基于灰色关联分析的碳纤维增强树脂复合材料控制臂铺层优化

蒋荣超; 慈树坤; 刘大维; 孙海霞; 王登峰

doi:10.13801/j.cnki.fhclxb.20210323.002

基于灰色关联分析的碳纤维增强树脂复合材料控制臂铺层优化

doi: 10.13801/j.cnki.fhclxb.20210323.002

1.
青岛大学　机电工程学院，青岛 266071
2.
海军航空大学　青岛校区航空机械系，青岛 266041
3.
吉林大学　汽车仿真与控制国家重点实验室，长春 130022

基金项目: 国家自然科学基金 (51805286)；山东省自然科学基金(2017PEE004)

详细信息

通讯作者:
蒋荣超，博士，副教授，硕士生导师，研究方向为汽车轻量化设计方法与应用　E-mail：jrch123@126.com

中图分类号: TB332
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- 被引次数: 0
出版历程
- 收稿日期: 2021-01-18
- 修回日期: 2021-03-08
- 录用日期: 2021-03-14
- 网络出版日期: 2021-03-25
- 刊出日期: 2022-01-15

Ply optimization of carbon fiber reinforced plastic control arm based on grey relational analysis

1.
College of Mechanical and Electrical Engineering, Qingdao University, Qingdao 266071, China
2.
Aviation Mechanics Department, Naval Aviation University Qingdao Campus, Qingdao 266041, China
3.
State Key Laboratory of Automotive Simulation and Control, Jilin University, Changchun 130022, China

摘要

摘要: 采用碳纤维增强树脂复合材料(CFRP)对悬架控制臂进行轻量化设计，为了充分发挥CFRP优异的力学性能，对CFRP控制臂进行多目标铺层优化。基于CFRP力学性能试验结果构建控制臂有限元模型，并通过有限元仿真对比分析钢质控制臂和CFRP控制臂结构性能。综合考虑质量、模态频率、刚度和强度等性能，基于正交试验设计方法，并结合灰色关联分析和主成分分析，对CFRP控制臂铺层参数进行多目标优化，确定最优铺层方案。结果表明，相比于原钢质控制臂，除纵向刚度略有下降外，CFRP控制臂其余结构性能指标均有所改善，并且质量降低40.23%，减重效果显著。
- 碳纤维增强树脂复合材料 /
- 控制臂 /
- 正交试验设计 /
- 灰色关联分析 /
- 轻量化
Abstract: Carbon fiber reinforced plastic (CFRP) was used for lightweight design of suspension control arm. In order to perform the excellent mechanical properties of CFRP, the multi-objective ply optimization of CFRP control arm was carried out. The finite element model of the control arm was constructed based on the test results of material mechanical properties of CFRP. And the structural properties of the steel control arm and the CFRP control arm were compared by finite element simulations. Considering the mass, modal frequency, stiffness and strength, the orthogonal experiment design method combined with grey relational analysis and principal component analysis were used to optimize the CFRP control arm ply parameters for determining the optimal ply scheme. The results show that the mass of the optimized CFRP control arm is reduced by 40.23% compared with the original steel control arm, which achieves a significant weight reduction. Meanwhile, the structural performance indexes of the optimized CFRP control arm are improved, except for a slight decrease in longitudinal stiffness.
- carbon fiber reinforced plastic /
- control arm /
- orthogonal experiment design /
- grey relational analysis /
- lightweighting

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图 1 试验设备及碳纤维增强树脂复合材料(CFRP)层合板试件

Figure 1. Test equipment and carbon fiber reinforced plastic (CFRP) laminates

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图 2 悬架钢质控制臂有限元模型

Figure 2. Finite element model of suspension steel control arm

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图 3 钢质控制臂模态试验

Figure 3. Modal test of steel control arm

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图 4 钢质控制臂前六阶模态振型

Figure 4. The first six modal shapes of steel control arm

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图 5 CFRP控制臂铺层示意图

Figure 5. Laminate layout diagram of CFRP control arm

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图 6 CFRP控制臂灰色关联分析结果

Figure 6. Results of grey correlation analysis of CFRP control arm

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图 7 CFRP控制臂各因素水平的主效应图

Figure 7. Main effect diagram of levels for each factor of CFRP control arm

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表 1 CFRP力学参数

Table 1. Mechanical parameters of CFRP

Property	Value
Density ρ/(g·cm⁻³)	1.65
Longitudinal elastic modulus E₁/GPa	51.77
Transverse elastic modulus E₂/GPa	51.77
Poisson’s ratio ν₁₂	0.0369
Longitudinal tensile strength X_t/MPa	757.08
Transverse tensile strength Y_t/MPa	757.08
Shear modulus G₁₂/GPa	2.07
Shear strength S/MPa	39.02

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表 2 钢质控制臂固有频率仿真与试验结果对比

Table 2. Comparison of simulation and test results of natural frequency for steel control arm

Modal order	Natural frequency /Hz		Relative error/%
Modal order	Simulation value	Experimental value	Relative error/%
1	211.9	204.7	3.4
2	246.0	235.7	4.2
3	396.0	378.8	4.3
4	714.2	674.1	5.6
5	927.0	909.5	1.9
6	993.2	970.2	2.3

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表 3 控制臂载荷条件

Table 3. Load cases of control arm

Position	Direction	Braking/N	Steering/N	Top speed/N
Outer point	F_x	−739.9	638.9	−2338.7
	F_y	−1086.6	2613.7	−3481.7
	F_z	−67.6	−175.9	143.4
Front point	F_x	221.8	−573.5	527.5
	F_y	−1886.2	2287.9	−6234.5
	F_z	−293.9	−407.4	−858.8
Rear point	F_x	116.5	73.8	166.7
	F_y	752.1	−551.7	2406.7
	F_z	293.7	407.1	856.8

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表 4 控制臂初始性能分析

Table 4. Initial performance analysis of control arm

Property	Ply-16	Ply-34	Ply-32	Steel
m/kg	1.17	1.44	1.71	2.66
f/Hz	201.8	279.7	343.5	211. 9
K_x/(kN·mm⁻¹)	1.49	3.64	9.52	5.65
K_y/(kN·mm⁻¹)	2.94	7.41	15.38	10.36
σ_b/MPa	58.8	26.3	15	92.6
σ_s/MPa	52.9	28.9	18.2	77.4
σ_v/MPa	184.65	88	50.1	295.1
Notes: m—Mass; f—The first order frequency; K_x—Longitudinal stiffness; K_y—Transverse stiffness; σ_b—Maximum braking stress; σ_s—Maximum steering stress; σ_v—Maximum top speed stress.

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表 5 CFRP控制臂正交试验表

Table 5. Orthogonal array for CFRP control arm simulation

No.	1	2	3	4	5	6	7	8	9
1	1	1	1	1	1	1	1	1	1
2	1	2	2	2	2	2	2	2	2
3	1	3	3	3	3	3	3	3	3
4	1	4	4	4	4	4	4	4	4
5	1	1	1	2	2	3	3	4	4
6	1	2	2	1	1	4	4	3	3
7	1	3	3	4	4	1	1	2	2
8	1	4	4	3	3	2	2	1	1
9	2	1	2	3	4	1	2	3	4
10	2	2	1	4	3	2	1	4	3
11	2	3	4	1	2	3	4	1	2
12	2	4	3	2	1	4	3	2	1
13	2	1	2	4	3	3	4	2	1
14	2	2	1	3	4	4	3	1	2
15	2	3	4	2	1	1	2	4	3
16	2	4	3	1	2	2	1	3	4
17	3	1	4	1	4	2	3	2	3
18	3	2	3	2	3	1	4	1	4
19	3	3	2	3	2	4	1	4	1
20	3	4	1	4	1	3	2	3	2
21	3	1	4	2	3	4	1	3	2
22	3	2	3	1	4	3	2	4	1
23	3	3	2	4	1	2	3	1	4
24	3	4	1	3	2	1	4	2	3
25	4	1	3	3	1	2	4	4	2
26	4	2	4	4	2	1	3	3	1
27	4	3	1	1	3	4	2	2	4
28	4	4	2	2	4	3	1	1	3
29	4	1	3	4	2	4	2	1	3
30	4	2	4	3	1	3	1	2	4
31	4	3	1	2	4	2	4	3	1
32	4	4	2	1	3	1	3	4	2
Notes: In the first row of the table, the factors 1-8 represent ply angle and the factor 9 represents ply thickness; The levels 1-4 of the factors 1-8 represent 0°, 45°, −45° and 90°, respectively; The level 1-4 of the factor 9 denotes 0.15 mm, 0.2 mm, 0.25 mm and 0.3 mm, respectively.

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表 6 CFRP控制臂性能指标仿真结果

Table 6. Simulation results of CFRP control arm performance

No.	m/kg	f/Hz	K_x/(kN·mm⁻¹)	K_y/(kN·mm⁻¹)	σ_v/MPa
1	1.10	127.4	1.486	3.058	202.0
2	1.27	246.1	2.006	4.287	101.0
3	1.43	277.6	2.690	5.696	71.9
4	1.59	208.5	3.675	7.111	79.0
5	1.59	316.8	5.206	10.777	46.9
6	1.43	268.0	4.126	8.591	66.5
7	1.27	225.0	3.057	6.470	98.5
8	1.10	183.7	2.029	4.406	155.0
9	1.59	328.5	4.806	9.999	47.0
10	1.43	278.9	3.941	8.272	64.9
11	1.27	234.5	2.922	6.229	94.5
12	1.10	194.7	1.886	4.096	148.0
13	1.10	194.1	1.886	4.097	148.0
14	1.27	235.3	2.924	6.230	93.8
15	1.43	279.9	3.943	8.273	64.5
16	1.59	328.0	4.807	10.003	47.0
17	1.43	282.5	4.102	8.561	61.5
18	1.59	320.3	4.533	9.499	49.5
19	1.10	190.0	1.791	3.929	157.0
20	1.27	237.3	3.036	6.430	87.8
21	1.27	236.6	2.990	6.352	90.4
22	1.10	193.4	1.847	4.028	152.0
23	1.59	325.9	4.693	9.793	46.8
24	1.43	281.6	4.037	8.448	62.0
25	1.27	220.6	3.042	6.460	102.0
26	1.10	186.5	2.035	4.407	152.0
27	1.59	320.8	5.215	10.776	46.3
28	1.43	262.9	4.107	8.578	68.0
29	1.43	264.1	4.155	8.663	66.6
30	1.59	320.6	5.177	10.710	46.2
31	1.10	186.5	2.023	4.387	154.0
32	1.27	221.5	3.075	6.518	99.4

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表 7 CFRP控制臂主成分分析结果

Table 7. Principal component analysis results of CFRP control arm

Property	Eigenvector					w
Property	PC1	PC2	PC3	PC4	PC5	w
m	−0.4195	0.7900	0.2013	0.3954	−0.0557	0.1759
f	0.4472	0.2075	0.7976	−0.3474	−0.0088	0.2000
K_x	0.4526	0.3711	−0.4201	−0.1430	−0.6786	0.2049
K_y	0.4536	0.3819	−0.3469	−0.0029	0.7267	0.2057
σ_v	0.4620	−0.2221	0.1627	0.8382	−0.0906	0.2135
Eigenvalue	4.5813	0.3022	0.1100	0.0061	0.0005	−
Contribution/%	91.63	6.04	2.20	0.12	0.01	−
Notes: PC1-PC5—The first to fifth principal components, respectively; w—Mass coefficient of the performance indicators.

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表 8 控制臂优化前后性能对比

Table 8. Performance comparison of original and optimized control arm

Property	Scheme No. 27	Optimal combination	Steel	Relative variation/%
m/kg	1.59	1.59	2.66	40.23
f/Hz	320.8	321.5	211. 9	51.72
K_x/(kN·mm⁻¹)	5.21	5.22	5.65	−7.61
K_y/(kN·mm⁻¹)	10.78	10.84	10.36	4.63
σ_b/MPa	25.1	25.5	92.6	72.46
σ_s/MPa	13.8	14.2	77.4	81.65
σ_v/MPa	46.3	47.5	295.1	83.90

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