Author Affiliations
1School of Mechanical and Electrical Engineering, Changchun University Of Technology, Changchun 130012, China2Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, Changchun 130033, Chinashow less
Fig. 1. Light-weighting structure of rectangular mirror
Fig. 2. Iteration curve of support point position optimization
Fig. 3. Positions of the support points by optimization
Fig. 4. The schematic diagram of key parameters of flexure hinge
Fig. 5. Curves of influence of t value of flexible hinge on RMS of self-weight surface of mirror
Fig. 6. Supporting structure constraint depth
Fig. 7. Curves of the self-weight surface of the mirror with respect to the support position
Fig. 8. Model of mirror assembly
Fig. 9. Finite element model of mirror assembly
Fig. 10. [in Chinese]
Fig. 10. The first three order mode shapes of mirror assembly
Fig. 11. Acceleration response curves of sinusoidal vibration
Fig. 12. Vibration test device of mirror assembly
Fig. 13. Result curves of dynamic test
| RB-SiC | Si | Be | ULE | Zerodur | Al | Fused silica | Poisson’s ratio μ | 0.2 | 0.278 | 0.08 | 0.17 | 0.24 | 0.33 | 0.17 | Elastic modulus E/GPa
| 340 | 131 | 287 | 67 | 91 | 78 | 72 | Density ρ/g·cm−3 | 3.05 | 2.33 | 1.85 | 2.21 | 2.53 | 2.68 | 2.19 | Specific stiffness E/ρ/GN·m·g−1 | 111.50 | 56.22 | 155.14 | 30.32 | 35.97 | 29.10 | 32.88 | Thermal conductivity λ/W·(m·K)−1 | 155 | 156 | 216 | 1.31 | 1.64 | 167 | 1.40 | Thermal expansion coefficient α/10−6·K−1 | 2.50 | 2.60 | 11.40 | 0.03 | 0.05 | 23.6 | 0.50 | Thermal stability λ/α/106 W·m−1 | 62 | 60 | 18.95 | 43.67 | 32.80 | 7.08 | 2.80 | Integrated quality (E/ρ) · (λ/α)
| 6913 | 3373.2 | 2939.40 | 1324.07 | 1179.76 | 206.03 | 92.06 |
|
Table 1. Performance and quality factors of rational materials for mirror
[9] t/mm
| X-direction
self-weight
RMS/nm
| X-direction
self-weight
RMS/nm
| X-direction
self-weight
RMS/nm
| Fundamental
frequency/Hz
| 2 | 13.69 | 8.92 | 11.54 | 252.6 | 2.5 | 13.68 | 8.66 | 11.46 | 256.1 | 3 | 12.43 | 8.81 | 10.10 | 259.3 | 3.5 | 13.63 | 8.96 | 11.32 | 262.3 | 4 | 13.62 | 9.09 | 11.47 | 265.0 |
|
Table 2. Influence of flexible hinge t value on mirror assembly
Material | Density ρ /
g·cm−3 | Elastic modulus
E /GPa
| Poisson’s
ratio μ | Thermal expansion
coefficient
α/10−6·℃−1 | RB-SiC | 3.05 | 340 | 0.2 | 2.5 | 4J32 | 8.1 | 150 | 0.28 | 2.5 | TC4 | 4.44 | 109 | 0.34 | 8.9 | SiC/Al | 2.95 | 190 | 0.2 | 8.1 |
|
Table 3. Material parameters of mirror assembly
| Maximum
deformation/μm
| PV/
nm
| RMS/
nm
| X-direction 1 g gravity
| 1.53 | 58.2 | 12.3 | Y
-direction 1 g gravity
| 2.82 | 51.5 | 10.7 | Z
-direction 1 g gravity
| 3.06 | 55.2 | 11.8 | 5 ℃ uniform temperature rise | 9.5 | 17.2 | 3.9 | Y-direction 1 g gravity + 5 ℃ uniform temperature rise
| 9.23 | 33.3 | 6.8 |
|
Table 4. Analysis results of the self-weight and temperature rise of the mirror assembly
Order | Frequency/Hz | Mode shapes | 1 | 259 | Mirror moves in the Z direction
| 2 | 311 | Mirror moves in the Y direction
| 3 | 335 | Mirror rotates around the X axis
| 4 | 408 | Mirror rotates around the Z axis
| 5 | 438 | Mirror rotates around the Y axis
| 6 | 484 | Mirror moves in the X direction
|
|
Table 5. Analysis results of the first six order mode shapes of mirror assembly
Frequency/Hz | Vibration amplitude | Incentive direction | 5−15 | 8.89 mm | | 15−70 | 8 g | X/Y/Z | 70−75 | 5.7 g | 75−100 | 5.7 g | |
|
Table 6. Sine vibration excitation conditions