Hierarchical Layout Optimization Of Surface-support Coupling System For Ultra-large Aperture Mirror

Passive Hydraulic Support Units(PHSUs)are frequently used in the in-situ fabrication and testing.However,the difference in PHSUs’ stiffness will affect the mirror surface figure.a 4 m aperture mirror was designed by theoretical analysis,empirical design,finite element analysis and structural optimization methods.For the difference of PHSUs’ stiffness,the joint optimization method of layout and stiffness studied.The accuracy of the support system after layout optimization is verified through experiments.The specific research contents are as follows:The first part is the mirror design.Taking the "solid circular plate" with 54 support points in 4 circles as the model,the quantitative relationship between the support radius and the diameter of the circular plate is determined according to the optimization result of its supporting position.Combined with the traditional empirical formula,a 4 m mirror was designed.Through the integrated optimization method,the structure of the mirror was optimized.After the optimization,the mass of the mirror was reduced from 3.15 t to 1.44 t,the mass was reduced by 54.13%.In the vertical direction of the optical axis with 1g acceleration,the Root Mean Square(RMS)of the mirror surface errors is 11.58 nm.The results meet the design requirement.The second part is the joint optimization of support stiffness and support position.The effect of the difference in the PHSUs’ stiffness on the mirror surface errors is analyzed.the joint optimization method of layout,stiffness and support force is studied.The equal-force support system is optimized through the optimization method of layout and stiffness.The unequal-force support system is optimized through the optimization method of support force,layout and stiffness.The two support schemes can meet the requirements after optimization.The influence of different stiffness schemes on the mirror surface errors is studied,and the optimization algorithm of stiffness schemes is optimized to improve the calculation efficiency.The third part introduces the technology of active optics,gives the method of fitting mirror deformation by using its modal shape and gives the process of calibration in free harmonic vibration modal.The active correction technology is used in the support system of the in-situ fabrication.Active correction is used in equal-force support system after layout optimization.After active correction,the RMS was reduced from 8.3 nm to 6.3 nm,resulting in better processing support accuracy.