Optimization of Laser Hardening and Polishing Parameters of H13 Steel Surfaces with Small Sample Data Driven Process

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

Abstract

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

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

CLC Number:

TN249

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.

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.

Figures/Tables 21

Fig.1 Flowchart of multi-objective optimization strategy

Fig.2 Flowchart of OOA algorithm to optimize XGBOOST model

Fig.3 Flowchart of the improved DNSGA-II algorithm

Fig.4 Flowchart of VIKOR-VRITIC

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

Fig.5 Schematic diagram of measurement method

Fig.6 Distribution of process parameters

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

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

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

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

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

Tab. 4 Algorithm performance comparison

评估

指标

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

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

Fig.9 Cross-section after laser scanning

Fig.10 Surface profile before and after polishing

Fig.11 Surface morphology before and after laser scanning

Fig.12 Schematic diagram of measurement method

Fig.13 Changing trend of hardness at different depths

Fig. 14 Cross-section organization of the hardened layer

Fig.15 Surface XRD before and after laser scanning

Fig.16 EDS line scanning results

References 36

[1]	VESELÝ Z， HONNEROVÁ P， HRUŠKA M， et al. Analysis of Laser Surface Absorptivity Modification for Selective Laser Hardening［J］. International Journal of Thermal Sciences， 2024， 200： 108982.
[2]	WAGH S V， MORE S R， VENU MADHAV V V， et al. Effects of Low-power Laser Hardening on the Mechanical and Metallurgical Properties of Biocompatible SAE 420 Steel［J］. Journal of Materials Research and Technology， 2024， 30： 1611-1619.
[3]	CHEN Zhenyu， YU Xiaodong， DING Ning， et al. Wear Resistance Enhancement of QT700-2 Ductile Iron Crankshaft Processed by Laser Hardening［J］. Optics & Laser Technology， 2023， 164： 109519.
[4]	杨仁人，林英华，彭龙生，等. 连续高功率激光辐照对55号钢组织和硬度的影响［J］. 中国激光， 2023， 50（16）： 163-174.
	YANG Renren， LIN Yinghua， PENG Longsheng， et al. Effect of Continuous High-power Laser Irradiation on Microstructure and Hardness of 55 Steel［J］. Chinese Journal of Lasers， 2023， 50（16）： 163-174.
[5]	ZHAO Shuang， YU Mingjie， YAN Ruopeng， et al. Surface Roughness and Microhardness Improvement of Laser Cladding Stainless-steel 316 by Laser Polishing Based on Multiple Remelting［J］. Optics & Laser Technology， 2024， 176： 110903.
[6]	LIU Bo， HONG Jing， QIAN Yongfeng， et al. Simultaneous Improvement in Surface Quality and Hardness of Laser Shock Peened Zr-based Metallic Glass by Laser Polishing［J］. Optics & Laser Technology， 2024， 179： 111323.
[7]	YI Chengnuo， CHEN Xiaoxiao， ZHOU Yuhang， et al. Effects of Scanning Speed and Scanning Times on Surface Quality of Line Spot Laser Polishing of Nickel-based Superalloys［J］. Journal of Materials Research and Technology， 2023， 26： 2179-2190.
[8]	周梦，吕志刚，邸若海，等. 基于小样本数据的BP神经网络建模［J］. 科学技术与工程， 2022， 22（7）： 2754-2760.
	ZHOU Meng， Zhigang LÜ， DI Ruohai， et al. BP Neural Network Modeling Based on Small Sample Data［J］. Science Technology and Engineering， 2022， 22（7）： 2754-2760.
[9]	赵腾远，宋超，何欢. 小样本条件下江苏软土路基回弹模量的贝叶斯估计——基于静力触探数据与高斯过程回归的建模分析［J］. 岩土工程学报， 2021， 43（）： 137-141.
	ZHAO Tengyuan， SONG Chao， HE Huan. Bayesian Estimation of Resilience Modulus of Soft Soil Subgrade in Jiangsu Province under Small Sample Conditions—Modeling Analysis Based on Cone Penetration Data and Gaussian Process Regression［J］. Chinese Journal of Geotechnical Engineering， 2021， 43（S2）： 137-141.
[10]	易茜，柳淳，李聪波，等. 基于小样本数据驱动的滚齿工艺参数低碳优化决策方法［J］. 中国机械工程， 2022， 33（13）： 1604-1612.
	YI Qian， LIU Chun， LI Congbo， et al. A Low Carbon Optimization Decision Method for Gear Hobbing Process Parameters Driven by Small Sample Data［J］. China Mechanical Engineering， 2022， 33（13）： 1604-1612.
[11]	李泽亚，罗敏，张超勇，等. 数控铣床低碳高质建模及工艺参数优化［J］. 中国机械工程， 2024， 35（10）： 1845-1851.
	LI Zeya， LUO Min， ZHANG Chaoyong， et al. Low Carbon and High Quality Modeling and Processing Parameter Optimization of CNC Milling Machines［J］. China Mechanical Engineering， 2024， 35（10）： 1845-1851.
[12]	李光保，高栋，路勇，等. 自适应卡尔曼滤波与PSO-GA-BP算法的机器人误差补偿［J］. 中国机械工程， 2023， 34（20）： 2456-2465.
	LI Guangbao， GAO Dong， LU Yong， et al. Adaptive Kalman Filtering and PSO-GA-BP Algorithm for Robot Error Compensation［J］. China Mechanical Engineering， 2023， 34（20）： 2456-2465.
[13]	龚伟，赵文华，王心田，等. 基于机器学习的激光微纳加工研究：应用和前景［J］. 中国激光， 2023， 50（20）： 2000001.
	GONG Wei， ZHAO Wenhua， WANG Xintian， et al. Machine Learning for Laser Micro/Nano Manufacturing： Applications and Prospects［J］. Chinese Journal of Lasers， 2023， 50（20）： 2000001.
[14]	CHEN Tianqi， GUESTRIN C. XGBoost： a Scalable Tree Boosting［C］∥ACM SIGKDD Conference on Knowledge Discovery and Data Mining. San Francisco，2016：785-794.
[15]	ZHANG Fan， ZHU Zhengyang， LIU Jiefeng， et al. A Novel Concentration Prediction Technique of Carbon Monoxide （CO） Based on Beluga Whale Optimization-extreme Gradient Boosting （BWO-XGBoost）［J］. Journal of the Taiwan Institute of Chemical Engineers， 2025， 171： 106045.
[16]	DEHGHANI M， TROJOVSKÝ P. Osprey Optimization Algorithm： a New Bio-inspired Metaheuristic Algorithm for Solving Engineering Optimization Problems［J］. Frontiers in Mechanical Engineering， 2023， 8： 1126450.
[17]	LIANG Qiang， XU Yonghang， XU Binyuan， et al. Parameter Optimization for In-situ Synthesized TiB₂/TiC Particle Composite Coatings by Laser Cladding Based on OOA-RFR and U-NSGA-III［J］. Optics & Laser Technology， 2025， 181： 111755.
[18]	YAN Pengcheng， LI Guodong， WANG Wenchang， et al. Qualitative and Quantitative Detection of Microplastics in Soil Based on LIF Technology Combined with OOA-ELM/SPA-PLS［J］. Microchemical Journal， 2024， 201： 110632.
[19]	GAO Yan， CAO Baifu， YU Wenhao， et al. Short-term Wind Speed Prediction for Bridge Site Area Based on Wavelet Denoising OOA-transformer［J］. Mathematics， 2024， 12（12）： 1910.
[20]	DEB K， PRATAP A， AGARWAL S， et al. A Fast and Elitist Multiobjective Genetic Algorithm： NSGA-II［J］. IEEE Transactions on Evolutionary Computation， 2002， 6（2）： 182-197.
[21]	郭庆辉，李媛，杨东升. 一种改进麻雀搜索算法的收敛性分析及应用［J］. 控制与决策， 2024， 39（8）： 2502-2510.
	GUO Qinghui， LI Yuan， YANG Dongsheng. Convergence Analysis and Application of an Improved Sparrow Search Algorithm［J］. Control and Decision， 2024， 39（8）： 2502-2510.
[22]	YANG Guangchao， WANG Liuhong， GU Wen， et al. Soil Ecological Risk Assessment of Ten Industrial Areas in China Based on the TRIAD and VIKOR Methods［J］. Ecological Indicators， 2024， 166： 112270.
[23]	ATANGANA NJOCK P G， SHEN Shuilong， ZHOU Annan， et al. A VIKOR-based Approach to Evaluate River Contamination Risks Caused by Wastewater Treatment Plant Discharges［J］. Water Research， 2022， 226： 119288.
[24]	LUO Yuyan， YANG Ziwei， QIN Yong. A Hybrid BWM-CRITIC-VIKOR Approach for Assessing Oil and Gas Risk Scenarios in Probabilistic Linguistic Term Set［J］. Heliyon， 2024， 10（19）： e38514.
[25]	DING Tingting， LIU Shushen， WANG Zejun， et al. A Novel Mixture Sampling Strategy Combining Latin Hypercube Sampling with Optimized One Factor at a Time Method： a Case Study on Mixtures of Antibiotics and Pesticides［J］. Journal of Hazardous Materials， 2024， 461： 132568.
[26]	BOURCET J， KUBILAY A， DEROME D， et al. Representative Meteorological Data for Long-term Wind-driven Rain Obtained from Latin Hypercube Sampling ― Application to Impact Analysis of Climate Change［J］. Building and Environment， 2023， 228： 109875.
[27]	MCKAY M D， BECKMAN R J， CONOVER W J. A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output from a Computer Code［J］. Technometrics， 2000， 42（1）： 55-61.
[28]	VOŘECHOVSKÝ M. Hierarchical Refinement of Latin Hypercube Samples［J］. Computer-Aided Civil and Infrastructure Engineering， 2015， 30（5）： 394-411.
[29]	WANG Yujing， ZHAO Yanqing. Predicting Bedrock Depth under Asphalt Pavement through a Data-driven Method Based on Particle Swarm Optimization-back Propagation Neural Network［J］. Construction and Building Materials， 2022， 354： 129165.
[30]	SHEN Qingkai， XUE Jiaxiang， ZHENG Zehong， et al. Machine Learning-based Prediction of CoCrFeNiMo_0.2 High-entropy Alloy Weld Bead Dimensions in Wire Arc Additive Manufacturing［J］. Materials Today Communications， 2024， 41： 110359.
[31]	RIVERA-LOPEZ R， CANUL-REICH J， MEZURA-MONTES E， et al. Induction of Decision Trees as Classification Models through Metaheuristics［J］. Swarm and Evolutionary Computation， 2022， 69： 101006.
[32]	BREIMAN L. Random Forests［J］. Machine Learning， 2001， 45（1）： 5-32.
[33]	HARANE P P， UNUNE D R， AHMED R， et al. Multi-objective Optimization for Electric Discharge Drilling of Waspaloy： a Comparative Analysis of NSGA-II， MOGA， MOGWO， and MOPSO［J］. Alexandria Engineering Journal， 2024， 99： 1-16.
[34]	YukuiMEN， DONG Yanfang， ZENG Si， et al. Multi-objective Optimization of Solar-driven Hollow Fiber Membrane Dehumidification System Based on MOPSO［J］. Energy， 2024， 304： 132084.
[35]	ZENG Quan， WANG Kelu， LU Shiqiang， et al. Modeling and Optimization of Energy Consumption， Surface Quality and Relative Density in GH3625 Superalloy by Laser Powder Bed Melting via RSM MOPSO and CRITIC-TOPSIS［J］. Optics & Laser Technology， 2025， 184： 112411.
[36]	ZHANG Hang， SUN Xiaoyu， XU Xuebo， et al. Numerical Simulation of Surface Structures in Single and Multi-track Laser Polishing of NiP Alloy［J］. Journal of Manufacturing Processes， 2024， 132： 404-415.