Study On Removal Function And Algorithm Of Bonnet Figuring For X-ray Focusing Mirror Mold

The detection of high-energy rays through X-ray telescopes is an important means to understand the physical phenomena such as star formation,black hole phenomenon and gas expansion after star explosion.The X-ray focusing mirror array is formed by nesting multiple layers of Wolter-I mirror,the manufacturing process of the focusing mirror puts extremely high requirements on the shape accuracy of the mold.Bonnet figuring is to use the bonnet as the processing tool and use CCOS(Computer Controlled Optical Surfacing)forming principle to correct low-frequency surface shape errors.Based on the X-ray focusing mirror shape characteristics and CCOS forming principles,this paper studies removal function and algorithm of bonnet figuring for X-ray focusing mirror mold and lay the technical foundation for the final high-precision figuring of the focusing mirror mold.According to the contact characteristics of the bonnet and the aspheric surface,firstly,this paper establishes the bonnet removal function model based on the Preston hypothesis.Secondly,based on the analysis of the surface shape of the X-ray focusing mirror mold,the removal function model is used to simulate and analyze the shape of the contact area and the amount of removed material at different positions on the surface of the focusing mirror mold.Finally,through the fixed-point removal function experiment,the shape difference between the actual removal function and the theoretical removal function is compared,the influence of the deformation of the bonnet on the material removal rate is analyzed,and the stability of the removal function over time under different combinations of polishing pads and polishing solutions is discussed.According to the surface shape characteristics of the X-ray focusing mirror mold,the dwell time iterative algorithm based on cylindrical coordinate projection is proposed.Then,using the method of simulation calculation,the influence of the relaxation factor on the iterative convergence speed is analyzed.Aiming at the edge effect in the dwell time algorithm,edge extension and "bonnet lifting" method are proposed to suppress the edge effect.Finally,in order to verify the adaptability of the iterative algorithm,different removal functions and surface shape errors are used for calculations simulation.The calculation results show that the closer the removal function shape is to the Gaussian shape,the smoother the surface shape error is and the faster the residence time convergence rate is.Aiming at the need of X-ray mirror mold deterministic shaping process,firstly,the position-attitude error during the mold surface shape measurement is analyzed,and the in-situ measurement of the surface shape is realized based on the separation principle of "reverse method".Then,according to the principle of CCOS,the correspondence between the position and attitude of the bonnet and the residence time distribution during the processing is determined.Finally,based on the analysis of the curvature effect and the additional dwell time,the mold figuring is simulated.After two iterations of machining,the surface shape error converges from 0.8?m to 0.2?m,meeting the mold surface accuracy requirements.