Design Method of Flexible Support and Lattice Structure for Long Strip Mirror

Fig. 6. Analysis results of influence of flexure hinge mounting angle. (a) Constrained model analysis; surface shape analysis of (b) gravity load; (c) temperature load; (d) forced displacement; (e) comprehensive factor

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Fig. 7. Analysis results of influence of axial position of flexure hinge installation. (a) Constrained model analysis; (b) surface shape analysis of gravity, temperature, and forced displacement; (c) surface shape analysis of comprehensive factor

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Fig. 8. Dimension parameters of flexible hinge with biaxial arc incision

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Fig. 9. Cell configuration of BCC

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Fig. 10. Lattice filling and point cloud generation

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Fig. 11. Grid reconstruction of point cloud triangulation

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Fig. 12. Simulation model of backplane skin lattice

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Fig. 13. Finite element model of mirror components

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Table 1. Parameters of materials for tertiary mirror components
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Table 1. Parameters of materials for tertiary mirror components
Material Density /（kg.m^-3） Elastic modulus /GPa Poisson ratio Linear expansion coefficient /（10^-6 ℃^-1）
ULE 2210 67.6 0.17 0.03
Invar 8180 145 0.25 0.05
TC4 4450 110 0.34 9.1
2216 epoxy adhesive 1000 0.689 0.43 102

Table 2. Mass distribution of mirror components
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Table 2. Mass distribution of mirror components
Part Mass distribution /kg
Reflector ≤4.5
Back support structure ≤0.5
Backplate support structure ≤2

Table 3. Structure parameters of tertiary mirror
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Table 3. Structure parameters of tertiary mirror
Caliber Panel thickness Base plate thickness Grid plate thickness Grid plate spacing Outer ring thickness
540×180 5 4 3 44 5

Table 4. Geometric parameters of flexible hinge
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Table 4. Geometric parameters of flexible hinge
r /mm t /mm b /mm A /（°） d /mm L /mm h /mm
1 2 3 65 1 2 50

Table 5. Structure parameters of backplane support
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Table 5. Structure parameters of backplane support
R a T
0.8 6 4.5

Table 6. Simulation results of mirror components

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Table 6. Simulation results of mirror components

First order fundamental frequency	20 g overload in X direction	20 g overload in Y direction	20 g overload in Z direction
237.3 Hz>120 Hz	Maximum stress：96.4 MPaSafety factor：9.1>1	Maximum stress：128.4 MPaSafety factor：6.8>1	Maximum stress：217.5 MPaSafety factor：4.0>1

Surface error under gravity of assembly direction	Uniform temperature rise of 2 ℃	Forced displacement of installation point 0.01 mm
PV：0.021λRMS：0.003λ（1.727 nm）	PV：0.046λRMS：0.006λ （3.505 nm）	PV：0.019λRMS：0.004λ （2.343 nm）

RMS of surface shape error	0.018λ（11.4 nm）＜λ/50
Rigid body displacement under gravity of assembly direction	0.007 mm<0.01 mm

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Pengpeng Liu, Jun Wu, Junlei Chang, Shoucheng Pang, Baocheng Zou, Zhuwei Zhang. Design Method of Flexible Support and Lattice Structure for Long Strip Mirror[J]. Acta Optica Sinica, 2024, 44(2): 0222002

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