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Article(id=1210590156747305386, tenantId=1146029695717560320, journalId=1149653034449285133, issueId=1210590152548807015, articleNumber=null, orderNo=null, doi=10.16790/j.cnki.1009-9239.im.2024.09.017, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=research-article, receivedDate=1694448000000, receivedDateStr=2023-09-12, revisedDate=1699718400000, revisedDateStr=2023-11-12, acceptedDate=null, acceptedDateStr=null, onlineDate=1766556785045, onlineDateStr=2025-12-24, pubDate=1726761600000, pubDateStr=2024-09-20, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1766556785045, onlineIssueDateStr=2025-12-24, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1766556785045, creator=13701087609, updateTime=1766556785045, updator=13701087609, issue=Issue{id=1210590152548807015, tenantId=1146029695717560320, journalId=1149653034449285133, year='2024', volume='57', issue='9', pageStart='1', pageEnd='165', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1766556784044, creator=13701087609, updateTime=1766563998200, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1210620410958312217, tenantId=1146029695717560320, journalId=1149653034449285133, issueId=1210590152548807015, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1210620410958312218, tenantId=1146029695717560320, journalId=1149653034449285133, issueId=1210590152548807015, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=158, endPage=165, ext={EN=ArticleExt(id=1210590157015740857, articleId=1210590156747305386, tenantId=1146029695717560320, journalId=1149653034449285133, language=EN, title=Finite element analysis on thermo-mechanical effects of smooth aluminium sheathed cables under serpentine laying, columnId=1192878364340924664, journalTitle=Insulating Materials, columnName=Test and Analysis, runingTitle=null, highlight=null, articleAbstract=

In recent years, attentions on smooth aluminium sheathed cables has continued to increase in China, but at present, the researches on the laying of smooth aluminium sheathed cables are still insufficient. Conductor heating caused by thermo-mechanical stress during laying process of cable may cause safety problems. In this paper, a finite element model of smooth aluminium sheathed cable under vertical serpentine laying was established, and the thermo-mechanical effect of the cable was calculated and analyzed. The results show that the vertical serpentine laying of cable would generate serpentine arc lateral slip, making the axial force induced by thermal effect much smaller than that of the straight laying of cable, which meet the long-term safe operation conditions of cable. With the increase of temperature, the lateral slip of vertical serpentine laying gradually increase, the increase trend is consistent with the theoretical calculation results, and the axial force changes from tensile force to compressive force and then gradually increase. By appropriately increasing the arc width and semi-serpentine pitch of vertical serpentine laying of cable, the axial force of cable can be reduced.

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近些年我国对平滑铝护套电缆的关注度持续提高，但目前相关敷设方面的研究尚有不足。针对电缆敷设过程中由于导体发热引起的热机械应力可能造成的安全问题，本文建立了平滑铝护套电缆在垂直蛇形敷设下的有限元模型，计算分析了垂直蛇形敷设情况下电缆的热机械效应。结果表明：垂直蛇形敷设电缆通过产生蛇形弧的侧向滑移，使其由于热效应引起的轴向力远小于直线敷设电缆，满足电缆长期安全运行条件；随着温度的升高，垂直蛇形敷设的侧向滑移量逐渐增大且增加趋势和理论计算结果相符，轴向力先从拉伸力转变为压缩力后逐渐增大；通过适当增大垂直蛇形敷设电缆的弧幅和半蛇形节距，可降低电缆产生的轴向力。

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李华强（1981-），男（汉族），陕西渭南人，副研究员，博士，主要从事绝缘、电缆、变压器方向的研究。
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金程逸畅（2000-），男（汉族），浙江金华人，硕士生，主要从事电力电缆多物理场仿真的研究。

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金程逸畅（2000-），男（汉族），浙江金华人，硕士生，主要从事电力电缆多物理场仿真的研究。

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金程逸畅（2000-），男（汉族），浙江金华人，硕士生，主要从事电力电缆多物理场仿真的研究。

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Distribution & Utilization,2009,26(6):1-5., articleTitle=Explanation on the snake laying design regulation of high voltage crosslinked cable, refAbstract=null)], funds=null, companyList=[AuthorCompany(id=1218262755744863085, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1210590156747305386, xref=1, ext=[AuthorCompanyExt(id=1218262755753251694, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1210590156747305386, companyId=1218262755744863085, language=EN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=1State Key Laboratory of Electrical Insulation and Power Equipment, Xi′an Jiaotong University, Xi′an 710049, China), AuthorCompanyExt(id=1218262755757445999, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1210590156747305386, companyId=1218262755744863085, language=CN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, 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电缆结构及材料厚度/mm外直径/mm
铜导体17.535.0
绝缘层20.075.0
缓冲层间隙1.578.0
平滑铝护套2.082.0
导电层外护套5.092.0
), ArticleFig(id=1218262764578066580, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1210590156747305386, language=CN, label=表1, caption=

电缆简化后结构参数

, figureFileSmall=null, figureFileBig=null, tableContent=
电缆结构及材料厚度/mm外直径/mm
铜导体17.535.0
绝缘层20.075.0
缓冲层间隙1.578.0
平滑铝护套2.082.0
导电层外护套5.092.0
), ArticleFig(id=1218262764653564055, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1210590156747305386, language=EN, label=Table 2, caption=Simulation results of force field at 90℃ under different laying methods, figureFileSmall=null, figureFileBig=null, tableContent=
电缆敷设方式铜导体最大应力/MPa铝护套最大应力/MPa轴向压缩力/N
垂直蛇形敷设31583 146.9
直线敷设62.5112.521 644.8
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90℃不同敷设方式下力场仿真结果

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电缆敷设方式铜导体最大应力/MPa铝护套最大应力/MPa轴向压缩力/N
垂直蛇形敷设31583 146.9
直线敷设62.5112.521 644.8
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平滑铝护套电缆蛇形敷设下热机械效应的有限元分析
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金程逸畅 1 , 李华春 2 , 任志刚 3 , 吴明 1 , 门业堃 3 , 高景晖 1 , 李华强 1
绝缘材料 | 测试与分析 2024,57(9): 158-165
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绝缘材料 | 测试与分析 2024, 57(9): 158-165
平滑铝护套电缆蛇形敷设下热机械效应的有限元分析
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金程逸畅1, 李华春2, 任志刚3, 吴明1, 门业堃3, 高景晖1, 李华强1
作者信息
  • 1西安交通大学 电工材料电气绝缘国家重点实验室,陕西 西安 710049
  • 2国网北京市电力公司,北京 100031
  • 3国网北京市电力公司电力科学研究院,北京 100075

    • 金程逸畅（2000-），男（汉族），浙江金华人，硕士生，主要从事电力电缆多物理场仿真的研究。

通讯作者:

李华强（1981-），男（汉族），陕西渭南人，副研究员，博士，主要从事绝缘、电缆、变压器方向的研究。
Finite element analysis on thermo-mechanical effects of smooth aluminium sheathed cables under serpentine laying
Chengyichang JIN1, Huachun LI2, Zhigang REN3, Ming WU1, Yekun MEN3, Jinghui GAO1, Huaqiang LI1
Affiliations
  • 1State Key Laboratory of Electrical Insulation and Power Equipment, Xi′an Jiaotong University, Xi′an 710049, China
  • 2State Grid Beijing Electric Power Company, Beijing 100031, China
  • 3Beijing Electric Power Research Institute of State Grid Beijing Electric Power Company, Beijing 100075, China
出版时间: 2024-09-20 doi: 10.16790/j.cnki.1009-9239.im.2024.09.017
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摘要
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近些年我国对平滑铝护套电缆的关注度持续提高，但目前相关敷设方面的研究尚有不足。针对电缆敷设过程中由于导体发热引起的热机械应力可能造成的安全问题，本文建立了平滑铝护套电缆在垂直蛇形敷设下的有限元模型，计算分析了垂直蛇形敷设情况下电缆的热机械效应。结果表明：垂直蛇形敷设电缆通过产生蛇形弧的侧向滑移，使其由于热效应引起的轴向力远小于直线敷设电缆，满足电缆长期安全运行条件；随着温度的升高，垂直蛇形敷设的侧向滑移量逐渐增大且增加趋势和理论计算结果相符，轴向力先从拉伸力转变为压缩力后逐渐增大；通过适当增大垂直蛇形敷设电缆的弧幅和半蛇形节距，可降低电缆产生的轴向力。

电力电缆  /  热机械效应  /  蛇形敷设  /  有限元分析  /  平滑铝护套

In recent years, attentions on smooth aluminium sheathed cables has continued to increase in China, but at present, the researches on the laying of smooth aluminium sheathed cables are still insufficient. Conductor heating caused by thermo-mechanical stress during laying process of cable may cause safety problems. In this paper, a finite element model of smooth aluminium sheathed cable under vertical serpentine laying was established, and the thermo-mechanical effect of the cable was calculated and analyzed. The results show that the vertical serpentine laying of cable would generate serpentine arc lateral slip, making the axial force induced by thermal effect much smaller than that of the straight laying of cable, which meet the long-term safe operation conditions of cable. With the increase of temperature, the lateral slip of vertical serpentine laying gradually increase, the increase trend is consistent with the theoretical calculation results, and the axial force changes from tensile force to compressive force and then gradually increase. By appropriately increasing the arc width and semi-serpentine pitch of vertical serpentine laying of cable, the axial force of cable can be reduced.

power cable  /  thermo-mechanical effect  /  serpentine laying  /  finite element analysis  /  smooth aluminium sheath
金程逸畅, 李华春, 任志刚, 吴明, 门业堃, 高景晖, 李华强. 平滑铝护套电缆蛇形敷设下热机械效应的有限元分析. 绝缘材料, 2024 , 57 (9) : 158 -165 . DOI: 10.16790/j.cnki.1009-9239.im.2024.09.017
Chengyichang JIN, Huachun LI, Zhigang REN, Ming WU, Yekun MEN, Jinghui GAO, Huaqiang LI. Finite element analysis on thermo-mechanical effects of smooth aluminium sheathed cables under serpentine laying[J]. Insulating Materials, 2024 , 57 (9) : 158 -165 . DOI: 10.16790/j.cnki.1009-9239.im.2024.09.017
正文
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0 引言
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随着城市化进程的加速，以交联聚乙烯为绝缘材料的电力电缆，由于其优异的性能，越来越广泛地应用于电力系统中[1-2]。同时随着电力需求的迅速增长，加剧了电缆所需承担的负荷电流。负荷电流的热效应和外界变化的温度导致电缆发生热胀冷缩，在电缆轴向上会产生非常庞大的热机械应力。热机械应力作用在电缆固定件及其支架上，使其面临被破坏的潜在风险[3]。由于受到热机械应力的作用，电缆金属护套在多次重复的变形弯曲下可能会发生疲劳应变和蠕变劣化[4-5]，而电缆则有可能会发生塑性变形，使其绝缘寿命和性能降低[6]。由此可见，热膨胀效应导致的热机械应力是影响电缆安全运行的重要因素，而电缆本体敷设方式在调控热机械应力方面起关键作用。
此外，我国高压交联聚乙烯电缆多采用波纹铝护套结构，因此波纹铝护套电缆在敷设方面的工程应用已较为成熟。但由于波纹铝护套电缆缓冲层烧蚀问题屡有发生，近些年我国对具有改善接触、提高散热和减轻质量等优点的平滑铝护套电缆的关注度持续提高，但对于平滑铝护套电缆的敷设问题，国内的相关理论研究和工程实践经验较少。
目前，国内在有关电缆蛇形敷设时热机械效应方面的研究主要通过经验公式的计算来指导工程实践，而对于真实工况下的电缆敷设问题进行的仿真分析较少，并缺乏针对平滑铝护套电缆敷设问题的研究。罗俊华等[7]分析计算了长距离大截面电缆线路的热机械效应，分析了电缆垂直蛇形敷设时温度、蛇形长度和蛇形弧幅对轴向力和蛇形弧侧向滑移量的影响；方建[8]推导了电缆热伸缩量的公式并对电缆蛇形敷设参数的选定给出了建议；徐伟等[9]分析了电缆蛇形敷设参数对电缆应力和应变的影响，讨论了选定蛇形敷设参数时应考虑的相关因素，并对比了在隧道中垂直蛇形和水平蛇形敷设方式的优缺点；张德等[10]使用COMSOL Multiphysics对垂直蛇形敷设电缆建立了热机械效应模型，用有限元方法分析了垂直蛇形敷设状态下电缆的应力和温度分布；刘英等[11]搭建了平滑铝护套XLPE电缆的四点弯曲三维仿真模型，研究了平滑铝护套XLPE电缆弯曲时的力学行为。
针对目前国内对于平滑铝护套电缆工程敷设过程中可能面临的热机械效应方面的问题，本文针对110 kV-800 mm2平滑铝护套电缆，建立了垂直蛇形敷设电缆的三维有限元模型，对垂直蛇形敷设下电缆的热机械效应进行仿真计算，研究电缆处于最大允许载流量工况下的位移、温度和应力分布，得到电缆在不同温度、弧幅和节距下轴向力和侧向滑移量的分布规律，为平滑铝护套电缆施工过程中敷设方式的选择提供参考。
1 电缆蛇形敷设模型建立
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1.1 蛇形敷设物理场模型
目前电缆的敷设方式按照敷设环境大致分为：直埋敷设、浅槽敷设、穿管敷设、电缆沟敷设、电缆隧道敷设和架空敷设。6种敷设方式均有可能由于受到热机械力的作用而对电缆及其附件造成损伤[6]。对于敷设在隧道或者电缆沟中的电缆，按照敷设形状可分为直线敷设和蛇形敷设[12]。
对于直线敷设的电缆，当电缆缆芯导体通过电流时，由于电流的热效应，会使得电缆整体温度升高，在热机械效应的作用下产生的形变会导致电缆中产生巨大的轴向力，有可能会损伤电缆本身并使得固定电缆的刚性连接件被破坏。电缆因热膨胀产生的轴向力F计算公式[13]如式（1）所示。
F=αΔθEA
式（1）中：α为电缆的线膨胀系数，℃-1；Δθ为电缆的温升，℃；E为电缆的杨氏模量，N/mm2；A为电缆的截面积，mm2。
图1为电缆蛇形敷设示意图。如图1所示，通过将电缆敷设成近似正弦曲线形状，电缆温升所产生的形变在很大程度上会转换为该段电缆蛇形弧侧向滑移，电缆的弯曲变形使得电缆产生的轴向力大幅减小，可有效提高电缆安全运行的可靠性。蛇形敷设电缆的侧向滑移量及轴向力可由公式（2）～（4）计算得出[14]。
n=B2+1.6αtL2-B
Fv1=+WL22B×0.8
Fv2=-8EIB2at2-8EI(B+n)2at2+WL22(B+n)×0.8
式（2）～（4）中：n为电缆的侧向滑移量，mm；t为温升，℃；B为蛇形弧幅，mm；L为半蛇形节距，mm；Fv1为电缆温度下降时蛇形弧轴向力；Fv2为电缆温度上升时蛇形弧轴向力；W为电缆单位长度的重量，N/mm；EI为电缆的弯曲刚度，N·mm2； “+”号代表拉伸力；“-”号代表压缩力。
1.2 电缆的仿真模型
本文以110 kV-800 mm2平滑铝套电缆为研究对象，电缆截面结构如图2所示。电缆从外到内依次分别为：导电层外护套、平滑铝护套、缓冲阻水层、绝缘屏蔽、XLPE绝缘、导体屏蔽、铜导体。其中平滑铝护套和铜导体是金属材料，其余为非金属材料。
为了降低模型的复杂程度，减少有限元计算量，需对电缆结构进行简化。电缆的导体屏蔽、XLPE绝缘和绝缘屏蔽通常采用三层共挤方式，它们的力学性能相似。在进行电缆结构的建模时，可以将这三层合并为一层，采用与绝缘层相同的力学参数。此外，本文主要针对电缆的热膨胀效应进行分析，在不影响仿真结果的基础上，对电缆缓冲阻水层进行合理简化，将缓冲阻水层分成两部分，即可压缩部分和不可压缩部分[11]。1 mm厚不可压缩部分归入绝缘层，1.5 mm厚可压缩部分用间隙进行等效，由此得到电缆简化后的结构参数，如表1所示。
1.3 蛇形敷设仿真模型
在电缆垂直蛇形敷设过程中，通常将蛇形节距设置在4～6 m之间，弧幅则取金属护套外径的1.5～2倍[5]。本文在此区间内选取半蛇形节距（L）为3 m、弧幅（B）为0.2 m的电缆进行建模。在电缆垂直蛇形敷设过程中，需在每个波峰位置使用夹具来固定电缆，而电缆的其他部分则处于自由状态，不受夹具限制。根据现场情况和相关标准，可以将电缆近似为三段圆弧拼接而成[15]。经过近似分析，中间段圆弧半径为11.5 m，旁边两段圆弧半径为11.2 m。建立的电缆三维模型如图3所示。
为了有效减少计算量，考虑到模型的对称性，将模型简化为1/4对称模型进行仿真分析。使用自动网格划分功能，对模型划分为四面体网格，这种网格划分方法可以保证网格质量和计算结果的精确度，同时减少计算时间和资源消耗。电缆的网格整体分布不均匀。在径向上，外侧网格分布相对中间更为密集，以确保电缆各层在厚度方向有两层以上网格以满足计算精确度需求。在轴向上，端面网格分布相比其他部位更为集中，两端区域是电缆最容易发生变形和损伤的地方，所以密集的网格分布可以更准确地捕捉到这些变形和损伤。
为了保证电缆可以在恶劣的情况下正常工作，应对电缆处于最大载流量负荷运行工况进行研究，分析电缆达到最高运行温度时产生的最大应力和应变。由于电缆运行时导体温度不能超过绝缘材料的长期允许最高工作温度，且交联聚乙烯的最高工作温度为90℃[16-17]，本文设置铜导体温度为90℃。在敷设的实际环境下，电缆外层暴露在空气中，符合第三类边界条件，即对流换热边界条件，设置环境温度为20℃，电缆外层和空气之间的对流换热系数为5 W/(m2·K)[18]。电缆内部各层之间按照热传导的方式进行热量交换。此外，由于缓冲阻水层可压缩部分简化成的间隙层并不代表实际工况下的空气间隙层，在热场分析中间隙层合并到绝缘层中充当导热载体。由于在波峰位置使用夹具来固定电缆，在对相邻波峰间的这段电缆进行分析时，应在电缆两端端面处设置固定约束的边界条件，并将整段电缆设置重力约束条件。
2 仿真结果及分析
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2.1 热场仿真结果
图4(a)是铜导体温度为90℃条件下的电缆内部温度分布截面图。由图4(a)可知，电缆中热量主要集中于铜导体和绝缘层中。铜导体整体温度为90℃，沿着电缆径向方向，温度逐渐降低。由于电缆绝缘层的热传导系数小，比热容大，绝缘层中温度下降幅值大。电缆最外层温度为60.1℃。
图4(b)是沿图4(a)所示截面中红色径向线的温度变化情况。由图4(b)可知，电缆径向温度曲线中心对称，中间层铜导体的温度最高，温度向外侧逐层递减。该折线图从对称中心线向两边由四段折线顺序连接，代表电缆内部由不同材料参数组成的四层简化结构。由于铜和铝是优良的导热体，温度基本保持不变，铜导体温度为90℃，铝导体温度为66.8℃。在非金属层中，温度沿径向方向逐渐递减，递减速率与材料的导热参数有关。
2.2 力场仿真结果
图5为垂直蛇形敷设电缆的位移分布图。由图5可知，除了电缆两端固定不动，其他部分均存在位移。沿电缆轴线方向，电缆两侧的位移量最小，中间的位移量最大，该变化趋势符合热机械效应的实际现象。蛇形弧侧向滑移量n为41.5 mm。
图6为垂直蛇形敷设电缆的热应力分布曲线。由图6可知，铜导体和平滑铝护套层的应力相较于其余各层明显更为集中。电缆各层热应力沿轴向从中间段向两边呈先减小再增大的变化趋势，其中铝护套层变化最为明显。
图6所示均为等效应力（Von Mises Stress）。有限元仿真计算中，应力的分析广泛采用等效应力的概念。等效应力在计算过程中不区分应力的方向而仅表示大小，其目的在于探究对于施加力的物体内部各点处的应力值是否会超过该点所能承受的最大应力，通过计算该点处各个方向应力分量合成后的总值，将其与材料本身所能承受的最大应力进行对比，从而可以判断该物体内部哪些部分最有可能发生危险，而考虑该点处应力的方向在此处无意义。由于图6中铝护套热应力从中间段向两边呈先减小再增大的变化趋势最明显，以下着重对铝护套层进行分析。
图7为垂直蛇形敷设电缆热膨胀示意图。针对图7中A到B点之间电缆段的所有横截面，分析了横截面铝护套层上侧点a和下侧点b的轴向应力分量变化趋势，对应于图8中的曲线a和曲线b。
由图8可知，对于曲线a而言，其对应的轴向应力分量在A处为正值，从A到B的过程中轴向应力分量逐渐减小为0后反向增加，代表横截面的点a在A处受拉力作用，在B处受压力作用；同理，横截面的点b在A处受压力作用，在B处受拉力作用。其现象符合真实情况，即热膨胀过程中A处电缆逐渐向下弯曲，电缆上侧受拉力下侧受压力；B处电缆两侧逐渐向上弯曲抬起，电缆下侧受拉力上侧受压力。即电缆段从A到B，电缆铝护套上侧点a先受拉力后受压力，下侧点b先受压力后受拉力。
将a点处铝护套的等效应力分布曲线（图6）和铝护套的轴向应力分量分布曲线（图8）进行对比分析，结果如图9所示。由图9可知，在数值上a点处的轴向应力分量和等效应力基本一致。说明铝护套的等效应力主要由轴向应力分量组成，而其他方向应力分量影响较小，因而通过分析轴向应力分量变化趋势来说明铝护套等效应力变化趋势是合理的。在此基础上，由于等效应力不区分应力的方向而仅表示大小，等效应力并不表现为从两边向中间一直减小而表现为先减小后增大。此外，图6中分析的是a点处的铝护套等效应力，其原因在于a点处和b点处的铝护套等效应力差别不大，且均高于铝护套中其他位置的等效应力。
由于有限元仿真的局限性，在对电缆两端边界整体设置固定约束条件在一定程度上会导致应力集中现象，使应力值与真实工况应力值有一定出入，故不将端面数值纳入考量。图6中除开端面，铝护套和铜导体出现的最大热应力分别不超过58 MPa和31 MPa。对照已有文献中1060铝材料的塑性参数[19]，铝护套少部分区域发生的最大塑性形变介于0.025 0和0.060 0之间，塑性形变程度极小。
在此基础上，对蛇形弧轴向力进行分析。电缆蛇形弧轴向力即电缆蛇形敷设后节点产生的轴向力，轴向力方向为电缆中心轴的方向。为了避免电缆端面由于受固定约束条件产生应力奇异现象而对轴向力分析产生较大影响，在电缆模型中选择了靠近固定端面的截面进行等效计算，如图10中红色截面所示。
通过对其截面上的轴向应力进行积分，可得到该截面上电缆所受的轴向力，结果如图11所示。由图11可知，仅在重力作用下，未受到热膨胀影响导体温度为20℃时，电缆整体受拉力，截面上轴向拉伸力为2 253.2 N，方向为图10蓝色箭头所示方向；而在导体升温导致电缆热膨胀情况下，电缆整体受压力，导体温度为90℃时，轴向压缩力值为3 146.9 N，方向为图10红色箭头所示方向。GB 50217—2018中6.16条规定，电缆蛇形敷设的参数选择应保证电缆因温度变化产生的轴向热应力无损电缆绝缘，不会对电缆金属护套长期使用产生应变疲劳断裂，且宜按允许拘束力条件确定[12]。查阅文献中的允许拘束力计算方法可知，本文中截面积约为490 mm2的铝护套容许应变的拘束力为19.6 kN[20]，其值远大于文中计算所得的蛇形敷设电缆的轴向力，说明蛇形敷设情况不会导致铝护套应变疲劳断裂问题的发生。
进一步研究过载情况下对电缆的影响，仿真分析了温度从20℃上升到130℃电缆轴向力随温度的变化趋势，结果如图11所示。
由图11可知，温度从20℃上升到130℃的过程中，电缆轴向拉伸力从2 253.2 N减小为0 N再变成压缩力并增大到3 992.9 N。在温度较低时，由于电缆整体受重力作用更多，电缆整体受拉伸力作用；当温度较高时，电缆由于热膨胀产生的热应力作用更大，电缆整体受压缩力作用。轴向压缩力随温度升高逐渐增大，但增大速率逐渐放缓并趋于平缓，其原因可能是电缆金属层和非金属层由于热膨胀系数和杨氏模量等参数不同导致的，温度升高时金属层和非金属层上的轴向力呈现不同的变化趋势，叠加后呈现增速放缓的趋势。
通过对公式（2）的理论计算和仿真分析，得到电缆蛇形弧侧向滑移量随温度变化的关系曲线如图12所示，其中理论计算中涉及的参数出自行业标准DL/T 5221—2016[14]。从图12可以看出，温度从20℃上升到130℃过程中，蛇形弧侧向滑移量从2.12 mm上升到61.75 mm。在20℃情况下电缆由于受到重力的作用，蛇形弧侧向滑移量不为0。此外，通过对仿真分析和理论计算结果进行对比分析，发现蛇形弧侧向滑移量随温度的变化趋势一致且数值接近，验证了仿真分析模型的可靠性。两者数值略有差异的原因在于行业标准DL/T 5221—2016给出的理论计算参数为简化后的电缆整体的线膨胀系数α，而仿真分析中考虑到了电缆各层材料不同的线膨胀系数，对问题因素的考虑更为全面。
2.3 敷设参数的影响
为了更直观地反映蛇形敷设电缆在实际工程中的具体作用，本文建立采用直线敷设的平滑铝护套电缆等效模型，轴向长度为6 m，在电缆两端设置固定约束条件，铜导体温度设置为90℃，其余边界条件与垂直蛇形敷设模型保持一致。采用有限元仿真计算直线敷设电缆的轴向力和各层的热应力，结果如表2所示。从表2可以看出，垂直蛇形敷设通过增加侧向滑移量有效降低了因热机械效应产生的热应力，将热膨胀产生的轴向力降低到3 146.9 kN，远小于铝护套容许应变的拘束力，有效避免了应变疲劳断裂问题的发生。直线敷设平滑铝护套电缆产生的轴向力为21 644.8 N，是垂直蛇形敷设电缆轴向力的6.9倍，已超过铝护套容许应变的拘束力19.6 kN，说明平滑铝护套长期使用会发生应变疲劳断裂，并有可能对电缆两端固定的附件造成损坏，在工程敷设过程中存在一定的安全隐患。因此，在工程中将平滑铝护套电缆敷设成垂直蛇形，可有效降低电缆本体及其附件由于热机械效应造成的安全隐患。
在此基础上，进一步探讨不同参数下垂直敷设电缆的轴向力和蛇形弧侧向滑移量的变化规律，研究垂直敷设的最优参数，为工程实际敷设过程中参数的选取提供依据。通过改变蛇形敷设电缆弧幅B和半蛇形节距L参数，仿真计算了在不同参数下垂直蛇形敷设电缆的轴向力和侧向滑移量，并对得到的结果进行了曲线拟合，结果如图13～14所示。
从图13可以看出，当垂直蛇形敷设电缆导体温度为90℃、半蛇形节距L为3 000 mm时，电缆蛇形弧侧向滑移量随着弧幅的增大而减小。此时电缆主要受到热膨胀引起的压缩力，随着弧幅的增大，压缩力逐渐减小。从图14可以看出，当垂直蛇形敷设电缆导体温度为90℃、弧幅B为200 mm时，随着半蛇形节距的增大，电缆蛇形弧侧向滑移量和轴向力也均减小。
在工程中，为了减小电缆的轴向力，应适当增大垂直蛇形敷设弧幅和半蛇形节距，但同时占据的隧道空间也会相应增大。
3 结论
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（1）对于110 kV-800 mm2垂直敷设情况下的平滑铝护套电缆，在最大允许载流量工况下，电缆侧向滑移量为41.5 mm，轴向力为3 146.9 N，满足电缆长期安全运行条件。
（2）在电缆过载情况下，当电缆温度上升到130℃过程中，电缆侧向滑移量增加到61.75 mm且增加趋势与理论计算结果相符，轴向力增加到3 992.9 N。
（3）相较于直线敷设，垂直蛇形敷设电缆的轴向力较小，有效避免了平滑铝护套应变疲劳和附件损坏断裂问题。在垂直蛇形敷设在参数选取方面，出于降低电缆轴向力的目的，应适当增大弧幅和半蛇形节距。
文献
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2024年第57卷第9期
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doi: 10.16790/j.cnki.1009-9239.im.2024.09.017
  • 接收时间：2023-09-12
  • 首发时间：2025-12-24
  • 出版时间：2024-09-20
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  • 收稿日期：2023-09-12
  • 修回日期：2023-11-12
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    1西安交通大学 电工材料电气绝缘国家重点实验室,陕西 西安 710049
    2国网北京市电力公司,北京 100031
    3国网北京市电力公司电力科学研究院,北京 100075

通讯作者:

李华强（1981-），男（汉族），陕西渭南人，副研究员，博士，主要从事绝缘、电缆、变压器方向的研究。
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2种不同金属材料的力学参数
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Family		 属数
Number of
genus		 种数
Number of
species		 占总种数比例
Percentage of
total species (%)		 属
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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