Lightweight Design of Multi-Objective Topology for a Large-Aperture Space Mirror
Abstract
:1. Introduction
2. Lightweight Design of the Primary Mirror
2.1. Fundamental Concepts
2.2. Formulation of the Optimization Problem
3. Application Examples of the Topology Optimization Method
3.1. Initial Design of the Primary Mirror
3.2. Topology Optimization Results
- (1)
- The additional ribs pass through the center of the areas without material filling to reduce the local deformation;
- (2)
- The additional ribs pass through the intersection of the main ribs to shorten the transmission path of the force;
- (3)
- The arrangement of the additional ribs must not affect the cyclic symmetry of the mirror;
- (4)
- Increasing lightening holes in the areas where the material is excessively concentrated.
3.3. Sensitive Analysis and Size Optimization
4. Performance Evaluation of the New Configuration
4.1. Comparison of Optical Performance of Three Naked Mirrors
4.2. Optical Performance of the PMA
5. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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γ, η, μ | α | D1 | D2 | P |
---|---|---|---|---|
0.33 | 0.3 | 25 nm | 160 nm | 0.2 kPa |
Outside Diameter | Inside Diameter | Outer Edge Thickness | SiC | ||
---|---|---|---|---|---|
E0 | μ | ρ | |||
610 mm | 86 mm | 70 mm | 280 GPa | 0.17 | 2800 kg/m3 |
Design Variable | Term | Value |
---|---|---|
DV1 | Front plate thickness | 5 mm |
DV2 | Outer ring thickness | 5 mm |
DV3 | Inner ring thickness | 5 mm |
DV4 | Rib1 thickness | 15 mm |
DV5 | Rib2 thickness | 8 mm |
DV6 | Rib3 thickness | 6 mm |
DV7 | Cylindrical structure radius | 162 mm |
DV8 | Auxiliary rib thickness | 4 mm |
Design Variable | Lower Bound | Upper Bound | Optimum Value |
---|---|---|---|
DV1 | 4 mm | 8 mm | 4 mm |
DV2 | 4 mm | 8 mm | 5.6 mm |
DV4 | 12 mm | 18 mm | 16.4 mm |
DV5 | 4 mm | 10 mm | 5.2 mm |
DV6 | 4 mm | 10 mm | 4 mm |
Terms | Tri-Configuration | Hex-Configuration | New Configuration |
---|---|---|---|
PVA & RMSA | 125.73 & 28.65 nm | 150.57 & 34.43 nm | 119.53 & 27.58 nm |
PVL & RMSL | 8.08 & 1.68 nm | 10.38 & 1.92 nm | 7.03 & 1.28 nm |
PVP & RMSP | 55.80 & 13.56 nm | 60.74 & 14.05 nm | 45.65 & 10.10 nm |
PV & RMS (+2 °C) | 61.6 & 10.48 nm | 100.5 & 17.5 nm | 50.1 & 8.78 nm |
Frequency | 1400.8 Hz | 1344.5 Hz | 1555.3 Hz |
Mass | 13.48 kg | 11.54 kg | 11.08 kg |
Lightweight ratio | 68.4% | 72.9% | 74.0% |
Name | Term | L = 1 mm, Coefficient/nm | L = 3.5 mm, Coefficient/nm | L = 6 mm, Coefficient/nm |
---|---|---|---|---|
Focus | 2r2 − 1 | 3.73 × 10−2 | 2.19 × 10−2 | 9.78 × 10−3 |
Pri Astig-A | r2cos(2θ) | 9.06 | 2.31 × 10−1 | −8.72 |
Pri Astig-B | r2sin(2θ) | −5.19 × 10−2 | −2.67 × 10−2 | −5.66 × 10−2 |
Pri Coma-A | (3r2 − 2r)cos(θ) | 1.37 × 10−2 | 2.15 × 10−2 | 1.65 × 10−2 |
Pri Coma-B | (3r2 − 2r)sin(θ) | 2.77 × 10−1 | 2.97 × 10−1 | 3.17 × 10−1 |
Pri Spherical | 6r4 − 6r2 − 1 | −2.15 × 10−2 | −9.32 × 10−3 | −3.46 × 10−4 |
Pri Trefoil-A | r3cos(3θ) | 9.62 × 10−1 | 1.04 × 10−2 | −1.02 × 10−2 |
Pri Trefoil-B | r3sin(3θ) | −6.53 × 10−3 | −7.83 × 10−3 | −8.05 × 10−3 |
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Qu, Y.; Jiang, Y.; Feng, L.; Li, X.; Liu, B.; Wang, W. Lightweight Design of Multi-Objective Topology for a Large-Aperture Space Mirror. Appl. Sci. 2018, 8, 2259. https://doi.org/10.3390/app8112259
Qu Y, Jiang Y, Feng L, Li X, Liu B, Wang W. Lightweight Design of Multi-Objective Topology for a Large-Aperture Space Mirror. Applied Sciences. 2018; 8(11):2259. https://doi.org/10.3390/app8112259
Chicago/Turabian StyleQu, Yanjun, Yanru Jiang, Liangjie Feng, Xupeng Li, Bei Liu, and Wei Wang. 2018. "Lightweight Design of Multi-Objective Topology for a Large-Aperture Space Mirror" Applied Sciences 8, no. 11: 2259. https://doi.org/10.3390/app8112259
APA StyleQu, Y., Jiang, Y., Feng, L., Li, X., Liu, B., & Wang, W. (2018). Lightweight Design of Multi-Objective Topology for a Large-Aperture Space Mirror. Applied Sciences, 8(11), 2259. https://doi.org/10.3390/app8112259