变拓扑空间可展桁架多体系统动力学建模与分析

Dynamic modeling and analysis on a deployable space truss multibody system

随着空间折叠式桁架可展长度的增大与结构的复杂化,对空间大型展开机构动力学分析的计算规模逐渐增大。为了减少系统的广义坐标个数,该研究取铰的相对坐标为系统的广义坐标,基于单向递推组集方法建立太空望远镜桁架展开过程的动力学模型。利用Jourdain速度变分原理建立了各柔性部件的动力学变分方程,根据各柔性部件之间的运动学递推关系,并引入切断铰的约束方程,建立了柔性多体系统的刚-柔耦合动力学方程。针对柔性部件展开锁定时容易出现的数值计算问题,提出了在缓冲减速的基础上施加相对角约束的变拓扑方法。基于动力学模型对11节桁架单元的太空望远镜桁架展开过程进行数值仿真。为了进一步缩减计算规模,根据系统结构的对称性和纵向载荷分布的均匀性,将多个桁架和主镜组成的多体系统简化为单个桁架与主镜的一部分组成的系统进行数值仿真。将单个桁架系统展开过程的数值仿真结果与多个桁架系统的仿真结果进行对比,验证了简化动力学模型的准确性和有效性。在此基础上进一步对30节桁架单元的桁架展开过程进行数值仿真,通过对比柔性桁架与刚性桁架在展开和碰撞锁定过程中仿真结果的差异,分析了弹性变形对系统动力学特性的影响。

With the increase of the deployable length and the complexity of a space folded truss,the time cost of the numerical analysis on the deployment dynamics of the space truss system is increasing.In order to reduce the number of system generalized coordinates,the relative coordinates of joints were selected as system generalized coordinates,and the dynamic model for the folded truss of a space diffraction telescope during its deployment process was established based on the forward recursive formulation.The Jourdain’s velocity variation principle was employed to derive the variational equations of a single flexible body,and then the kinematic recursive relationship and the constraint equations of the cut joints were used to derive the rigid-flexible coupled dynamic equations of the system.In addition,concerning the numerical problem arising in the period of locking flexible components,a variable topology method was proposed,in which relative angle constraints were added on the revolute joints after the rotating speed was significantly reduced by damping torques.Based on the dynamic model,the numerical simulation and analysis of a folded truss system with 11 truss elements were carried out.In order to further reduce the time cost,according to the symmetric characteristics of the structure and the uniform distribution of the load in longitudinal direction,the deployable system,composed of multiple trusses and main mirror,was simplified to a single truss attached with a part of the main mirror.The correctness and effectiveness of the simplified method were verified by comparison of the simulation results with those obtained by the complex model.Finally,a folded truss system with 30 truss elements was analysed accordingly.The dynamic performance of the flexible truss in the process of deployment and locking was compared with that of the rigid truss system and the effect of the elatic deformation was analyzed.