基于小样本数据驱动的H13钢表面激光硬化及抛光工艺参数优化

doi:10.3969/j.issn.1004-132X.2026.08.011

摘要/Abstract

摘要：

为实现通过激光加工对H13模具钢表面进行硬化处理并改善表面形貌，以激光功率、扫描速度和搭接率3个工艺参数为变量，对试样的淬透深度和相邻扫描道次的峰谷差值、表面粗糙度进行了优化。首先采用拉丁超立方抽样进行试验设计，并基于得到的小样本数据建立了多目标优化模型。然后采用多目标优化算法进行工艺参数寻优。最后采用多准则妥协解排序法结合客观赋权法构建了一种综合评价方法，对非劣解集进行排序以得到最佳工艺参数组合。在最佳工艺参数组合下进行试验，结果表明H13钢表面硬化效果显著，同时有效降低了表面粗糙度。

关键词: H13钢, 激光抛光, 激光硬化, 小样本数据驱动, 参数优化

Abstract:

This paper investigated the optimization of processing parameters for surface hardening and morphology improvement of H13 mold steels using laser processing. Laser power， scanning speed， and overlap ratio were selected as processing variables， and their effects on hardening depth， peak-valley height between adjacent scanning tracks， and surface roughness were optimized. Initially， Latin hypercube sampling was employed for experimental design， followed by the development of a multi-objective optimization model based on the obtained small-sample data. A multi-objective optimization algorithm was then used to optimize the processing parameters. Finally， a comprehensive evaluation method was proposed by integrating the multi-criteria decision-making approach with an objective weighting method to rank the non-dominated solutions and identify the optimal parameter combination. Experimental results conducted under the optimal parameter combination demonstrate significant surface hardening of H13 steels along with effective reduction in surface roughness.

Key words: H13 steel, laser polishing, laser hardening, small sample data driven, parameter optimization

中图分类号:

TN249

梁强, 徐彬源, 徐永航, 胡开群, 陈伟灵, 陈红. 基于小样本数据驱动的H13钢表面激光硬化及抛光工艺参数优化[J]. 中国机械工程, 2026, 37(8): 1917-1927.

LIANG Qiang, XU Binyuan, XU Yonghang, HU Kaiqun, CHEN Weiling, CHEN Hong. Optimization of Laser Hardening and Polishing Parameters of H13 Steel Surfaces with Small Sample Data Driven Process[J]. China Mechanical Engineering, 2026, 37(8): 1917-1927.

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链接本文: https://www.cmemo.org.cn/CN/10.3969/j.issn.1004-132X.2026.08.011

https://www.cmemo.org.cn/CN/Y2026/V37/I8/1917

图/表 21

图1 多目标优化策略流程图

Fig.1 Flowchart of multi-objective optimization strategy

图2 OOA算法优化XGBOOST模型训练流程图

Fig.2 Flowchart of OOA algorithm to optimize XGBOOST model

图3 改进DNSGA-Ⅱ算法流程图

Fig.3 Flowchart of the improved DNSGA-II algorithm

图4 VIKOR-VRITIC流程图

Fig.4 Flowchart of VIKOR-VRITIC

表1 H13钢主要化学成分（质量分数） (%)

Tab.1 Main chemical compositions of H13 steel（mass fraction）

w（C）	w（Si）	w（Mn）	w（Cr）	w（Mo）	w（V）	w（P）	w（S）	w（Fe）
0.32～0.45	0.80～1.20	0.20～0.50	4.75～5.50	1.10～1.75	0.80～1.20	≤0.03	≤0.03	其余

图5 加工与测量方式示意图

Fig.5 Schematic diagram of measurement method

图6 工艺参数分布情况

Fig.6 Distribution of process parameters

表2 试验方案及结果

Tab.2 Test program and results

序号	P/W	v/（mm·s $- 1$ ）	δ/%	H/μm	ΔH/μm	Ra/μm
1	534	10	31	712.7033	473.9808	2.4318
2	547	6	65	764.7600	69.0054	2.7549
3	567	14	24	659.2067	659.2067	2.7285
4	581	14	41	706.8433	254.5815	2.6617
5	586	11	54	753.3067	76.4454	3.4433
6	606	10	68	816.2033	34.7314	3.2717
7	617	10	27	763.1167	251.2191	3.3295
8	647	8	32	844.8267	184.5580	3.4072
9	650	8	35	919.3367	108.0334	2.8930
10	677	7	20	994.9333	286.3463	2.8464
11	681	6	37	1011.3400	167.0627	3.7995
12	707	15	50	735.7467	111.0918	3.1009
13	726	14	26	730.7833	230.8106	3.5365
14	731	9	11	856.8400	387.3315	3.0025
15	755	8	63	1129.2933	254.8948	2.9192
16	776	12	66	826.0200	66.7878	2.3739
17	778	9	43	1067.8363	140.6478	2.3718
18	801	6	16	1131.5800	399.9582	3.0312
19	811	11	53	856.7667	115.4971	2.9085
20	826	13	18	863.1000	366.2251	2.6999
21	852	7	45	1140.0633	76.7062	3.1529
22	861	13	57	863.1600	69.4323	4.3345
23	877	12	48	893.1933	108.8696	4.8046
24	904	5	59	1540.2567	216.6558	4.3540
25	916	11	14	1040.8467	352.9074	4.3978

表2 试验方案及结果

Tab.2 Test program and results

序号	P/W	v/（mm·s $- 1$ ）	δ/%	H/μm	ΔH/μm	Ra/μm
1	534	10	31	712.7033	473.9808	2.4318
2	547	6	65	764.7600	69.0054	2.7549
3	567	14	24	659.2067	659.2067	2.7285
4	581	14	41	706.8433	254.5815	2.6617
5	586	11	54	753.3067	76.4454	3.4433
6	606	10	68	816.2033	34.7314	3.2717
7	617	10	27	763.1167	251.2191	3.3295
8	647	8	32	844.8267	184.5580	3.4072
9	650	8	35	919.3367	108.0334	2.8930
10	677	7	20	994.9333	286.3463	2.8464
11	681	6	37	1011.3400	167.0627	3.7995
12	707	15	50	735.7467	111.0918	3.1009
13	726	14	26	730.7833	230.8106	3.5365
14	731	9	11	856.8400	387.3315	3.0025
15	755	8	63	1129.2933	254.8948	2.9192
16	776	12	66	826.0200	66.7878	2.3739
17	778	9	43	1067.8363	140.6478	2.3718
18	801	6	16	1131.5800	399.9582	3.0312
19	811	11	53	856.7667	115.4971	2.9085
20	826	13	18	863.1000	366.2251	2.6999
21	852	7	45	1140.0633	76.7062	3.1529
22	861	13	57	863.1600	69.4323	4.3345
23	877	12	48	893.1933	108.8696	4.8046
24	904	5	59	1540.2567	216.6558	4.3540
25	916	11	14	1040.8467	352.9074	4.3978

图7 预测模型对H、ΔH和Ra的拟合效果

Fig.7 Effectiveness of fitting the prediction model to H、ΔH and Ra

表3 模型准确性对比

Tab.3 Comparison of model accuracy

评估指标	BPNN
评估指标	R²	MAPE值	RMSE值
Ra	0.904	5.411	0.236
H	0.939	4.332	44.002
ΔH	0.876	27.652	15.883
评估指标	DT
评估指标	R²	MAPE值	RMSE值
Ra	0.903	6.024	0.238
H	4.362	42.955	0.899
ΔH	41.352	0.903	6.024
评估指标	RF
评估指标	R²	MAPE值	RMSE值
Ra	0.912	6.240	0.227
H	4.580	43.433	0.933
ΔH	33.629	0.912	6.240
评估指标	XGBOOST
评估指标	R²	MAPE值	RMSE值
Ra	0.943	4.185	0.168
H	0.952	3.493	39.125
ΔH	0.989	8.243	13.918
评估指标	OOA-XGBOOST
评估指标	R²	MAPE值	RMSE值
Ra	0.961	3.988	0.151
H	0.973	3.172	29.117
ΔH	0.991	4.366	11.998

图8 各优化算法所得Pareto解集

Fig.8 The set of Pareto solutions obtained by each optimization algorithm

表4 算法性能对比

Tab. 4 Algorithm performance comparison

评估

指标

表5 综合评价排名前5组解

Tab.5 Top 5 groups of solutions ranked by comprehensive evaluation

序号	P/W	v/（mm·s $- 1$ ）	δ/%	Ra/μm	H/μm	ΔH/μm	S_i	R_i	Q_i
1	793.0291	9.2820	41.8260	2.5715	982.6173	144.3267	0.0570	0.0570	0.0009
2	787.7155	9.4735	41.9124	2.5759	978.6181	145.5351	0.0645	0.0578	0.0070
3	774.4715	9.0337	43.5136	2.5765	969.5222	143.4933	0.0726	0.0564	0.0101
4	774.4715	9.0337	41.0374	2.5760	975.5882	152.6799	0.0725	0.0627	0.0197
5	792.5727	10.3157	41.8353	2.6071	901.2695	131.3647	0.1516	0.0819	0.1003

表5 综合评价排名前5组解

Tab.5 Top 5 groups of solutions ranked by comprehensive evaluation

序号	P/W	v/（mm·s $- 1$ ）	δ/%	Ra/μm	H/μm	ΔH/μm	S_i	R_i	Q_i
1	793.0291	9.2820	41.8260	2.5715	982.6173	144.3267	0.0570	0.0570	0.0009
2	787.7155	9.4735	41.9124	2.5759	978.6181	145.5351	0.0645	0.0578	0.0070
3	774.4715	9.0337	43.5136	2.5765	969.5222	143.4933	0.0726	0.0564	0.0101
4	774.4715	9.0337	41.0374	2.5760	975.5882	152.6799	0.0725	0.0627	0.0197
5	792.5727	10.3157	41.8353	2.6071	901.2695	131.3647	0.1516	0.0819	0.1003

图9 激光扫描后的截面

Fig.9 Cross-section after laser scanning

图10 抛光前后表面轮廓

Fig.10 Surface profile before and after polishing

图11 激光扫描前后表面形貌

Fig.11 Surface morphology before and after laser scanning

图12 测量方式示意图

Fig.12 Schematic diagram of measurement method

图13 不同深度硬度变化规律

Fig.13 Changing trend of hardness at different depths

图14 硬化层截面组织

Fig. 14 Cross-section organization of the hardened layer

图15 激光扫描前后的表面XRD

Fig.15 Surface XRD before and after laser scanning

图16 EDS线扫描结果

Fig.16 EDS line scanning results

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