• Infrared and Laser Engineering
  • Vol. 50, Issue 10, 20210118 (2021)
Lei Zhao, Qiuxing Liu, Bo Hu, Hu Wang..., Liang Liang and Heng Lu|Show fewer author(s)
Author Affiliations
  • Xi'an Institute of Applied Optics, Xi'an 710065, China
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    DOI: 10.3788/IRLA20210118 Cite this Article
    Lei Zhao, Qiuxing Liu, Bo Hu, Hu Wang, Liang Liang, Heng Lu. Design and application of bi-axial half-butterfly flexure hinges in fast steering mirrors[J]. Infrared and Laser Engineering, 2021, 50(10): 20210118 Copy Citation Text show less

    Abstract

    A bi-axial half-butterfly flexure hinge for an fast steering mirror (FSM) was presented to adapt high stability accuracy of beam-pointing control performance in laser weapon systems. According to the requirements of reciprocating movements and high bandwidth provided for the FSM, the solid model of the bi-axial half-butterfly flexure hinge was designed. By applying Castigliano’s displacement theorem, the numerical model was simplified and deduced. Furthermore, to quantify the numerical model, natural frequencies of the finite-element analysis and experiments were carried out, of which the results were compared with the analytic solutions. The experiment results show that the in-plane natural frequency is 165.29 Hz. The comparison shows that the error between numerical analytic and experimentation is 1.3%, and the error between FEA and experimentation is 3.2%. It is proven that the bi-axial half-butterfly flexure hinge is an appropriate structure as a guide mechanism for an FSM system.
    $\left\{ {{uhe}{ule}} \right\} = \left[ {[Che]00[Cle]} \right]\left\{ {{Lhe}{Lle}} \right\}$(1)

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    $\left[ {{C^{he}}} \right] = \left[ {Cx,Fx000Cy,FyCy,Mz0Cθz,FyCθz,Mz} \right]$(2)

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    $\left[ {{C^{le}}} \right] = \left[ {Cz,FzCz,MyCθy,FzCθy,My} \right]$(3)

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    $\left[ {Cx,FxCy,FyCy,MzCθz,Mz} \right]{\rm{ = }}\left[ {1Ew00065Gw12Ew000012Ew000012Ew} \right]\left[ {0ldxt0lx2dxt30lxdxt30ldxt3} \right]$(4)

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    $\left[ {Cz,FCz,MyCθy,My} \right] = \left[ {12Ew3065Gw012Ew300012Ew3} \right]\left[ {0lx2dxt0lxdxt0ldxt} \right]$(5)

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    ${C_{se}} = {C_1} + {C_2}$(6)

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    ${C_{co}} = \frac{{{C_1}{C_2}}}{{{C_1} + {C_2}}}$(7)

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    ${C_l} = \frac{{12\left( {{l_1}{{\cos }^4}{\varphi _1} + {l_3}{{\cos }^4}{\varphi _3}} \right)}}{{Ew{t^3}}}$(8)

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    $\left\{ {ux=UFx=0uy=UFy=0θz=UMz=0} \right.$(9)

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    $\left\{ {Ch=ClcosψCrsin(ψ)Ch=Clsinψ+Crcos(ψ)} \right.$(10)

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    $\psi = \frac{{{\varphi _1} + {\varphi _3}}}{2}$(11)

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    $\left\{ {Cl=CrCh=1(cosψ+sinψ)Cl} \right.$(12)

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    ${C_h} = \frac{{12\left( {{l_1}{{\cos }^4}{\varphi _1} + {l_3}{{\cos }^4}{\varphi _3}} \right)}}{{\left( {\cos \psi + \sin \psi } \right)Ew{t^3}}}$(13)

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    $\left\{ {fin=12π1ChJzfs2=200Hzfout2fs=565.5Hz} \right.$(14)

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    ${R_{h1}} = {R_{h3}} = {R_{h4}} = {R_{h6}} = 0.5\;{\rm{mm}}$(15)

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    ${f_{\rm in}}{\rm{ = }}163.13\;{\rm{Hz}} \leqslant 200\;{\rm{Hz}}$(16)

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    Lei Zhao, Qiuxing Liu, Bo Hu, Hu Wang, Liang Liang, Heng Lu. Design and application of bi-axial half-butterfly flexure hinges in fast steering mirrors[J]. Infrared and Laser Engineering, 2021, 50(10): 20210118
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