Reliability-based Optimization of Selective Laser Melting Process Parameters for Co-Cr Alloy

doi:10.12382/bgxb.2023.0923

Abstract

Abstract:

Selective laser melting (SLM) is one of the most common additive manufacturing technologies at present. The process parameters, material properties and atmosphere stability have important impacts on the forming quality. A multi-factor and multi-level experiment is designed by taking the nominal value of laser power, scanning speed and scanning pitch as design variables, and the laser power, local distribution mean value of Co-Cr alloy powder diameters, and wind speed fluctuation strength as random parameters. Based on the principle of rank correlation, the probabilistic augmentation of incomplete data is achieved to obtain the response surface among design variables, random parameters and properties of samples. The reliability-based design optimization (RBDO) model for SLM process parameters of Co-Cr alloy is established with the optimization goal of maximizing forming efficiency under the probability constraint of meeting the allowable tensile strength. Aiming at non-normal random parameters and non-linear performance function in the Co-Cr alloy SLM process, the universal generation function is introduced, discrete enumeration and random sampling are integrated, and an innovative RBDO algorithm based on adaptive subdivision-importance sampling strategy is proposed to obtain the optimal solution of SLM process parameters for achieving the highest forming efficiency under reliability constraints.

Key words: selective laser melting, reliability-based design optimization, Co-Cr alloy, process parameter, universal generating function, rank correlation

CLC Number:

ZHOU Jinyu, WANG Xinyuan, CHENG Jinxiang, WANG Lin. Reliability-based Optimization of Selective Laser Melting Process Parameters for Co-Cr Alloy[J]. Acta Armamentarii, 2024, 45(12): 4530-4538.

Figures/Tables 11

Fig.1 Technology principle of SLM

Table 1 Chemical composition of Co-Cr alloy powder

元素组成	钴	铬	钨	硅	铁	锰
占比/%	61.5	27.75	8.5	1.5	0.5	0.25

Fig.2 Distribution of power particle size

Fig.3 Tensile specimens

Table 2 Design of experiments

因素	水平
因素	-2	-1	0	1	2
P_m /W	120	140	160	180
v/(mm·s^-1)	1000	1200	1400	1600	1800
h/mm	0.06	0.07	0.08

Table 3 Test results of tensile strength (partially)

编号	P_m/ W	v/ (mm·s^-1)	h/ mm	σ₁/ MPa	σ₂/ MPa	σ₃/ MPa
1	120	1000	0.06	1034.61	1048.21	1065.21
2	140	1000	0.07	967.49	1043.90	1064.48
3	160	1000	0.08	1038.29	1049.98	1058.25
4	180	1000	0.06	970.48	1003.72	1019.47
5	120	1000	0.07	1060.08	1089.45	1100.81
6	120	1200	0.07	1053.07	1108.34	1132.05
7	140	1200	0.08	1027.81	1095.79	1113.43
8	160	1200	0.08	1070.51	1083.22	1127.67
9	180	1200	0.06	984.53	1013.28	1037.55
10	140	1200	0.06	1012.73	1056.96	1073.91
11	120	1400	0.08	814.01	895.21	911.73
12	140	1400	0.07	966.58	1062.39	1099.09
13	160	1400	0.08	998.11	1082.37	1165.05
14	180	1400	0.06	984.72	1015.36	1028.18
15	160	1400	0.07	995.20	1050.17	1083.77
16	120	1600	0.06	679.88	896.29	946.10
17	140	1600	0.07	900.60	947.05	1009.10
18	160	1600	0.06	972.97	1078.37	1096.74
19	180	1600	0.07	1042.13	1086.49	1107.93
20	180	1600	0.08	1069.77	1093.74	1116.56
21	120	1800	0.08	502.59	617.80	709.61
22	140	1800	0.06	853.33	944.61	1072.16
23	160	1800	0.07	764.34	909.13	1049.10
24	180	1800	0.08	775.43	928.35	1005.69
25	180	1800	0.06	962.38	1067.77	1085.42

Fig.4 Main effect of the process parameters on the tensile strength of specimen

Table 4 Mapping of random parameters and tensile strengths (for a group of experiments)

P/W	d_m /μm	δ/(m·s^-1)	σ/MPa
117.14	37.83	0.39	502.59
118.09	37.50	0.35	588.74
118.65	37.17	0.32	606.65
119.09	36.83	0.30	611.11
119.47	36.50	0.28	611.55
119.83	36.17	0.26	615.16
120.17	35.83	0.24	617.80
120.53	35.50	0.22	621.28
120.91	35.17	0.20	644.93
121.35	34.83	0.18	668.51
121.91	34.50	0.15	681.18
122.86	34.17	0.11	709.61

Table 5 Analysis of variance of response surface model for tensile strength

来源	自由度	F值	p值	评价
模型	10	196.06	<0.0001	显著
P	1	331.78	<0.0001	显著
v	1	615.77	<0.0001	显著
h	1	38.94	<0.0001	显著
δ	1	163.59	<0.0001	显著
Pv	1	365.98	<0.0001	显著
Ph	1	14.90	0.0001	显著
vh	1	74.42	<0.0001	显著
P²	1	54.66	<0.0001	显著
v²	1	118.32	<0.0001	显著
$d m 2$	1	6.93	0.0089	显著

Table 5 Analysis of variance of response surface model for tensile strength

来源	自由度	F值	p值	评价
模型	10	196.06	<0.0001	显著
P	1	331.78	<0.0001	显著
v	1	615.77	<0.0001	显著
h	1	38.94	<0.0001	显著
δ	1	163.59	<0.0001	显著
Pv	1	365.98	<0.0001	显著
Ph	1	14.90	0.0001	显著
vh	1	74.42	<0.0001	显著
P²	1	54.66	<0.0001	显著
v²	1	118.32	<0.0001	显著
$d m 2$	1	6.93	0.0089	显著

Fig.5 Flowchart of AS-IS-based RBDO framework for SLM process parameters

Table 6 Comparison of calculated results of given methods

方法	设计点位置向量	β_MCS	ε_i/ %	迭代次数	功能函数调用次数	时间/ s
1	×	×	×	×	×	×
2	×	×	×	×	×	×
3	×	×	×	×	×	×
4	$165.6 1733.2 0.08$	1.9917	0.42	5	153279	1.08
5	$165.7 1733.2 0.079$	2.0092	0.46	3	30400000	318

Table 6 Comparison of calculated results of given methods

方法	设计点位置向量	β_MCS	ε_i/ %	迭代次数	功能函数调用次数	时间/ s
1	×	×	×	×	×	×
2	×	×	×	×	×	×
3	×	×	×	×	×	×
4	$165.6 1733.2 0.08$	1.9917	0.42	5	153279	1.08
5	$165.7 1733.2 0.079$	2.0092	0.46	3	30400000	318

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