Research On The Design Of Large-aperture Mirror And Its Supporting Technology

With the increasing requirements for space telescope detection accuracy,the large aperture of the primary mirror of space telescope becomes one of the development trends.As the core component of a space telescope,the performance of the primary mirror directly affects the imaging quality of the space telescope.However,the deformation of large-aperture mirrors is extremely sensitive to external loads,and the increase of the aperture also makes the mass of the mirror increase.In order to reduce the launch cost of the space telescope and to operate properly in the harsh space environment,it is necessary to design the mirror in a lightweight way and to enhance the mirror’s ability to resist the mirror surface degradation caused by external load changes,thus making the structural design of the mirror assembly more difficult.The design and optimization of the main mirror and its support components is one of the key technologies that must be carried out during the development of the space telescope.In this thesis,the primary mirror of a pre-study XX large-aperture space telescope is used as the research object.Aiming at the lightweight design of the primary mirror and the performance design of the support structure,the research is carried out on the Φ1.6m aperture mirror assembly from theoretical calculation,structural optimization and simulation analysis.(1)The design requirements of space mirrors and the principles of optimized design are described.Firstly,the environment faced by the space telescope from development to orbit operation is outlined,and the design guidelines to be followed in the design of the large-aperture mirror as the core component of the space telescope are clarified.Secondly,the topology optimization method and the dimensional optimization method used in the structural optimization design of the mirror are introduced.Finally,the theoretical calculation methods of the mirror surface accuracy and rigid body displacement are analyzed.The Zernike fitting method and the one-dimensional iterative method based on the spherical formula are analyzed for the theoretical calculation of the surface shape accuracy and the homogeneous coordinate transformation method for the theoretical calculation of the rigid body displacement.The above work lays the foundation for the next design optimization.(2)The initial structure of the mirror was designed using traditional empirical methods.Firstly,the material for the production of the mirror was analyzed and determined.Next,the back structure form of the mirror and the dimensional parameters were determined using the theoretical formula combined with the empirical design method.A mirror with an open back structure was initially designed with a weight of 174.6Kg and a light weight rate of 84.51%.After finite element analysis,the surface shape accuracy of the mirror under the action of gravity of 1g in the radial direction is 0.0102λ(λ=632.8nm).(3)A comprehensive optimization method based on the secondary developed topology optimization software combined with Isight parameter optimization software is proposed to optimize the initial structure of the mirror.Firstly,a one-dimensional iterative method based on the spherical formula is developed and integrated into the software to address the problem that the RMS value of the surface shape accuracy cannot be used as a constraint or objective function in the finite element software.A topology optimization model with the minimum volume of the mirror as the optimization objective and the RMS value of the mirror surface shape accuracy as the constraint is established.Next,based on the topology optimization results,a dimensional optimization model with the objective of minimizing the face shape accuracy is established using Isight integrated simulation optimization software to extract the conceptual configuration of the 1/6 mirror.After double optimization,the weight of the mirror is 130.01 Kg,and the lightness rate is 88.46%.Finally,after the finite element analysis,the accuracy of the mirror surface shape under the radial 1g gravity is 0.00965λ(λ=632.8nm).Compared with the initial mirror structure,the mass is reduced by 25.54% and the surface shape accuracy is improved by 5.56%.(4)The flexible support structure and support plate were designed and optimized using the sensitivity analysis method.First,the functions that the support structure should have were analyzed and a preliminary design of a flexible support structure was designed.The optimal installation depth of the flexible support structure in the optical axis direction was optimized to 161 mm.The flexibility matrix of the flexible hinge is calculated and the force of the mirror assembly is analyzed.The deformation of the mirror is decoupled from the flexibility characteristics of the flexible support structure,and the sensitivity analysis of the dimensional parameters of the flexible support structure is performed separately,and the parameters with a large contribution to the deformation of the flexible support structure are prioritized for optimization based on the analysis results.The finite element analysis of the optimized and improved design solution shows that the surface shape accuracy of the mirror is0.01087λ(λ=632.8 nm)under the radial 1g gravitational force,0.00949λ(λ=632.8 nm)under the 2°С temperature rise load,0.0141λ(λ= 632.8 nm),all of which meet the design requirements.Finally,the support plate of the mirror was designed with a weight of 186 Kg,and the overall weight of the mirror assembly was better than the design requirement.(5)Simulation verification analysis of the design-optimized mirror assembly.The face shape accuracy of the mirror assembly is 0.01081λ(λ=632.8nm)under 1g of gravity in the radial direction,and the rigid body displacement is 15.86μm.The face shape accuracy of the mirror assembly under 2°С temperature load is 0.00817λ(λ =632.8 nm)and the rigid body displacement is 4.95 μm.The accuracy of the face shape under the joint action of the two loads is 0.0134λ(λ=632.8nm),and the rigid body displacement is 15.88μm.In the sine vibration analysis and random vibration analysis,the maximum response stress of the mirror assembly is located in the flexible support structure,and the maximum response stress values are 288.66 MPa and 164.51 MPa,respectively,which are less than the allowable stress of the material.After the simulation verification analysis,it is clear that the large-aperture mirror assembly designed in this paper meets the design specification requirements.In this paper,the traditional empirical design method,the topology optimization method based on secondary development and the dimensional parameter optimization method are combined to achieve high efficiency and fast performance for the design of circular large-aperture mirrors.The flexible support structure can isolate the effect of environmental disturbances on the mirror surface shape accuracy.The results of the work obtained are useful for the design of similar mirror assemblies.