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Article(id=1154021706680226556, tenantId=1146029695717560320, journalId=1146120084050784272, issueId=1154021703362532078, articleNumber=null, orderNo=null, doi=10.19562/j.chinasae.qcgc.2024.12.001, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1714406400000, receivedDateStr=2024-04-30, revisedDate=1718726400000, revisedDateStr=2024-06-19, acceptedDate=null, acceptedDateStr=null, onlineDate=1753069815558, onlineDateStr=2025-07-21, pubDate=1735056000000, pubDateStr=2024-12-25, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1753069815558, onlineIssueDateStr=2025-07-21, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1753069815558, creator=13701087609, updateTime=1753069815558, updator=13701087609, issue=Issue{id=1154021703362532078, tenantId=1146029695717560320, journalId=1146120084050784272, year='2024', volume='46', issue='12', pageStart='2143', pageEnd='2354', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=0, articleOrder=1, issueType=-1, specialIssue=null, createTime=1753069814768, creator=13701087609, updateTime=1753074363847, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1154040783624724753, tenantId=1146029695717560320, journalId=1146120084050784272, issueId=1154021703362532078, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1154040783624724754, tenantId=1146029695717560320, journalId=1146120084050784272, issueId=1154021703362532078, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=2143, endPage=2153, ext={EN=ArticleExt(id=1154021707095462654, articleId=1154021706680226556, tenantId=1146029695717560320, journalId=1146120084050784272, language=EN, title=Integrated Optimization Design of Lightweight and Fatigue Life for the Integrated Structure of Cell-To-Frame, columnId=1170310431202619715, journalTitle=Automotive Engineering, columnName=Feature Topic： Automotive Structural Integration Design and Manufacturing Technology, runingTitle=null, highlight=null, articleAbstract=

To improve the lightweight level of electric cargo vehicles，a Cell To Frame （CTF） structure that integrates the frame and battery compartment is proposed in this paper. Firstly，a finite element model of the benchmark vehicle frame is established，and its static performance and free mode are calculated. The accuracy of the finite element model is verified through free mode experiments. Then，the fatigue life analysis of the frame is carried out using the nominal stress method in the time domain using the multi working condition combination fatigue load spectrum obtained from road sampling. Next，experimental design is conducted on the initial design of the CTF structure，which has been validated by finite element analysis，and a surrogate model is established. Finally，the global response search method is used for optimization design to obtain the optimal lightweight solution. The results show that after optimized design，the weight of the CTF structure is reduced by 139.95 kg compared to the traditional separation design of the frame and battery compartment，with a lightweight rate of 14.09%. At the same time，the mechanical properties and fatigue life of the CTF structure both meet the design requirements.

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为提高电动载货汽车轻量化水平，本文提出了一种车架与电池舱一体化（cell to frame-简称“CTF”）结构。首先建立对标车型车架有限元模型，计算了其静力学性能与自由模态，并通过自由模态试验验证有限元模型的准确性。然后采用道路实采的多工况组合疲劳载荷谱在时域内运用名义应力法进行车架疲劳寿命分析。接着对经有限元分析验证合理的CTF结构初始设计进行试验设计并建立代理模型。最后采用全局响应面法进行优化设计，获得最佳轻量化方案。结果表明，优化设计后，CTF结构质量相较于传统的车架与电池舱分离设计结构轻量139.95 kg，轻量化率达14.09%，同时CTF结构力学性能与疲劳寿命均满足设计要求。

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王登峰，教授，博士，E-mail：。
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工况 满载弯曲 满载扭转 紧急制动 紧急转弯
左前悬架前吊耳约束情况 UY，UZ UY，UZ UY，UZ UY，UZ
左前悬架后吊耳约束情况 UY，UZ UY，UZ UY，UZ UY，UZ
右前悬架前吊耳约束情况 UY，UZ UY，UZ UY，UZ
右前悬架后吊耳约束情况 UY，UZ UY，UZ UY，UZ
左后悬架前吊耳约束情况 UX，UY，UZ UX，UY，UZ UX，UY，UZ UX，UY，UZ
左后悬架后吊耳约束情况 UY，UZ UY，UZ UY，UZ UY，UZ
右后悬架前吊耳约束情况 UX，UY，UZ UX，UY，UZ UX，UY，UZ UX，UY，UZ
右后悬架后吊耳约束情况 UY，UZ UY，UZ UY，UZ UY，UZ
惯性载荷施加 0.6g 制动惯性力 0.4g侧向惯性力
动载荷系数 2 1.2 1.2 1.2
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车架在4种工况下的吊耳约束情况、惯性载荷施加情况与动载荷系数

, figureFileSmall=null, figureFileBig=null, tableContent=
工况 满载弯曲 满载扭转 紧急制动 紧急转弯
左前悬架前吊耳约束情况 UY，UZ UY，UZ UY，UZ UY，UZ
左前悬架后吊耳约束情况 UY，UZ UY，UZ UY，UZ UY，UZ
右前悬架前吊耳约束情况 UY，UZ UY，UZ UY，UZ
右前悬架后吊耳约束情况 UY，UZ UY，UZ UY，UZ
左后悬架前吊耳约束情况 UX，UY，UZ UX，UY，UZ UX，UY，UZ UX，UY，UZ
左后悬架后吊耳约束情况 UY，UZ UY，UZ UY，UZ UY，UZ
右后悬架前吊耳约束情况 UX，UY，UZ UX，UY，UZ UX，UY，UZ UX，UY，UZ
右后悬架后吊耳约束情况 UY，UZ UY，UZ UY，UZ UY，UZ
惯性载荷施加 0.6g 制动惯性力 0.4g侧向惯性力
动载荷系数 2 1.2 1.2 1.2
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阶数 振型 仿真频率/Hz 试验频率/Hz 误差/%
1 1阶扭转 7.25 7.31 0.82
2 1阶垂向弯曲 12.52 12.60 0.63
3 1阶横向弯曲 19.72 19.71 -0.05
4 2阶横向弯曲 20.92 20.62 -1.45
5 2阶扭转 25.52 26.03 1.96
), ArticleFig(id=1170310950952382866, tenantId=1146029695717560320, journalId=1146120084050784272, articleId=1154021706680226556, language=CN, label=表2, caption=

仿真模态与试验模态对比

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阶数 振型 仿真频率/Hz 试验频率/Hz 误差/%
1 1阶扭转 7.25 7.31 0.82
2 1阶垂向弯曲 12.52 12.60 0.63
3 1阶横向弯曲 19.72 19.71 -0.05
4 2阶横向弯曲 20.92 20.62 -1.45
5 2阶扭转 25.52 26.03 1.96
), ArticleFig(id=1170310951036268947, tenantId=1146029695717560320, journalId=1146120084050784272, articleId=1154021706680226556, language=EN, label=null, caption=null, figureFileSmall=null, figureFileBig=null, tableContent=
材料 抗拉强度/MPa 弹性模量/MPa
ZQS500L 650 2.0×105
QSTE420TM 560 2.0×105
Q355B 510 2.0×105
20#钢管 410 2.0×105
), ArticleFig(id=1170310951099183508, tenantId=1146029695717560320, journalId=1146120084050784272, articleId=1154021706680226556, language=CN, label=表3, caption=

各材料抗拉强度和弹性模量

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材料 抗拉强度/MPa 弹性模量/MPa
ZQS500L 650 2.0×105
QSTE420TM 560 2.0×105
Q355B 510 2.0×105
20#钢管 410 2.0×105
), ArticleFig(id=1170310951149515157, tenantId=1146029695717560320, journalId=1146120084050784272, articleId=1154021706680226556, language=EN, label=null, caption=null, figureFileSmall=null, figureFileBig=null, tableContent=
序号 DV1 DV2 DV3 DV4 DV5 ··· DV18 DV19 DV20 DV21
1 5.74 3.76 8.26 16.96 6.51 ··· 4.84 5.31 7.35 11.26
2 6.58 4.72 7.42 13.12 5.82 ··· 5.69 6.63 8.29 10.51
3 7.42 3.28 6.58 18.88 6.48 ··· 5.25 5.92 8.20 9.31
4 8.26 4.24 5.74 15.04 6.84 ··· 5.63 6.46 7.30 10.66
5 5.07 4.91 6.41 20.03 6.85 ··· 5.22 4.54 9.07 10.81
··· ··· ··· ··· ··· ··· ··· ··· ··· ··· ···
172 7.29 3.21 8.45 14.86 5.26 ··· 5.33 5.35 7.62 10.38
173 8.13 4.17 7.61 20.63 6.22 ··· 5.04 5.20 8.43 9.28
··· ··· ··· ··· ··· ··· ··· ··· ··· ··· ···
275 4.95 3.58 8.85 15.21 5.72 ··· 4.88 5.63 8.57 9.50
276 5.79 4.54 8.01 11.37 6.86 ··· 5.33 4.81 6.62 9.81
277 6.63 3.10 7.17 17.13 4.82 ··· 5.50 4.15 7.58 8.17
278 7.47 4.06 6.33 13.29 5.49 ··· 5.27 4.64 8.83 9.95
279 8.31 5.02 5.49 19.05 5.84 ··· 5.64 5.18 7.93 11.30
), ArticleFig(id=1170310951225012630, tenantId=1146029695717560320, journalId=1146120084050784272, articleId=1154021706680226556, language=CN, label=表4, caption=

试验设计矩阵

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序号 DV1 DV2 DV3 DV4 DV5 ··· DV18 DV19 DV20 DV21
1 5.74 3.76 8.26 16.96 6.51 ··· 4.84 5.31 7.35 11.26
2 6.58 4.72 7.42 13.12 5.82 ··· 5.69 6.63 8.29 10.51
3 7.42 3.28 6.58 18.88 6.48 ··· 5.25 5.92 8.20 9.31
4 8.26 4.24 5.74 15.04 6.84 ··· 5.63 6.46 7.30 10.66
5 5.07 4.91 6.41 20.03 6.85 ··· 5.22 4.54 9.07 10.81
··· ··· ··· ··· ··· ··· ··· ··· ··· ··· ···
172 7.29 3.21 8.45 14.86 5.26 ··· 5.33 5.35 7.62 10.38
173 8.13 4.17 7.61 20.63 6.22 ··· 5.04 5.20 8.43 9.28
··· ··· ··· ··· ··· ··· ··· ··· ··· ··· ···
275 4.95 3.58 8.85 15.21 5.72 ··· 4.88 5.63 8.57 9.50
276 5.79 4.54 8.01 11.37 6.86 ··· 5.33 4.81 6.62 9.81
277 6.63 3.10 7.17 17.13 4.82 ··· 5.50 4.15 7.58 8.17
278 7.47 4.06 6.33 13.29 5.49 ··· 5.27 4.64 8.83 9.95
279 8.31 5.02 5.49 19.05 5.84 ··· 5.64 5.18 7.93 11.30
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序号 masstotal/kg dispt max/mm stressbd max/MPa stresst max/MPa stressbk max/MPa stresst max/MPa freq1/Hz lifemin/循环
1 13.42 12.91 389.34 487.31 424.14 356.89 10.75 289 900
2 13.47 11.58 339.45 438.98 366.55 316.34 10.58 2 139 000
3 13.46 11.72 252.64 330.27 275.04 260.98 10.59 5 066 000
4 13.55 10.51 205.07 279.77 212.07 217.28 10.50 75 490 000
5 13.42 12.81 369.77 440.92 382.32 348.91 10.49 329 300
··· ··· ··· ··· ··· ··· ··· ··· ···
172 13.45 12.02 380.04 478.04 405.48 339.72 10.36 5 538 000
173 13.53 10.70 212.31 316.42 219.15 214.69 10.36 39 390 000
··· ··· ··· ··· ··· ··· ··· ··· ···
275 13.34 14.17 402.87 416.23 318.26 412.85 10.04 265 000
276 13.44 12.26 306.17 325.61 261.44 312.09 10.63 443 700
277 13.41 13.15 394.03 492.93 423.23 365.26 9.99 874 400
278 13.49 11.25 321.18 413.66 345.74 296.75 10.52 11 410 000
279 13.57 10.21 273.89 308.58 251.67 239.46 10.37 89 560 000
), ArticleFig(id=1170310951359230363, tenantId=1146029695717560320, journalId=1146120084050784272, articleId=1154021706680226556, language=CN, label=表5, caption=

试验设计结果

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序号 masstotal/kg dispt max/mm stressbd max/MPa stresst max/MPa stressbk max/MPa stresst max/MPa freq1/Hz lifemin/循环
1 13.42 12.91 389.34 487.31 424.14 356.89 10.75 289 900
2 13.47 11.58 339.45 438.98 366.55 316.34 10.58 2 139 000
3 13.46 11.72 252.64 330.27 275.04 260.98 10.59 5 066 000
4 13.55 10.51 205.07 279.77 212.07 217.28 10.50 75 490 000
5 13.42 12.81 369.77 440.92 382.32 348.91 10.49 329 300
··· ··· ··· ··· ··· ··· ··· ··· ···
172 13.45 12.02 380.04 478.04 405.48 339.72 10.36 5 538 000
173 13.53 10.70 212.31 316.42 219.15 214.69 10.36 39 390 000
··· ··· ··· ··· ··· ··· ··· ··· ···
275 13.34 14.17 402.87 416.23 318.26 412.85 10.04 265 000
276 13.44 12.26 306.17 325.61 261.44 312.09 10.63 443 700
277 13.41 13.15 394.03 492.93 423.23 365.26 9.99 874 400
278 13.49 11.25 321.18 413.66 345.74 296.75 10.52 11 410 000
279 13.57 10.21 273.89 308.58 251.67 239.46 10.37 89 560 000
), ArticleFig(id=1170310951443116446, tenantId=1146029695717560320, journalId=1146120084050784272, articleId=1154021706680226556, language=EN, label=null, caption=null, figureFileSmall=null, figureFileBig=null, tableContent=
验证方法 响应量 交叉验证 额外采点验证
R 2 质量 0.999 9 0.999 9
扭转工况下的最大位移 0.999 7 0.999 3
弯曲工况下的最大应力 0.958 0 0.939 0
制动工况下的最大应力 0.957 4 0.974 5
扭转工况下的最大应力 0.995 8 0.992 8
转弯工况下的最大应力 0.968 3 0.966 4
1阶模态频率 0.980 4 0.985 9
疲劳寿命 0.863 6 0.857 9
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近似模型的决定系数

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验证方法 响应量 交叉验证 额外采点验证
R 2 质量 0.999 9 0.999 9
扭转工况下的最大位移 0.999 7 0.999 3
弯曲工况下的最大应力 0.958 0 0.939 0
制动工况下的最大应力 0.957 4 0.974 5
扭转工况下的最大应力 0.995 8 0.992 8
转弯工况下的最大应力 0.968 3 0.966 4
1阶模态频率 0.980 4 0.985 9
疲劳寿命 0.863 6 0.857 9
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设计变量 代号 初始值/mm 优化值/mm 圆整值/mm
纵梁厚度 DV1 7 6.29 7
加强梁厚度 DV2 4 2.80 3
前横梁厚度 DV3 7 4.90 5
前横梁连接板厚度 DV4 16 10.80 11
前圆管梁厚度 DV5 6 4.80 5
前圆管梁连接板厚度 DV6 8 6.40 7
后圆管梁厚度 DV7 6 4.80 5
后圆管梁连接板厚度 DV8 8 6.40 7
第1电池舱底梁厚度 DV9 10 9.2 10
第1电池舱底梁连接板厚度 DV10 8 9.6 10
第2电池舱底梁厚度 DV11 10 8.0 8
第2电池舱底梁连接板厚度 DV12 8 6.4 7
第3电池舱底梁连接板厚度 DV13 8 9.6 10
第1钢板横梁厚度 DV14 5 4.0 4
第1钢板横梁连接板厚度 DV15 7 8.99 9
第2钢板横梁厚度 DV16 5 4.0 4
第2钢板横梁连接板厚度 DV17 6 5.0 5
尾梁厚度 DV18 5 4.0 4
尾梁连接板厚度 DV19 5 4.0 4
电池舱底梁连接板加强肋厚度 DV20 8 9.6 10
第3电池舱底梁厚度 DV21 10 10.99 11
), ArticleFig(id=1170310951682191782, tenantId=1146029695717560320, journalId=1146120084050784272, articleId=1154021706680226556, language=CN, label=表7, caption=

CTF结构优化后各变量取值

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设计变量 代号 初始值/mm 优化值/mm 圆整值/mm
纵梁厚度 DV1 7 6.29 7
加强梁厚度 DV2 4 2.80 3
前横梁厚度 DV3 7 4.90 5
前横梁连接板厚度 DV4 16 10.80 11
前圆管梁厚度 DV5 6 4.80 5
前圆管梁连接板厚度 DV6 8 6.40 7
后圆管梁厚度 DV7 6 4.80 5
后圆管梁连接板厚度 DV8 8 6.40 7
第1电池舱底梁厚度 DV9 10 9.2 10
第1电池舱底梁连接板厚度 DV10 8 9.6 10
第2电池舱底梁厚度 DV11 10 8.0 8
第2电池舱底梁连接板厚度 DV12 8 6.4 7
第3电池舱底梁连接板厚度 DV13 8 9.6 10
第1钢板横梁厚度 DV14 5 4.0 4
第1钢板横梁连接板厚度 DV15 7 8.99 9
第2钢板横梁厚度 DV16 5 4.0 4
第2钢板横梁连接板厚度 DV17 6 5.0 5
尾梁厚度 DV18 5 4.0 4
尾梁连接板厚度 DV19 5 4.0 4
电池舱底梁连接板加强肋厚度 DV20 8 9.6 10
第3电池舱底梁厚度 DV21 10 10.99 11
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性能指标 对标车架 CTF结构 对比
弯曲工况最大应力/MPa 347.36 326.70 -5.95%
扭转工况最大应力/MPa 365.48 325.64 -10.90%
制动工况最大应力/MPa 303.72 226.24 -25.51%
转弯工况最大应力/MPa 335.91 325.81 -3.01%
弯曲工况最大变形/mm 4.40 4.34 -
弯曲工况车架部分最大变形/mm 4.40 4.34 -1.36%
扭转工况最大变形/mm 11.80 16.31 -
扭转工况车架部分最大变形/mm 11.80 11.38 -3.56%
制动工况最大变形/mm 3.42 3.17 -
制动工况车架部分最大变形/mm 3.42 3.17 -7.31%
转弯工况最大变形/mm 5.86 8.09 -
转弯工况车架部分最大变形/mm 5.86 8.09 38.05%
1阶模态频率/Hz 7.31 10.64 45.55%
2阶模态频率/Hz 12.63 12.24 -3.09%
3阶模态频率/Hz 19.84 20.43 2.97%
4阶模态频率/Hz 20.38 23.14 13.54%
5阶模态频率/Hz 25.71 28.32 10.15%
最危险点疲劳寿命（循环次数） 2.82E+06 2.66E+06 -5.67%
最危险点疲劳寿命/万km 107.79 101.67 -5.68%
车架质量/kg 654.00 586.40 -10.34%
电池舱质量（不含动力电池）/kg 339.27 266.92 -21.33%
车架与电池舱质量之和/kg 993.27 853.32 -14.09%
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优化后CTF结构与对标车架对比

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性能指标 对标车架 CTF结构 对比
弯曲工况最大应力/MPa 347.36 326.70 -5.95%
扭转工况最大应力/MPa 365.48 325.64 -10.90%
制动工况最大应力/MPa 303.72 226.24 -25.51%
转弯工况最大应力/MPa 335.91 325.81 -3.01%
弯曲工况最大变形/mm 4.40 4.34 -
弯曲工况车架部分最大变形/mm 4.40 4.34 -1.36%
扭转工况最大变形/mm 11.80 16.31 -
扭转工况车架部分最大变形/mm 11.80 11.38 -3.56%
制动工况最大变形/mm 3.42 3.17 -
制动工况车架部分最大变形/mm 3.42 3.17 -7.31%
转弯工况最大变形/mm 5.86 8.09 -
转弯工况车架部分最大变形/mm 5.86 8.09 38.05%
1阶模态频率/Hz 7.31 10.64 45.55%
2阶模态频率/Hz 12.63 12.24 -3.09%
3阶模态频率/Hz 19.84 20.43 2.97%
4阶模态频率/Hz 20.38 23.14 13.54%
5阶模态频率/Hz 25.71 28.32 10.15%
最危险点疲劳寿命（循环次数） 2.82E+06 2.66E+06 -5.67%
最危险点疲劳寿命/万km 107.79 101.67 -5.68%
车架质量/kg 654.00 586.40 -10.34%
电池舱质量（不含动力电池）/kg 339.27 266.92 -21.33%
车架与电池舱质量之和/kg 993.27 853.32 -14.09%
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车架与电池舱一体化结构轻量化与疲劳寿命集成优化设计*
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孟子皓 , 王登峰 , 张小朋 , 张子峰 , 连丰民 , 陈静
汽车工程 | 专题：汽车结构一体化设计与制造技术 2024,46(12): 2143-2153
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汽车工程 | 专题：汽车结构一体化设计与制造技术 2024, 46(12): 2143-2153
车架与电池舱一体化结构轻量化与疲劳寿命集成优化设计*
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孟子皓, 王登峰 , 张小朋, 张子峰, 连丰民, 陈静
作者信息
  • 吉林大学，汽车底盘集成与仿生全国重点实验室，长春 130022

通讯作者:

王登峰，教授，博士，E-mail：。
Integrated Optimization Design of Lightweight and Fatigue Life for the Integrated Structure of Cell-To-Frame
Zihao Meng, Dengfeng Wang , Xiaopeng Zhang, Zifeng Zhang, Fengmin Lian, Jing Chen
Affiliations
  • Jilin University，National Key Laboratory of Automotive Chassis Integration and Bionics，Changchun 130022
出版时间: 2024-12-25 doi: 10.19562/j.chinasae.qcgc.2024.12.001
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摘要
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为提高电动载货汽车轻量化水平，本文提出了一种车架与电池舱一体化（cell to frame-简称“CTF”）结构。首先建立对标车型车架有限元模型，计算了其静力学性能与自由模态，并通过自由模态试验验证有限元模型的准确性。然后采用道路实采的多工况组合疲劳载荷谱在时域内运用名义应力法进行车架疲劳寿命分析。接着对经有限元分析验证合理的CTF结构初始设计进行试验设计并建立代理模型。最后采用全局响应面法进行优化设计，获得最佳轻量化方案。结果表明，优化设计后，CTF结构质量相较于传统的车架与电池舱分离设计结构轻量139.95 kg，轻量化率达14.09%，同时CTF结构力学性能与疲劳寿命均满足设计要求。

电动载货汽车车架  /  疲劳分析  /  轻量化  /  优化设计  /  汽车结构一体化设计

To improve the lightweight level of electric cargo vehicles，a Cell To Frame （CTF） structure that integrates the frame and battery compartment is proposed in this paper. Firstly，a finite element model of the benchmark vehicle frame is established，and its static performance and free mode are calculated. The accuracy of the finite element model is verified through free mode experiments. Then，the fatigue life analysis of the frame is carried out using the nominal stress method in the time domain using the multi working condition combination fatigue load spectrum obtained from road sampling. Next，experimental design is conducted on the initial design of the CTF structure，which has been validated by finite element analysis，and a surrogate model is established. Finally，the global response search method is used for optimization design to obtain the optimal lightweight solution. The results show that after optimized design，the weight of the CTF structure is reduced by 139.95 kg compared to the traditional separation design of the frame and battery compartment，with a lightweight rate of 14.09%. At the same time，the mechanical properties and fatigue life of the CTF structure both meet the design requirements.

electric truck frame  /  fatigue analysis  /  lightweight  /  optimization design  /  integrated design of automotive structure
孟子皓, 王登峰, 张小朋, 张子峰, 连丰民, 陈静. 车架与电池舱一体化结构轻量化与疲劳寿命集成优化设计*. 汽车工程, 2024 , 46 (12) : 2143 -2153 . DOI: 10.19562/j.chinasae.qcgc.2024.12.001
Zihao Meng, Dengfeng Wang, Xiaopeng Zhang, Zifeng Zhang, Fengmin Lian, Jing Chen. Integrated Optimization Design of Lightweight and Fatigue Life for the Integrated Structure of Cell-To-Frame[J]. Automotive Engineering, 2024 , 46 (12) : 2143 -2153 . DOI: 10.19562/j.chinasae.qcgc.2024.12.001
正文
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前言
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根据国家统计局最新发布的数据，2023年我国原油进口量56 399万t[1]，对外依存度高达72.97%，能源安全问题已成为当今我国迫切需要关注和解决的重大课题[2]。新能源汽车的发展有助于削弱对传统石油资源的依赖，这对于解决当前紧迫的能源安全问题具有深远的战略意义，新能源汽车的发展已经引起了国家和业界普遍关注和高度重视[3-6]。
新能源汽车由于配备有较大的动力电池，使得整备质量较传统燃油车高很多，因此轻量化变得更为重要。汽车轻量化主要通过采用轻质材料、引入先进制造工艺和优化结构设计这3种途径来实现[7]。然而，由于轻质材料和先进制造工艺的成本较高，使得它们在经济取向的商用车领域难以得到广泛应用。因此，优化结构设计对于电动商用车的轻量化至关重要。近年来，许多学者从不同角度对车辆结构进行了优化设计。张凯成等[8]对钢铝材料结合的商用车车架进行了多工况轻量化优化设计研究。Wang等[9]提出了一种集贡献分析、试验设计、近似模型和偏好选择指数（PSI）法于一体的优化策略，建立了一种高效的多目标重型商用车车架轻量化设计方法。刘莹等[10]基于隐式全参数化技术对动力电池舱进行轻量化设计研究。谷先广等[11]研究了精密铸铝件一体化设计对车身轻量化的影响。但是，上述研究仅考虑了车架或电池舱本身，并没有考虑电池舱对车架的耦合作用。廉玉波等[12]基于扭转刚度对乘用车电池包与车身一体化集成设计进行了研究，开启了车身与电池舱一体化研究的先河。段利斌等[13]基于VRB/OW-GFRP混合结构对CTB电池包上盖总成进行了轻量化设计研究。但这些研究仅局限于乘用车领域，商用车车架与电池舱一体化集成的研究目前尚处在空白阶段。
商用车常处于满载运行状态，其使用场景极为复杂多变，车架作为支撑驾驶室、动力电池、货箱以及各类附件的核心结构体，长期承受着不断变化的动态载荷，导致车架极易产生疲劳破坏。国内外学者就车架疲劳寿命预测分析进行了大量研究[14-17]，但其基本局限于匀速工况下疲劳寿命的分析，并没有考虑到加速、制动和转向工况对车架疲劳寿命的影响。
1 对标车架性能仿真与试验
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1.1 对标车架有限元模型建立
本文以某量产重型电动载货汽车作为对标车型，提取设计指标，该对标车型车架总体尺寸为：长×前宽（后宽）×高=8560 mm×958（858） mm×243 mm，车架质量为654 kg。有限元模型如图1所示，使用5 mm网格进行离散，网格总数为610 878个，其中四边形单元603 404个，三角形单元7 474个，使用328组RBE2和Bar单元模拟螺栓和铆钉连接，依据GB/T 33582—2017《机械产品结构有限元力学分析通用规则》[18]的相关规则进行网格质量控制。
1.2 对标车架静力学性能分析
车架的典型工况包括：满载弯曲工况、满载扭转工况、紧急制动工况和紧急转弯工况，在进行静力学性能分析时上述4种工况采用吊耳约束和惯性载荷施加的方式实现，由于车架在行驶过程会受到各种随机载荷的作用，所以就需要对静载荷乘上动载荷系数来模拟车架的真实受载情况，各工况下的吊耳约束、惯性载荷施加与动载荷系数如表1所示，求解结果如图2所示。
根据图2所示的分析结果得到对标车架在弯曲工况、扭转工况、制动工况、转弯工况下的最大应力和最大位移分别为347.36、365.48、303.72、335.91 MPa和4.40、11.80、3.42、5.86 mm，全部出现在材料为ZQS500L的结构上，该材料的屈服强度为500 MPa，因此得到安全系数分别为1.43、1.37、1.65和1.49。
1.3 对标车架有限元模态分析与试验验证
为验证上文建立的对标车架有限元模型的准确性，本文采用锤击法对车架样件进行自由模态试验，获取对标车架的主要低阶固有频率和模态振型参数与有限元分析结果进行对比验证。模态试验选用选取美国PCB压电传感器技术有限公司的冲击力锤（086D05）和三轴加速度传感器（356A16）来产生激励和测量车架结构的振动响应，采用江苏东华测试技术股份有限公司的DH5920动态信号测试分析系统和DHDAS分析软件采集测试信号与分析试验数据。
如图3所示，被测对标车架样件放置在空气弹簧支座上，保持被测结构水平，图中黄色圆圈表示空气弹簧支座的支撑位置。在正式试验开始前测得对标车架在空气弹簧支座上的刚体模态频率为0.56 Hz，小于车架1阶固有模态频率的10%，满足自由模态试验测试要求。为全面反映对标车架结构的几何特征与保证测试数据信息的完整性，在被测车架结构上布置32个响应测点，设置1个激励点。响应点和激励点的布置如图3所示，其中蓝色方框表示响应点，其上安装加速度传感器，红色矩形框表示激励点，冲击力锤在此处敲击。
本次试验采用单点激励多点拾取的方法，选用灵敏度为2.2 mV/N的冲击力锤，采用力锤敲击法进行激励，保证力锤每次敲击都有足够大的激励能量，对32个响应点分4组进行测量。设置采样频率为1 000 Hz，通过DH5920动态信号测试分析系统采集各组激励和响应试验数据并进行储存，采用PolyLSCF识别方法进行模态分析，在稳态图中选取竖直方向上S点布满的频率值作为频率输出值，通过分析得到对标车架前5阶整体弹性模态频率和振型如图4所示。
本文在有限元分析中使用兰索士方法求解对标车架的模态性能参数，为了剔除固有频率在0附近的前6阶刚体模态，设置有限元分析的频率下限为1 Hz，提取出车架的前5阶整体弹性模态频率和振型，如图5所示。
车架有限元分析与试验得到的模态频率和振型对比如表2所示。
2 车架多工况疲劳寿命分析
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2.1 车架疲劳载荷谱的测量
研究团队依托某车企采集的电动载货车车联网行车大数据，以车辆行驶道路、里程、速度和加、减速度与转向和制动等作为用户运行工况表征参数，采用无监督自学习的K-means聚类分析法对电动载货车使用场景和运行工况进行分类，并据此确定了不同场景和工况的时长为20 s的车架疲劳分析载荷分配比例，如图6所示。
为了获取电动载货车在典型工况下的车架疲劳载荷，本文在车辆试验场进行了实车道路试验，试验中，采用应变片来测量不同工况下各测点的应变-时间历程信号，试验过程的图片如图7所示。经过车架载荷台架标定试验，得到了各测试位置在x、y、z 3个方向上的载荷-时间历程数据。
根据图6的疲劳载荷谱工况分配和实车道路试验测得的各工况载荷-时间历程数据，本文编制了一个时长20 s的车架实际使用工况载荷谱用于多工况疲劳分析，受制于篇幅限制，本文仅展示了1号与2号测点的载荷谱，如图8所示，其中红色、蓝色和绿色曲线分别表示x、y、z方向的载荷谱。
2.2 材料S-N曲线的拟合
本文根据材料的抗拉强度和弹性模量利用疲劳分析软件计算出各个材料的S-N曲线，对标车架各个材料的抗拉强度和弹性模量如表3所示，拟合出的材料S-N曲线如图9所示。
2.3 对标车架疲劳寿命分析
本文在时域内应用名义应力法进行车架多工况疲劳寿命分析，选用临界面（CriticalPlane）法进行应力组合，选用德国机械工程学会编制的FKM方法进行平均应力修正，存活率选择95%，经疲劳分析软件计算后得到对标车架各节点疲劳寿命结果如图10所示。
由图10可以看出对标车架的前部横梁和纵梁与其他总成的连接处均为疲劳寿命相对较短的部位，其中最危险点出现在车架纵梁与前横梁的连接处，该节点由于此处距离驾驶室悬置和前轴悬架固定吊耳较近，所以该处受到的交变应力较大，该节点的疲劳寿命2.82E+06次循环，约为106.35万km。
3 CTF结构轻量化与疲劳寿命优化
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3.1 CTF结构初始设计与有限元模型建立
对标车架采用车架与电池舱分离结构，电池舱与车架的连接关系如图11所示，电池舱支架通过螺栓连接在车架纵梁上，其上挂有电池舱。电池舱可以容纳9组容量为35.09 kW·h的电池组，共储存315.81 kW·h电能。该结构设计的电池舱与电池舱支架对车架的强度与刚度几乎起不到加强作用，存在较大的设计冗余，造成车架与电池舱总成质量较大，不利于车辆轻量化。
本文提出了一种车架与电池舱一体化（cell to frame-简称“CTF”）结构，初始设计如图12所示，CTF结构在左右纵梁中部外侧设置有3对电池舱支架，3根底梁连接在3对电池舱支架底部，电池舱框架固定安装在3根底梁上，电池舱框架与3根底梁可以整体与电池舱支架进行分离以实现快速换电。电池舱可以容纳4组或6组容量为70.86 kW·h的电池组，共储存283.44或425.16 kW·h电能，考虑到可以整体换电，本文后续以电量为283.44 kW·h的电池组结构为例进行分析。CTF结构可将动力电池舱与车架集成为一体，电池舱支架和底梁对车架的强度与刚度起到了一定的加强作用。
根据CTF结构初始设计建立的有限元模型如图13所示，使用5 mm网格进行离散，网格总数为720 517个，其中四边形单元712 061个，三角形单元8 456个，使用378组RBE2和Bar单元模拟螺栓和铆钉连接。
3.2 CTF结构初始设计性能分析
对CTF结构初始设计进行4种典型工况的静力学性能分析，各工况下的吊耳约束、加速度施加与动载荷系数见表1，得到其在4种典型工况下最大应力和车架部分最大位移分别为267.35、363.25、304.07、304.40 MPa和4.20、11.87、3.07、7.54 mm，全部出现在材料为ZQS500L的结构上，安全系数分别为1.87、1.38、1.64和1.64。对其进行模态分析，得到其前5阶模态频率分别为10.44、12.43、20.54、23.34和28.8 Hz。对其进行多工况疲劳寿命分析，得到其最危险点疲劳寿命为2.26E+06次循环，约合86.38万km。
从CTF结构初始设计性能分析可以看出，该设计基本合理，且存在一定的优化空间。
3.3 CTF结构多目标优化设计
3.3.1 设计变量
本文选择了CTF结构上21个尺寸变量作为设计变量，如图14所示。
3.3.2 数学模型
CTF结构多目标优化要考虑静力学性能指标、低阶模态、疲劳寿命以及质量等多个方面。本文的首要优化目标为CTF结构的质量最小化，其次考虑车架在扭转工况下的变形最小化和CTF结构疲劳寿命最大化。将弯曲、扭转、制动和转弯工况下的CTF结构最大应力、1阶模态频率作为约束条件。其中，弯曲、扭转、制动和转弯工况下CTF结构各部分的最大应力应该小于所用材料的许用应力；同时约束1阶模态频率高于对标车架的1阶模态频率。综上所述，建立CTF结构多目标优化设计的数学模型如下：
f i n d D V i m i n ≤ D V i ≤ D V i m a x i = 1,2 , … , 21 s . t . s t r e s s j   b d m a x ≤ σ j    j = 1,2 , … , 6 s t r e s s j   t o m a x ≤ σ j j = 1,2 , … , 6 s t r e s s j   b k m a x ≤ σ j j = 1,2 , … , 6 s t r e s s j   t n m a x ≤ σ j    j = 1,2 , … , 6 d i s p t o m a x ≤ 15   m m l i f e m i n ≥ 1.83 × 10 6   f r e q 1 ≥ 7.31   H z o p t i m a l   o b j e c t i v e    m i n m a s s   ,   m i n d i s p t o m a x   ,   m a x l i f e m i n  
式中：DVi 为第i个设计变量的取值；DVi max和DVi min分别为第i个设计变量取值的上限和下限；stressj bd max为CTF结构第j种材料的部件在弯曲工况下所受的最大应力；stressj to max为CTF结构第j种材料的部件在扭转工况下所受的最大应力；stressj bk max为CTF结构第j种材料的部件在制动工况下所受的最大应力；stressj tn max为CTF结构第j种材料的部件在转弯工况下所受的最大应力；[σ j ]为CTF结构第j种材料的许用应力；disp to max为扭转工况下车架部分的最大位移；lifemin为CTF结构的最小疲劳循环次数；freq1为CTF结构的1阶模态频率；mass是CTF结构的质量。
3.3.3 试验设计和近似模型的建立
（1）试验设计矩阵。可扩展的格栅序列（Mels）法是一种准随机序列、无差别序列的方法，它是在空间内均匀撒点，能最大限度地避免团块和空白区间的出现，对于结构疲劳寿命这种高度非线性的响应面，Mels方法相比拉丁超立方采样方法具有更好的空间填充效果。因此本文选用Mels方法对CTF结构的21个设计变量进行样本采集，总计279组样本点。构造的试验设计矩阵如表4所示。
（2）试验设计结果。将试验设计矩阵中的279组样本点分别赋予给有限元模型进行仿真分析和计算，获得对应响应量的值。响应量包括CTF结构的质量、4种工况下CTF结构的最大应力、CTF结构的低阶模态频率、CTF结构的疲劳寿命以及扭转工况下车架部分的最大变形，计算得到的结果如表5所示。
（3）近似模型的建立。试验设计完成后，下一步须拟合出一个近似模型，从而更高效地寻找最优解。CTF结构的质量、弯曲、扭转、制动工况下的最大应力和疲劳寿命以及车架在扭转工况下的最大位移采用最小二乘法进行拟合，CTF结构在转弯工况下的最大应力采用移动最小二乘法进行拟合，1阶模态频率采用径向基函数响应面拟合算法进行拟合。响应面拟合完成之后，须对响应面的拟合精度进行评估，一般用决定系数（R 2）评价响应面的拟合精度，其值越接近于1，表明拟合精度越高。本文各响应量的决定系数R 2如表6所示。
3.3.4 多目标优化设计
本文采用全局响应面法进行优化设计，其广泛适用于多目标优化领域，对于连续变量、离散变量和混合类型变量都具有较好的全局搜索能力。本文共进行500次迭代运算，最终得到Pareto最优解集，如图15所示。
由图15可知，CTF结构的轻量化与扭转刚度和疲劳寿命相互冲突，不存在多目标的最优解。车架的扭转刚度对包括车辆操纵稳定性[19]在内的多项性能影响显著，因此在车架轻量化优化设计过程中应尽可能保证车架扭转刚度不下降。根据中华人民共和国商务部颁布的《机动车强制报废标准规定》，载货汽车的安全行驶里程应当超过70万km，车架作为车辆承载的核心部件，应具有与车辆服役期限相当的疲劳寿命，因此本文选择车架在扭转刚度不下降、疲劳寿命满足法规要求（1.25倍安全系数下）并且满足其他约束条件下，CTF结构质量最小的解作为最终妥协解，再依据车架的制造工艺要求将方案中变量采用向上取整的方式进行圆整，得到CTF结构各个纵横梁以及连接板厚度，如表7所示。
4 优化后CTF结构性能分析对比
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为验证CTF结构多目标优化设计结果的可信度，将上文得到的最优解代入有限元模型进行仿真运算，得到最终CTF结构各性能参数以及疲劳寿命，如图16所示，由于篇幅限制，图中仅列出最危险的满载扭转工况下的位移与应力云图、1阶模态振型图和CTF结构多工况疲劳分析得到的各节点疲劳寿命云图，完整结果以及与对标车架的对比信息在表8中列出。
根据表8中的对比结果可知，优化后的CTF结构在保证多工况疲劳载荷下安全行驶百万公里且大多数性能有提升的前提下，相较于传统的车架与电池舱分离设计轻量高达14.09%，其中车架部分也轻量高达10.34%，轻量化效果显著。这主要得益于CTF结构的独特设计，它将动力电池舱与车架融为一体，使得电池舱与车架之间相互作用，从而显著提升了整体的强度与刚度。此外，这一设计还减少了零部件的数量。值得注意的是，尽管CTF结构在紧急转弯工况下的最大变形出现了38.05%的劣化，这主要是由于动力电池的集中布置所导致，然而8.09 mm的变形量仍处于车架许用的最大变形范围之内。因此，CTF结构仍然能够满足安全行驶的需求。
5 结论
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（1）建立了某电动载货车车架的有限元模型，并进行了车架模态试验以验证所建有限元模型的准确性，通过有限元分析获得了车架静力学性能及低阶模态性能，为后续轻量化与疲劳寿命集成优化设计提供了基础。
（2）创新性地提出了综合考虑匀速、加速、制动和转弯的多工况疲劳分析方法，通过道路实车载荷测量试验构建了多工况疲劳分析载荷谱，成功完成了研究对象的疲劳寿命高精度预测分析。
（3）提出了一种车架与电池舱一体化（cell to frame-简称“CTF”）的创新结构，将动力电池舱与车架集成为一体，实现了两者之间结构强度与刚度的相互增强，大幅提升了车架整体结构的性能。经过轻量化与疲劳寿命多目标集成优化设计后，在CTF结构满足性能要求的条件下，实现轻量139.95 kg，降低14.09%，展现出CTF结构在实际工程应用中巨大的潜力和价值。
基金
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  • *国家重点研发计划(2022YFB2503502)
  • 吉林大学研究生创新基金资助项目(2024CX078)
文献
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2024年第46卷第12期
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doi: 10.19562/j.chinasae.qcgc.2024.12.001
  • 接收时间：2024-04-30
  • 首发时间：2025-07-21
  • 出版时间：2024-12-25
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  • 收稿日期：2024-04-30
  • 修回日期：2024-06-19
基金
*国家重点研发计划(2022YFB2503502)
吉林大学研究生创新基金资助项目(2024CX078)
作者信息
    吉林大学，汽车底盘集成与仿生全国重点实验室，长春 130022

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王登峰，教授，博士，E-mail：。
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2种不同金属材料的力学参数
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Number of
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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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