基于应变梯度理论的准晶扭转微镜驱动器的稳定性分析

黄允祗; 冯淼林; 陈秀华

doi:10.1007/s10409-021-09031-x

Stability analysis of quasicrystal torsion micromirror actuator based on the strain gradient theory

doi: 10.1007/s10409-021-09031-x

Huang Yunzhi¹,
Feng Miaolin^{1,*
, ,},
Chen Xiuhua^{2,*
, ,}

1.
Department of Engineering Mechanics, School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University,Shanghai 200240, China
2.
School of Aeronautics and Astronautics, Shanghai Jiao Tong University, Shanghai 200240, China

Funds:

the National Natural Science Foundation of China Grant

Corresponding authors: Corresponding authors. E-mail addresses: mlfeng@sjtu.edu.cn (M. L. Feng); chenxiuhua@sjtu.edu.cn (X. H. Chen); Corresponding authors. E-mail addresses: mlfeng@sjtu.edu.cn (M. L. Feng); chenxiuhua@sjtu.edu.cn (X. H. Chen)

摘要

摘要: 静电扭转微镜广泛应用于微米光开关、光衰减器、光学扫描仪和光学显示器等领域. 过去微镜镜面主要沿单轴或双轴方向偏转, 从而限制了入镜光线的反射范围. 本文通过建立圆形静电驱动微镜的动力学模型, 设计了一种可任意方向偏转的准晶微镜驱动器. 然后基于应变梯度理论进行数值求解, 分析了其静态和动态现象以及吸合失稳特性, 并比较了反射镜面在三种偏转方向下的结果. 研究表明, 镜面沿着不同方向偏转的结果存在显著差异. 当沿斜轴的偏转角度达到45°时, 吸合失稳电压值最小. 失稳电压还随着准晶的声子场-相位子场耦合弹性模量和相位子场弹性模量的增加而增加. 准晶的介电常数、应变梯度参数和空气阻尼都会影响到微镜动态系统的扭转. 此外, 微镜表面分布力的减小也会导致更大的吸合失稳电压.
Abstract: Electrostatic torsional micromirrors are widely applied in the fields of micro-optical switches, optical attenuators, optical scanners, and optical displays. In previous lectures, most of the micromirrors were twisted along the uniaxial or biaxial direction, which limited the range of light reflection. In this paper, a quasicrystal torsional micromirror that can be deflected in any direction is designed and the dynamic model of the electrostatically driven micromirror is established. The static and dynamic phenomena and pull-in characteristics are analyzed through the numerical solution of the strain gradient theory. The results of three kinds of mirror deflection directions are compared and analyzed. The results show the significant differences in the torsion models with different deflection axis directions. When the deflection angle along the oblique axis reaches 45°, the instability voltage is the smallest. The pull-in instability voltage increases with the increment of phonon-phason coupling elastic modulus and phason elastic modulus. The permittivity of quasicrystal, the strain gradient parameter, and the air damping influence the torsion of the micromirror dynamic system. A larger pull-in instability voltage generates with the decrease of surface distributed forces.
- Quasicrystals /
- Torsion micromirror /
- Instability /
- Strain gradient theory

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1. A schematic view of the round, double-gimbaled system, showing the various relevant parameters: a the main view of the system; b the top view of the circular plate; c the bottom view of the circular plate; d the top view of the substrate.

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2. Schematic diagram of electrostatic torsional mirror with model considering coupled torsion and bending effects.

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3. A schematic view of the circular plate rotating along a the inner axis, b the outer axis, and c the oblique axis under the action of the electrostatic force in different areas.

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4. The static behaviors of macro reference model analyzed by finite element simulation: stress amplitude for rotating along a the inner axis, b the outer axis, and c the oblique axis; displacement amplitude for rotating along d the inner axis, e the outer axis, and f the oblique axis.

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5. Comparison of torsions in three directions (the inner, outer, and oblique axes) using FES and present model for macro mirror: a curve for torsion angle Θ; b curve for maximum displacement Δ.

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6. Influences of a phonon-phason coupling elastic modulus R₁ and b phason elastic modulus K₁, and influences of c horizontal deflection angle φ and d strain gradient parameter-induced additional stiffness J_s/J₀ on the dimensionless pull-in tilting angle Θ and voltage β, respectively.

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7. Comparison of time history curves of a the tilting angle Θ with different strain gradient parameter-induced additional stiffness J_s/J₀ and b the velocity of rotation ξ with different damping effects ${\bar{C}}_{vq}$ and ${\bar{C}}_{sq}$ , respectively.

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8. Influence of QC permittivity ε₁ on the maximum torsion angle Θ_m with different a damping effects ${\bar{C}}_{vq}$ ( = ${\bar{C}}_{sq}$ ) and b parameters of outer electrode position and width λ = b/a₁.

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9. Comparison of the phase portrait on the phase plane: a without damping effects ( ${\bar{C}}_{vq}$ = ${\bar{C}}_{sq}$ = 0 ) and b with damping effects ( ${\bar{C}}_{vq}$ = ${\bar{C}}_{sq}$ = 0.05).

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10. Influence of a van der Waals moment (α₃ = 0) and b thermal Casimir moment (α₄ = 0) on the pull-in voltage β_cp with different initial gap g₀.

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Table 1. Geometrical and material parameters of the combination structure of beam and plate

Geometrical parameters		QC material parameters
H = 20 μm, R = 200 μm, a = 200 μm,b = a/2, g₀ = H, a₁ = a, a₁ = 3a/2,L = b/2, L₁ = b/2, L₂ = 1.2R, L₃ = L₁, h₁ = 10 μm, h₂ = h₁		E = 197.5 × 10⁹ N/m²,K₁ = 122 × 10⁹ N/m²,R₁ = 17.7 × 10⁹ N/m²,ν = 0.25

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Stability analysis of quasicrystal torsion micromirror actuator based on the strain gradient theory

doi: 10.1007/s10409-021-09031-x

Corresponding authors: Corresponding authors. E-mail addresses: mlfeng@sjtu.edu.cn (M. L. Feng); chenxiuhua@sjtu.edu.cn (X. H. Chen); Corresponding authors. E-mail addresses: mlfeng@sjtu.edu.cn (M. L. Feng); chenxiuhua@sjtu.edu.cn (X. H. Chen)

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Stability analysis of quasicrystal torsion micromirror actuator based on the strain gradient theory

doi: 10.1007/s10409-021-09031-x

Corresponding authors: Corresponding authors. E-mail addresses: mlfeng@sjtu.edu.cn (M. L. Feng); chenxiuhua@sjtu.edu.cn (X. H. Chen); Corresponding authors. E-mail addresses: mlfeng@sjtu.edu.cn (M. L. Feng); chenxiuhua@sjtu.edu.cn (X. H. Chen)

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