Multi-objective optimal design of elliptic flexible hinge in fast steering mirror

Songhang Wu; Jihong Dong; Shuyan Xu; Funan Yu; Boqian Xu

doi:10.3788/IRLA20200286

Journals >Infrared and Laser Engineering >Volume 50 >Issue 4 >Page 20200286 > Article

Infrared and Laser Engineering
Vol. 50, Issue 4, 20200286 (2021)

Multi-objective optimal design of elliptic flexible hinge in fast steering mirror

Songhang Wu^1、2, Jihong Dong¹, Shuyan Xu¹, Funan Yu¹, and Boqian Xu¹

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

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DOI: 10.3788/IRLA20200286 Cite this Article

Songhang Wu, Jihong Dong, Shuyan Xu, Funan Yu, Boqian Xu. Multi-objective optimal design of elliptic flexible hinge in fast steering mirror[J]. Infrared and Laser Engineering, 2021, 50(4): 20200286 Copy Citation Text

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Fig. 1. Elliptical flexible hinge

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Fig. 2. Front view of elliptic flexible hinge

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Fig. 3. Relationship curve of I/I₀ and s

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Fig. 4. Optimization design process of elliptic flexible hinge

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Fig. 5. Correlation factors between structural parameters and axial compliance

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Fig. 6. Pareto solution distribution

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Fig. 7. Three-axis rotation analysis results

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	t₀/mm	w/mm	C_z-Mz/rad·Nm⁻¹	C_y-My/rad·Nm⁻¹	C_x-Mx/rad·Nm⁻¹	y_c/m
EQU	1	5	0.1130	8.699×10⁻³	7.572×10⁻²	1.000×10⁻⁷
FEM	1	5	0.1106	8.989×10⁻³	7.380×10⁻²	9.993×10⁻⁸
EQU	0.5	5	0.6479	1.360×10⁻²	0.4095	4.194×10⁻⁷
FEM	0.5	5	0.6419	1.403×10⁻²	0.3996	4.179×10⁻⁷
EQU	1	3	0.1884	4.028×10⁻²	0.1426	1.668×10⁻⁷
FEM	1	3	0.1874	4.141×10⁻²	0.1329	1.677×10⁻⁷
EQU	0.2	3	10.80	0.1089	4.508	4.501×10⁻⁶
FEM	0.2	3	10.51	0.1098	4.790	4.487×10⁻⁶

Table 1. [in Chinese]

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J_θx/ kg·m²	J_θy/kg·m²	J_θz/ kg·m²
3.46×10⁻⁶	3.46×10⁻⁶	6.33×10⁻⁶

Table 2. [in Chinese]

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	a/mm	b/mm	t₀/mm	w/mm	C_z-Mz/rad·Nm⁻¹	C_y-My/rad·Nm⁻¹	C_x-Mx/rad·Nm⁻¹
Initial value	9	5	0.5	6	0.4859	7.079×10⁻³	0.2966
Optimized value	9.67	6.63	0.661	9.74	0.1390	1.343×10⁻³	8.870×10⁻²

Table 3. [in Chinese]

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Algorithm	C_z-Mz/rad·Nm⁻¹	C_y-My/rad·Nm⁻¹	C_x-Mx/rad·Nm⁻¹	R_C	Pareto solution number	Pareto solution efficiency
MIGA	0.1320	1.329×10⁻²	6.999×10⁻²	−0.6	153	38.2%
PSO	0.1301	4.630×10⁻²	7.075×10⁻²	0.4	110	27.5%
NSGA-II	0.1390	1.343×10⁻²	8.870×10⁻²	−0.8	210	52.5%

Table 4. [in Chinese]

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	C_z-Mz/rad·Nm⁻¹	C_y-My/rad·Nm⁻¹	C_x-Mx/rad·Nm⁻¹
EQU	0.1390	1.343×10⁻³	8.870×10⁻²
FEM	0.1320	1.340×10⁻³	8.290×10⁻²

Table 5. [in Chinese]

Songhang Wu, Jihong Dong, Shuyan Xu, Funan Yu, Boqian Xu. Multi-objective optimal design of elliptic flexible hinge in fast steering mirror[J]. Infrared and Laser Engineering, 2021, 50(4): 20200286

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