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Article(id=1236276118311989903, tenantId=1146029695717560320, journalId=1235980550691926019, issueId=1236276104999268557, articleNumber=null, orderNo=null, doi=10.3969/j.issn.0253-6099.2025.04.033, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1740326400000, receivedDateStr=2025-02-24, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1772680795504, onlineDateStr=2026-03-05, pubDate=1753977600000, pubDateStr=2025-08-01, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1772680795504, onlineIssueDateStr=2026-03-05, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1772680795504, creator=13701087609, updateTime=1772680795504, updator=13701087609, issue=Issue{id=1236276104999268557, tenantId=1146029695717560320, journalId=1235980550691926019, year='2025', volume='45', issue='4', pageStart='1', pageEnd='200', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=1, specialIssue=null, createTime=1772680792331, creator=13701087609, updateTime=1772681498687, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1236279067746562719, tenantId=1146029695717560320, journalId=1235980550691926019, issueId=1236276104999268557, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1236279067746562720, tenantId=1146029695717560320, journalId=1235980550691926019, issueId=1236276104999268557, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=180, endPage=185, ext={EN=ArticleExt(id=1236276120115540768, articleId=1236276118311989903, tenantId=1146029695717560320, journalId=1235980550691926019, language=EN, title=Finite Element Analysis of Electron Beam Welding Performance of TU2 Oxygen-Free Copper, columnId=1236276108207902848, journalTitle=Mining and Metallurgical Engineering, columnName=MATERIALS, runingTitle=null, highlight=null, articleAbstract=

For reducing energy consumption while ensuring weld joint quality, the welding process parameters for electron beam welding of TU2 oxygen-free copper were optimized with SYSWELD simulation software, and a finite element model with appropriate boundary conditions was established for a 30-mm-thick TU2 copper plate. A heat source model was determined based on the actual situation of electron beam welding, and simulation analysis was made by imputing varied energy consumption value in the welding process, with the obtained simulation results compared with actual welding results. It is shown that with a double-ellipsoidal heat source input of 1260 J/mm and a 3D Gaussian heat source input of 5 000 J/mm, a full penetration weld with the lowest energy consumption can be achieved. The simulation results show that the obtained morphology of molten pool is almost the same with that in the actual welding, proving that the welding parameters set in the simulation analysis are feasible for TU2 welding. It is concluded that this study can provide a reliable reference for optimizing the parameters in welding of TU2 oxygen-free copper.

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为了在保证焊接接头质量的同时降低焊接能量消耗，通过SYSWELD仿真软件对TU2无氧铜电子束焊接时的焊接工艺参数进行优化。建立了30 mm厚TU2无氧铜板焊接模型与边界条件，根据电子束焊接的实际情况确定热源模型，改变焊接过程中能量消耗数值进行焊接仿真分析，并与实际焊接结果进行对比验证。结果表明，当双椭球热源能量输入为1 260 J/mm、3D高斯热源能量输入为5 000 J/mm时，不仅能保证铜板焊透，而且焊接消耗能量低，仿真得到的焊接熔池形貌和实际焊接结果基本一致，证明仿真设定的焊接参数在TU2焊接中的可行性，可为TU2焊接工艺参数优化提供依据。

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王慧纯（1999—），女，江西抚州人，硕士研究生，主要从事矿山机械和特种焊接研究。E-mail：
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尹中会（1970—），女，安徽六安人，副教授，硕士研究生导师，主要从事矿山机械和特种焊接研究。E-mail：

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尹中会（1970—），女，安徽六安人，副教授，硕士研究生导师，主要从事矿山机械和特种焊接研究。E-mail：

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尹中会（1970—），女，安徽六安人，副教授，硕士研究生导师，主要从事矿山机械和特种焊接研究。E-mail：

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Welded Pipe and Tube, 2022, 45(6): 14-18., articleTitle=Electron beam welding test and analysis of oxygen-free copper, refAbstract=null)], funds=[Fund(id=1236348229227442537, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1236276118311989903, awardId=2021SW1005, language=CN, fundingSource=安徽省重点实验室开放基金(2021SW1005), fundOrder=null, country=null)], companyList=[AuthorCompany(id=1236348221216322330, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1236276118311989903, xref=1., ext=[AuthorCompanyExt(id=1236348221220516635, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1236276118311989903, companyId=1236348221216322330, language=EN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=1.School of Mechanical Engineering, Anhui University of Science and Technology, Huainan 232001, Anhui, China), AuthorCompanyExt(id=1236348221228905244, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1236276118311989903, companyId=1236348221216322330, language=CN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=1.安徽理工大学　机械工程学院，安徽　淮南　232001)]), AuthorCompany(id=1236348221400871719, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1236276118311989903, xref=2., ext=[AuthorCompanyExt(id=1236348221409260328, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1236276118311989903, companyId=1236348221400871719, language=EN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=2.Anhui Provincial Key Laboratory of Special Welding Technology, Institute of Plasma Physics, Chinese Academy of Science, Huainan 232000, Anhui, China), AuthorCompanyExt(id=1236348221417648938, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1236276118311989903, companyId=1236348221400871719, language=CN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=2.中国科学院等离子体物理研究所　特种焊接技术安徽省重点实验室，安徽　淮南　232000)])], figs=[ArticleFig(id=1236348225393848450, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1236276118311989903, language=EN, label=Fig.1, caption=Schematic diagram of grid in simulation model, figureFileSmall=G+jK7hY8UlaSXGf1H98VRg==, figureFileBig=h5Z6D5WQwWbo8XvS+YP1mw==, tableContent=null), ArticleFig(id=1236348225532260490, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1236276118311989903, language=CN, label=图1, caption=仿真网格模型示意图, figureFileSmall=G+jK7hY8UlaSXGf1H98VRg==, figureFileBig=h5Z6D5WQwWbo8XvS+YP1mw==, tableContent=null), ArticleFig(id=1236348225687449742, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1236276118311989903, language=EN, label=Fig.2, caption=Schematic diagram of boundary condition, figureFileSmall=H8iTzz8PZ9sOdYxHSx+6Bg==, figureFileBig=nmRtA0HmdDWX9CQMQpVfMQ==, tableContent=null), ArticleFig(id=1236348225762947220, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1236276118311989903, language=CN, label=图2, caption=边界条件示意图, figureFileSmall=H8iTzz8PZ9sOdYxHSx+6Bg==, figureFileBig=nmRtA0HmdDWX9CQMQpVfMQ==, tableContent=null), ArticleFig(id=1236348225918136473, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1236276118311989903, language=EN, label=Fig.3, caption=Composite heat source model, figureFileSmall=QlQ9WdFPXoqcwnGr/Z4fsg==, figureFileBig=28Q0ZsVg+rf7yGJ9hkKIYQ==, tableContent=null), ArticleFig(id=1236348226077520037, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1236276118311989903, language=CN, label=图3, caption=复合热源模型, figureFileSmall=QlQ9WdFPXoqcwnGr/Z4fsg==, figureFileBig=28Q0ZsVg+rf7yGJ9hkKIYQ==, tableContent=null), ArticleFig(id=1236348226207543472, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1236276118311989903, language=EN, label=Fig.4, caption=Temperature fields in the middle stage of three sets of welding simulation, figureFileSmall=qBdECNwWKSwhQPUO1SGomQ==, figureFileBig=MtKKZ7GFX3oupRLxWjKj+g==, tableContent=null), ArticleFig(id=1236348226375315640, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1236276118311989903, language=CN, label=图4, caption=3组焊接仿真中段的温度云场

（a）A组；（b）B组；（c）C组

, figureFileSmall=qBdECNwWKSwhQPUO1SGomQ==, figureFileBig=MtKKZ7GFX3oupRLxWjKj+g==, tableContent=null), ArticleFig(id=1236348226530504895, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1236276118311989903, language=EN, label=Fig.5, caption=Local temperature fields in three sets of welding simulation after cooling for 3 600 seconds, figureFileSmall=rtA/xo9mPPrsLEi35FPk6Q==, figureFileBig=l6DS3QVQSLyrDp+DZxjd+A==, tableContent=null), ArticleFig(id=1236348226647945418, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1236276118311989903, language=CN, label=图5, caption=3组焊接仿真冷却3 600 s时的局部温度云场

（a）A组；（b）B组；（c）C组

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（a）t=30 s；（b）t=50 s；（c）t=1 700 s

, figureFileSmall=mnr9LYsDbDg1UgKsxUSlRw==, figureFileBig=1zZwb3hZFzKOwQyPJn6aag==, tableContent=null), ArticleFig(id=1236348227096735979, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1236276118311989903, language=EN, label=Fig.7, caption=Residual stress distribution after welding in three sets of simulation, figureFileSmall=W6yc8dgCvZCtfptzJCkOfg==, figureFileBig=u8BLrdKhByGmR37bIstUmQ==, tableContent=null), ArticleFig(id=1236348227239342321, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1236276118311989903, language=CN, label=图7, caption=3组焊接模拟焊后的残余应力云图

（a）A组；（b）B组；（c）C组

, figureFileSmall=W6yc8dgCvZCtfptzJCkOfg==, figureFileBig=u8BLrdKhByGmR37bIstUmQ==, tableContent=null), ArticleFig(id=1236348227360977143, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1236276118311989903, language=EN, label=Fig.8, caption=Transverse residual stress distribution after welding in three sets of welding simulation, figureFileSmall=M4D35hnjsU0/3BtcdQEOgg==, figureFileBig=F0NNvT83C2Y/nmaqtpcr7w==, tableContent=null), ArticleFig(id=1236348227461640444, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1236276118311989903, language=CN, label=图8, caption=3组焊接仿真焊后横向残余应力云图

（a）A组；（b）B组；（c）C组

, figureFileSmall=M4D35hnjsU0/3BtcdQEOgg==, figureFileBig=F0NNvT83C2Y/nmaqtpcr7w==, tableContent=null), ArticleFig(id=1236348227658772744, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1236276118311989903, language=EN, label=Fig.9, caption=Longitudinal residual stress distribution after welding in three set of simulation, figureFileSmall=YUnsZWuaftQ0lv6PZZV63w==, figureFileBig=bExpIqpaq5LCYo8qRe97Pg==, tableContent=null), ArticleFig(id=1236348227797184784, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1236276118311989903, language=CN, label=图9, caption=3组焊接仿真焊后纵向残余应力云图

（a）A组；（b）B组；（c）C组

, figureFileSmall=YUnsZWuaftQ0lv6PZZV63w==, figureFileBig=bExpIqpaq5LCYo8qRe97Pg==, tableContent=null), ArticleFig(id=1236348227914625303, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1236276118311989903, language=EN, label=Fig.10, caption=Comparison of morphology of molten pool between actual and simulated welding, figureFileSmall=coDu9NPTtF7Pg2V+uAysVw==, figureFileBig=JDblRgypxzQD0Qql83oA0g==, tableContent=null), ArticleFig(id=1236348228061425950, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1236276118311989903, language=CN, label=图10, caption=实际焊接熔池形貌与仿真结果对比

（a）A组；（b）B组；（c）C组

, figureFileSmall=coDu9NPTtF7Pg2V+uAysVw==, figureFileBig=JDblRgypxzQD0Qql83oA0g==, tableContent=null), ArticleFig(id=1236348228166283557, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1236276118311989903, language=EN, label=Table 1, caption=

Data checking of simulation model

, figureFileSmall=null, figureFileBig=null, tableContent=
组别3D高斯热源能量输入/（J·mm－1）双椭球热源能量输入/（J·mm－1）仿真结果
13 0003 000未焊透
24 0002 000未焊透
35 0001 000未焊透
43 5003 000未焊透
54 5002 000焊透
65 5001 000焊透
74 0002 500未焊透
85 0001 500焊透
95 0001 260焊透
105 0001 250未焊透
115 2601 000未焊透
124 2602 000未焊透
134 0002 260未焊透
), ArticleFig(id=1236348228283724079, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1236276118311989903, language=CN, label=表1, caption=

仿真校核数据

, figureFileSmall=null, figureFileBig=null, tableContent=
组别3D高斯热源能量输入/（J·mm－1）双椭球热源能量输入/（J·mm－1）仿真结果
13 0003 000未焊透
24 0002 000未焊透
35 0001 000未焊透
43 5003 000未焊透
54 5002 000焊透
65 5001 000焊透
74 0002 500未焊透
85 0001 500焊透
95 0001 260焊透
105 0001 250未焊透
115 2601 000未焊透
124 2602 000未焊透
134 0002 260未焊透
), ArticleFig(id=1236348228422136122, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1236276118311989903, language=EN, label=Table 2, caption=

Three sets of heat inputs in oxygen-free copper welding simulation

, figureFileSmall=null, figureFileBig=null, tableContent=
组别3D高斯热源能量输入/（J·mm－1）双椭球热源能量输入/（J·mm－1）
A4 0001 260
B5 0001 260
C5 0002 260
), ArticleFig(id=1236348228543770943, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1236276118311989903, language=CN, label=表2, caption=

3组无氧铜焊接仿真热源能量输入

, figureFileSmall=null, figureFileBig=null, tableContent=
组别3D高斯热源能量输入/（J·mm－1）双椭球热源能量输入/（J·mm－1）
A4 0001 260
B5 0001 260
C5 0002 260
), ArticleFig(id=1236348228648628552, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1236276118311989903, language=EN, label=Table 3, caption=

Welding simulation results

, figureFileSmall=null, figureFileBig=null, tableContent=
组别熔池顶部宽度/mm熔池中部宽度/mm熔池底部宽度/mm
A5.54.0（深3.0 mm处）0.62（深26 mm处）
B7.84.6（深3.5 mm处）1.20（深30 mm处）
C8.75.9（深4.0 mm处）2.30（深30 mm处）
), ArticleFig(id=1236348228774457681, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1236276118311989903, language=CN, label=表3, caption=

焊接仿真结果

, figureFileSmall=null, figureFileBig=null, tableContent=
组别熔池顶部宽度/mm熔池中部宽度/mm熔池底部宽度/mm
A5.54.0（深3.0 mm处）0.62（深26 mm处）
B7.84.6（深3.5 mm处）1.20（深30 mm处）
C8.75.9（深4.0 mm处）2.30（深30 mm处）
), ArticleFig(id=1236348228883509590, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1236276118311989903, language=EN, label=Table 4, caption=

Actual welding test results

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组别熔池顶部宽度/mm熔池中部宽度/mm熔池底部宽度/mm
A53.0（深3.0 mm处）0.5（深26 mm处）
B73.5（深3.5 mm处）0.7（深30 mm处）
C85.0（深4.0 mm处）1.5（深30 mm处）
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实际焊接试验结果

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组别熔池顶部宽度/mm熔池中部宽度/mm熔池底部宽度/mm
A53.0（深3.0 mm处）0.5（深26 mm处）
B73.5（深3.5 mm处）0.7（深30 mm处）
C85.0（深4.0 mm处）1.5（深30 mm处）
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TU2无氧铜的真空电子束焊接性能的有限元数值模拟分析
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尹中会 1 , 王慧纯 1 , 王少秋 1 , 马建国 2 , 刘振飞 2
矿冶工程杂志 | 材料 2025,45(4): 180-185
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矿冶工程杂志 | 材料 2025, 45(4): 180-185
TU2无氧铜的真空电子束焊接性能的有限元数值模拟分析
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尹中会1 , 王慧纯1 , 王少秋1, 马建国2, 刘振飞2
作者信息
  • 1.安徽理工大学　机械工程学院，安徽　淮南　232001
  • 2.中国科学院等离子体物理研究所　特种焊接技术安徽省重点实验室，安徽　淮南　232000

    • 尹中会（1970—），女，安徽六安人，副教授，硕士研究生导师，主要从事矿山机械和特种焊接研究。E-mail：

通讯作者:

王慧纯（1999—），女，江西抚州人，硕士研究生，主要从事矿山机械和特种焊接研究。E-mail：
Finite Element Analysis of Electron Beam Welding Performance of TU2 Oxygen-Free Copper
Zhonghui YIN1 , Huichun WANG1 , Shaoqiu WANG1, Jianguo MA2, Zhenfei LIU2
Affiliations
  • 1.School of Mechanical Engineering, Anhui University of Science and Technology, Huainan 232001, Anhui, China
  • 2.Anhui Provincial Key Laboratory of Special Welding Technology, Institute of Plasma Physics, Chinese Academy of Science, Huainan 232000, Anhui, China
出版时间: 2025-08-01 doi: 10.3969/j.issn.0253-6099.2025.04.033
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摘要
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为了在保证焊接接头质量的同时降低焊接能量消耗，通过SYSWELD仿真软件对TU2无氧铜电子束焊接时的焊接工艺参数进行优化。建立了30 mm厚TU2无氧铜板焊接模型与边界条件，根据电子束焊接的实际情况确定热源模型，改变焊接过程中能量消耗数值进行焊接仿真分析，并与实际焊接结果进行对比验证。结果表明，当双椭球热源能量输入为1 260 J/mm、3D高斯热源能量输入为5 000 J/mm时，不仅能保证铜板焊透，而且焊接消耗能量低，仿真得到的焊接熔池形貌和实际焊接结果基本一致，证明仿真设定的焊接参数在TU2焊接中的可行性，可为TU2焊接工艺参数优化提供依据。

TU2  /  无氧铜  /  焊接  /  电子束焊接  /  焊接熔池  /  温度场  /  应力场  /  仿真分析

For reducing energy consumption while ensuring weld joint quality, the welding process parameters for electron beam welding of TU2 oxygen-free copper were optimized with SYSWELD simulation software, and a finite element model with appropriate boundary conditions was established for a 30-mm-thick TU2 copper plate. A heat source model was determined based on the actual situation of electron beam welding, and simulation analysis was made by imputing varied energy consumption value in the welding process, with the obtained simulation results compared with actual welding results. It is shown that with a double-ellipsoidal heat source input of 1260 J/mm and a 3D Gaussian heat source input of 5 000 J/mm, a full penetration weld with the lowest energy consumption can be achieved. The simulation results show that the obtained morphology of molten pool is almost the same with that in the actual welding, proving that the welding parameters set in the simulation analysis are feasible for TU2 welding. It is concluded that this study can provide a reliable reference for optimizing the parameters in welding of TU2 oxygen-free copper.

TU2  /  oxygen-free copper  /  welding  /  electron beam welding  /  molten pool  /  temperature field  /  stress field  /  simulation analysis
尹中会, 王慧纯, 王少秋, 马建国, 刘振飞. TU2无氧铜的真空电子束焊接性能的有限元数值模拟分析. 矿冶工程杂志, 2025 , 45 (4) : 180 -185 . DOI: 10.3969/j.issn.0253-6099.2025.04.033
Zhonghui YIN, Huichun WANG, Shaoqiu WANG, Jianguo MA, Zhenfei LIU. Finite Element Analysis of Electron Beam Welding Performance of TU2 Oxygen-Free Copper[J]. Mining and Metallurgical Engineering, 2025 , 45 (4) : 180 -185 . DOI: 10.3969/j.issn.0253-6099.2025.04.033
正文
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国际热核聚变实验堆（ITER）计划旨在通过托卡马克装置验证核聚变作为清洁能源的可行性，集成了国际聚变能源研究的最新成果，综合了大型超导磁体技术、中能高流强加速器技术等世界顶尖技术[1]。我国承担ITER项目中的任务之一是制造超导磁体馈线（Feeder）系统，Feeder系统的重要部件之一是高温超导电流引线，其中室温终端、翅片换热器和高温超导段均使用TU2无氧铜[2]。无氧铜材料熔点较高，又具有极好的导热性，常规焊接方法热量不集中导致热量瞬间散失，并且厚度越大热量散失越明显，从而使焊接难度大大增加。近年来，有许多学者研究了铜及铜合金与异种金属的焊接性能，使用的主要焊接方式[3]有激光焊、搅拌摩擦焊、MIG焊等，但对于无氧铜电子束焊接研究较少。真空电子束焊接相较于传统焊接拥有更高的能量级和能效比，能量损失更小，并且避免了空气污染，较其他热源更容易控制和计算，更容易实现精准焊接[4]。电子束焊接为高能束焊接，属于自熔焊接，无需焊材填充，主要依赖调整焊接工艺参数来降低热裂纹倾向。因此，本文使用有限元软件仿真分析与试验相结合的方法进一步优化焊接参数。
1　仿真模型的建立与焊接参数的设置
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1.1　仿真试验条件及几何模型
近年来，科研人员在使用SYSWELD软件的过程中发现该软件在建模与网格划分上操作复杂，不够直观，针对这一问题，ESI集团研发了Visual-Environment系列软件，使软件建模、网格划分、前后处理更加直观方便，但其核心仍为SYSWELD分析系统。本文采用Visual-Environment软件进行建模、网格划分和处理操作，并用SYSWELD软件对TU2无氧铜电子束焊接接头的温度场、应力场和变形场进行模拟分析，探讨焊接工艺参数对焊接接头残余应力、焊接变形的影响。
首先建立焊接模型。电子束焊接的能量可以调节，被焊接金属厚度范围为0.05～300 mm，可以不开坡口，一次焊接成型，因此直接建立理想焊件模型。试板尺寸为150 mm×150 mm×30 mm。电子束焊接光束集中在对接的焊缝处，为了使仿真更加准确和方便，网格划分时焊接区域的网格需要更加精细，远离焊接区域的网格需稍微稀疏（即从板材边缘到焊缝区域，网格细化程度逐渐提高），最终建立如图1所示的仿真网格模型。
1.2　边界条件与材料性能参数
边界条件主要是确保焊件不发生刚性位移，同时不产生过度约束，焊接时，要对焊件X方向、Y方向、Z方向进行位移约束，固定住其6个自由度，不让其产生位移。边界条件如图2所示，两侧为装夹位置。
本文研究所采用材料为TU2无氧铜，材料的高温物性参数通过查阅航空航天材料手册及外延得到，为了简化计算，密度取8 930 kg/m3，泊松比取0.33。
1.3　热源模型
焊缝的热力学耦合由材料的相变、高温热集中度和热传导组成，焊接温度场是影响焊缝组织性能的主要参数，是影响焊缝质量的关键。因此要保证其仿真计算的可靠性，必须保证焊接热循环曲线的准确性。合理的热源模型是计算精度的关键。当前可采用的热源模型有面热源、柱热源、双椭球热源、高斯锥体热源、高斯面热源、混合热源以及其他热源。电子束焊接特有的“匙孔”效应会导致焊缝成型的机理更加复杂，熔池内部存在空腔等各种物化反应[5]。因此选择合适的热源模型能够更好地反映电子束焊接的熔池特征。
随着电子束焊接有限元研究的逐步推进，单一热源已经不能满足研究需要，也无法反映焊接过程中的真实情况，组合热源模型更适合电子束的有限元模拟，焊接焊缝的形貌大多呈V形，因此可以采用双椭球热源模型和高斯面热源模型的复合模型。复合热源模型见图3。
双椭球热源模型的前、后半部分椭球内热源分布函数为：
式中：x，y，z分别为空间点的坐标值；f1和f2分别作为热流密度的分布函数，f1+f2=2；Q为输入的热源有效功率，Q=ηUI（η为热源效率；U为焊接电压，kV；I为焊接电流，mA）；a1、a2、c均为定义椭圆的参数，互不影响，可取不同的值，其确定方法见文献[6]。
高斯面热源模型为：
式中：e为常数，取2.718；r0为光束直径；r为试件上任意点至电弧加热斑点的距离；ze、zi分别为试件上、下表面z轴坐标；re、ri分别为板材上、下表面热流密度半径。
1.4　焊接参数
焊接过程中，电子束流高速冲击试件产生巨大热量，使焊件温度产生剧烈变化，导致焊接残余应力和焊接变形的产生。本文在3 mm/s的焊接速度下，通过改变电子束流的大小对30 mm厚TUZ无氧铜板进行焊接模拟。焊接热源输入量计算公式为：
式中，v为焊接速度，mm/s。
根据已完成试验[7]可知，加速电压150 kV、电子束流120 mA时可焊透无氧铜板。焊接速度为3 mm/s时，由公式计算可得，复合热源总能量输入为6 000 J/mm，具体能量输入通过仿真软件调整复合热源数值获得，挑选具有代表性的13组仿真校核数据汇成表1。由表1可知，焊透30 mm厚无氧铜板所需的最低能量为：双椭球热源能量输入1 260 J/mm、3D高斯热源能量输入5 000 J/mm。
为研究热源数值大小对无氧铜的温度场与应力场分布的影响，以能量输入为变量，进行3组温度场与应力场的仿真分析对比，热源能量输入数据如表2所示。
2　焊接仿真温度场模拟分析
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为了更好地预测与评估残余应力与变形对焊接强度的影响，焊接温度场的模拟准确性至关重要。图4为3组焊接仿真中段（焊接稳定25 s时）的温度云场分布。焊接温度云场沿焊缝对称分布，截取左侧图，余下图同理。由图4可知，由于电子束焊接能力集中且无氧铜导热率较高，在焊接过程中，3组焊接热影响区整体呈椭圆状，区域较小，且随着热源能量输入增加而增大。
图5为3组焊接仿真真空冷却3 600 s时的局部温度云场。由图5可知，冷却3 600 s后，A组温度为36 ℃，B组温度为39 ℃，C组温度为42 ℃。出现这种情况的原因是在真空环境下只有热辐射在进行散热，冷却速度慢，3组样品冷却后温度递增也是热输入的增加使得热辐射散热需要更多的时间。
3　焊接仿真应力场模拟分析
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由于3组模拟B组为最佳参数，取B组模拟进行焊接残余应力规律的研究，不同时刻的焊接应力云图如图6所示。由图6可知，t=30 s时，焊接残余应力主要分布在焊接热源经过区域和边界条件加持区域，距离焊接热源较远的区域为无应力状态，热源中心熔池区域也处于无应力状态，这是因为在热源的加载下熔池区域内的金属状态为熔融液态，而液态金属是不存在残余应力的。t=50 s时，在焊接结束时刻，残余应力主要存在于焊缝以及焊缝两边热影响区域，从焊接起始点到热源经过的区域残余应力较大，焊接刚结束时刻在结束点的残余应力较低。这是由于焊接刚刚结束，材料还在处于较高的温度状态，焊缝金属还没有冷却，残余应力还没有形成。t=1 700 s时，焊接初始点的残余应力开始降低，焊缝两边的残余应力由初始点到结束点逐渐增大，随着距离焊缝处越来越远，残余应力也越来越低。
图7为3组焊接模拟焊后的残余应力云图。从图7可以看出，t=3600 s时，残余应力在热影响区域最大，在热影响区域和边界条件加持区域之间残余应力逐渐降低，在充分冷却后边界加持区域也有残余应力的产生，比焊接过程中只有边界加持产生的残余应力大，这是由于热源影响到边界加持区域，残余应力增大。且随着焊接时电子束能量增加，最大残余应力区域逐渐增大。
在焊接过程中，焊接样板由于受到非线性温度场变化产生的热应力而产生塑性形变，在焊接完成后，由于温度降低，一部分热应力被释放，但残余的应力仍在焊件内存在，从而导致焊件出现形变。因此研究焊接板材焊后的横向与纵向残余应力是非常有必要的。
图8为3组焊接板材的焊后横向残余应力云图。由图8可知，焊件的横向残余应力主要集中在焊缝周围并表现为拉应力，其应力值大小由焊缝中心处向外递减。随着电子束能量增加，横向残余应力增大，3组焊接板材的最大拉应力分别为309、343和334 MPa。
图9为3组焊接板材的焊后纵向残余应力云图。由图9可知，纵向残余应力主要集中在焊缝、热影响区域与边界条件加持区域。且随着输入能量增加，板材的纵向残余应力逐渐增大。焊缝两侧与装夹侧的纵向残余应力表现为拉应力，而焊缝处的区域表现为压应力，纵向残余应力的截面图清晰表现了焊缝处拉应力与压应力的范围，3种焊接板材的纵向最大拉应力分别为173、190和212 MPa。
4　仿真结果验证
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为了验证不同热源能量输入下的TU2无氧铜真空电子束焊接的温度场与应力场的仿真结果的可靠性，本文采用优化后焊接工艺参数得出的仿真结果与实际试验结果[7]进行了比较。采用特种焊接技术安徽省重点实验室的真空电子束焊接系统，试验材料为150 mm×150 mm×30 mm的TU2无氧铜板，焊接设备为高压真空电子束焊接系统，电子束功率0～60 kW，真空室容积66 m3，采用150 kV的加速电压，3组焊接电子束流分别为100、120与140 mA。3组熔池数据如表3与表4所示。结果显示，试验材料的形貌、尺寸与仿真模型基本一致。
3组试验结果和有限元模拟结果对比，试验的熔池形貌均略小于模拟的熔池形貌，误差在1 mm左右。这是由于仿真结果是在完全理想的情况下进行的，并且对仿真热源参数进行了优化调整。受实际条件限制，试验使用的电子束流大小有些许不同，导致试验结果与模拟结果的差异，但在焊缝熔池轮廓上试验结果与仿真结果都是“铁钉”形貌，二者基本吻合。图10为真空电子束焊接熔池形貌与仿真结果对比图，上部为实际焊接体，下部为仿真结果。
5　结论
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1）采用高斯面热源与双椭球热源的复合热源模型能够较好地表现出真空电子束焊接的匙孔效应。
2）3D高斯热源数值为5 000 J/mm、双椭球热源数值为1 260 J/mm时，能在保证铜板焊透的同时能量输入最小。
3）仿真热源能量输入数值略大于实际焊接热源能量输入值，但熔池形貌特征基本吻合，验证了本文所建立的热源模型与仿真的准确性。
基金
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  • 安徽省重点实验室开放基金(2021SW1005)
文献
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doi: 10.3969/j.issn.0253-6099.2025.04.033
  • 接收时间：2025-02-24
  • 首发时间：2026-03-05
  • 出版时间：2025-08-01
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  • 收稿日期：2025-02-24
基金
安徽省重点实验室开放基金(2021SW1005)
作者信息
    1.安徽理工大学　机械工程学院，安徽　淮南　232001
    2.中国科学院等离子体物理研究所　特种焊接技术安徽省重点实验室，安徽　淮南　232000

通讯作者:

王慧纯（1999—），女，江西抚州人，硕士研究生，主要从事矿山机械和特种焊接研究。E-mail：
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2种不同金属材料的力学参数
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鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
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