• Infrared and Laser Engineering
  • Vol. 50, Issue 6, 20200450 (2021)
Weifan Zhang1、2, Changxiang Yan1、3, Zhiliang Gao1, Siyu Wang1, Xiao Shen1、2, Jing Yuan1、2, and Youzhi Dong1、2
Author Affiliations
  • 1Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, Changchun 130033, China
  • 2University of Chinese Academy of Sciences, Beijing 100049, China
  • 3Center of Materials Science and Optoelectrics Engineering, University of Chinese Academy of Sciences, Beijing 100049, China
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    DOI: 10.3788/IRLA20200450 Cite this Article
    Weifan Zhang, Changxiang Yan, Zhiliang Gao, Siyu Wang, Xiao Shen, Jing Yuan, Youzhi Dong. Optimal design of natural frequency of two-degree-of-freedom fast steering mirror system[J]. Infrared and Laser Engineering, 2021, 50(6): 20200450 Copy Citation Text show less
    (a) Overall structure of fast steering mirror; (b) Flexible support system structure
    Fig. 1. (a) Overall structure of fast steering mirror; (b) Flexible support system structure
    (a) Plan view of deep-cut flexure hinge; (b) Schematic diagram of deep-cut flexure hinge
    Fig. 2. (a) Plan view of deep-cut flexure hinge; (b) Schematic diagram of deep-cut flexure hinge
    (a) First-order mode; (b) Second-order mode; (c) Third-order mode; (d) Fourth-order mode
    Fig. 3. (a) First-order mode; (b) Second-order mode; (c) Third-order mode; (d) Fourth-order mode
    (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. 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
    Simplified model of third-order modal stiffness
    Fig. 5. Simplified model of third-order modal stiffness
    (a) Non-linear fitting curve diagram; (b) Non-linear fitting determination coefficient
    Fig. 6. (a) Non-linear fitting curve diagram; (b) Non-linear fitting determination coefficient
    Finite element verification of the working stiffness of the deep-cut flexure hinge
    Fig. 7. Finite element verification of the working stiffness of the deep-cut flexure hinge
    Third-order mode shape simulation diagram
    Fig. 8. Third-order mode shape simulation diagram
    Optimization flow chart of genetic algorithm
    Fig. 9. Optimization flow chart of genetic algorithm
    (a) Front view; (b) Right view; (c) Bottom view
    Fig. 10. (a) Front view; (b) Right view; (c) Bottom view
    (a) First-order mode; (b) Second-order mode; (c) Third-order mode; (d) Fourth-order mode
    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·rad1Finite element simulation results /N·m·rad1Error percentage
    1081825.379926.0417−2.54%
    1061833.839932.65133.64 %
    530.588.46008.25272.45%
    530.555.28755.14662.74%
    520.557.93127.29228.76%
    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
    43.550.823284.40286.250.61%
    1088115218.90220.17−0.58%
    658115434.29427.111.68%
    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
    108182510015
    Table 3. Initial structure parameters of the fast steering mirror system
    ParameterValue
    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·rad1K2/N·m·rad1K3/N·m·rad1K4/N·m1G(x)
    Initial value108150.0450.04844.62961.323e+060.0279
    Optimized value4.840.840.5140.513.3602e+032.343e+060.0181
    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/HzSecond-order mode/HzThird-order mode/HzFourth-order mode/Hz
    Initial structure60.71560.814236.93549.97
    Optimized structure55.80757.533503.68642.38
    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
    Weifan Zhang, Changxiang Yan, Zhiliang Gao, Siyu Wang, Xiao Shen, Jing Yuan, Youzhi Dong. Optimal design of natural frequency of two-degree-of-freedom fast steering mirror system[J]. Infrared and Laser Engineering, 2021, 50(6): 20200450
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