为满足30 m望远镜(TMT)三镜系统(M3S)对质量和刚度的要求, 研究了合理分配该系统各部分刚度的方法。针对M3S的第一阶谐振频率不小于15 Hz的要求, 本文基于M3S的结构组成对模型进行适当地简化, 然后使用前期设计数据建立了四质量点弹簧-质点模型。研究了三镜支撑系统支撑刚度的组成, 使用特征值反解的方法得到了简化模型在6个广义方向上的刚度矩阵。最后,给出了系统中所有弹簧代表的刚度, 并将这一简化模型和计算结果用来指导后期的结构设计和控制设计。使用运动学仿真软件Adams对分配结果进行了验证, 验证结果显示, M3S各部分刚度配比合理, 系统的基频能够达到15.1 Hz, 满足设计要求。采用本文的刚度分配方法, 可以有效地提高系统设计的效率与合理性。

To meet the requirements of the Tertiary Mirror System (M3S) in a Thirty Meter Telescope(TMT) for mass and stiffness, how to allocate rationally the stiffness for different parts in the system was researched. As the first-order resonant frequency of M3S should not be less than 15 Hz, the composition of M3S was researched, then a four-point lumped-mass model was established by the pre-designed data. Furthermore, the stiffness of the mirror support system was calculated, and an eigenvalue inverse solution was used to obtain the stiffness matrix of a simplified model in six global directions. Finally, stiffness of all springs in the system was given, and the simplified model and the calculated results were used to guide the structure design and control design later. The simulation software Adams was used to verify the stiffness allocation and analysis process. The results show that the stiffness allocation of the M3S is reasonable and the first modal frequency of the system can achieve to 15.2 Hz, which meets the design requirements. With the stiffness allocation, the system design can offer higher efficiency and rationality.