Study on four-point support inversion method for removing gravity-induced deformation of quasi-cylindrical low-stiffness shell

Abstract The X-ray mirror is the critical optical component in X-ray telescopes. Multilayered quasi-cylindrical mirrors are nested in the X-ray mirror to capture enough X-ray photons from space, which decreases the stiffness of the mirror. Additionally, residual stress induced by the grinding process can cause the warping of the low-stiffness mirror. During the deformation measurements, the coupled influence of residual stress and gravity requires isolation of the gravity-induced deformation ( GID ) effect to ensure the evaluation of the residual stress-induced deformation ( RID ). This study proposed a four-point support inversion measurement method to eliminate the GID of a low-stiffness quasi-cylindrical shell. The method provided the selection methods of supporting parameters to reduce the gravity-induced deformation error ( ∆l ) of the mirror before and after inversion. To verify the effectiveness of the inversion method, this paper conducted grinding and deformation measurement experiments. The experimental results showed that the four-point support inversion method can realize the separation of RID and GID . Comparison of the finite element results of the GID with the experimental measurements verified the validity of the inversion method and explained that the presence of residual stress led to an increase in the GID .