Article(id=1239167206131552950, tenantId=1146029695717560320, journalId=1238841944844054536, issueId=1239167201161302658, articleNumber=null, orderNo=null, doi=10.12347/j.ycyk.20241217006, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1734364800000, receivedDateStr=2024-12-17, revisedDate=1739116800000, revisedDateStr=2025-02-10, acceptedDate=null, acceptedDateStr=null, onlineDate=1773370084555, onlineDateStr=2026-03-13, pubDate=1741968000000, pubDateStr=2025-03-15, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1773370084555, onlineIssueDateStr=2026-03-13, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1773370084555, creator=13701087609, updateTime=1773370084555, updator=13701087609, issue=Issue{id=1239167201161302658, tenantId=1146029695717560320, journalId=1238841944844054536, year='2025', volume='46', issue='2', pageStart='1', pageEnd='142', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1773370083370, creator=13701087609, updateTime=1773370146323, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1239167465285014189, tenantId=1146029695717560320, journalId=1238841944844054536, issueId=1239167201161302658, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1239167465285014190, tenantId=1146029695717560320, journalId=1238841944844054536, issueId=1239167201161302658, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=20, endPage=33, ext={EN=ArticleExt(id=1239167206395794114, articleId=1239167206131552950, tenantId=1146029695717560320, journalId=1238841944844054536, language=EN, title=Analysis and Study on the Impact of Rapid Link Establishment of Interstellar Laser in External Heat Flux Environment, columnId=1239133503154081962, journalTitle=Journal of Telemetry, Tracking and Command, columnName=TT & C Communication and Navigation, runingTitle=null, highlight=null, articleAbstract=

As one of the important means of data transmission between satellites, laser communication has a direct impact on the performance of the constellation system due to its fast and stable link establishment ability. The laser communication terminal relies on a high-precision optical tracking system to achieve continuous and stable pointing of the signal beam to the target satellite. However, space environmental factors can interfere with the pointing accuracy of laser terminals, and their influence can reach the level of milliarcsecond measurements. The deformation of the satellite structure caused by thermal expansion, cold contraction and stress changes during the satellite operation in orbit leads to the rigid displacement of the laser terminal pointing accuracy compared with the reference position of the satellite platform. In this paper, based on the application background of the rapid and stable chain construction of inter-satellite laser communication links, the finite element analysis method is used to study the pointing error caused by the thermally induced deformation of the laser terminal datum and the satellite platform star sensitive datum. By analyzing the installation reference error caused by the thermal deformation of satellites at different orbit altitudes, the variation law of laser communication link pointing error is obtained, which provides an analytical basis for the rapid and stable chain construction, and provides a design reference for the module layout and overall thermal control of the whole satellite.

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激光通信作为卫星间数据传输的重要手段之一,其快速稳定的建链能力直接影响着星座系统的性能。激光通信终端依赖高精度光学跟瞄系统以实现信号光束持续稳定指向目标卫星。然而,空间环境因素会干扰激光终端的指向精度,其影响程度可达毫弧度量级。卫星在轨运行中因热胀冷缩和应力变化产生的星体结构形变,导致激光终端指向精度相较卫星平台基准位置发生刚体位移。本文以星间激光通信链路快速稳定建链为应用背景,采用有限元分析方法对激光终端基准与卫星平台星敏基准因热致形变产生的指向误差进行研究。通过分析不同轨道高度卫星在轨受热变形产生的安装基准误差量,获取激光通信链路指向误差变化规律,为实现快速稳定建链提供分析基础,同时为整星响应单机布局及总体热控提供设计参考。

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张萍 1998年生,硕士研究生。

成飞 1980年生,博士研究生,研究员。

关哲 1988年生,博士,高级工程师。

贺文正 2001年生,硕士研究生。

韩轶丹 1992年生,硕士,工程师。。

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张萍 1998年生,硕士研究生。

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成飞 1980年生,博士研究生,研究员。

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成飞 1980年生,博士研究生,研究员。

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贺文正 2001年生,硕士研究生。

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贺文正 2001年生,硕士研究生。

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韩轶丹 1992年生,硕士,工程师。。

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韩轶丹 1992年生,硕士,工程师。。

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Thermal distortion optimization design and simulation of a large high precision satellite antenna[J]. Journal of Mechanical Engineering, 2022, 58(9): 41-48., articleTitle=Thermal distortion optimization design and simulation of a large high precision satellite antenna, refAbstract=null)], funds=[Fund(id=1239285176627425332, tenantId=1146029695717560320, journalId=1238841944844054536, articleId=1239167206131552950, awardId=D010105, language=CN, fundingSource=科工局民用航天技术预先研究项目(D010105), fundOrder=null, country=null)], companyList=[AuthorCompany(id=1239285167290905287, tenantId=1146029695717560320, journalId=1238841944844054536, articleId=1239167206131552950, xref=null, ext=[AuthorCompanyExt(id=1239285167299293897, tenantId=1146029695717560320, journalId=1238841944844054536, articleId=1239167206131552950, companyId=1239285167290905287, language=EN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=Shanghai Institute of Satellite Engineering, Shanghai 201109, China), AuthorCompanyExt(id=1239285167303488202, tenantId=1146029695717560320, 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Thermal deformation analysis steps performed by finite element software

, figureFileSmall=null, figureFileBig=null, tableContent=
步骤详细流程内容
前处理建几何模型使用建模软件PATRAN (有限元分析前/后处理软件)创建结构的几何模型,定义模型的尺寸、形状和结构特征。
定义材料属性指定结构所使用材料的热物理和机械属性,如热膨胀系数、导热系数、密度和弹性模量。
网格划分对几何模型进行网格划分,将其离散为有限元单元。选择合适的单元类型和网格密度,以平衡计算精度和计算量。
定义工况指定温度载荷,如环境温度变化、内部热源等。确定分析工况,包括静态、瞬态或周期性热分析。
求解设置分析类型选择适当的分析类型,如热分析、热-结构耦合分析等。对于热变形分析,通常需要进行热分析后进行结构分析(即热-结构耦合分析)。
生成求解输入文件根据前处理的设置,生成NASTRAN求解器所需的输入文件。确保所有材料属性、边界条件、载荷和工况定义正确。
运行求解使用NASTRAN求解器运行分析,解决热分析和随后的结构分析。监控求解过程,确保计算顺利进行并得到收敛解。
后处理查看结果使用后处理软件PATRAN查看分析结果,检查温度分布、热流分布、热应力和热变形等结果。
结果分析通过结果后处理,分析温度变化对结构变形和应力分布的影响,识别可能的热应力集中区域和变形最大值。
验证与优化验证分析结果是否符合预期,检查是否存在异常或错误。根据分析结果,对结构设计进行优化,如调整材料、改变几何形状或改进边界条件,以减小热应力和变形。
), ArticleFig(id=1239285175490768899, tenantId=1146029695717560320, journalId=1238841944844054536, articleId=1239167206131552950, language=CN, label=表1, caption=

开展热变形分析步骤

, figureFileSmall=null, figureFileBig=null, tableContent=
步骤详细流程内容
前处理建几何模型使用建模软件PATRAN (有限元分析前/后处理软件)创建结构的几何模型,定义模型的尺寸、形状和结构特征。
定义材料属性指定结构所使用材料的热物理和机械属性,如热膨胀系数、导热系数、密度和弹性模量。
网格划分对几何模型进行网格划分,将其离散为有限元单元。选择合适的单元类型和网格密度,以平衡计算精度和计算量。
定义工况指定温度载荷,如环境温度变化、内部热源等。确定分析工况,包括静态、瞬态或周期性热分析。
求解设置分析类型选择适当的分析类型,如热分析、热-结构耦合分析等。对于热变形分析,通常需要进行热分析后进行结构分析(即热-结构耦合分析)。
生成求解输入文件根据前处理的设置,生成NASTRAN求解器所需的输入文件。确保所有材料属性、边界条件、载荷和工况定义正确。
运行求解使用NASTRAN求解器运行分析,解决热分析和随后的结构分析。监控求解过程,确保计算顺利进行并得到收敛解。
后处理查看结果使用后处理软件PATRAN查看分析结果,检查温度分布、热流分布、热应力和热变形等结果。
结果分析通过结果后处理,分析温度变化对结构变形和应力分布的影响,识别可能的热应力集中区域和变形最大值。
验证与优化验证分析结果是否符合预期,检查是否存在异常或错误。根据分析结果,对结构设计进行优化,如调整材料、改变几何形状或改进边界条件,以减小热应力和变形。
), ArticleFig(id=1239285175566266375, tenantId=1146029695717560320, journalId=1238841944844054536, articleId=1239167206131552950, language=EN, label=Table 2, caption=

The model uses a material parameter table

, figureFileSmall=null, figureFileBig=null, tableContent=
材料E/GPaG/GPaV σS/MPa ρ/(kg/m3)A
铝合金2A12T470.6270.32502 7802.27E-005
镁合金40.2-0.31201 7802.37E-005
碳纤维M55J2 8884.60.266-16 000-1.3E-006
3.24E-005
蜂窝芯8.04×10-51.5081/3-33-
), ArticleFig(id=1239285175654346761, tenantId=1146029695717560320, journalId=1238841944844054536, articleId=1239167206131552950, language=CN, label=表2, caption=

模型使用材料参数表

, figureFileSmall=null, figureFileBig=null, tableContent=
材料E/GPaG/GPaV σS/MPa ρ/(kg/m3)A
铝合金2A12T470.6270.32502 7802.27E-005
镁合金40.2-0.31201 7802.37E-005
碳纤维M55J2 8884.60.266-16 000-1.3E-006
3.24E-005
蜂窝芯8.04×10-51.5081/3-33-
), ArticleFig(id=1239285175738232847, tenantId=1146029695717560320, journalId=1238841944844054536, articleId=1239167206131552950, language=EN, label=Table 3, caption=

Changes in the pointing error of a LEO satellite in one circle

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工况星敏感器变形量/″光学头变形量/″指向误差/″指向误差/mrad
高温极限工况115.993 483.5867.148 290.034 7
低温极限工况115.900 7161.508 9105.165 80.51
1063.171 226.917 316.607 50.080 5
2013.262 925.17.1110.034 5
3027.009 427.124 720.326 70.098 5
4032.798 525.901 425.943 10.125 8
5030.137 021.896 833.276 20.161 3
6027.558 325.573 848.447 60.234 9
7033.179 328.281 160.8610.295 1
8022.356 923.99746.065 50.223 3
9010.107 314.996 512.788 10.062
10027.247 911.025 913.2450.064 2
11039.082 310.135 616.746 20.081 2
12047.236 327.184 08.185 90.039 7
1309.664 125.074 57.496 60.036 3
), ArticleFig(id=1239285175834701843, tenantId=1146029695717560320, journalId=1238841944844054536, articleId=1239167206131552950, language=CN, label=表3, caption=

低轨卫星指向误差变化情况表

, figureFileSmall=null, figureFileBig=null, tableContent=
工况星敏感器变形量/″光学头变形量/″指向误差/″指向误差/mrad
高温极限工况115.993 483.5867.148 290.034 7
低温极限工况115.900 7161.508 9105.165 80.51
1063.171 226.917 316.607 50.080 5
2013.262 925.17.1110.034 5
3027.009 427.124 720.326 70.098 5
4032.798 525.901 425.943 10.125 8
5030.137 021.896 833.276 20.161 3
6027.558 325.573 848.447 60.234 9
7033.179 328.281 160.8610.295 1
8022.356 923.99746.065 50.223 3
9010.107 314.996 512.788 10.062
10027.247 911.025 913.2450.064 2
11039.082 310.135 616.746 20.081 2
12047.236 327.184 08.185 90.039 7
1309.664 125.074 57.496 60.036 3
), ArticleFig(id=1239285175964725275, tenantId=1146029695717560320, journalId=1238841944844054536, articleId=1239167206131552950, language=EN, label=Table 4, caption=

Simulation results under high and low temperature limit conditions

, figureFileSmall=null, figureFileBig=null, tableContent=
工况星敏感器变形量/(″/mrad)光学头变形量/(″/mrad)指向误差/(″/mrad)
低温212.879 5/1.032 1110.371 1/0.535 1273.715 3/1.33
高温199.08/0.965 2112.328 9/0.544 6220.469 3/1.07
), ArticleFig(id=1239285176132497440, tenantId=1146029695717560320, journalId=1238841944844054536, articleId=1239167206131552950, language=CN, label=表4, caption=

高低温极限工况下仿真结果

, figureFileSmall=null, figureFileBig=null, tableContent=
工况星敏感器变形量/(″/mrad)光学头变形量/(″/mrad)指向误差/(″/mrad)
低温212.879 5/1.032 1110.371 1/0.535 1273.715 3/1.33
高温199.08/0.965 2112.328 9/0.544 6220.469 3/1.07
), ArticleFig(id=1239285176220577828, tenantId=1146029695717560320, journalId=1238841944844054536, articleId=1239167206131552950, language=EN, label=Table 5, caption=

Pointing error of the optical head relative to the star sensor

, figureFileSmall=null, figureFileBig=null, tableContent=
时间星敏感器变形量/″光学头变形量/″指向误差/″指向误差/mrad
冬至1 h201.731 2111.600 8229.2961.111 7
冬至3 h211.24111.116 9235.3681.141 1
冬至5 h212.879 5103.870 4230.600 41.118
冬至7 h220.216 5104.611 3232.871.129
冬至9 h215.581115.842 2235.690 51.142 7
冬至11 h207.336 5121.402 8230.704 21.118 5
冬至13 h196.050 2122.874 4214.924 61.042
冬至15 h180.447 5121.308 3191.654 60.929 2
冬至17 h177.784 8102.069 8175.771 80.852 2
冬至19 h175.25895.741 7169.167 40.820 1
冬至21 h173.257 595.009 3169.583 40.822 2
冬至23 h182.689 6101.113 7186.928 70.906 3
), ArticleFig(id=1239285176308658213, tenantId=1146029695717560320, journalId=1238841944844054536, articleId=1239167206131552950, language=CN, label=表5, caption=

光学头相对于星敏感器的指向误差

, figureFileSmall=null, figureFileBig=null, tableContent=
时间星敏感器变形量/″光学头变形量/″指向误差/″指向误差/mrad
冬至1 h201.731 2111.600 8229.2961.111 7
冬至3 h211.24111.116 9235.3681.141 1
冬至5 h212.879 5103.870 4230.600 41.118
冬至7 h220.216 5104.611 3232.871.129
冬至9 h215.581115.842 2235.690 51.142 7
冬至11 h207.336 5121.402 8230.704 21.118 5
冬至13 h196.050 2122.874 4214.924 61.042
冬至15 h180.447 5121.308 3191.654 60.929 2
冬至17 h177.784 8102.069 8175.771 80.852 2
冬至19 h175.25895.741 7169.167 40.820 1
冬至21 h173.257 595.009 3169.583 40.822 2
冬至23 h182.689 6101.113 7186.928 70.906 3
), ArticleFig(id=1239285176388349994, tenantId=1146029695717560320, journalId=1238841944844054536, articleId=1239167206131552950, language=EN, label=Table 6, caption=

Comparative analysis of the magnitude of pointing error of high and low orbit satellites under high and low temperature limit conditions

, figureFileSmall=null, figureFileBig=null, tableContent=
不同轨道卫星高温工况下指向误差/mrad低温工况下指向误差/mrad
高轨卫星1.071.33
低轨卫星0.034 70.51
), ArticleFig(id=1239285176476430378, tenantId=1146029695717560320, journalId=1238841944844054536, articleId=1239167206131552950, language=CN, label=表6, caption=

高低轨卫星在高低温极限工况下指向误差大小对比分析

, figureFileSmall=null, figureFileBig=null, tableContent=
不同轨道卫星高温工况下指向误差/mrad低温工况下指向误差/mrad
高轨卫星1.071.33
低轨卫星0.034 70.51
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外热流环境中星间激光快速建链影响分析研究
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张萍 , 成飞 , 关哲 , 贺文正 , 韩轶丹
遥测遥控 | 测控通信与导航 2025,46(2): 20-33
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遥测遥控 | 测控通信与导航 2025, 46(2): 20-33
外热流环境中星间激光快速建链影响分析研究
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张萍, 成飞, 关哲, 贺文正, 韩轶丹
作者信息
  • 上海卫星工程研究所 上海 201109
  • 张萍 1998年生,硕士研究生。

    成飞 1980年生,博士研究生,研究员。

    关哲 1988年生,博士,高级工程师。

    贺文正 2001年生,硕士研究生。

    韩轶丹 1992年生,硕士,工程师。。

Analysis and Study on the Impact of Rapid Link Establishment of Interstellar Laser in External Heat Flux Environment
Ping ZHANG, Fei CHENG, Zhe GUAN, Wenzheng HE, Yidan HAN
Affiliations
  • Shanghai Institute of Satellite Engineering, Shanghai 201109, China
出版时间: 2025-03-15 doi: 10.12347/j.ycyk.20241217006
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激光通信作为卫星间数据传输的重要手段之一,其快速稳定的建链能力直接影响着星座系统的性能。激光通信终端依赖高精度光学跟瞄系统以实现信号光束持续稳定指向目标卫星。然而,空间环境因素会干扰激光终端的指向精度,其影响程度可达毫弧度量级。卫星在轨运行中因热胀冷缩和应力变化产生的星体结构形变,导致激光终端指向精度相较卫星平台基准位置发生刚体位移。本文以星间激光通信链路快速稳定建链为应用背景,采用有限元分析方法对激光终端基准与卫星平台星敏基准因热致形变产生的指向误差进行研究。通过分析不同轨道高度卫星在轨受热变形产生的安装基准误差量,获取激光通信链路指向误差变化规律,为实现快速稳定建链提供分析基础,同时为整星响应单机布局及总体热控提供设计参考。

激光通信  /  稳定建链  /  热变形  /  指向误差  /  有限元分析

As one of the important means of data transmission between satellites, laser communication has a direct impact on the performance of the constellation system due to its fast and stable link establishment ability. The laser communication terminal relies on a high-precision optical tracking system to achieve continuous and stable pointing of the signal beam to the target satellite. However, space environmental factors can interfere with the pointing accuracy of laser terminals, and their influence can reach the level of milliarcsecond measurements. The deformation of the satellite structure caused by thermal expansion, cold contraction and stress changes during the satellite operation in orbit leads to the rigid displacement of the laser terminal pointing accuracy compared with the reference position of the satellite platform. In this paper, based on the application background of the rapid and stable chain construction of inter-satellite laser communication links, the finite element analysis method is used to study the pointing error caused by the thermally induced deformation of the laser terminal datum and the satellite platform star sensitive datum. By analyzing the installation reference error caused by the thermal deformation of satellites at different orbit altitudes, the variation law of laser communication link pointing error is obtained, which provides an analytical basis for the rapid and stable chain construction, and provides a design reference for the module layout and overall thermal control of the whole satellite.

Laser communication  /  Stable link establishment  /  Thermal deformation  /  Pointing error  /  Finite element analysis
张萍, 成飞, 关哲, 贺文正, 韩轶丹. 外热流环境中星间激光快速建链影响分析研究. 遥测遥控, 2025 , 46 (2) : 20 -33 . DOI: 10.12347/j.ycyk.20241217006
Ping ZHANG, Fei CHENG, Zhe GUAN, Wenzheng HE, Yidan HAN. Analysis and Study on the Impact of Rapid Link Establishment of Interstellar Laser in External Heat Flux Environment[J]. Journal of Telemetry, Tracking and Command, 2025 , 46 (2) : 20 -33 . DOI: 10.12347/j.ycyk.20241217006
星间激光通信以激光为载波在空间中传输信息,其频率比无线电波高4~5个数量级[1],具有数据传输速率高、波束方向性好、抗干扰能力强、安全保密性好等优点。与传统微波通信载荷产品相比,激光通信终端体积更小、重量更轻、功耗更低,可进一步节约卫星发射与运行成本,符合通信、导航、遥感等卫星对宇航产品小型化、低功耗的要求。
星间激光通信一般包括LEO (近地轨道)与LEO、LEO与GEO (地球静止轨道)、GEO与GEO等通信链接关系,其通信距离通常至少为几百千米,甚至到几万千米。在星间激光快速建链和长期稳定通信时,由于通信距离较远且激光光束发散角较小等原因,激光终端光学跟瞄系统对卫星平台姿态测量精度和自身指向精度都提出了较高要求。
卫星平台和激光通信终端在结构系统间相互耦合、相互关联。激光通信终端涉及光学、结构、材料、空间环境等多学科、多领域[2]。目前,星间激光通信技术在快速稳定建链方面面临多项工程难题,最为突出的是对复杂空间环境下涉及多学科的多源耦合因素的把控不到位。目前制约星间激光通信的误差来源可分为固定误差和随机误差两个方面[3]。固定误差主要包括结构安装误差、轨道姿态确定误差、终端轴系误差、跟踪控制误差、光路系统误差、星历误差、时延误差等。随机误差主要包括星上热致形变、微振动等。在激光终端完成在轨标校及首次链路建立后,可通过指向修正措施对固定误差进行校正[3]。但是,随卫星在轨运行过程中持续随机变化的随机误差,则难以通过简单指向修正实现一次性标定校正,需开展专项分析与研究。
针对星上影响激光通信的随机误差,其中微振动误差主要由活动部件转动造成,通常影响量级较小,一般在微弧度量级,可通过激光终端的微振动抑制手段进行缓解。但是,空间环境中热致形变误差主要由星体在轨受到太阳光照、其他单机热辐射和整星热控等因素共同影响,其对激光终端指向精度的影响程度可达毫弧度量级,已远超激光终端抑制能力[4-8]
本文针对激光终端在轨受热致形变产生的指向误差进行研究,分析卫星在轨受热变形影响产生的激光终端与卫星平台星敏感器之间的安装基准误差量,以获取星间激光通信链路指向误差的变化规律。
卫星在轨工作时受空间热环境、自身单机热辐射、整星热控等因素共同影响,其结构将会由于热胀冷缩和应力应变等而产生热形变。由于空间环境的不确定性和热变形的非线性[9-10],在轨的热变形难以通过量化来表征。卫星平台在轨运行产生热形变主要受到外因和内因的影响[11-12]。所谓外因,即随着卫星绕地球飞行,卫星的轨道位置和姿态不断变化,它所接受的空间热流也随之呈现出周期性的变化,加之轨道阴影区以及结构部件之间的各种遮挡关系的影响,在卫星的结构中会产生周期性冷热变化且分布不均匀的瞬态温度场,恶劣的温度交变环境或较大的温度梯度可引起材料的尺寸变化,从而引发结构的变形,影响卫星在轨精度。所谓内因,即卫星机械组件的材料本身的“热胀冷缩”的属性。大多数材料在温度发生变化时,由于其内部粒子的振动而引起结构外形尺寸的变化。对于高精度机械系统而言,一般要求其组成材料和结构在空间温度发生变化时能保持尺寸和精度的稳定,因此所使用的材料应有较小的热膨胀系数。
卫星在天基环境中产生的热形变具有复杂性的特点。不同的轨道和卫星姿态条件下,卫星平台各部分温度分布不同,当卫星平台在轨运行时,温度分布会随轨道和姿态的变化而变化[13-14],从而使得星间激光通信终端等高精度载荷机械精度也会呈现复杂变化,且地面试验很难对在轨温度环境进行精确模拟,无法直接对其在轨变形情况进行验证。
热形变对激光通信终端的影响主要表现在以下三个方面[15-16]
① 影响光学天线面型精度
激光终端的光学材料受到太阳光照容易引起变形,以光学天线为例,天线增益表示天线辐射集中程度的参数,天线增益与天线面型精度误差之间的关系如下所示[17-19]
式中,G、G0表示实际反射面与理想反射面的天线增益;δ代表实际反射面的形面精度误差(RMS),可通过实际反射面与理想反射面的尺寸偏差求出;λ代表光学天线的工作波长。当波长一定的情况下,改变天线的形面精度会使光学天线的增益下降,影响光束传输距离。
② 影响激光终端的指向误差
激光终端的光学头单机安装在卫星舱外,很容易受到卫星平台热形变的影响,使得光学头相对星敏感器安装位置发生变化,最终导致光学天线理论指向角度与目标实际角度产生偏差,影响激光光轴的指向精度。
③ 影响激光终端光学头后光路光学元件安装位置和镜面面型
温度对后光路收发光路一致性的影响主要体现在两个方面:一方面,激光终端后光路组件一般位于激光终端光学头单机底部,靠近卫星平台安装面,卫星平台热形变会导致激光终端光学头单机安装面产生应变扭曲,影响后光路上相应镜组原有装调位置及面型精度;另一方面,激光终端单机内部自身由于外热流及工作产能产生的温度变化,影响后光路上相应镜组原有装调位置及面型精度;破坏信号光发射光路及接收光路的同轴度,影响系统耦合效率。
热变形分析研究是航天器热变形控制的重要环节[20]。在卫星方案设计阶段,可根据以往型号经验和历史仿真数据,创建热变形分析初步模型,进行典型工作状态下的热变形分析,了解航天器结构应力、应变以及变形等情况;同时进行设计参数敏感度分析,指导高稳定结构设计,为方案选型和优化设计提供技术支撑。在地面试验阶段,根据热变形分析的温度场结果,设定各个部件温度条件,制定试验工况,地面热试验的结果可用于修正热变形分析模型。在详细设计阶段,进行全周期内温度环境仿真分析,获取关键部件的详细温度环境,基于修正后的热变形分析模型,预测恶劣环境下的热变形情况及对载荷性能的影响,也为在轨变形测量和主动控制提供选型依据。
热变形分析的一般分析流程包括轨道外热流计算、温度场分析和热弹性分析等[20]
① 轨道外热流计算,根据卫星轨道参数计算光照角度系数等,获取轨道外热流;
② 温度场分析,根据卫星设计要求建立卫星的CAD (计算机辅助设计)模型,在此基础上建立热分析模型,获得卫星系统内各个设备的温度分布;
③ 热弹性分析,将温度场分析结果作为体载荷加载到结构有限元模型进行力学分析,通过对变形值的处理可以得到敏感元件的刚体位移和形面变化[21];温度场映射,即温度场分析结果传递至热弹性分析工况,旨在解决温度场分析模型和热弹性分析模型网格不一致的情况。
温度场指的是在特定时间和空间范围内的温度变化,它可以作为空间坐标和时间的函数[22]。由于温度是标量,因此温度场属于标量场。常用的空间坐标系有直角坐标系、柱坐标系和球坐标系。在直角坐标系中,温度场的表达形式为:
式中,t表示温度,xyz为三个空间坐标,τ表示时间。若温度场各点的温度均不随时间变化,即∂t/∂τ=0,则该温度场称为稳态温度场;如果温度随时间变化,则称该温度场为非稳态温度场。
物体形状的变化与各点位移之间属于完全几何关系,所以热弹性方程里的几何方程和弹性力学中的相同。在弹性物体内出现∆T的温度变化时,若研究对象不受约束,其内部各点的微小长度会产生αT的正应变(α为弹性体材料的线热膨胀系数)。对于各向同性材料而言,线热膨胀系数不随方向改变,所以也不会产生剪切应变。
式中,εxyz方向上的正应变,γxyz方向上的剪应力。
通常而言,受温度载荷影响的物体不会出现自由变形的情况。这是由于存在边界约束,且物体内部各个区域之间相互制约,于是便产生了热应力。而热应力的存在又会促使物体发生变形。所以,物体在温度载荷下各个方向上的总变形量为:
理论上,针对给定温度场的热变形分析问题,通过求解上述微分方程组,就可以得到弹性物体的应力、应变和位移分布。一般情况下,方程组不易求解,通常需要借助一些特殊的求解方法,例如位移法、应力函数法、有限元方法等。
将弹性体离散为结构单元,采用有限元方法开展热变形仿真分析。弹性体承受载荷时产生应变{ε}和应力{σ},将温度变化产生相应的应变定义为{ε0},弹性体的应力-应变关系写为:
式中,[Q]为弹性矩阵。弹性体的应力表示为:
单元体的势能由以下两部分组成:
① 单元的应变能
上式中,[K]为刚度矩阵,{L}为热载荷向量,{C}为与节点位移无关的项。
② 外力势能
外力可分为三类:体积力{Pv}、表面力{Ps}、和节点集中力{Fe},单元体的外力势能为:
式中,{f}为单元体任一点的位移,[N]为形函数矩阵,{F}为等效节点力。将单元势能的各部分相加后可以得到总势能泛函的表达式。
利用最小势能原理,对上式变法后并整理可以得到:
根据上式及边界条件,可以求解出节点的位移、结构的应变及应力。
NASTRAN(有限元分析软件)在航空航天与汽车工业中应用广泛,在结构分析领域表现尤为卓越,能够精确处理线性和非线性的静态、动态结构问题,并且具备精度高、兼容性好的优点[23]。运用该软件开展热变形分析时,主要包含前处理、求解以及后处理这三个关键步骤,详细内容可参照表1。在前处理阶段进行精细建模并准确定义材料属性,求解阶段正确设置并运行,后处理阶段对结果加以分析和优化,这确保了热变形分析的准确性与有效性。在卫星结构设计时,合理运用仿真软件进行热变形分析,有助于工程师预测结构在温度变化时的表现,从而优化设计,提升结构的可靠性和性能。
按照上述流程,能够利用NASTRAN开展全面的热变形分析[24]
指向精度是光学天线指向机构的关键技术指标,它直接关系到整个系统工作的可靠性。在初始扫描捕获阶段,激光通信终端要对整个不确定区域进行螺旋扫描,借助探测器判断捕获是否成功并测定对方光束的方向,根据测得的光斑脱靶量计算出目标激光通信终端在本地激光通信终端空间坐标系中的矢量方向,然后调整机构指向,让入射光斑进入精跟踪视场范围。激光通信终端的指向误差会直接对不确定区域的范围和扫描精度产生影响,指向误差较大时,会使扫描捕获时间变长、捕获概率变低,甚至可能导致系统失效。电子科技大学李晓峰[25]等人经分析研究可得:在光束发散角α一定的情况下,指向误差σ增大1.732倍,此时突发误码将提升4个数量级。由此可知指向误差对激光通信链路性能的影响非常大。掌握卫星激光通信终端在轨指向误差和通信误码率的变化规律,对我们进行系统指标设计和在轨温控指标的确定是有帮助的。
采用有限元方法计算卫星平台在不同的观测姿态和日照环境下的非均匀温度分布及其变化规律,探讨激光终端光学头安装面面形与星敏感器安装面在实时变化的光照影响下的演变规律。
激光终端光学头一般安装于卫星平台舱外,以低轨倾斜轨道卫星为例设置其轨道高度为1 150 km,倾斜角度为50°左右,轨道周期是108.34 min。太阳光照面在–74°~74°之间变化。卫星在轨温度变化的外界影响因素主要是空间外热流。光照角为0°时轨道上阴影期最长为35 min,光照角在58°~74°、–74°~–58°范围内无阴影期,在轨道面光照角为60°和–60°时为全光照期,该卫星的–Y侧与+Y侧位置受太阳光照长期照射,卫星受到空间外热流总和最大。
针对该低轨卫星配置的一台激光终端光学头和一台平台星敏感器,建立分析模型,经网格划分后的模型如图1图2所示。
网格划分要求为:① 承力筒和结构板考虑为壳单元;② 贮箱和推进剂考虑为壳单元,推进剂考虑为均布质量;③ 各种仪器设备:激光终端,星敏感器等模型考虑质量点载荷或均布质量。
边界条件属于在轨自由状态情况,模型具体参数如表2所示:
设计光学头与星敏感器通过4个安装点实现支撑框架连接,考虑光学头支撑框架选用零膨胀复合材料制成,在结构模型中将光学头安装位置连接到4个点上,设卫星材料参考温度为20 ℃并进行热变形分析。完成上述模型构建、约束条件定义和载荷施加之后,基于结构有限元计算软件进行仿真求解。在MATLAB中调用Nastran[26-28]进行结构热变形的仿真计算。对于该低轨卫星光学头指向误差的仿真分析,一方面选取高低温极限工况下进行计算,另一方面选用卫星运行一个轨道周期(130 min)每隔10 min一个工况进行计算。
低轨卫星光学头高低温极限工况下的温度云图和热变形云图如图3所示。
低轨卫星星敏感器高低温极限工况下的温度云图和热变形云图如图4所示。
经仿真计算,在高温极限工况下,光学头安装面相对于星敏感器的变化量为7.148 297角秒(等于0.034 7 mrad),光学头安装面相对于基准面的变形量为83.586角秒(0.405 mrad),星敏感器相对于基准面的变形量为115.993 4角秒(等于0.562 mrad)。在低温极限工况下,光学头安装面相对于星敏感器的变化量为105.165 8角秒(等于0.51 mrad),光学头安装面相对于基准面的变形量为161.508 9角秒(0.783 mrad),星敏感器相对于基准面的变形量为115.900 7角秒(0.562 mrad)。
为了进一步研究光学头在天基环境中指向误差的变化规律,此次仿真不仅讨论高低温极限工况下指向误差的大小,还针对该卫星在轨运行一轨的情况开展仿真分析研究,选取运行10 min为一个工况,总计选取13个工况,即在轨运行130 min,在该卫星一个轨道周期内,选取13个时间节点进行分析,低轨卫星光学头对应时间点温度云图和热变形云图如图5所示。鉴于篇幅受限,本文只附7个时间点(每隔20 min)的工况。
高轨卫星星敏感器对应时间点温度云图和热变形云图如图6所示。
经仿真计算,在一个轨道周期内,激光终端光学头安装面相对于基准面的变形量最大为28.281 1角秒(0.137 mrad),星敏感器相对于基准面的变形量最大为63.171 2角秒(0.306 mrad),综合激光终端光学头安装面相对于星敏感器的变化量最大为60.861角秒(0.295 1 mrad)。仿真结果如表3所示。
将高低温工况与上述低轨卫星在轨运行一圈的13个工况下的数据整理成图7所示。
图7可得,该低轨卫星激光终端光学头指向误差最大时对应在低温极限工况下,指向误差大小为0.51 mrad,指向误差最小时对应在高温极限工况下,指向误差大小为0.034 7 mrad,最大指向误差与最小指向误差相差0.475 3 mrad;该低轨卫星在一轨中激光终端光学头指向误差最小为20 min时的变形量0.034 5 mrad,指向误差最大为70 min时的变形量0.295 mrad;在轨一圈中相邻10 min内产生指向误差的变化梯度为最大0.161 3 mrad,最小为0.034 5 mrad。
设计该高轨卫星配置一台激光终端光学头和1台星敏感器,卫星网格划分后的模型如图8图9所示。
对该高轨卫星的模型进行仿真计算,一方面分析高低温极限工况下激光终端光学头指向误差的变化情况,另一方面分析卫星在轨运行24 h内每2 h一次的激光终端光学头指向误差变化情况。
高低温工况下激光终端光学头的温度云图和热变形云图如图10所示。
高低温工况下的星敏感器温度云图和热变形云图如图11所示。
仿真分析激光终端光学头相对不同星敏感器的指向误差,结果如表4所示。
图10可以清晰得知,在高低温极限工况下激光终端光学头指向误差最大为1.33 mrad (低温),指向误差最小为1.07 mrad (高温)。
冬至12个工况下光学头温度场及热变形云图如图12所示,鉴于篇幅受限,本文只附7个时间点(每隔4小时选取一个工况)的工况。
冬至12个工况下星敏感器温度场及热变形云图如图13所示。
表5的数据是激光终端光学头相对于星敏感器的指向误差。从表中可以得到,星敏感器最大变形量为220.216 5 "(1.07 mrad),光学头最大变形量为122.874 4 "(0.596 mrad)。
对上面的指向误差参数进行整理分析可得图14
图14可知,在冬至24小时中,指向误差最大在冬至1 h达到了1.111 7 mrad,最小在冬至19 h时为0.820 1 mrad;星敏感器一天中的变化量波动较小,相邻2 h间波动最大为0.163 7 mrad,最小为0.000 1 mrad;若在轨使用时选用该星敏感器获取信息时需要再次建链时,需要再次采取恒星标校措施。
综合上述研究,对高低轨卫星在高低温极限工况下激光终端光学头因热致产生的指向误差大小进行对比分析,分析结果如表6所示。
综上可得,高轨卫星相对低轨卫星的激光终端光学头产生的指向误差较大,所以针对高轨卫星激光终端自身结构,热控设计及其在整星的布局应考虑更加全面,采取相应的解决措施,如增加激光终端底座与后光路安装底板的厚度,优化热控设计使其在轨工作时温度梯度符合其使用要求等。
以星间激光通信链路快速稳定建链为应用背景,采用有限元分析方法对激光终端基准与卫星平台星敏基准因热致形变产生的指向误差进行研究,通过分别建立低轨、高轨两型卫星仿真模型,开展卫星在轨运行中,基于太阳光照角度变化、星上单机热辐射、整星热控等多因素复合影响情况下的星体结构形变分析。在低轨卫星仿真模型中,获得激光终端光学头与卫星平台星敏之间因热致形变产生的指向误差最大为0.51 mrad;在高轨卫星仿真模型中,获得激光终端光学头与卫星平台星敏之间因热致形变产生的指向误差最大为1.33 mrad。通过分析高、低两型卫星激光终端受热形变影响产生指向误差,计算不同轨道高度卫星在轨受热变形影响产生的激光终端与卫星平台星敏之间的安装基准误差量,分析获取星间激光通信链路指向误差变化规律,为星间激光通信终端在轨应用及数据分析基础,同时为整星响应单机布局及总体热控提供设计参考。
  • 科工局民用航天技术预先研究项目(D010105)
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doi: 10.12347/j.ycyk.20241217006
  • 接收时间:2024-12-17
  • 首发时间:2026-03-13
  • 出版时间:2025-03-15
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  • 收稿日期:2024-12-17
  • 修回日期:2025-02-10
基金
科工局民用航天技术预先研究项目(D010105)
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    上海卫星工程研究所 上海 201109
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