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

	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 2. [in Chinese]
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Table 2. [in Chinese]
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 3. [in Chinese]

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Table 3. [in Chinese]

	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 4. [in Chinese]

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Table 4. [in Chinese]

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 5. [in Chinese]
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Table 5. [in Chinese]
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

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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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