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摘要: 为了精确分析外载荷作用下米级口径经纬仪保护窗口镜面变形，本文基于接触有限元理论建立了米级口径经纬仪保护窗口带摩擦接触的有限元分析模型，对比了线性刚性连接和非线性摩擦接触方法的差异。采用齐次坐标变换法去除刚体位移，得到米级口径经纬仪保护窗口镜面畸变数据，使用Zernike多项式作为光机集成分析的接口工具，并将Zernike多项式系数导入ZEMAX中，以波前像差RMS值衡量镜面变形对成像质量的影响，并与干涉仪检测结果进行比较。考虑摩擦接触条件得到的保护窗口镜面波前像差RMS值为38.095 nm、PV为205.027 nm，使用干涉仪检测得到的保护窗口镜面波前像差RMS值为40.626 nm、PV值为235.654 nm。实验结果表明，考虑摩擦接触条件的仿真实验与干涉仪检测实验的镜面波前像差RMS值偏差为6.23%，能更准确地反映米级口径保护窗口镜面变形。
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关键词:
- 经纬仪 /
- 有限元理论 /
- 齐次坐标变换 /
- Zernike多项式
Abstract: In order to accurately analyze the mirror deformation of the one-meter theodolite protective window under exterior loads, the model of one-meter theodolite protective window is built on the base of frictional contact finite element theory, the differences between linear rigid joint and nonlinear frictional contact simulation methods are compared. Homogeneous coordinate transformation method is used to remove the rigid body displacement, and the mirror distortion data of the protection window of the meter-caliber theodolite is obtained. The Zernike polynomial is used as an interface tool for the integrated optomechanical analysis, and Zernike polynomial coefficients are introduced into ZEMAX. The effect of mirror distortion on image quality is measured by the RMS value of wavefront aberration, and is compared with the results of the interferometer test. The RMS value of the mirror wavefront aberration is 38.095 nm and the PV is 205.027 nm. The RMS value of the wavefront aberration is 40.626 nm and the PV is 235.654 nm. The experimental results show that the deviation of the RMS value of the specular wavefront aberration between the simulation experiment and the interferometer detection experiment considering the frictional contact condition is 6.23%, thus more accurately reflect the mirror deformation of the meter-level aperture protection window. -
图 5 保护窗口面形的干涉仪检测结果
Figure 5. Interferometer test results of contour diagram of protective window surface
表 1 材料属性参数
Table 1. Material property parameters
Material Density/
(kg·m-3)Young′s
Modulus/GpaPoisson′s
Ratio45 7 890 209 0.27 HT250 7 280 138 0.156 Fused silica 2 205 73 0.17 Rubber 1 150 0.006 1 0.49 
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表 2 Zernike前五项表达式及意义
Table 2. The first five polynomials of Zernike and their meanings
NO Polynomial Meaning 1 1 piston 2 2x x tilt 3 2y y tilt 4 
defocus 5 2 
astigmatism
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