带多充液贮箱及柔性附件航天器模块化建模与耦合动力学研究

Modern large spacecraft are generally designed to install with multiple liquid-filled tanks and flexible appendages. The attitude and orbit motion of spacecraft, the liquid sloshing in tanks and the free vibration of appendages will give rise to the result of complex coupling dynamics, by which produced the unbalanced interference cannot be treated as a bounded and regular external force. It may unlikely affect the efficiency and accuracy of the spacecraft control system, and even results in failure of the flight mission. In view of the disadvantages that the incompletely described the sloshing dynamics are always existed in all of traditional mechanical equivalent model of liquid sloshing. And for most of the coupled analysis methods of liquid-filled spacecraft, the disadvantage of the unidirectional mode of liquid sloshing is considered. In the present project, an attitude-orbit-liquid-flexible coupling dynamic analysis method and modular modeling method for spacecraft with multiple liquid-filled cylindrical tanks, spherical tanks or ellipsoidal tanks, along with flexible appendages, are systematically obtained by considered the influence of multi-order and multi-directional full liquid sloshing mode. Through theoretical analysis, experimental research and numerical simulation, coupled dynamic characteristics of total spacecraft system or subsystem will be studied. The unknown potential coupling dynamics and unstable factors of the spacecraft system will be mainly researched, and some dependable theoretical references will be provided for practical engineering.

现代大型航天器一般均安装有多个充液贮箱和柔性附件，航天器主体的姿态与轨道运动、贮箱内的液体晃动和柔性附件的自由振动之间会共同产生复杂的耦合动力学效应，其产生的非平衡干扰将不能简单处理为有界、规则的外力，且极易影响航天器控制系统的执行效率和精度，甚至导致飞行任务的失败。针对传统液体晃动等效力学模型均存在不能完整描述晃动特性的缺点，以及现有大部分充液航天器耦合动力学分析方法中仅考虑液体晃动单向模态时的不足，本项目将充分考虑贮箱内液体多阶、多向晃动全模态的影响，分别较系统的得到带多充液圆柱贮箱、球形贮箱或椭球贮箱以及柔性附件航天器的模块化建模方法和姿-轨-液-柔耦合动力学分析体系，编制出相应的窗口化、可视化仿真平台。通过理论分析、实验研究和数值仿真，具体研究航天器系统整体或各子系统的耦合动力学特性，重点探讨和分析航天器系统中未知的潜在耦合动力学特性和不稳定性因素，为实际工程中提供可靠的理论参考。

针对现代航天器因携带多类型充液贮箱及大型可机动柔性附件而导致的动力学建模困难，本项目的研究内容主要围绕充液贮箱内的液体晃动特性分析、柔性附件的动力学建模和航天器整体模块化动力学建模等领域较系统开展相关理论与实验分析，具体工作内容分别有：（1）设计了一种能同时实现充液贮箱整体固定安装和液体动态晃动力、力矩精确测量的实验装置，给出了相应的实验数据采集、分析和处理方法。通过开展大量实验，将实验数据与CFD仿真结果进行细致对比后发现：在旋转晃动状态下，CFD仿真结果存在明显的计算偏差，不便被独立的用于完整揭示贮箱内液体晃动的真实特性。进一步，归纳了贮箱内液体的非线性稳态晃动行为随横向外激励频率的变化规律，并对比分析了驻波晃动、拍振晃动、多类复杂的旋转晃动等多种不同形式的非线性稳态晃动行为及其对运载工具控制系统的任务执行效率和稳定性的影响。(2)针对传统等效力学模型在描述贮箱内液体晃动特性时存在准确性和完整性等方面不足的现状。运用势流理论推导出部分充液贮箱液体的动力学状态方程，依据方程中液体晃动速度势函数与晃动波高函数中傅立叶-贝塞尔级数展开系数的正交性条件，将不同类型贮箱内液体晃动的求解区域向与之外相切的圆柱贮箱求解区域内进行扩展，建立用于描述球形贮箱内液体晃动问题的参数化等效灰度模型。利用MATLAB的灰箱辨识函数对所建立的参数化等效灰度模型中的待定系数进行准确的辨识，实现了球形贮箱内液体横向晃动问题的高精度等效建模。（3）基于薄板小幅振动理论，运用有限单元法建立了柔性附件四边形板单元动力学模型，将附件相对航天器变化的姿态角代入坐标转换矩阵构造柔性附件作大范围机动时的时变坐标转换矩阵。基于凯恩方程推导了航天器整体系统的动力学状态方程，利用MATLAB软件编制出相应的模块化建模程序。最后，通过数值算例分析，研究了典型构型航天器中柔性附件以不同方式机动的系统整体耦合动力学性能，验证了该建模方法的通用性、适用性和准确性。