空间可展天线精度测量、热分析、可靠性分析及间隙影响研究
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摘要
可展结构作为一种新型结构形式,近些年来在许多领域都得到了广泛的应用,根据其用途不同可分为空间可展结构和地面可展结构。随着空间科技的发展,各相关学科对空间可展天线提出了更高的要求,主要体现在大口径、高精度两方面,为此各国研究机构研究并设计了多种形式的空间可展天线。本文对空间可展天线的精度测量、热分析、结构分析、可靠性分析、间隙影响及展开过程分析进行了深入系统的研究。
论文首先在查阅大量国内外文献的基础上,介绍了空间可展天线的应用情况,分别从反射面精度测量、可展天线热-结构分析、可展天线可靠性分析、间隙对结构的影响分析和可展结构展开分析五个方面介绍了空间可展天线结构的研究现状,进而阐述了课题的研究意义。
对摄影测量中影响系统测量精度的因素进行了分析,并对提高系统测量精度的方法进行了深入分析。利用最小二乘法原理推导了最佳吻合抛物面拟合公式,利用牛顿法推导了反射面形面精度RMS的数值计算方法,并通过程序实现。针对于尺寸较大反射面的精度测量,提出了分片测量拼装组合方法,并对此方法的测量过程及测量中的一些数值计算方法进行了研究。基于PhotoModeler软件构建了摄像测量系统,对3.2m口径的充气可展天线进行了精度测量试验,分别采用整体一次测量和分片测量拼装组合方法进行测量,两种方法所得结果十分接近,表明分片测量拼装组合的数值计算方法在天线反射面形面精度测量中具有足够的精度,可用于大口径天线反射面的精度测量。之后采用分片测量拼装组合的方法对一个6.2m口径的充气可展天线进行了精度测量试验。
讨论了空间可展开天线的热传递方式和热平衡关系,讨论了三种空间外热流的计算,即太阳辐射外热流,地球反照外热流和地球红外辐射外热流,并从几何上推导了一种太阳同步轨道条件下三种外热流及阴影的数值计算方法。基于有限元理论,建立了一维两节点杆单元和二维三节点三角形单元的瞬态导热一辐射微分方程,通过引入边界条件得到了相应的泛函公式,进而建立了空间可展天线温度场计算迭代方程。利用上述理论编制了基于FORTRAN语言的有限元程序。针对一个算例计算了一种太阳同步轨道条件下在春分、夏至、秋分、冬至四个时刻在一个周期内结构的温度场随时间的动态变化关系。通过分析得出了此轨道条件下对天线不利的时刻,可用于指导热控制设计。
对多场耦合问题的数学模型和耦合关系进行了深入分析。针对空间可展桁架天线结构的特点,利用非线性有限元理论,建立了结构热变形计算方程。将可展桁架天线热分析与结构分析进行了耦合,并编制了基于FORTRAN语言的程序。实现了热分析与结构分析的直接转化和耦合。利用上述理论对一个算例进行了分析,用反射面形面误差RMS作为衡量热变形的指标。针对一种太阳同步轨道条件,计算了春分、夏至、秋分、冬至四个特定时刻在一个周期内结构的温度场随时间和反射面形面误差RMS随时间的动态变化关系,通过分析得出对天线不利的时刻。利用ANSYS对结构进行了热致动力响应分析,比较了上述四个特定时刻在一个周期内节点加速度随时间的变化,通过分析验证了前面对天线不利的时刻的判断。
构建了单元的失效概率函数；将天线系统看作是各个单元组成的串联系统,推导了串联系统中,单元的可靠度与整体系统的可靠度的关系。利用故障树理论构建了天线的失效模型,分析了底事件失效概率和重要度的计算方法,在此基础上利用概率理论建立了天线系统失效概率方程。利用动力学理论建立桁架式可展开天线展开分析方程,对不同位置处扭簧失效时天线的展开过程进行分析,进而得出失效时使天线无法完全展开或使其展开形面精度很差的扭簧位置和失效后对天线展开及其展开形面精度基本没有影响的扭簧位置,并将其引入到天线可靠性分析模型中。分别运用常规的故障树理论和基于模糊原理的故障树理论对天线的可靠度进行了分析。
从几何上对桁架式可展天线节点间隙进行了推导,结合概率理论得到节点间隙引起杆长变化的概率分布函数。利用将杆件变形等效为单元内力的方法推导了确定天线形状的方法。构建了Monte Carlo随机分析模型。最后通过一个算例分析了节点间隙对天线形面精度的影响,得出结论,对于一般的天线来说,间隙所引起的形面变化对反射面精度的影响较小,设计时可以忽略；但对于高精度的天线来说,在结构设计时仍然需要考虑间隙的影响,并尽量减小其影响。
从几何方面分析了二维折纸模型的折叠准则。从刚体运动学出发,用刚体来描述板壳结构,利用广义逆矩阵原理,推导了可展板壳结构运动分析方程。对基于二维折纸模型的二维可展板壳结构进行了分析,发现此类结构在折叠、展开过程中各块板之间需要发生一定的弹塑性变形,进行了相应的约束处理,并通过一个例子模拟了此类结构的展开过程。
As a new kind of structure, deployable structures are more and more widely used in many fields recent years. They can be divided into space deployable structures and ground deployable structures by differentiations. Following the development of the aerospace technology, higher performance requirements are brought forward to deployable antennas on satellites from each relative field, which mainly focus on larger caliber and less surface error. And because of it, many kinds of space deployable antennas are studied and designed by research institutes from many countries. Measurement of surface precision, thermal analysis, structural analysis, reliability analysis, influence of clearance and deployment process for space deployable antennas have been studied systematically in this dissertation.
Firstly, after referring a lot of pertinent literature worldwidely, applications of space deployable antennas are introduced and the research actuality on measurement of surface precision, thermal analysis, structural analysis, reliability analysis, influence analysis of clearance and deployment process analysis for space deployable antennas are summarized, then the research significance is presented.
Factors which affect measuring accuracy of the system in photogrammetry are analyzed, and methods that can improve measuring accuracy of the system are analyzed systematically. Fitting formulas for the best fitting paraboloid are deduced, and numerical computation method on surface error of the reflector'RMS'is deduced based on Newton method, and the program is made. According to surface precision measurement of the reflector with large caliber, the method by which each part of the reflector is measured independently then combined together is proposed, measuring process of the method and some numerical computation methods in the measuring process are studied. A non-contact photogrammetric measure system is built on the base of Photomodeler software packages, and a surface precision experiment on a membrane inflatable antenna with 3.2m caliber is made. The method by which the whole reflector is measured once and the method by which each part of the reflector is measured independently then combined together are both used. And the two results obtained through the two methods are very close, and it is concluded that the method by which each part of the reflector is measured independently then combined together is precise enough for surface precision measurement of the antenna, and it can be used in surface precision measurement of antennas with large caliber. Then using the method by which each part of the reflector is measured independently then combined together, another surface precision experiment on a membrane inflatable antenna with 6.2m cal iber is made.
Heat transfer, heat balance, computation of three kinds of space external thermal flow, external thermal flow of sun, external thermal flow of earth shine and external thermal flow of earth infrared radiation are discussed. And a numerical computation method on the three kinds of external thermal flow and shadow for an antenna in a sun-synchronous orbit is deduced based on geometric theory. Based on finite element theory, the transient conduction-radiation differential equation is established using one-dimensional bar element with two nodes and two-dimensional triangular element with three nodes. Corresponding functional formulas are obtained through introducing boundary conditions. Then iterative equations for temperature field computation of deployable antennas are established. Using FORTRAN, a finite element program based on the theory above is built. According to an example, temperature fields changing with time for an antenna in a sun-synchronous orbit in a cycle are calculated respectively at vernal equinox, summer solstice, autumn equinox and winter solstice. Time that is unfavorable for the antenna in the orbit is concluded through analysis, and it can be used for thermal controlling design.
Mathematical models for coupling of many fields and coupling relationships are analyzed in detailed. According to characteristics of space deployable truss antennas, using non-liner finite element theory, formulations to analyze thermal deformation are established. Then the thermal analysis and structural analysis for deployable truss antennas are coupled, and a program is made based on FORTRAN. Direct conversion and coupling from thermal analysis to structural analysis for deployable truss antenna is real ized. An example is analyzed by the theory above, the reflector surface error RMS is used as the index to reflect the deformation. Temperature fields and reflector surface errors RMS changing with time for an antenna in a sun-synchronous orbit in a cycle are calculated respectively at vernal equinox, summer solstice, autumn equinox and winter solstice. Time that is unfavorable for the antenna in the orbit is concluded through analysis. Dynamic responses by temperature fields are analyzed. Accelerations of a joint changing with time in a cycle at four special times above are compared and the time obtained before that is unfavorable for the antenna in the orbit is verified.
The failure probability function of an element is established. The antenna is a serial system made up of each element. The relationship between reliability degree of an element and that of the whole system in a serial system is deduced. Failure model of the truss deployable antenna is established using faulty tree theory, computational methods for failure probability and importance degree of basic events are analyzed and based on it failure probability formulations for the antenna are established using probability theory; deployment analysis formulations for deployable truss antenna are established using dynamic theory and deployment process of the antenna is analyzed when there are torsional spring failures at different positions, then those positions where the antenna could not deploy fully or the surface error is very high when torsional springs fail are obtained, and those positions where the antenna could deploy smoothly and the surface error is low when torsional springs fail are also obtained. These results and reliability analysis are combined. The reliability analysis on the antenna is made using conventional faulty tree theory and faulty tree theory based on fuzzy theory relatively.
The clearance at the joint of the truss deployable antenna is calculated based on geometric theory. And combing probability theory, the probability distribution function of elongation of the rod caused by clearance is obtained. A model for random analysis is established based on Monte Carlo theory. The effect of clearance at the joint on reflector surface precision is analyzed through an example. And it is concluded that the effect of clearance on reflector surface precision is weak for a common antenna, it can be neglected. But the effect should be considered during design for antennas with high precision, and the effect should be reduced.
Folding code of 2D paper-folding models is analyzed based on geometric theory. Based on rigid body kinematics, equations for motion analysis of deployable panel and shell structures are deduced using Moore-Penrose generalized inverse matrix theory. Two-dimensional deployable panel and shell structures based on a two-dimensional paper-folding models are analyzed. It is shown that there are elastic-plastic deformations between panels in these kinds of structures during folding and deployment process, and the deformations are simulated by corresponding constraint handling. The deployment process is simulated through an example.
论文首先在查阅大量国内外文献的基础上,介绍了空间可展天线的应用情况,分别从反射面精度测量、可展天线热-结构分析、可展天线可靠性分析、间隙对结构的影响分析和可展结构展开分析五个方面介绍了空间可展天线结构的研究现状,进而阐述了课题的研究意义。
对摄影测量中影响系统测量精度的因素进行了分析,并对提高系统测量精度的方法进行了深入分析。利用最小二乘法原理推导了最佳吻合抛物面拟合公式,利用牛顿法推导了反射面形面精度RMS的数值计算方法,并通过程序实现。针对于尺寸较大反射面的精度测量,提出了分片测量拼装组合方法,并对此方法的测量过程及测量中的一些数值计算方法进行了研究。基于PhotoModeler软件构建了摄像测量系统,对3.2m口径的充气可展天线进行了精度测量试验,分别采用整体一次测量和分片测量拼装组合方法进行测量,两种方法所得结果十分接近,表明分片测量拼装组合的数值计算方法在天线反射面形面精度测量中具有足够的精度,可用于大口径天线反射面的精度测量。之后采用分片测量拼装组合的方法对一个6.2m口径的充气可展天线进行了精度测量试验。
讨论了空间可展开天线的热传递方式和热平衡关系,讨论了三种空间外热流的计算,即太阳辐射外热流,地球反照外热流和地球红外辐射外热流,并从几何上推导了一种太阳同步轨道条件下三种外热流及阴影的数值计算方法。基于有限元理论,建立了一维两节点杆单元和二维三节点三角形单元的瞬态导热一辐射微分方程,通过引入边界条件得到了相应的泛函公式,进而建立了空间可展天线温度场计算迭代方程。利用上述理论编制了基于FORTRAN语言的有限元程序。针对一个算例计算了一种太阳同步轨道条件下在春分、夏至、秋分、冬至四个时刻在一个周期内结构的温度场随时间的动态变化关系。通过分析得出了此轨道条件下对天线不利的时刻,可用于指导热控制设计。
对多场耦合问题的数学模型和耦合关系进行了深入分析。针对空间可展桁架天线结构的特点,利用非线性有限元理论,建立了结构热变形计算方程。将可展桁架天线热分析与结构分析进行了耦合,并编制了基于FORTRAN语言的程序。实现了热分析与结构分析的直接转化和耦合。利用上述理论对一个算例进行了分析,用反射面形面误差RMS作为衡量热变形的指标。针对一种太阳同步轨道条件,计算了春分、夏至、秋分、冬至四个特定时刻在一个周期内结构的温度场随时间和反射面形面误差RMS随时间的动态变化关系,通过分析得出对天线不利的时刻。利用ANSYS对结构进行了热致动力响应分析,比较了上述四个特定时刻在一个周期内节点加速度随时间的变化,通过分析验证了前面对天线不利的时刻的判断。
构建了单元的失效概率函数；将天线系统看作是各个单元组成的串联系统,推导了串联系统中,单元的可靠度与整体系统的可靠度的关系。利用故障树理论构建了天线的失效模型,分析了底事件失效概率和重要度的计算方法,在此基础上利用概率理论建立了天线系统失效概率方程。利用动力学理论建立桁架式可展开天线展开分析方程,对不同位置处扭簧失效时天线的展开过程进行分析,进而得出失效时使天线无法完全展开或使其展开形面精度很差的扭簧位置和失效后对天线展开及其展开形面精度基本没有影响的扭簧位置,并将其引入到天线可靠性分析模型中。分别运用常规的故障树理论和基于模糊原理的故障树理论对天线的可靠度进行了分析。
从几何上对桁架式可展天线节点间隙进行了推导,结合概率理论得到节点间隙引起杆长变化的概率分布函数。利用将杆件变形等效为单元内力的方法推导了确定天线形状的方法。构建了Monte Carlo随机分析模型。最后通过一个算例分析了节点间隙对天线形面精度的影响,得出结论,对于一般的天线来说,间隙所引起的形面变化对反射面精度的影响较小,设计时可以忽略；但对于高精度的天线来说,在结构设计时仍然需要考虑间隙的影响,并尽量减小其影响。
从几何方面分析了二维折纸模型的折叠准则。从刚体运动学出发,用刚体来描述板壳结构,利用广义逆矩阵原理,推导了可展板壳结构运动分析方程。对基于二维折纸模型的二维可展板壳结构进行了分析,发现此类结构在折叠、展开过程中各块板之间需要发生一定的弹塑性变形,进行了相应的约束处理,并通过一个例子模拟了此类结构的展开过程。
As a new kind of structure, deployable structures are more and more widely used in many fields recent years. They can be divided into space deployable structures and ground deployable structures by differentiations. Following the development of the aerospace technology, higher performance requirements are brought forward to deployable antennas on satellites from each relative field, which mainly focus on larger caliber and less surface error. And because of it, many kinds of space deployable antennas are studied and designed by research institutes from many countries. Measurement of surface precision, thermal analysis, structural analysis, reliability analysis, influence of clearance and deployment process for space deployable antennas have been studied systematically in this dissertation.
Firstly, after referring a lot of pertinent literature worldwidely, applications of space deployable antennas are introduced and the research actuality on measurement of surface precision, thermal analysis, structural analysis, reliability analysis, influence analysis of clearance and deployment process analysis for space deployable antennas are summarized, then the research significance is presented.
Factors which affect measuring accuracy of the system in photogrammetry are analyzed, and methods that can improve measuring accuracy of the system are analyzed systematically. Fitting formulas for the best fitting paraboloid are deduced, and numerical computation method on surface error of the reflector'RMS'is deduced based on Newton method, and the program is made. According to surface precision measurement of the reflector with large caliber, the method by which each part of the reflector is measured independently then combined together is proposed, measuring process of the method and some numerical computation methods in the measuring process are studied. A non-contact photogrammetric measure system is built on the base of Photomodeler software packages, and a surface precision experiment on a membrane inflatable antenna with 3.2m caliber is made. The method by which the whole reflector is measured once and the method by which each part of the reflector is measured independently then combined together are both used. And the two results obtained through the two methods are very close, and it is concluded that the method by which each part of the reflector is measured independently then combined together is precise enough for surface precision measurement of the antenna, and it can be used in surface precision measurement of antennas with large caliber. Then using the method by which each part of the reflector is measured independently then combined together, another surface precision experiment on a membrane inflatable antenna with 6.2m cal iber is made.
Heat transfer, heat balance, computation of three kinds of space external thermal flow, external thermal flow of sun, external thermal flow of earth shine and external thermal flow of earth infrared radiation are discussed. And a numerical computation method on the three kinds of external thermal flow and shadow for an antenna in a sun-synchronous orbit is deduced based on geometric theory. Based on finite element theory, the transient conduction-radiation differential equation is established using one-dimensional bar element with two nodes and two-dimensional triangular element with three nodes. Corresponding functional formulas are obtained through introducing boundary conditions. Then iterative equations for temperature field computation of deployable antennas are established. Using FORTRAN, a finite element program based on the theory above is built. According to an example, temperature fields changing with time for an antenna in a sun-synchronous orbit in a cycle are calculated respectively at vernal equinox, summer solstice, autumn equinox and winter solstice. Time that is unfavorable for the antenna in the orbit is concluded through analysis, and it can be used for thermal controlling design.
Mathematical models for coupling of many fields and coupling relationships are analyzed in detailed. According to characteristics of space deployable truss antennas, using non-liner finite element theory, formulations to analyze thermal deformation are established. Then the thermal analysis and structural analysis for deployable truss antennas are coupled, and a program is made based on FORTRAN. Direct conversion and coupling from thermal analysis to structural analysis for deployable truss antenna is real ized. An example is analyzed by the theory above, the reflector surface error RMS is used as the index to reflect the deformation. Temperature fields and reflector surface errors RMS changing with time for an antenna in a sun-synchronous orbit in a cycle are calculated respectively at vernal equinox, summer solstice, autumn equinox and winter solstice. Time that is unfavorable for the antenna in the orbit is concluded through analysis. Dynamic responses by temperature fields are analyzed. Accelerations of a joint changing with time in a cycle at four special times above are compared and the time obtained before that is unfavorable for the antenna in the orbit is verified.
The failure probability function of an element is established. The antenna is a serial system made up of each element. The relationship between reliability degree of an element and that of the whole system in a serial system is deduced. Failure model of the truss deployable antenna is established using faulty tree theory, computational methods for failure probability and importance degree of basic events are analyzed and based on it failure probability formulations for the antenna are established using probability theory; deployment analysis formulations for deployable truss antenna are established using dynamic theory and deployment process of the antenna is analyzed when there are torsional spring failures at different positions, then those positions where the antenna could not deploy fully or the surface error is very high when torsional springs fail are obtained, and those positions where the antenna could deploy smoothly and the surface error is low when torsional springs fail are also obtained. These results and reliability analysis are combined. The reliability analysis on the antenna is made using conventional faulty tree theory and faulty tree theory based on fuzzy theory relatively.
The clearance at the joint of the truss deployable antenna is calculated based on geometric theory. And combing probability theory, the probability distribution function of elongation of the rod caused by clearance is obtained. A model for random analysis is established based on Monte Carlo theory. The effect of clearance at the joint on reflector surface precision is analyzed through an example. And it is concluded that the effect of clearance on reflector surface precision is weak for a common antenna, it can be neglected. But the effect should be considered during design for antennas with high precision, and the effect should be reduced.
Folding code of 2D paper-folding models is analyzed based on geometric theory. Based on rigid body kinematics, equations for motion analysis of deployable panel and shell structures are deduced using Moore-Penrose generalized inverse matrix theory. Two-dimensional deployable panel and shell structures based on a two-dimensional paper-folding models are analyzed. It is shown that there are elastic-plastic deformations between panels in these kinds of structures during folding and deployment process, and the deformations are simulated by corresponding constraint handling. The deployment process is simulated through an example.
引文
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