变F-RD型点阵结构的参数分析与验证

doi:10.12068/j.issn.1005-3026.2024.09.010

摘要/Abstract

摘要：

针对常规F-RD型点阵结构进行变形设计，提出一种基于隐式表达式的TPMS（three?period minimal surface）参数设计方法，通过改变输入隐式表达式的变形参数来设计点阵结构；研究了F-RD型点阵结构变形参数和阈值对孔隙率的影响规律，提出了针对孔隙率分析的单参数和混合参数方法，建立了变形参数和阈值对变F-RD型点阵结构的映射关系，可以生成特定形状和孔隙率的F-RD型点阵结构；通过金属激光烧结成型原理制备AlSi10Mg样件，验证了变形参数和阈值对实际孔隙率的影响关系，为F-RD型点阵结构的工程设计和应用提供参考.

关键词: 变F-RD型点阵结构, 参数分析, TPMS, 孔隙率, 点阵结构设计

Abstract:

Aiming at the conventional F-RD-type lattice structure for deformation design， a TPMS parameter design method based on implicit expression is proposed to design the lattice structure by changing the deformation parameter inputted into the implicit expression； the influence law of the deformation parameter and the threshold value on the porosity of the F-RD-type lattice structure is investigated， the single parameter and mixed parameter methods for porosity analysis are proposed， the mapping relationship between the deformation parameter and the threshold value on the variable F-RD-type lattice structure is established， and the F-RD-type lattice structure with specific shapes and porosity can be generated； through the AlSi10Mg samples prepared by the metal laser sintering molding principle， the influence relationship of the deformation parameter and the threshold value on the actual porosity is verified， which provides a reference for the engineering design and application of TPMS lattice structures.

Key words: variable F-RD-type lattice structure, parametric analysis, TPMS, porosity, lattice structure design

中图分类号:

TH 122

郝博, 张鹏, 朱枳名. 变F-RD型点阵结构的参数分析与验证[J]. 东北大学学报（自然科学版）, 2024, 45(9): 1294-1300.

Bo HAO, Peng ZHANG, Zhi-ming ZHU. Parameter Analysis and Verification of Variable F-RD-Type Lattice Structure[J]. Journal of Northeastern University(Natural Science), 2024, 45(9): 1294-1300.

图/表 11

图1 常规F-RD型曲面和单元（a）—F-RD型曲面；（b）—F-RD型单元.

Fig.1 Conventional F-RD surfaces and elements

图2 TPMS型点阵结构参数化设计运算器

Fig.2 TPMS lattice structure parametric design calculator

图3 a值对F-RD型点阵结构形状的影响

Fig.3 Influence of a value on the shape of the F-RD lattice structure

图4 b值对F-RD型点阵结构形状的影响

Fig.4 Influence of b value on the shape of the F-RD lattice structure

图5 C值对F-RD型点阵结构形状的影响

Fig.5 Influence of C value on the shape of the F-RD lattice structure

表1 变形参数a与孔隙率P的关系

Table 1 Relationship between deformation parameter a and porosity P

C=-0.4		C=-0.2		C=0		C=0.2		C=0.4
a	P/%	a	P/%	a	P/%	a	P/%	a	P/%
1.0	85.84	1.0	85.85	1.0	85.87	1.0	86.08	1.0	86.46
1.4	86.00	1.4	86.01	1.4	86.17	1.4	86.40	1.4	86.71
1.8	86.07	1.8	86.15	1.8	86.32	1.8	86.55	1.8	86.90
2.2	86.13	2.2	86.22	2.2	86.40	2.2	86.63	2.2	86.93
2.6	86.19	2.6	86.26	2.6	86.45	2.6	86.67	2.6	86.98
3.0	86.20	3.0	86.26	3.0	86.46	3.0	86.66	3.0	86.97
3.4	86.18	3.4	86.28	3.4	86.46	3.4	86.70	3.4	86.95
3.8	86.16	3.8	86.28	3.8	86.45	3.8	86.68	3.8	86.93
4.2	86.11	4.2	86.26	4.2	86.46	4.2	86.66	4.2	86.91
4.6	86.08	4.6	86.21	4.6	86.45	4.6	86.65	4.6	86.90
5.0	86.00	5.0	86.16	5.0	86.43	5.0	86.66	5.0	86.87

表2 阈值C与孔隙率P的关系

Table 2 Relationship between threshold C and porosity P

a=1.5，b=0.4		a=2.0，b=0.4		a=2.0，b=0.6		a=2.5，b=0.6
C	P/%	C	P/%	C	P/%）	C	P/%
-0.8	86.95	-0.8	86.39	-0.8	86.24	-0.8	86.04
-0.6	86.24	-0.6	86.04	-0.6	86.11	-0.6	86.01
-0.4	86.06	-0.4	85.94	-0.4	86.07	-0.4	86.04
-0.2	86.11	-0.2	86.03	-0.2	86.17	-0.2	86.13
0	86.44	0	86.43	0	86.46	0	86.41
0.2	87.10	0.2	87.04	0.2	86.86	0.2	86.81
0.4	88.34	0.4	88.07	0.4	87.52	0.4	87.34
0.6	89.59	0.6	89.13	0.6	88.46	0.6	88.27
0.8	90.45	0.8	89.86	0.8	89.45	0.8	89.12

图6 当C=0.4时的混合参数对孔隙率P的影响（a）—3D散点图；（b）—3D映射图.

Fig.6 Effect of mixing parameters on porosity P when C=0.4

图7 当C=-0.4时的混合参数对孔隙率P的影响（a）—3D散点图；（b）—3D映射图.

Fig.7 Effect of mixing parameters on porosity P when C=-0.4

图8 变F-RD型点阵结构AlSi10Mg样件

Fig.8 AlSi10Mg sample of the variable F-RD lattice structure

图9 不同参数的理论孔隙率和实际孔隙率关系（a）—a=4.5，C=-0.4时变形参数b对孔隙率P的影响；（b）—b=1.0，C=0时变形参数a对孔隙率P的影响；（c）—a=2.0，b=0.3时变形参数C对孔隙率P的影响.

Fig.9 Relationship of theoretical porosity and actual porosity for different parameters

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