基于刚度等效模型的减重孔板结构快速分析方法

那景新; 任俊铭; 谭伟; 陈立军

doi:10.19818/j.cnki.1671-1637.2019.03.010

基于刚度等效模型的减重孔板结构快速分析方法

doi: 10.19818/j.cnki.1671-1637.2019.03.010

吉林大学汽车仿真与控制国家重点实验室, 吉林长春 130022

基金项目:

国家自然科学基金项目 51775230

详细信息

作者简介:
那景新(1957-), 男, 黑龙江哈尔滨人, 吉林大学教授, 从事车身结构设计理论与轻量化技术研究

通讯作者:
陈立军(1960-), 男, 吉林延吉人, 吉林大学副研究员

中图分类号: U270.2
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出版历程
- 收稿日期: 2019-01-07
- 刊出日期: 2019-06-25

Rapid analysis method of weight-reduced orifice plate structure based on stiffness equivalence model

State Key Laboratory of Automotive Simulation and Control, Jilin University, Changchun 130022, Jilin, China

More Information

Author Bio:
NA Jing-xin(1957-), male, professor, najx@jlu.edu.cn

Corresponding author: CHENLi-jun(1960-), male, associate professor, chenlijun@jlu.edu.cn

摘要

摘要: 为了能够更有效率地对减重孔板结构进行计算分析, 提出一种快速分析方法; 研究了减重孔板结构模型与平面板结构模型间的一般刚度等效关系, 建立了减重孔板孔径、孔距与相应平面板等效杨氏模量、等效板厚间的关系表达式, 以等效平面板结构模型代替原孔板结构模型进行变形分析; 将局部节点位移施加到相应目标孔位模型上, 计算了目标孔位区域的应力分布; 结合试验与仿真验证了方法的准确性; 通过对某实际减重孔板结构施加不同载荷, 对刚度等效关系的稳定性进行了验证; 通过某车体底架带孔板结构实例, 对方法应用于实际工程中的有效性进行了验证。分析结果表明: 与试验结果相比, 快速分析方法仿真变形最大误差约为3%, 应变的最大误差约为5%;不同载荷下的等效杨氏模量偏差约为2.5%, 等效板厚的偏差约为1.3%;快速分析方法对变形与局部应力的平均计算误差小于6.7%, 计算时间缩短了约50%。可见, 快速分析方法可以替代传统方法对减重孔板结构进行性能分析。
- 车辆工程 /
- 城市轨道客车 /
- 减重孔板结构 /
- 结构轻量化 /
- 有限元分析 /
- 刚度等效模型
Abstract: In order to calculate and analyze the structure of weight-reduced orifice plate more efficiently, a rapid analysis method was proposed. The general stiffness equivalence relationship between weight-reduced orifice plate structure model and planar plate structure model was researched. The relational expressions were established between the aperture, hole distance of weight-reduced orifice plate, the equivalent Young's modulus, and thickness of corresponding planar plate. The orifice plate structure model was replaced with equivalent planar plate structure model for deformation analysis. The local node displacement was applied to corresponding target hole model, and the stress distribution of target hole area was calculated. The accuracy of proposed method was verified by experiments and simulations. The stability of stiffness equivalence relationship was verified by applying different loads to an actual weight-reduced orifice plate structure. The effectiveness of the method in practical engineering was verified by an example of a car body chasis with orifice plate. Analysis result shows that compared with experimental results, the maximum error of deformation of rapid analysis method is about 3%, and the maximum error of strain is about 5%. Under different loads, the deviation of equivalent Young's modulus is about 2.5%, and the deviation of equivalent plate thickness is about 1.3%. The average calculation error of deformation and local stress of rapid analysis method is less than 6.7%, and the calculation time is shortened by about 50%. So, the rapid analysis method can replace the traditional method to analyze the performance of weight-reduced orifice plate structure.
- vehicle engineering /
- urban rail passenger coach /
- weight-reduced orifice plate structure /
- structure lightweight /
- finite element analysis /
- stiffness equivalence model

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图 1 抽取的矩形孔板

Figure 1. Extracted rectangular orifice plate

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图 2 孔径为5、6 mm的矩形孔板应力结果

Figure 2. Rectangular orifice plate stress results with apertures of 5 and 6 mm

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图 3 孔径为7、8 mm的矩形孔板应力结果

Figure 3. Rectangular orifice plate stress results with apertures of 7 and 8 mm

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图 4 孔板与平面板边界节点位置

Figure 4. Positions of orifice plate and planar plate boundary nodes

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图 5 变形测试现场

Figure 5. Deformation test site

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图 6 有限元变形结果

Figure 6. Finite element deformation result

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图 7 DIC试验现场

Figure 7. DIC test site

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图 8 目标孔位测点

Figure 8. Target hole measuring points

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图 9 底架减重孔板结构

Figure 9. Structure of chasis weight-reduced orifice plate

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图 11 在2种工况下模型的变形

Figure 11. Deformations of models under two conditions

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图 10 等效平面板与底架减重孔板结构模型

Figure 10. Structure models of equivalence planar plate and chasis weight-reduced orifice plate

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图 12 孔板分块方式与目标孔位分块区域

Figure 12. Orifice plate block method and target hole block area

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图 13 平面板分块方式与相应分块区域

Figure 13. Planar plate block method and corresponding block area

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图 14 目标孔分块区域的有限元模型

Figure 14. Finite element model of target hole block area

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图 15 快速分析方法得到的目标孔区域应力

Figure 15. Target hole region stress obtained by rapid analysis method

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图 16 传统方法得到的目标孔区域应力

Figure 16. Target hole region stress obtained by traditional method

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表 1 孔径与孔距组合

Table 1. Aperture and hole distance combinations mm

孔径	5	5	5	6	6	6	7	7	7	8	8	8
孔距	20	25	30	20	25	30	20	25	30	20	25	30

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表 2 材料参数

Table 2. Material parameters

参数	密度/ (kg·m^-3)	泊松比	弹性模量/MPa	屈服极限/MPa
数值	7 800	0.3	2.06×10⁵	235

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表 3 矩形平面板平均位移与平均转角

Table 3. Average displacements and angles of rectangular planar plates

平面板序号	杨氏模量/10¹¹ Pa	板厚/mm	平均位移/10^-7 mm	平均转角/rad
1	1.0	1.0	3.006	3.563
2	1.0	1.5	2.004	1.056
3	1.0	2.0	1.503	0.445
4	1.0	2.5	1.203	0.228
5	1.5	1.0	2.004	2.376
6	1.5	1.5	1.336	0.704
7	1.5	2.0	1.002	0.297
8	1.5	2.5	0.802	0.152
9	2.0	1.0	1.503	1.782
10	2.0	1.5	1.002	0.528
11	2.0	2.0	0.752	0.223
12	2.0	2.5	0.601	0.114
13	2.5	1.0	1.202	1.425
14	2.5	1.5	0.802	0.422
15	2.5	2.0	0.601	0.178
16	2.5	2.5	0.481	0.091

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表 4 孔板的等效杨氏模量与板厚

Table 4. Equivalent Young's moduli and thicknesses of orifice plates

组合序号	孔径/mm	孔距/mm	等效杨氏模量/10¹¹ Pa	等效板厚/mm
1	5	20	1.234	2.06
2	5	25	1.474	2.05
3	5	30	1.714	2.03
4	6	20	0.998	2.06
5	6	25	1.305	2.06
6	6	30	1.502	2.05
7	7	20	0.747	2.07
8	7	25	1.115	2.06
9	7	30	1.322	2.06
10	8	20	0.497	2.07
11	8	25	0.929	2.07
12	8	30	1.209	2.06

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表 5 不同测点3个方向的应变

Table 5. Strains in three directions of different measuring points

测点	方法	ε₁/10^-4	ε₂/10^-5	ε₃/10^-6
1	DIC试验	-3.99	8.67	9.70
1	快速分析方法	-3.67	8.55	10.20
2	DIC试验	-0.28	-9.41	1.02
2	快速分析方法	-0.31	-9.38	1.03
3	DIC试验	-3.99	8.71	-11.40
3	快速分析方法	-3.69	8.68	-10.50
4	DIC试验	-0.26	-7.81	-1.23
4	快速分析方法	-0.31	-7.88	-1.18

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表 6 不同力系下的等效杨氏模量与等效板厚

Table 6. Equivalent Young's moduli and thicknesses under different force systems

力系	拉力/N	弯矩/ (N·m)	等效杨氏模量/10¹¹ Pa	等效板厚/mm
1	3	3	1.58	2.06
2	6	6	1.55	2.05
3	9	9	1.60	2.04
4	12	12	1.64	2.03
5	15	15	1.61	2.04

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表 7 不同载荷下的垂向挠度

Table 7. Vertical deflections under different loads

工况	外载荷/N	模型	挠度/cm	误差/%
1	20	底架减重孔板	13.40	6.7
		等效平面板	12.50
2	4	底架减重孔板	2.68	6.6
		等效平面板	2.50

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表 8 快速分析方法与传统方法应力对比

Table 8. Stress comparison between rapid analysis method and traditional method

孔位序号	快速分析方法得到最大应力/10¹¹ Pa	传统方法得到最大应力/10¹¹ Pa	误差率/%	平均误差率/%
1	1.58	1.63	3.1	4.5
2	1.72	1.65	4.2
3	1.79	1.86	3.7
4	1.76	1.64	7.3
5	1.73	1.66	4.2

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