Mechanism analysis and process parameter optimization of high-intensity shot peening for aerospace gears based on real rough tooth surfaces
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摘要:
针对高性能航空齿轮高强韧表面性能需求，提出一种考虑真实粗糙齿面的喷丸工艺参数优化方法。建立具有磨削表面形貌的喷丸强化有限元-离散元（FEM-DEM）耦合模型，研究表面覆盖率、弹丸直径、喷丸强度对喷丸效果的影响规律。采用曲面响应法，制定关于表面覆盖率、弹丸流量、空气压力的三因素三水平喷丸仿真试验方案，获得最大残余压应力及表面粗糙度。建立工艺参数与残余应力和表面粗糙度的多项式函数模型，分析各因素之间的交互作用及对喷丸强化效果的影响规律。以残余应力最大化和表面粗糙度最小化为目标，以覆盖率、弹丸流量、空气压力在固定范围内为约束条件，使用多起点单纯形搜索算法（MS-NM）优化喷丸工艺，并在不同初始表面粗糙度模型上进行仿真验证。结果表明：响应面预测模型与仿真结果误差小于2%，可用于喷丸效果预测和复合工艺优化。
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关键词:
- 喷丸强化 /
- 有限元-离散元（FEM-DEM） /
- 残余压应力 /
- 粗糙表面 /
- 预测函数
Abstract:An optimization method for shot peening parameters considering real rough tooth surfaces was proposed to meet the high strength and toughness requirements of high-performance aeronautical gears. A coupled finite element method-discrete element method (FEM-DEM） model incorporating ground surface topography was developed to investigate the effects of surface coverage, shot diameter, and shot peening intensity on shot peening performance. A three-factor (surface coverage, shot flow rate, air pressure) and three-level shot peening simulation scheme was designed using response surface methodology to achieve maximum residual compressive stress and minimum roughness. Polynomial models were established to analyze the interactions among these factors and their influence on shot peening effectiveness. The MS-NM algorithm was utilized to optimize the shot peening process with constraints on surface coverage, shot flow rate, and air pressure. The proposed process was then validated through simulations on different initial roughness models. The results showed that the prediction error between the response surface model and simulation results is less than 2%, indicating that the model can be effectively used for shot peening effect prediction and process optimization.
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图 1 布鲁克Contour GT-K测量流程图
Figure 1. Measurement process flowchart of Bruker Contour GT-K
图 3 弹丸直径为0.2 mm，弹丸速度为90 m/s的弹坑直径及临界塑性应变
Figure 3. Crater diameter and critical plastic strain for a projectile with a diameter of 0.2 mm and a velocity of 90 m/s
图 4 不同表面覆盖率下的残余应力曲线和表面粗糙度
Figure 4. Residual stress curves and surface roughness at different surface coverage rates
图 5 不同喷丸强度下的残余应力曲线和表面粗糙度
Figure 5. Residual stress curves and surface roughness at different shot peening intensities
图 6 不同弹丸直径下的残余应力曲线和表面粗糙度
Figure 6. Residual stress curves and surface roughness at different projectile diameters
图 8 最大残余压应力预测值残差分析
Figure 8. Residual analysis of the predicted maximum residual compressive stress
图 10 各因素对最大残余压应力的影响
Figure 10. Influence of various factors on maximum residual compressive stress
图 11 各因素交互作用对最大残余压应力的响应面图
Figure 11. Response surface plots of the interaction effects of various factors on the maximum residual compressive stress
图 13 各因素交互作用对靶材表面粗糙度Ra的响应面图
Figure 13. Response surface plots of the interaction effects of various factors on the surface roughness （Ra） of the target material
图 15 不同表面粗糙度的磨削形貌
Figure 15. Grinding morphologies at different surface roughness levels
表 1 以表面覆盖率为自变量的喷丸仿真试验方案
Table 1. Simulation experiment scheme for shot peening with surface coverage as the independent variable
表面覆盖率/% 弹丸直径/mm 弹丸速度/（m/s） 100 0.2 90 200 0.2 90 300 0.2 90 
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表 2 BBD方案及仿真结果
Table 2. BBD scheme and simulation results
序号 设计参数 响应值 覆盖率A/% 弹丸流量B/（kg/min） 空气压力C/MPa 最大残余压应力σmax/MPa 表面粗糙度Ra/μm 1 100 6 0.25 − 1409 1.83 2 150 10 0.25 − 1458 1.77 3 200 3 0.35 − 1517 2.24 4 150 10 0.45 − 1472 2.35 5 150 3 0.25 − 1466 1.89 6 200 10 0.35 − 1498 2.11 7 150 6 0.35 − 1468 2.10 8 150 6 0.35 − 1467 2.11 9 100 3 0.35 − 1439 2.15 10 100 10 0.35 − 1428 1.93 11 200 6 0.25 − 1466 1.87 12 150 6 0.35 − 1469 2.10 13 150 6 0.35 − 1467 2.11 14 150 6 0.35 − 1473 2.11 15 200 6 0.45 − 1502 2.31 16 100 6 0.45 − 1418 2.27 17 150 3 0.45 − 1475 2.48
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表 3 最大残余压应力预测值方差分析
Table 3. Analysis of variance for the predicted maximum residual compressive stress
数据
来源平方和/
MPa2自由度 均方/
MPa2F值 P值 模型 12697.09 9 1410.79 69.56 < 0.0001 A 10260.00 1 10260.00 505.88 < 0.0001 B 210.12 1 210.12 10.36 0.0147 C 580.41 1 580.41 28.62 0.0011 AB 13.92 1 13.92 0.6864 0.4347 AC 182.25 1 182.25 8.99 0.0200 BC 2.91 1 2.91 0.1434 0.7161 A2 315.04 1 315.04 15.53 0.0056 B2 511.62 1 511.62 25.23 0.0015 C2 547.20 1 547.20 26.98 0.0013
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表 4 表面粗糙度预测值方差分析
Table 4. Analysis of variance for predicted surface roughness
数据来源 平方和/μm2 自由度 均方/μm2 F值 P值 模型 0.5829 3 0.1943 93.14 < 0.0001 A 0.0153 1 0.0153 7.34 0.0179 B 0.0423 1 0.0423 20.28 0.0006 C 0.5253 1 0.5253 251.81 < 0.0001
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表 5 约束条件及权重设置
Table 5. Constraint conditions and weight settings
名称 目标 下限 上限 下限权重 上限权重 重要性 A/% 范围内 100 200 1 1 3 B/（kg/min） 范围内 3 10 1 1 3 C/MPa 范围内 0.25 0.45 1 1 3 σmax/MPa 最小化 − 1517 − 1409 1 1 3 Ra/μm 最小化 1.77 5 1 0.2 2
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表 6 最大残余压应力及表面粗糙度的仿真值与预测值
Table 6. Simulated and predicted values of maximum residual compressive stress and surface roughness
试验组编号 最大残余压应力σmax 表面粗糙度Ra 仿真值/MPa 预测值/MPa 误差/% 仿真值/μm 预测值/μm 误差/% #1 − 1511 − 1517 0.40 2.43 2.41 0.83 #2 − 1502 0.98 2.41 #3 − 1489 1.84 2.44 1.24
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