Design and optimization of integrated flexure mounts for unloading lateral gravity of a lightweight mirror for space application

Liu Zhang; Liu Zhang; Tailei Wang; Tailei Wang; Fan Zhang; Fan Zhang; Huanyu Zhao; Huanyu Zhao; Yu Zhao; Xiaoyi Zheng; Xiaoyi Zheng

doi:10.1364/AO.414054

Applied Optics
Vol. 60,
Issue 2,
pp. 417-426
(2021)
•https://doi.org/10.1364/AO.414054

Design and optimization of integrated flexure mounts for unloading lateral gravity of a lightweight mirror for space application

Liu Zhang, Tailei Wang, Fan Zhang, Huanyu Zhao, Yu Zhao, and Xiaoyi Zheng

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Liu Zhang, Tailei Wang, Fan Zhang, Huanyu Zhao, Yu Zhao, and Xiaoyi Zheng, "Design and optimization of integrated flexure mounts for unloading lateral gravity of a lightweight mirror for space application," Appl. Opt. 60, 417-426 (2021)

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Abstract

This paper presents an integrated flexure mount (IFM) to unload the lateral gravity of a lightweight mirror. The significance of the position relationship between the plane of mirror centroid and the center of flexure pivot is analyzed using the coupling kinematic stiffness model of the flexure mounts derived in this paper. Based on the analysis, an IFM with S-type flexure hinges was designed, and the structure and assembly are described. Then, the optimal position and size parameters of an S-type flexure hinge were obtained by optimization. The optimization results attained by finite element analysis (FEA) indicate that the optimization objectives and constraints were satisfied. Moreover, the degradation of the mirror’s optical performance caused by lateral gravity was minimized, and the effects of temperature variation and assembly tolerance were reduced. The IFMs were fabricated based on the optimization results and assembled with a mirror prototype for a pointing precision test and sine-frequency sweep test. A FEA and test results for the IFMs confirm the validity and feasibility of the flexure mounts model and structure design, and we believe the IFM meets the requirements of a lightweight mirror for space application.

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	$x$	$y$	$z$
$p_{i}$	$θ_{p i} = 0$	$ϕ_{p i} = \frac{π}{2}$	$ψ_{p i} = \frac{π}{2}$
$q_{i}$	$θ_{q i} = \frac{π}{2}$	$ϕ_{q i} = \frac{(i - 1) π}{6}$	$ψ_{q i} = \frac{π}{2} - \frac{(i - 1) π}{6}$
$r_{i}$	$θ_{r i} = \frac{π}{2}$	$ϕ_{r i} = \frac{π}{2} + \frac{(i - 1) π}{6}$	$ψ_{r i} = \frac{(i - 1) π}{6}$

Design Variable	Value Range (mm)	Initial Value (mm)	Optimal Value (mm)	Design Value (mm)
$l$	[1.5,6.5]	4	2.9	3
$d$	[0.5,2]	1	0.54	0.5
$h$	[5,7]	6	6.45	6.5
$b$	[2,4]	3	2.85	3

	$x$	$y$	$z$
$p_{i}$	$θ_{p i} = 0$	$ϕ_{p i} = \frac{π}{2}$	$ψ_{p i} = \frac{π}{2}$
$q_{i}$	$θ_{q i} = \frac{π}{2}$	$ϕ_{q i} = \frac{(i - 1) π}{6}$	$ψ_{q i} = \frac{π}{2} - \frac{(i - 1) π}{6}$
$r_{i}$	$θ_{r i} = \frac{π}{2}$	$ϕ_{r i} = \frac{π}{2} + \frac{(i - 1) π}{6}$	$ψ_{r i} = \frac{(i - 1) π}{6}$

Design Variable	Value Range (mm)	Initial Value (mm)	Optimal Value (mm)	Design Value (mm)
$l$	[1.5,6.5]	4	2.9	3
$d$	[0.5,2]	1	0.54	0.5
$h$	[5,7]	6	6.45	6.5
$b$	[2,4]	3	2.85	3

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Equations (12)

Applied Optics