车用复合材料螺旋弹簧的设计与优化

詹博文; 孙凌玉; 黄彬城; 赵冠博; 王倩

doi:10.13700/j.bh.1001-5965.2017.0548

车用复合材料螺旋弹簧的设计与优化

doi: 10.13700/j.bh.1001-5965.2017.0548

北京航空航天大学交通科学与工程学院, 北京 100083

基金项目:

国家自然科学基金 U1664250

国家自然科学基金 51575023

国家重点研发计划 2016YFB0101606

详细信息

作者简介:
詹博文男, 硕士研究生。主要研究方向：结构优化和智能材料开发等

孙凌玉女, 博士, 教授, 博士生导师。主要研究方向：汽车轻量化和智能材料开发等

通讯作者:
孙凌玉.E-mail:lysun@buaa.edu.cn

中图分类号: U465.6
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出版历程
- 收稿日期: 2017-08-31
- 录用日期: 2017-11-23
- 网络出版日期: 2018-07-20

Design and optimization of automotive composite helical spring

School of Transportation Science and Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100083, China

Funds:

National Natural Science Foundation of China U1664250

National Natural Science Foundation of China 51575023

National Key R & D Program of China 2016YFB0101606

More Information

Corresponding author: SUN Lingyu.E-mail:lysun@buaa.edu.cn

摘要

摘要:
利用复合材料可设计性强和树脂基体轻量化的特点，并解耦“材料-结构-性能”之间的相互关联，是汽车复合材料结构件设计的难点。螺旋弹簧是汽车悬架系统的主要承载部件，工况复杂，一般采用性能极佳的弹簧钢；若用轻质复合材料替代，必须兼顾安全性与轻量化，设计难度很大。针对上述问题，提出了一种复合材料螺旋弹簧“材料-结构-性能”集成设计方法。依据弹簧受压缩载荷时，簧丝截面应力分布，确定选择±45°铺层的碳纤维复合材料（CFRP）；在满足刚度、强度和安装空间约束条件下，根据复合材料力学和弹簧刚度、强度理论模型，确定初始弹簧几何参数；再进一步利用有限元数值仿真进行校验；将正交实验设计法和有限元数值模拟结合，建立轴向压缩刚度和强度随几何参数变化的响应面模型；采用遗传算法获得满足弹簧性能要求下轻量化效果最佳的设计结果。优化后的复合材料弹簧方案比金属弹簧质量减轻34.4%，为复合材料汽车结构件设计提供了可行的整体解决方案和产品开发实例。
- 汽车轻量化 /
- 有限元法 /
- 复合材料 /
- 螺旋弹簧 /
- 响应面模型 /
- 优化设计
Abstract:
A major problem in designing automotive structures is how to make full use of the flexible designability of composites and light weight of polymer matrix, and also consider the close connection among the material, structure and properties. Since the helical spring is one of the major load-bearing parts of suspension and subjected to complex loads, it is generally manufactured by spring steel with ultra-high performance. If replaced by lightweight composites, both safety and light weight should be satisfied, which makes the design of composite helical spring rather difficult. In this paper, an integrated materials-structure-performance design method of composite helical spring is proposed. According to the stress distribution on the cross section of spring under compression, carbon fiber reinforce polymer (CFRP) material with ±45° ply sequence is selected. Under the constraint conditions of stiffness, strength and installation space, the initial geometric parameters of helical spring are derived by analytical models based on spring stiffness and strength and composite material mechanics. Furthermore, the initial result is verified numerically by finite element simulation. Combining the design of orthogonal experiment with numerical simulation, the response surface model of stiffness and strength of helical spring to its geometric parameters is established. Finally, the optimal design of helical spring satisfying both required performance and weight reduction is obtained by genetic optimization algorithm. Compared with the metal helical spring, the CFRP one reduces the mass by 34.4%. As a representative product development case, it has demonstrated that the proposed method is a feasible integrated solution for design of automotive structural components with composite materials.
- automotive light weight /
- finite element method /
- composite /
- helical spring /
- response surface model /
- optimal design

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图 1 弹簧及簧丝截面受力情况

Figure 1. Force analysis of spring and cross section of wire

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图 2 RVE的铺层结构示意图

Figure 2. Schematic of layer structure of RVE

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图 3 初始参数理论设计流程

Figure 3. Theoretical design process of inital parameters

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图 4 仿真模型中的载荷与边界条件

Figure 4. Loads and boundary condition in simulation model

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图 5 压缩量最大时弹簧整体及截面的剪切应力分布

Figure 5. Shear stress distribution of whole spring and cross section at ultimate compression

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图 6 κ与d、D和n的响应面

Figure 6. Response surface of κ with geometric parameters d, D and n

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图 7 τ_smax与d、D和n的响应面

Figure 7. Response surface of τ_smax with geometric parameters d, D and n

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表 1 CFRP的材料参数^[12]

Table 1. Material parameters of CFRP^[12]

参　数	E₁/GPa	E₂/GPa	G₁₂/GPa	ν₁₂	X_T/MPa	X_C/MPa	Y_T/MPa	Y_C/MPa	S₁₂/MPa
数　值	115.142	6.894	12.41	0.332	1 447	1 172	6.89	262	279

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表 2 弹簧几何参数的理论设计初值

Table 2. Theoretically designed initial value of spring geometric parameters

参　数	簧丝直径/mm	弹簧中径/mm	弹簧有效圈数
数　值	21.2	123.5	5.4

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表 3 Hashin失效准则^[15]

Table 3. Hashin failure criterion^[15]

失效模式	失效准则
纤维拉伸断裂(σ₁₁≥0)
纤维压缩断裂(σ₁₁ < 0)
基体拉伸断裂(σ₂₂≥0)
基体压缩断裂(σ₂₂ < 0)

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表 4 弹簧几何结构正交实验样本及仿真结果

Table 4. Orthogonal experimental samples and their simulation results of spring geometric structure

d/mm	D/mm	n	κ	S
19.27	120	5.2	64.94	1.18
20.83	121.06	6	84.29	1.33
19.66	122.11	4.93	66.37	1.22
20.05	123.17	5.87	71.53	1.26
20.44	124.23	4.13	68.57	1.27
20.25	125.28	4.53	72.13	1.29
19.08	126.34	5.47	61.8	1.31
19.86	127.4	4.8	55.5	1.14
21.03	128.45	4.67	74.13	1.38
21.22	129.51	5.33	75.59	1.39
20.64	130.57	5.07	80.87	1.38
21.81	131.62	5.73	66.42	1.29
22	132.68	5.6	81.3	1.40
21.42	133.74	4.27	70.64	1.35
19.47	134.79	4.4	48	1.29
21.61	135.85	4	69.81	1.41

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表 5 金属弹簧及优化前后复合材料弹簧性能比较

Table 5. Performance comparison of metal spring and composite spring before and after optimization

弹簧	W/kg	κ/(N·mm^-1)	S	d/mm	D/mm	n
金属弹簧	5.23	75	2.74	16.4	142.1	7.3
初始理论设计复合材料弹簧	3.74	73.2	1.38	21.2	123.5	5.4
有限元优化后的复合材料弹簧	3.43	75	1.33	19.1	121.4	5.0

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表 6 优化结果误差分析

Table 6. Error analysis of optimized results

约束参数	优化结果	优化结构的数值仿真	误差/%
κ	75	72.7	3.1
τ_smax	270.3	276.4	2.2

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