0.08 总和 40.64 30 R2=0.932 5
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表 4 Dd的方差分析
Table 4. Variance analysis of Dd
项目 平方和 自由度 均方值 F值 P值 备注 模型 41 019.85 14 2 929.99 32.58 <0.000 1 非常显著 n 4 916.29 1 4 916.29 54.67 <0.000 1 3 vf 14 885.82 1 14 885.82 165.52 <0.000 1 1 ap 7 550.43 1 7 550.43 83.96 < 0.000 1 2 A 68.33 1 68.33 0.76 0.396 3 4 n−vf 274.71 1 274.71 3.05 0.099 7 n−ap 154.60 1 154.60 1.72 0.208 3 n−A 4 842.00 1 4 842.00 53.84 < 0.0001 vf−ap 1 399.13 1 1 399.13 15.56 0.001 2 vf−A 2 169.56 1 2 169.56 24.12 0.000 2 ap−A 741.04 1 741.04 8.24 0.011 1 n2 422.38 1 422.38 4.70 0.045 7 vf2 1 471.65 1 1 471.65 16.36 0.000 9 ap2 527.39 1 527.39 5.86 0.027 7 A2 1 242.08 1 1 242.08 13.81 0.001 9 残差 1 438.94 16 89.93 失拟项 942.49 10 94.25 1.14 0.456 3 不显著 纯误差 496.46 6 82.74 总和 42 458.79 30 R2=0.966 1
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表 5 不同权重占比下的优化结果
Table 5. Optimized results under different weight ratios
组号 权重因素 优化结果 参数 结果 ${W_{{S_{\rm{a}}}}} $ ${W_{{D_{\rm{d}}}}} $ ${W_{{V_{{\rm{MRR}}}}}} $ n
(r·min−1)vf
(mm·min−1)ap
mmA
μmSa
μmDd
μmVMRR
(mm3·min−1)1 1/3 1/3 1/3 23 693 882.36 0.90 4.41 3.34 81.21 2 902.41 2 3/5 1/5 1/5 23 864 999.98 0.72 4.69 1.93 68.59 2 630.45 3 1/5 3/5 1/5 23 602 714.27 0.97 4.05 3.50 52.18 2 512.22 4 1/5 1/5 3/5 23 999 745.94 1.30 4.49 5.09 105.01 3 538.53 中心点 — — — 16 000 600.00 1.00 6.00 5.72 116.78 2 184.00
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表 6 Sa和Dd试验值与预测值对比
Table 6. Comparison of Sa and Dd test values with predicted values
项目 三维表面粗糙度
Sa /μm表面层损伤深度
Dd /μm试验值 4.67 95.13 预测值 5.09 105.01 相对误差绝对值 8.25% 9.41%
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