Author Affiliations
1Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, Changchun 130033, China2University of Chinese Academy of Sciences, Beijing 100049, China3Center of Materials Science and Optoelectrics Engineering, University of Chinese Academy of Sciences, Beijing 100049, Chinashow less
Fig. 1. (a) Overall structure of fast steering mirror; (b) Flexible support system structure
Fig. 2. (a) Plan view of deep-cut flexure hinge; (b) Schematic diagram of deep-cut flexure hinge
Fig. 3. (a) First-order mode; (b) Second-order mode; (c) Third-order mode; (d) Fourth-order mode
Fig. 4. (a) Simplified diagram of first-order mode shape stiffness; (b) Simplified diagram of second-order mode shape stiffness; (c) Simplified diagram of third-order mode shape stiffness;(d) Simplified diagram of fourth-order mode shape stiffness
Fig. 5. Simplified model of third-order modal stiffness
Fig. 6. (a) Non-linear fitting curve diagram; (b) Non-linear fitting determination coefficient
Fig. 7. Finite element verification of the working stiffness of the deep-cut flexure hinge
Fig. 8. Third-order mode shape simulation diagram
Fig. 9. Optimization flow chart of genetic algorithm
Fig. 10. (a) Front view; (b) Right view; (c) Bottom view
Fig. 11. (a) First-order mode; (b) Second-order mode; (c) Third-order mode; (d) Fourth-order mode
a/mm
| b/mm
| t/mm
| w/mm
| Theoretical
calculation results
/N·m·rad−1 | Finite element
simulation results
/N·m·rad−1 | Error
percentage
| 10 | 8 | 1 | 8 | 25.3799 | 26.0417 | −2.54% | 10 | 6 | 1 | 8 | 33.8399 | 32.6513 | 3.64 % | 5 | 3 | 0.5 | 8 | 8.4600 | 8.2527 | 2.45% | 5 | 3 | 0.5 | 5 | 5.2875 | 5.1466 | 2.74% | 5 | 2 | 0.5 | 5 | 7.9312 | 7.2922 | 8.76% |
|
Table 1. Comparison of theoretical calculation and finite element simulation of working stiffness of deep-cut flexure hinge
a/mm
| b/mm
| w/mm
| t/mm
| Mirror
thickness: h/mm
| Theoretical
calculation
value of
third-order
mode/Hz
| Three-order
mode finite
element simulation
value/Hz
| Error
percentage
| 4 | 3.5 | 5 | 0.8 | 23 | 284.40 | 286.25 | 0.61% | 10 | 8 | 8 | 1 | 15 | 218.90 | 220.17 | −0.58% | 6 | 5 | 8 | 1 | 15 | 434.29 | 427.11 | 1.68% |
|
Table 2. Comparison of theoretical calculation and finite element simulation of three-boundary natural frequency of fast mirror system
a/mm
| b/mm
| t/mm
| w/mm
| L/mm
| D/mm
| h/mm
| 10 | 8 | 1 | 8 | 25 | 100 | 15 |
|
Table 3. Initial structure parameters of the fast steering mirror system
Parameter | Value | a/mm
| 4.8 | b/mm
| 4 | t/mm
| 0.8 | G(x)
| 0.0181 |
|
Table 4. Optimization results of genetic algorithm
| a/mm
| b/mm
| t/mm
| K1/N·m·rad−1 | K2/N·m·rad−1 | K3/N·m·rad−1 | K4/N·m−1 | G(x)
| Initial value | 10 | 8 | 1 | 50.04 | 50.04 | 844.6296 | 1.323e+06 | 0.0279 | Optimized value | 4.8 | 4 | 0.8 | 40.51 | 40.51 | 3.3602e+03 | 2.343e+06 | 0.0181 | Optimization rate | | | | −19.04% | −19.04% | 297.83% | 77.09% | 41.58% |
|
Table 5. Comparison of system stiffness between multi-objective optimized structure and initial structure
| First-order mode/Hz | Second-order mode/Hz | Third-order mode/Hz | Fourth-order mode/Hz | Initial structure | 60.715 | 60.814 | 236.93 | 549.97 | Optimized structure | 55.807 | 57.533 | 503.68 | 642.38 | Optimization rate | −8.08% | −5.40% | 112.59% | 16.80% |
|
Table 6. Comparison of the fourth-order natural frequency between the optimized structure and the initial structure