张拉薄膜结构力学特性分析及三棱柱式薄膜支撑臂设计.pdf

嗨thesis 博士学位论文博士学位论文 张拉薄膜结构力学特性分析及三棱柱式薄膜 支撑臂设计 MECHANICAL CHARACTERISTICS ANALYSIS OF TENSIONED MEMBRANE STRUCTURE AND DESIGN OF TRIANGULAR PRISM MEMBRANE SUPPORT MAST 李冰岩李冰岩 哈尔滨工业大学哈尔滨工业大学 2021 年年 6 月月 国内图书分类号V443.4 国际图书分类号621 学校代码10213 密级公开 工学博士学位论文工学博士学位论文 张拉薄膜结构力学特性分析及三棱柱式薄膜 支撑臂设计 博 士 研 究 生李冰岩 导师刘荣强 教授 申 请 学 位工学博士 学科航空宇航科学与技术 所 在 单 位机电工程学院 答 辩 日 期2021 年 6 月 授予学位单位哈尔滨工业大学 Classifi ed Index V443.4 U.D.C 621 Dissertation for the Doctoral Degree in Engineering MECHANICAL CHARACTERISTICS ANALYSIS OF TENSIONED MEMBRANE STRUCTURE AND DESIGN OF TRIANGULAR PRISM MEMBRANE SUPPORT MAST CandidateLi Bingyan SupervisorProfessor Liu Rongqiang Academic Degree Applied for Doctor of Engineering SpecialtyAeronautical and Astronautical Science and Technology Affi liationSchool of Mechatronics Engineering Date of DefenceJune, 2021 Degree-Conferring-Institution Harbin Institute of Technology 摘要 摘要 随着大型航天器在空间探索中发挥着越来越重要的作用，大型轻量化结构的 发展越来越受到重视。薄膜结构质量轻、展收比大， 具有在未来航天器上应用的巨 大潜力，主要包括天线、太阳帆、太阳电池阵、遮光罩和光学成像镜等应用领域。 作为一种预应力结构，薄膜在刚度和稳定性方面相比传统结构具有不同力学特性， 在空间应用中会产生更为复杂的技术问题，只有继续完善薄膜理论才能从根本上 打破技术层面的制约。薄膜在空间中的应用依赖于展开结构的支撑，而薄膜结构 对边界条件敏感的特性对大尺度支撑结构提出了更高的设计要求。虽然弹性伸杆 适合展开薄膜，但其个体刚度较低，承载能力较弱，在大尺度空间薄膜结构上的应 用受到了限制，无法充分发挥其可展开、质量轻的优势。在使用薄膜结构服务于 空间探索任务时，既需要解决分析薄膜时的理论难点，提高对薄膜结构力学特性 的认知程度，又需要丰富薄膜支撑结构设计，增强薄膜结构在空间中的应用能力， 本文从这两个角度出发，一方面进行了薄膜结构理论建模和力学特性分析，另一 方面进行了基于豆荚杆展开的三棱柱式薄膜支撑臂设计。 本文基于前褶皱薄膜结构张拉的对称性，提出张拉薄膜结构应力叠加法。通 过应力叠加组的划分，将多点张拉矩形薄膜的应力分布求解解耦为角点拉力、长 边点拉力和宽边点拉力这三种拉力分别作用下的应力分布计算，提出每种作用力 下应力区域划分方式和应力计算方法，从而实现对薄膜结构应力分布的解析求解。 考虑了薄膜的几何刚度、网格划分和空气附加质量，建立薄膜自由振动方程。给 出薄膜内任一点受力确定方法，构建基于应力叠加法的自由振动计算流程。 基于应力叠加法理论，计算角点张拉和多点张拉薄膜的应力分布，通过与有 限元仿真结果的对比，对张拉薄膜结构应力分布的理论结果进行验证。基于多点 张拉薄膜结构地面实验要求，设计薄膜动力学实验平台，构建薄膜振动测试系统。 对比理论结果与文献中现有实验数据，并结合不同张拉薄膜研究对象，通过仿真、 实验和理论计算三种方式，综合比较薄膜应力分布和结构模态，验证应力叠加法 及基于此方法的薄膜自由振动计算结果。 利用提出的应力叠加法和自由振动计算理论，研究张拉边界参数对薄膜应力 分布与前六阶模态的影响。在角点张拉的矩形薄膜中分析花边弧度在不同长宽比 条件下对薄膜力学特性的影响；提出大气和真空环境下各阶对应频率比值变化公 式；分析薄膜应力分布和结构模态随长宽比的变化；对比分析长、宽边点拉力值和 - I - 哈尔滨工业大学工学博士学位论文 拉力点密度对薄膜应力分布、纵向模态和横向模态影响的差异，根据力学特性分 析，提出长条形薄膜的张拉设计方法，得到薄膜结构的设计依据。 基于大尺度薄膜结构的空间应用背景，设计基于豆荚杆展开的三棱柱式空间 薄膜支撑臂构型，采用双层绳索张拉方式提高对薄膜的支撑刚度。在豆荚杆建模 基础上，根据能量等效原理，推导三棱柱桁架等效梁模型，结合并联机构理论，建 立支撑臂张拉等效 23-SPS-S 机构模型。以桁架单位长度质量最小为目标建立三 棱柱桁架弯曲性能指标，设计豆荚杆截面参数。以支撑臂张拉支撑刚度最大为优 化目标设计支撑臂张拉参数，并通过有限元仿真验证等效模型的正确性，确定质 量与刚度综合特性最优的薄膜支撑臂结构参数。结合薄膜在三棱柱桁架上的应用 背景，设计三棱柱式薄膜支撑臂原理样机，通过实验验证三棱柱桁架与薄膜之间 的动力学耦合模型，为薄膜在空间结构中的设计和应用提供参考依据。 关键词薄膜结构；应力叠加法；自由振动；三棱柱式支撑臂；等效机构 - II - Abstract Abstract With large spacecraft playing a more and more important role in space exploration, the development of large lightweight structure is paid more and more attention. Due to its light weight and high aspect ratio, the membrane structure has a huge potential to be used in future spacecraft, including antennas, solar sails, solar arrays, sunshields and optical imaging mirrors. As a kind of tensioned structure, membrane has diff erent characteristics in terms of stiff ness and stability compared with the traditional structures, which will produce more complex technical problems in the space application. Only by continuing to develop the membrane theory can the technical constraints be fundamentally broken through. The application of membrane in space depends on the support of deployable structures, but the sensitivity of membrane structure to boundary conditions puts forward higher design requirements for the large-scale support mast. Due to its low stiff ness and weak bearing capacity, the collapsible tubular mast suitable for deploying membrane is limited in the application of large-scale space membrane structures, which can not give full play to its advantages of foldability and lightweight. When the membrane structure serves the space exploration task, it is necessary to solve the diffi culties and shortcomings of membrane theory, develop the understanding of the mechanical characteristics of membrane structure, enrich the design of membrane support structure, and enhance the application ability of membrane structure in space. From these two angles, on the one hand, thispaperconductsthetheoreticalmodelingandmechanicalcharacteristicsanalysis of the membrane structure. On the other hand, the triangular prism membrane support mast based on collapsible tubular masts is designed. In this paper, based on the tension symmetry of the pre-wrinkling membrane, the stress superposition of tensioned membrane is proposed. Through the division of stress superposition group, the stress distribution of multi-point tensioned rectangular membraneisdecoupledintothecalculationofstressdistributionsundereachvertexcorner load, length corner load and width corner load, respectively. The division s of stress regionsandthestresscalculationmeansundereachtensionareproposed,thusestablishing the analytical solution for the membrane stress distribution. Considering the geometric stiff ness, mesh generation and air added mass of the membrane, the free vibration equation of the membrane is established. The to determine the eff ective - III - 哈尔滨工业大学工学博士学位论文 forces for any point in the membrane is given, and the calculation fl ow of free vibration based on stress superposition is established. Based on the stresssuperposition , the stressdistributions of corner tensioned and multi-point tensioned membranes are calculated.By comparing with the results of fi nite element simulation, the theoretical results of stress distribution of tensioned membrane structure are verifi ed. Based on the requirements of multi-point tensioned membrane ground experiment, the membrane dynamic experiment plat is designed, and the membrane vibration test system is established. The theoretical results are com- pared with the experimental data available in the literature. Analyzing diff erent research objects of tensioned membrane structures through simulation, experiment and theoretical computation, the stress distribution and modal results of membrane structures are com- pared comprehensively to verify the stress superposition and the membrane free vibration calculation based on this . Based on the established stress superposition and free vibration calculation theory, the eff ects of tension boundary parameters on membrane stress distribution and the fi rst six modes are studied. The infl uence of edge arcs on the mechanical character- istics is analyzed for the corner tensioned rectangular membranes with diff erent aspect ratios. The ula for each order’s fundamental frequency ratio of atmospheric to spatial environment is proposed. The change of membrane stress distribution and modes with aspect ratio is analyzed. The eff ects of the value and density of the length and width tension on the stress distribution, longitudinal modes and transverse modes are compared and analyzed. According to the analysis of mechanical characteristics, the tension design of the strip membrane is proposed, and the basis of membrane structure parameters is obtained. Based on the space application background of large-scale membrane structure, a triangularprismmembranesupportmastbasedonthecollapsibletubularmastisproposed, and the double-level guyed confi guration is adopted to improve the support stiff ness for the membrane. Based on the modeling of the collapsible tubular mast, according to the principle of energy equivalence, the equivalent beam model of the triangular prism mast is deduced. Combined with the theory of parallel mechanism, the equivalent 23-SPS-S mechanism model of the guyed support mast is established. Taking the minimum mass perunitlengthofmastastheoptimizationobjective,thebendingperanceindexofthe triangular prism mast is established, and the cross-section parameters of the collapsible - IV - Abstract tubular mast are designed. Taking the maximum support stiff ness of the guyed mast as the optimization objective, the parameters of the guyed support mast are designed. The correctnessoftheequivalentmodelisverifi edbyfi niteelementsimulation. Thestructural parameters of the membrane support mast with the optimal comprehensive characteristics of mass and stiff ness are obtained. Based on the application background of membrane in triangular prism truss, the experimental prototype of triangular prism membrane support mast is designed. The dynamic coupling model between the triangular prism truss and the membrane is verifi ed through experiments, which provides reference for the design and application of space membrane structures. Keywords Membrane structure, stress superposition , free vibration, triangular prism support mast, equivalent mechanism - V - 哈尔滨工业大学工学博士学位论文 目录 摘要 ...............................................................................................I ABSTRACT ......................................................................................III 第 1 章绪论 ..................................................................................... 1 1.1 课题来源及研究目的和意义 ........................................................... 1 1.1.1 课题来源 .............................................................................. 1 1.1.2 研究目的和意义 ..................................................................... 1 1.2 国内外研究现状及分析 ................................................................. 2 1.2.1 国外空间薄膜结构研究现状 ...................................................... 2 1.2.2 国内空间薄膜结构研究现状 ...................................................... 7 1.2.3 薄膜结构力学特性研究现状 .....................................................10 1.3 空间薄膜结构研究现状简析 ..........................................................14 1.4 本文的主要研究内容 ...................................................................15 第 2 章张拉薄膜结构应力叠加法与自由振动方程 ....................................17 2.1 引言 ........................................................................................17 2.2 角点张拉矩形薄膜的应力叠加 .......................................................17 2.3 多点张拉矩形薄膜的应力叠加 .......................................................23 2.3.1 矩形薄膜应力叠加组 ..............................................................23 2.3.2 角点拉力作用下的应力计算 .....................................................25 2.3.3 长边点拉力作用下的应力计算 ..................................................27 2.3.4 宽边点拉力作用下的应力计算 ..................................................30 2.4 张拉薄膜结构的自由振动方程 .......................................................33 2.4.1 薄膜单元 .............................................................................33 2.4.2 薄膜自由振动方程 .................................................................35 2.4.3 基于应力叠加法的结构模态分析流程 .........................................38 2.5 本章小结 ..................................................................................40 第 3 章张拉薄膜结构应力叠加法仿真与实验验证 ....................................41 3.1 引言 ........................................................................................41 3.2 张拉薄膜应力分布仿真验证 ..........................................................41 - VI - 目录 3.2.1 角点张拉薄膜应力分布仿真验证 ...............................................41 3.2.2 多点张拉薄膜应力分布仿真验证 ...............................................44 3.3 张拉薄膜结构模态实验验证 ..........................................................46 3.3.1 薄膜动力学实验平台设计 ........................................................46 3.3.2 角点张拉薄膜结构模态实验验证 ...............................................49 3.3.3 多点张拉薄膜结构模态实验验证 ...............................................54 3.4 本章小结 ..................................................................................59 第 4 章基于应力叠加法的张拉薄膜结构力学特性分析 ..............................60 4.1 引言 ........................................................................................60 4.2 角点张拉薄膜结构力学特性分析 ....................................................60 4.2.1 应力分布分析 .......................................................................60 4.2.2 结构模态分析 .......................................................................63 4.3 多点张拉薄膜结构应力分析 ..........................................................66 4.3.1 长宽比对应力分布的影响 ........................................................66 4.3.2 长边拉力点密度对应力分布的影响 ............................................71 4.3.3 宽边拉力点密度对应力分布的影响 ............................................73 4.4 拉力值对张拉薄膜力学特性影响分析 ..............................................76 4.4.1 长边点拉力值 .......................................................................76 4.4.2 宽边点拉力值 .......................................................................78 4.5 本章小结 ..................................................................................80 第 5 章三棱柱式展开薄膜支撑臂优化设计与实验 ....................................82 5.1 引言 ........................................................................................82 5.2 三棱柱式薄膜支撑臂构型设计与建模 ..............................................82 5.2.1 三棱柱式薄膜支撑臂构型设计 ..................................................82 5.2.2 豆荚杆建模 ..........................................................................85 5.2.3 三棱柱桁架单元 ....................................................................87 5.2.4 三棱柱桁架等效梁模型 ...........................................................91 5.2.5 支撑臂张拉等效模型 ..............................................................92 5.3 基于豆荚杆的三棱柱桁架设计 .......................................................98 5.3.1 三棱柱桁架弯曲变形分析 ........................................................98 5.3.2 豆荚杆截面参数优选 ............................................................ 100 5.4 支撑臂张拉参数优化设计 ........................................................... 102 5.4.1 张拉支撑臂优化模型 ............................................................ 102 - VII - 哈尔滨工业大学工学博士学位论文 5.4.2 支撑臂张拉参数优化 ............................................................ 104 5.5 薄膜支撑臂原理样机动力学实验 .................................................. 107 5.5.1 原理样机设计 ..................................................................... 107 5.5.2 动力学测试 ........................................................................ 109 5.6 本章小结 ................................................................................ 110 结论 ........................................................................................... 112 参考文献 ........................................................................................ 114 攻读博士学位期间发表的论文及其他成果 .............................................. 124 哈尔滨工业大学学位论文原创性声明和使用权限 ..................................... 126 致谢 ........................................................................................... 127 个人简历 ........................................................................................ 129 - VIII - Contents Contents Abstract In Chinese.............................................................................I Abstract In English ...........................................................................III Chapter 1 Introduction......................................................................... 1 1.1 Source, objective and signifi cance of the subject ..................................... 1 1.1.1 Source of issues..........................................................