磨料水射流抛光熔石英玻璃的多目标参数优化

李倩; 姚鹏; 邓红星; 冯辰宇; 许崇海; 屈硕硕; 杨玉莹; 朱洪涛; 黄传真

doi:10.37188/CO.EN-2025-0006

磨料水射流抛光熔石英玻璃的多目标参数优化

李倩^{1, 2, 3,},
姚鹏^{2, 3, ,},
邓红星^{2, 3},
冯辰宇^{2, 3},
许崇海¹,
屈硕硕^{2, 3},
杨玉莹¹,
朱洪涛^{2, 3},
黄传真⁴

1.
齐鲁工业大学(山东省科学院) 机械工程学部, 济南 250353
2.
山东大学机械工程学院, 先进射流工程技术研究中心, 济南 250061
3.
山东大学机械工程学院, 高效洁净机械制造教育部重点实验室, 济南 250061
4.
燕山大学机械工程学院, 秦皇岛 066004

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出版历程
- 收稿日期: 2025-02-08
- 录用日期: 2025-04-17
- 网络出版日期: 2025-07-16

Multi-objective parameter optimization of abrasive water jet polishing for fused silica

doi: 10.37188/CO.EN-2025-0006

LI Qian^{1, 2, 3
,},
YAO Peng^{2, 3
, ,},
DENG Hong-xing^{2, 3},
FENG Chen-yu^{2, 3},
XU Chong-hai¹,
QU Shuo-shuo^{2, 3},
YANG Yu-ying¹,
ZHU Hong-tao^{2, 3},
HUANG Chuan-zhen⁴

1.
School of Mechanical Engineering, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, PR China
2.
Center for Advanced Jet Engineering Technologies (CaJET), School of Mechanical Engineering, Shandong University, Jinan 250061, PR China
3.
Key Laboratory of High Efficiency and Clean Mechanical Manufacture, Shandong University, Ministry of Education, Jinan, 250061, PR China
4.
School of Mechanical Engineering, Yanshan University, Qinhuangdao, 066004, PR China

Funds: Supported by National Key Research and Development Program of China (No. 2023YFC2413301); National Natural Science Foundation of China (No. U23A20632); Major Basic Research of Shandong Provincial Natural Science Foundation (No. ZR2023ZD34)

More Information

Author Bio:
LI Qian (1993—), female, born in Jinan, Shandong Province. She obtained her bachelor's degree from Dezhou University in 2017. Currently, she is a postgraduate jointly cultivated by the School of Mechanical Engineering of Qilu University of Technology and the School of Mechanical Engineering of Shandong University. Her main research directions are ultra-precision machining and abrasive water jet polishing technology. E-mail: qluliqian@163.com

YAO Peng (1979—), male, born in Dalian, Liaoning Province, PhD, Professor, Doctoral Supervisor. He received his doctoral degree from Northeastern University (Japan) in 2011, Mainly engaged in research on grinding and ultra precision machining technology, multi energy field composite precision machining technology, and laser micro/nano machining technology. E-mail: yaopeng@sdu.edu.cn

Corresponding author: yaopeng@sdu.edu.cn

摘要

摘要:
磨料水射流抛光技术作为一种非接触式超精密加工方法，凭借其稳定的材料去除函数、无亚表面损伤特性及强形状适应性，在光学元件加工领域具有重要应用价值。本研究通过计算流体动力学（CFD）数值模拟方法，系统分析了射流压力、喷嘴直径及入射角度对抛光流场压力分布、速度分布及壁面剪切力分布的作用规律。基于Box-Behnken实验设计，构建了响应面回归模型，系统研究了工艺参数对熔石英玻璃的材料去除率（MRR）和表面粗糙度（Ra）的影响机制。实验结果表明：通过增大射流压力和喷嘴直径可显著提高MRR，该规律与流场仿真揭示的剪切应力分布特征一致；但增大射流压力和入射角度会导致Ra增大，不利于表面质量提升。通过遗传算法（GA）多目标优化建立Pareto解集，成功实现了加工效率与表面质量的协同优化，在射流压力2 MPa、喷嘴直径0.3mm和入射角度30°的参数组合下MRR达169.05 μm³/s、Ra低至0.50 nm；实验验证表明，模型预测值与实测值误差仅为4.4%（MRR）和3.8%（Ra），验证了模型的可靠性。本研究建立的参数优化体系为复杂曲面光学元件的超精密抛光提供了理论依据与技术支持。
- 磨粒 /
- 计算流体动力学 /
- 去除函数 /
- 材料去除率 /
- 表面粗糙度
Abstract:
As a non-contact ultra-precision machining method, abrasive water jet polishing (AWJP) has significant application in optical elements processing due to its stable tool influence function (TIF), no subsurface damage and strong adaptability to workpiece shapes. In this study, the effects of jet pressure, nozzle diameter and impinging angle on the distribution of pressure, velocity and wall shear stress in the polishing flow field were systematically analyzed by computational fluid dynamics (CFD) simulation. Based on the Box-Behnken experimental design, a response surface regression model was constructed to investigate the influence mechanism of process parameters on material removal rate (MRR) and surface roughness (Ra) of fused silica. And experimental results showed that increasing jet pressure and nozzle diameter significantly improved MRR, consistent with shear stress distribution revealed by CFD simulations. However, increasing jet pressure and impinging angle caused higher Ra values, which was unfavorable for surface quality improvement. Genetic algorithm (GA) was used for multi-objective optimization to establish Pareto solutions, achieving concurrent optimization of polishing efficiency and surface quality. A parameter combination of 2 MPa jet pressure, 0.3 mm nozzle diameter, and 30° impinging angle achieved MRR of 169.05 μm³/s and Ra of 0.50 nm. Experimental verification showed prediction errors of 4.4% (MRR) and 3.8% (Ra), confirming model reliability. This parameter optimization system provides theoretical basis and technical support for ultra-precision polishing of complex curved optical components.
- abrasive /
- computational fluid dynamics /
- tool influence function /
- material removal rate /
- surface roughness

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Figure 1. Schematic diagram of AWJP

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Figure 2. Experimental setup

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Figure 3. The SEM image of CeO₂ abrasive

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Figure 4. The white light 3D interferometer image of (a) the removal profile and (b) cross-sectional TIF

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Figure 5. Polished surface topography via white light interferometry

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Figure 6. Velocity cloud plots at different impinging angles (a) 30°; (b) 45° and (c) 60°

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Figure 7. Simulation curves for different impinging angles (a) velocity curve; (b) static pressure curve and (c) wall shear stress curve

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Figure 8. Simulation curves for different jet pressure (a) velocity curve; (b) static pressure curve and (c) wall shear stress curve

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Figure 9. Simulation curves for different nozzle diameters (a) velocity curve; (b) static pressure curve and (c) wall shear stress curve

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Figure 10. Normal plots of residuals for (a) MRR and (b) Ra

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Figure 11. Perturbation plots obtained from RSM analysis showing the influence of individual process variables on (a) MRR and (b) Ra

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Figure 12. The material removal process under different jet impinging (a) Small impinging angle and (b) Large impinging angle

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Figure 13. 3D response surface plots depicting the interactions between independent variables and their effect on MRR (a-c) and Ra (d-f)

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Figure 14. Pareto footprint diagram of the objective function

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Table 1. AWJP parameters

AWJP parameters	levels
AWJP parameters	−1	0	1
Jet pressure (MPa)	2	3	4
Nozzle diameter (mm)	0.3	0.5	0.7
Impinging angle (°)	30	45	60

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Table 2. The results of the response surface regression experiments

AWJP parameters				Output responses
Run	jet pressure (MPa)	nozzle diameter (mm)	impinging angle (°)	MRR (μm³/s)	Ra (nm)
1	2	0.5	30	262.75	0.56
2	4	0.3	45	907.42	1.12
3	3	0.5	45	735.50	0.81
4	3	0.5	45	846.42	0.87
5	2	0.3	45	221.42	0.55
6	3	0.5	45	766.75	0.86
7	3	0.5	45	821.33	0.80
8	4	0.7	45	1873.25	1.22
9	2	0.5	60	208.67	0.71
10	4	0.5	30	1391.92	0.94
11	3	0.3	60	439.33	0.91
12	3	0.3	30	613.08	0.72
13	4	0.5	60	1011.42	1.35
14	3	0.5	45	831.25	0.92
15	2	0.7	45	470.08	0.63
16	3	0.7	60	961.42	0.93
17	3	0.7	30	1304.92	0.78

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Table 3. Analysis of variance for MRR

Source	Sum of squares	Degree of Freedom	Mean square	F-value	P-value	Significance
Model	3.082$ e $+06	9	3.425$ e $+05	187.33	< 0.0001	significant
A-jet pressure	2.021$ e $+06	1	2.021$ e $+06	1105.56	< 0.0001
B-nozzle diameter	7.372$ e $+05	1	7.372$ e $+05	403.22	< 0.0001
C-impinging angle	1.132$ e $+05	1	1.132$ e $+05	61.95	0.0001
AB	1.286$ e $+05	1	1.286$ e $+05	70.33	< 0.0001
AC	26637.50	1	26637.50	14.57	0.0066
BC	7203.77	1	7203.77	3.94	0.0875
A²	1964.92	1	1964.92	1.07	0.3343
B²	33648.28	1	33648.28	18.41	0.0036
C²	15136.43	1	15136.43	8.28	0.0237
Residual	12797.12	7	1828.16
Lack of Fit	3945.28	3	1315.09	0.5943	0.6512	not significant
Pure Error	8851.85	4	2212.96
Cor Total	3.095$ \mathrm{e} $$ e $+06	16

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Table 5. Fit statistics of ANOVA

	Std.Dev.	Mean	C.V.%	R²	Adjusted R²	Predicted R²	Adeq Precision
MRR	42.76	803.94	5.32	0.9959	0.9905	0.9751	51.073
Ra	0.0524	0.8635	6.07	0.9743	0.9413	0.7717	19.1547

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Table 4. Analysis of variance for Ra

Source	Sum of squares	Degree of Freedom	Mean square	F-value	P-value	Significance
Model	0.7290	9	0.0810	29.48	< 0.0001	significant
A-jet pressure	0.5940	1	0.5940	216.24	< 0.0001
B-nozzle diameter	0.0084	1	0.0084	3.08	0.1229
C-impinging angle	0.1012	1	0.1012	36.86	0.0005
AB	0.0001	1	0.0001	0.0364	0.8541
AC	0.0169	1	0.0169	6.15	0.0422
BC	0.0004	1	0.0004	0.1456	0.7141
A²	0.0073	1	0.0073	2.64	0.1483
B²	0.0008	1	0.0008	0.2793	0.6135
C²	0.0001	1	0.0001	0.0188	0.8949
Residual	0.0192	7	0.0027
Lack of Fit	0.0098	3	0.0033	1.37	0.3720	not significant
Pure Error	0.0095	4	0.0024
Cor Total	0.7482	16

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Table 6. Partial Pareto solution set for multi-objective optimization

run	A	B	C	$ f(MRR) $	$ f(Ra) $
1	2.00	0.3	30	176.86	0.52
2	2.10	0.3	30	218.77	0.53
3	3.90	0.7	30	1955.06	0.99
4	2.32	0.7	30	743.00	0.64
5	2.00	0.6	30	390.57	0.59
6	2.68	0.7	30	1045.99	0.70
7	3.93	0.7	30	1982.46	1.00
8	2.10	0.7	30	512.08	0.60
9	4.00	0.7	30	2036.53	1.02
10	3.25	0.7	30	1473.19	0.82
11	2.96	0.7	30	1253.51	0.76
12	3.20	0.7	30	1433.27	0.81
···	···	···	···

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Table 7. Comparative analysis of experiments

Run	Indicator	Pareto solutions	Experimental value	Error
1	MRR (μm³/s)	176.86	169.05	4.4%
8		512.08	507.65	0.9%
11		1253.51	1247.25	0.5%
1	Ra(nm)	0.52	0.50	3.8%
8		0.60	0.58	3.3%
11		0.76	0.78	2.6%

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