Author Affiliations
1Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, Changchun 130033, China2University of Chinese Academy of Sciences, Beijing 100049, China3Ji Hua Laboratory, Foshan 528200, Chinashow less
Fig. 1. Lens shape and dimension parameters
Fig. 2. Schematic diagram of the overall structure of lens assembly
Fig. 3. Lens support assembly and its structural parts
Fig. 4. Schematic diagram of flexible hinge structure
Fig. 5. Schematic diagram of force analysis of flexure hinge
Fig. 6. Schematic diagram of equivalent analysis of elastic sheet flexure hinge
Fig. 7. Equal mechanical model for flexible supports in the X-axis direction
Fig. 8. Relationship between flexibility Cx and design parameters
柔度
随各设计参数间的变化关系
Fig. 9. Radial flexible support structure and its finite element model
Fig. 10. Test test equipment
Fig. 11. Mesh division
Fig. 12. Simulation results under various working conditions
Fig. 13. The first three order mode shapes of the lens assembly
Fig. 14. Schematic diagram of spherical data fitting principle
Fig. 15. Static surface cloud map of the upper surface of the lens
Materials | H-K9L | 4J32 | TC4 | Density ρ/kg·m−3 | 2520 | 8300 | 4400 | Elastic modulus E/GPa
| 79.2 | 150 | 114 | Poisson’s ratio μ | 0.21 | 0.30 | 0.34 | Thermal expansion coefficient α/10-6·K−1 | 7.60 | 7.50 | 9.10 |
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Table 1. Material properties
Parameter | Initial | Optimized | r1/mm
| 0.1 | 0.5 | r2/mm
| 0.2 | 0.5 | l/mm
| 15 | 40 | t/mm
| 1.2 | 0.6 | t1/mm
| 6 | 3 | t2/mm
| 7 | 6 | Surface and position accuracy RMS/nm
| 39.498 | 11.272 | Maximum deformation x/mm
| 0.0532 | 0.0515 |
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Table 2. Optimization results of flexure hinge support structure
Number | Parameter/mm | | Stiffness/105 N·m−1 | Error | l | t | h | | FEA | An | 1 | 40 | 0.6 | 16 | | 0.991 | 0.985 | 0.62% | 2 | 40 | 0.6 | 20 | | 1.229 | 1.231 | 0.16% | 3 | 40 | 1.0 | 16 | | 4.762 | 4.560 | 4.24% | 4 | 36 | 0.8 | 16 | | 3.203 | 3.417 | 6.74% | 5 | 36 | 1.0 | 16 | | 6.255 | 6.515 | 4.16% | 6 | 36 | 1.0 | 20 | | 7.819 | 8.183 | 4.65% | 7 | 46 | 1.0 | 16 | | 2.998 | 2.840 | 5.27% | 8 | 46 | 1.0 | 20 | | 3.748 | 3.545 | 5.42% | 9 | 46 | 1.2 | 16 | | 5.181 | 5.225 | 0.85% | 10 | 46 | 1.2 | 20 | | 6.476 | 6.575 | 1.53% |
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Table 3. Comparison of theoretical stiffness (An) and FEA of radial flexible support structure
Number | Stiffness/105 N·m−1 | Error | Ex | An | 1 | 1.000 | 0.985 | 1.52% | 2 | 0.923 | 0.985 | 6.29% | 3 | 1.025 | 0.985 | 4.06% | 4 | 1.039 | 0.985 | 5.48% |
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Table 4. Comparison of theoretical (An) and teststiffness (Ex) of radial flexible support structures
Load case | Maximum deformation x/mm
| Grav _X | 7.61×10−3 | Grav _Y | 7.61×10−3 | Grav _Z | 4.62×10−3 | Temp_−10 | 7.66×10−2 | Temp_+40 | 5.10×10−2 |
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Table 5. Deformation and displacement data of lens statics simulation under various working conditions
Order | Frequency/Hz | Mode shapes | 1 | 183.97 | Move along X-axis
| 2 | 183.97 | Move along Y-axis
| 3 | 234.35 | Move along Z-axis
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Table 6. Modal analysis results of lens subassembly
Load case | PV/nm | RMS/nm | Grav _X | 16.636 | 6.0695 | Grav _Y | 16.514 | 6.0758 | Grav _Z | 25.506 | 9.9347 | Temp_−10 ℃ | 6.4467 | 1.5756 | Temp_+40 ℃ | 4.3959 | 1.0709 |
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Table 7. Analysis results of surface precision on lens assembly