Wolter-I型聚焦镜热变形数值研究

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.