为了给聚焦镜热控及支撑结构优化设计提供依据, 对爱因斯坦探针项目中的后随X射线望远镜的镜片组进行了三维全尺寸建模与有限元分析.研究了轴向、径向两种温度梯度, 以及有、无支 撑结构对镜片组形变的影响, 并对面形误差与温差范围的关系进行了探究.结果表明: 对于无支撑结构, 轴向温度梯度下面形误差与半径关系接近线性关系, 径向温度梯度下则接近分段二次关系; 支撑结构发生热变形时, 会使镜片组产生与之对应的面形误差, 令同相圆度误差转变为异相圆度误差, 并使镜片组整体面型误差峰谷值增加32.25%~123.01%, 均方根值增加4.13%~5.14%; 对于有支 撑结构, 热致面形误差与温差成正比, 温差每增加1℃, 轴向温度梯度下, 面形误差峰谷值与均方根值分别增加7.76 μm、1.12 μm, 而对于径向温度梯度则分别增加9.67 μm、1.60 μm.聚焦镜片 热致面形误差在一定情况下与镜片尺寸、温差成线性关系, 并受到支撑结构变形的显著影响.

In order to provide a basis for the thermal control of the focusing telescope and the optimal design of the support structure, the three-dimensional full-size modeling and finite element analysis of the follow-up X-ray telescope′s mirrors group in the Einstein probe project are carried out. The influence of axial and radial temperature gradients, as well as the supported and unsupported structures on the deformation of the mirrors group is studied. The relationship between the surface error and the temperature difference is explored. The results show that the relation between the surface error and the mirrors′ radius for unsupported structures under the axial temperature gradient is close to the linear relation, while the relation under the radial temperature gradient is close to the piecewise quadratic relation. When the support structure is thermally deformed, the surface error corresponding to that occurs in the mirrors group. That transforms the in-phase roundness error into the out-of- phase roundness error, and increases the Peak-to-Valley value of the overall surface error of the mirrors group by 32.25%~123.01%, and the Root-Mean-Square value by 4.13%~5.14%. For supported structures, the thermally induced surface error is proportional to the temperature difference. When the temperature difference increases by 1℃, the Peak-to-Valley value and Root-Mean-Square value of surface error increase by 7.76 μm and 1.12 μm respectively under the axial temperature gradient, while 9.67 μm and 1.60 μm, respectively, under radial temperature gradient. The thermal-induced surface error of the focusing mirrors has a linear relationship with the mirrors size and temperature difference under certain conditions, and is significantly affected by the deformation of the support structure.