Article(id=1200070652918072202, tenantId=1146029695717560320, journalId=1189918454225211397, issueId=1200070647759078025, articleNumber=null, orderNo=null, doi=10.20104/j.cnki.1674-6546.20240061, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=null, receivedDateStr=null, revisedDate=1711555200000, revisedDateStr=2024-03-28, acceptedDate=null, acceptedDateStr=null, onlineDate=1764048739890, onlineDateStr=2025-11-25, pubDate=1726329600000, pubDateStr=2024-09-15, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1764048739890, onlineIssueDateStr=2025-11-25, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1764048739890, creator=13701087609, updateTime=1764048739890, updator=13701087609, issue=Issue{id=1200070647759078025, tenantId=1146029695717560320, journalId=1189918454225211397, year='2024', volume='', issue='9', pageStart='1', pageEnd='48', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1764048738660, creator=13701087609, updateTime=1764049380600, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1200073340305109868, tenantId=1146029695717560320, journalId=1189918454225211397, issueId=1200070647759078025, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1200073340309304173, tenantId=1146029695717560320, journalId=1189918454225211397, issueId=1200070647759078025, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=27, endPage=30, ext={EN=ArticleExt(id=1200070653232645029, articleId=1200070652918072202, tenantId=1146029695717560320, journalId=1189918454225211397, language=EN, title=Analysis of Stiffness Characteristics of Leaf Spring with Few Piece Variable Cross-Section with Cracks, columnId=null, journalTitle=Automotive Engineer, columnName=null, runingTitle=null, highlight=null, articleAbstract=

A three-dimensional simulation model of leaf spring with few piece variable cross-section with crack is established using SolidWorks and ANSYS. The influence laws of crack location, angle, and depth on the stiffness of few leaf spring are explored by analyzing stiffness characteristics of few leaf spring under different crack locations, angles and depths. The results show that the transverse crack has a significant influence on the stiffness of the leaf spring. The closer the crack location is to the 1/3 length of the straight section at the root of the leaf spring, the closer the crack angle is to 90° and the deeper the crack is, the greater the influence is and the smaller the stiffness is. The longitudinal crack has a slight influence on the stiffness of the leaf spring and the variation of the stiffness is small. The stiffness of the leaf spring with crack is slightly bigger than that of the leaf spring without crack in a certain depth range.

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利用SolidWorks和ANSYS软件建立了含裂纹的少片变截面钢板弹簧三维仿真模型,通过分析不同位置、角度、深度的裂纹影响下钢板弹簧的刚度特性,探究了裂纹位置、角度、深度对弹簧刚度的影响规律。结果表明:横向裂纹对钢板弹簧刚度影响显著,裂纹位置越接近板簧根部平直段1/3长度处、裂纹角度越接近90°、裂纹越深,影响程度越大,钢板弹簧刚度越小;纵向裂纹对钢板弹簧刚度的影响轻微,刚度变化很小;一定深度范围内,含裂纹钢板弹簧的刚度较无裂纹钢板弹簧的刚度略大。

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结构参数 取值 结构参数 取值
板簧片数/片 1 端部平直段的厚度
/mm
5.7
板簧1/2长度/mm 560 根部平直段的厚度
/mm
10
根部平直段1/2长度
/mm
52 厚度比 0.57
斜线段长度/mm 418 宽度/mm 63
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试验板簧结构参数

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结构参数 取值 结构参数 取值
板簧片数/片 1 端部平直段的厚度
/mm
5.7
板簧1/2长度/mm 560 根部平直段的厚度
/mm
10
根部平直段1/2长度
/mm
52 厚度比 0.57
斜线段长度/mm 418 宽度/mm 63
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对比对象 最大载荷下的变形量
/mm
刚度/N·mm-1
板簧试验 148.30 23.74
模型仿真 143.00 24.62
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力学特性对比结果

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对比对象 最大载荷下的变形量
/mm
刚度/N·mm-1
板簧试验 148.30 23.74
模型仿真 143.00 24.62
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裂痕位置/mm 变形量/mm 刚度/N·mm-1 影响程度/%
m=2.00 144.84 24.30 -1.27
m=17.00 145.62 24.17 -1.80
m=52.00 145.32 24.22 -1.60
m=350.00 144.79 24.31 -1.24
m=470.00 143.68 24.50 -0.47
m=500.00 143.23 24.58 -0.16
n=10.00 142.93 24.63 0.05
n=20.00 142.97 24.62 0.02
n=31.50 142.99 24.62 0.01
n=43.00 142.97 24.62 0.02
n=53.00 142.93 24.63 0.05
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裂纹位置对刚度的影响

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裂痕位置/mm 变形量/mm 刚度/N·mm-1 影响程度/%
m=2.00 144.84 24.30 -1.27
m=17.00 145.62 24.17 -1.80
m=52.00 145.32 24.22 -1.60
m=350.00 144.79 24.31 -1.24
m=470.00 143.68 24.50 -0.47
m=500.00 143.23 24.58 -0.16
n=10.00 142.93 24.63 0.05
n=20.00 142.97 24.62 0.02
n=31.50 142.99 24.62 0.01
n=43.00 142.97 24.62 0.02
n=53.00 142.93 24.63 0.05
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角度/(°) 变形量/mm 刚度/N·mm-1 影响程度/%
α=30.00 143.68 24.50 -0.47
α=60.00 144.98 24.28 -1.37
α=90.00 145.62 24.17 -1.80
α=120.00 145.00 24.28 -1.38
α=150.00 143.70 24.50 -0.49
β=30.00 142.93 24.63 0.05
β=60.00 142.96 24.62 0.03
β=90.00 142.97 24.62 0.02
β=120.00 142.95 24.62 0.03
β=150.00 142.92 24.63 0.06
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裂纹角度对刚度的影响

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角度/(°) 变形量/mm 刚度/N·mm-1 影响程度/%
α=30.00 143.68 24.50 -0.47
α=60.00 144.98 24.28 -1.37
α=90.00 145.62 24.17 -1.80
α=120.00 145.00 24.28 -1.38
α=150.00 143.70 24.50 -0.49
β=30.00 142.93 24.63 0.05
β=60.00 142.96 24.62 0.03
β=90.00 142.97 24.62 0.02
β=120.00 142.95 24.62 0.03
β=150.00 142.92 24.63 0.06
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深度/mm 变形量/mm 刚度/N·mm-1 影响程度/%
hx=5.00 143.06 24.605 -0.042
hx=15.00 143.92 24.458 -0.639
hx=30.00 145.62 24.173 -1.799
hx=45.00 147.58 23.851 -3.103
hy=5.00 142.88 24.636 0.084
hy=15.00 142.90 24.633 0.070
hy=30.00 142.97 24.621 0.021
hy=45.00 142.99 24.617 0.007
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裂纹深度对刚度的影响

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深度/mm 变形量/mm 刚度/N·mm-1 影响程度/%
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hx=15.00 143.92 24.458 -0.639
hx=30.00 145.62 24.173 -1.799
hx=45.00 147.58 23.851 -3.103
hy=5.00 142.88 24.636 0.084
hy=15.00 142.90 24.633 0.070
hy=30.00 142.97 24.621 0.021
hy=45.00 142.99 24.617 0.007
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含裂纹少片变截面钢板弹簧的刚度特性分析
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杨林 , 李靖 , 李飞 , 韩雪雯
汽车工程师 | 2024,(9): 27-30
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汽车工程师 | 2024, (9): 27-30
含裂纹少片变截面钢板弹簧的刚度特性分析
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杨林, 李靖, 李飞, 韩雪雯
作者信息
  • 山东劳动职业技术学院, 济南 250399
Analysis of Stiffness Characteristics of Leaf Spring with Few Piece Variable Cross-Section with Cracks
Lin Yang, Jing Li, Fei Li, Xuewen Han
Affiliations
  • Shandong Labor Vocational and Technical College, Jinan 250399
出版时间: 2024-09-15 doi: 10.20104/j.cnki.1674-6546.20240061
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利用SolidWorks和ANSYS软件建立了含裂纹的少片变截面钢板弹簧三维仿真模型,通过分析不同位置、角度、深度的裂纹影响下钢板弹簧的刚度特性,探究了裂纹位置、角度、深度对弹簧刚度的影响规律。结果表明:横向裂纹对钢板弹簧刚度影响显著,裂纹位置越接近板簧根部平直段1/3长度处、裂纹角度越接近90°、裂纹越深,影响程度越大,钢板弹簧刚度越小;纵向裂纹对钢板弹簧刚度的影响轻微,刚度变化很小;一定深度范围内,含裂纹钢板弹簧的刚度较无裂纹钢板弹簧的刚度略大。

车辆悬架  /  少片变截面钢板弹簧  /  叶片裂纹  /  刚度

A three-dimensional simulation model of leaf spring with few piece variable cross-section with crack is established using SolidWorks and ANSYS. The influence laws of crack location, angle, and depth on the stiffness of few leaf spring are explored by analyzing stiffness characteristics of few leaf spring under different crack locations, angles and depths. The results show that the transverse crack has a significant influence on the stiffness of the leaf spring. The closer the crack location is to the 1/3 length of the straight section at the root of the leaf spring, the closer the crack angle is to 90° and the deeper the crack is, the greater the influence is and the smaller the stiffness is. The longitudinal crack has a slight influence on the stiffness of the leaf spring and the variation of the stiffness is small. The stiffness of the leaf spring with crack is slightly bigger than that of the leaf spring without crack in a certain depth range.

Vehicle suspension  /  Leaf spring with few piece variable cross-section  /  Crack  /  Stiffness
杨林, 李靖, 李飞, 韩雪雯. 含裂纹少片变截面钢板弹簧的刚度特性分析. 汽车工程师, 2024 , (9) : 27 -30 . DOI: 10.20104/j.cnki.1674-6546.20240061
Lin Yang, Jing Li, Fei Li, Xuewen Han. Analysis of Stiffness Characteristics of Leaf Spring with Few Piece Variable Cross-Section with Cracks[J]. Automotive Engineer, 2024 , (9) : 27 -30 . DOI: 10.20104/j.cnki.1674-6546.20240061
少片变截面钢板弹簧对汽车行驶平顺性具有重要影响,目前对其的研究主要集中于刚度特性及应力特性解析计算、有限元仿真分析等。如:周长城等利用解析法推导了板簧刚度的计算公式[1-2],唐应时等利用有限元法分析了片间摩擦[3]、材料[4]等因素对板簧刚度特性的影响,Savaidis[5]采用CAE建模仿真和板簧台架试验对板簧的力学特性进行了对比分析。在实际工作过程中,受复杂的道路情况和多变的车辆运行工况以及钢板弹簧制造过程中原材料和加工工艺的影响[6-7],钢板弹簧叶片出现裂纹的情况时有发生,而对于含裂纹的少片变截面钢板弹簧的刚度特性有待进一步研究。
针对这一问题,本文利用SolidWorks和ANSYS软件建立含裂纹的少片变截面钢板弹簧三维仿真模型,探究裂纹位置、角度、深度对板簧刚度的影响规律。
根据少片变截面钢板弹簧的实际结构尺寸,利用SolidWorks软件建立相应的仿真模型。考虑到钢板弹簧沿片长度方向的对称性,取一半板簧模型作为初始模型,以加快仿真分析时的求解速度。将初始模型导入ANSYS静力学仿真模块,利用DesignModeler软件添加裂纹面,因叶片裂纹形状多样,为探究其对钢板弹簧刚度影响的一般规律,以长方形作为裂纹面形状,生成含裂纹的钢板弹簧模型。
定义单元类型为SOLID187,材料为60Si2Mn,设置板簧单元尺寸为6 mm并生成四面体网格。引入缺陷特征(Fracture),选择随机裂纹(Arbirary Crack),网格划分方式设置为四面体,最大轮廓半径(Largest Contour Radius)设置为1 mm,通过细化裂纹网格提高计算精度,网格划分效果如图1所示。在叶片根部施加宽度方向上的固定约束,叶片端部为自由端,允许其自由变形。
集中载荷以分步加载的方式加载在板簧端部的节线上,加载-卸载过程分解为14个载荷步,最大载荷为1 760 N。打开求解控制中的几何大变形选项,添加总位移(Total Deformation)分布云图分析求解。
为保证裂纹分析的准确性,需要对所建立初始模型的正确性进行验证,以某少片斜线型变截面钢板弹簧为例,其结构参数如表1所示。
根据GB/T 19844—2018所规定的试验方法,对表1所示钢板弹簧进行力学特性试验,试验平台如图2所示。试验中,为提高安全性,取3片同样的钢板弹簧进行加载和卸载,测试其变形参数,本文所提到的变形均为最大载荷下的板簧端部变形。通过有限元软件对初始模型进行仿真,所得到的试验数据与仿真数据对比结果如图3所示,力学特性对比结果如表2所示。
由于簧片间摩擦等因素的存在,板簧刚度往往呈现出非线性特性,具有迟滞现象,导致试验过程中显示滞回环曲线,见图3,可以看出,加载至最大载荷时,初始模型仿真结果与板簧试验结果中变形量的相对偏差为3.57%,刚度的相对偏差为3.71%,吻合度较高,证明了该模型的准确性。
利用所建立的含裂纹的少片变截面钢板弹簧三维仿真模型分析裂纹位置、角度、深度对板簧刚度特性的影响。分析时,以板簧根部为原点O,沿片长方向为x轴,沿片宽方向为y轴,沿片厚方向为z轴,建立坐标系,如图4所示,考虑板簧的纵向(x方向)和横向(y方向)裂纹。定义横向裂纹面与板簧底面交线的x坐标m、纵向裂纹面与板簧底面交线的y坐标n为裂纹位置,定义横向、纵向裂纹面与Oxy面的夹角αβ为裂纹角度,定义横向裂纹面与x轴、纵向裂纹面与y轴的最远距离hxhy为裂纹深度。
图5所示为α=β=90°、hx=hy=30 mm时,仿真所得的不同裂纹位置影响下的板簧端部的最大变形量,其中,不同裂纹位置下的板簧刚度如表3所示。
图5表3可以看出,当板簧不同厚度段出现横向裂纹时,端部变形量呈现不同的变化趋势:当裂纹出现在根部平直段时,随着m的增大,端部变形量先增加后降低,最大变形量对应的裂纹位置接近根部平直段1/3长度位置处(m=17 mm),在此处,裂纹对板簧刚度的影响程度最大,板簧刚度达到最小值;在根部平直段范围内,裂纹对板簧刚度的影响程度较大,板簧变形量较大,刚度较小;当裂纹出现在斜线段时,变形量随着m的增大而逐渐减小,减小趋势成非线性,板簧刚度相应增大,裂纹对板簧刚度的影响程度逐渐减小;当裂纹出现在端部平直段时,变形量随着m的增大而显著减小,最小变形量对应的裂纹位置为板簧端部,在此处,裂纹对板簧刚度的影响程度最小,板簧刚度达到最大值。当板簧出现纵向裂纹时,裂纹位置越接近板簧1/2宽度位置处(n=31.5 mm),端部变形量越大,刚度越小,但整体看来,纵向裂纹位置对板簧刚度的影响程度轻微,刚度变化量很小。
图6所示为m=n=20 mm、hx=hy=30 mm时仿真所得的不同裂纹角度影响下的板簧端部的最大变形量变化曲线,其中,不同裂纹角度下的板簧刚度如表4所示。
图6表4可以看出,在不同裂纹角度的影响下,板簧的端部变形量和刚度的变化具有一定的对称性:α越接近90°,裂纹对板簧刚度的影响程度越大,板簧的变形量越大,刚度越小,整体看来,纵向裂纹角度对板簧刚度的影响显著;β越接近90°,板簧的变形量越大,刚度越小,但整体看来,纵向裂纹角度对板簧刚度的影响轻微,刚度变化量很小。
图7所示为m=n=20 mm、α=β=90°时仿真所得的不同裂纹深度影响下的板簧端部变形量的变化曲线,其中,不同裂纹深度下的板簧刚度如表5所示。
图7表5可以看出:随着hx的增大,横向裂纹深度对板簧刚度的影响程度显著增大,板簧端部变形量增加,刚度减小;随着hy的增加,端部变形量略有增加,刚度略有减小,整体看来,纵向裂纹深度对板簧刚度的影响程度轻微。特别地,在一定深度范围内,hy对板簧刚度的影响程度为正值,即此时含裂纹的板簧刚度较初始模型刚度大,造成这种现象的原因可能是:板簧端部受力,纵向裂纹方向与弯矩方向垂直,对变形量影响较小,故纵向裂纹对板簧刚度的影响程度较小,且在端部力的作用下,裂纹面间相互挤压抵消了一部分作用力,使得板簧变形减小,刚度略有增大。
本文利用SolidWorks和ANSYS软件建立了含裂纹的少片变截面钢板弹簧三维仿真模型,探究了裂纹位置、角度、深度对板簧刚度的影响规律,所得结论如下:
a. 横向裂纹位置对板簧刚度的影响显著,裂纹位置越接近板簧根部平直段1/3长度位置处,影响程度越大,板簧刚度越小;纵向裂纹位置对板簧刚度的影响程度轻微,随着裂纹向板簧1/2宽度位置处移动,板簧刚度略有减小。
b. 横向裂纹角度对板簧刚度的影响显著,影响规律具有一定对称性,裂纹角度越接近90°,影响程度越大,板簧刚度越小;纵向裂纹角度对板簧刚度的影响程度轻微,也呈现一定对称性,但刚度变化量很小。
c. 横向裂纹深度对板簧刚度的影响显著,裂纹越深,影响程度越大,板簧刚度越小;纵向裂纹深度对板簧刚度的影响程度轻微,在一定深度范围内,纵向裂纹对板簧刚度的影响程度为正值,即此时含裂纹的板簧刚度较无裂纹板簧刚度大。
所得结论可为少片变截面钢板弹簧的刚度计算和疲劳寿命预测提供有效的理论参考和技术借鉴。
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doi: 10.20104/j.cnki.1674-6546.20240061
  • 首发时间:2025-11-25
  • 出版时间:2024-09-15
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  • 修回日期:2024-03-28
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    山东劳动职业技术学院, 济南 250399
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2种不同金属材料的力学参数

Family
属数
Number of
genus
种数
Number of
species
占总种数比例
Percentage of
total species (%)

Genus
种数
Number of
species
占总种数比例
Percentage of total
species (%)
鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
小菇科 Mycenaceae 2 12 5.74 丝盖伞属 Inocybe 5 2.39
多孔菌科 Polyporaceae 8 14 6.70 蜡蘑属 Laccaria 5 2.39
红菇科 Russulaceae 3 23 11.00 小皮伞属 Marasmius 6 2.87
小菇属 Mycena 11 5.26
光柄菇属 Pluteus 5 2.39
红菇属 Russula 17 8.13
栓菌属 Trametes 5 2.39
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