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由于反射镜本身结构的关系,有筋区域和无筋区域的刚度不同,在正压力加工过程中,有筋支撑的区域弹性变形小,材料去除量大,而无筋支撑的区域弹性变形大,材料去除量小。当加工结束后,反射镜有筋区域呈下凹现象,无筋区域呈上凸现象,当反射镜的面形精度较高时,就会产生和镜面背部支撑结构相关的变形分布,这种现象被称为“压印效应”,即“网格效应”。
根据弹性力学理论,反射镜在加工过程中产生的“网格效应”与其结构参数存在下列关系[14-15]:
$$ \delta=\frac{12 \varphi P B^{4}\left(1-\mu^{2}\right)}{E t_{f}^{3}} $$ (1) 式中:δ为“网格效应”的最大值;
$\varphi $ 为与形状有关的因子;P为反射镜加工过程中的抛光压力;B为反射镜蜂窝结构的内切圆直径;E为反射镜材料的弹性模量;tf为反射镜面板厚度。由公式(1)可知,当反射镜材料确定后,格子效应主要受抛光压力、蜂窝尺寸大小和面板厚度等因素的影响,其中抛光压力越大、蜂窝结构尺寸越大、面板厚度越薄,反射镜在加工过程中产生的格子效应就越明显。为了抑制网格效应的产生,在设计时反射镜的蜂窝结构尺寸和面板厚度就会有一定的限制,同时加工过程中抛光压力也不能选择太大,这些都影响着反射镜的轻量化设计和抛光加工效率。
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ULE反射镜的具体结构如图1所示,口径为Ø350 mm,高度为60 mm,上下两镜面均为平面,将反射镜上表面定为镜面A,下表面定为镜面B,面板厚度均为4 mm;反射镜内部是六边形蜂窝夹芯结构,蜂窝外接圆直径为150 mm,筋厚度为2 mm,各筋处开Ø20 mm的孔相互连通;反射镜外壁厚3 mm,外壁上开12个Ø20 mm的孔,其中六个孔用于在反射镜内部粘贴应变传感器,另外六个孔用于外接气嘴,整个镜坯质量约为2.4 kg,面密度为25.95 kg/m2。反射镜的材料为ULE,其力学性能如表1所示。
表 1 ULE主镜的力学性能参数表
Table 1. Mechanical property parameters of ULE primary mirror
Mechanical property parameters Value Modulus of elasticity/GPa 67 Density/t·mm−3 2.21×10−9 Poisson's ratio 0.17 -
HyperMesh是一个高性能的有限元前后处理器,它能让CAE分析工程师在高度交互及可视化的环境下进行仿真分析工作,与其他有限元前后处理器相比,HyperMesh的图形用户界面易于学习,在处理几何模型和有限元网格的效率和质量方面具有很好的速度、适应性和可定制性,故文中采用HyperMesh对其进行有限元分析。
因该反射镜轻量化程度高,壁很薄,选用二维壳体单元建模,共有41717个节点,42696个单元,反射镜光轴方向为Y轴,如图2所示。正常加工状态下,研抛盘按照加工轨迹对整个镜面进行依次加工,反射镜受力是随着研抛盘的移动不断变化的,属于动态力学分析,在仿真时很难准确模拟,但可以通过静力学仿真进行定性分析,即用反射镜整个镜面均匀受力后的变形来简化模拟加工过程中的网格效应问题,该仿真分析方法简单有效且具有通用性,不受反射镜刚度和背部轻量化等形式的影响。针对该反射镜具体施加的边界条件为:沿–Y方向,给整个镜面施加2000 Pa的压力,同时约束反射镜底面X、Y、Z三个方向的平动和转动。
仿真面形结果见图3,图3(a)为2000 Pa压力作用下的反射镜的面形,因网格效应主要是带来与反射镜支撑结构相关的中高频误差,故对面形进行滤波,滤掉低频误差后,中高频误差如图3(b)所示,可以看出反射镜中高频误差面形分布与镜面背部的蜂窝结构呈明显的相关形式。
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对反射镜A面和B面的加工结果进行面形检测,因加工边缘效应的影响,反射镜边缘有极大的翘边,取有效口径Ø260 mm的面形检测,结果如图6所示。可以看出,A面的面形图已经出现与反射镜背部支撑结构相关的图形,B面则无明显相关性。对两面形图进行高斯滤波,频段误差大于30 mm的结果如图7所示。可以看出,相比于B面,滤波后A面反射镜的蜂窝结构已经清晰的印在面形上,网格效应十分明显,可见在保证加工参数相同的情况下,当面形精度RMS加工到1/10λ以内时,不充气加工的面形发现有明显的网格效应,而充气加工的网格效应大大改善,可见充气平衡式加工可有效减小网格效应。
图 6 (a) A面面形检测结果;(b) B面面形检测结果
Figure 6. (a) Surface detection result of surface A; (b) Surface detection result of surface B
图 7 (a) A面高斯滤波结果;(b) B面高斯滤波结果
Figure 7. (a) Gaussian filtering result of surface A; (b) Gaussian filtering result of surface B
垂直于平面镜支撑筋处,选取两块小区域:区域1和区域2,小区域内A面和B面的面形对比如图8所示。可以看出,在该区域内没有充气加工的面形呈现明显的高低高,有筋处加工量多,无筋处加工量小;而充气加工后,有筋区域和无筋区域的变形趋于一致。
图 8 两支撑筋区域内A面和B面的面形对比图
Figure 8. Surface precision comparison of surface A and surface B in the area of two support ribs
对区域1和区域2处的A面、B面面形PV值和RMS值进行分析,结果如表2所示。可以看出,无充气加工时,区域1、区域2内的PV值和RMS值都比较大,而充气加工后,区域1、区域2内的PV值和RMS值相比于未充气可降低50%以上,可见通过充气平衡法加工反射镜有助于减少中高频误差的产生,加快收敛效率。
表 2 支撑筋处面形PV值和RMS值分析
Table 2. Analysis of PV and RMS values of surface shape at support ribs
Surface A Surface B The reduction rate PV of area 1/nm 182.9 50.7 72.3% RMS of area 1/nm 41.3 13.2 68.5% PV of area 2/nm 133.9 59.3 55.7% RMS of area 2/nm 38.7 10.3 73.4%
Reduction of grid effect in ultra-light mirror machining by inflatable balanced method (invited)
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摘要: 对于传统蜂窝夹芯结构的反射镜,因加工过程中网格效应的存在,反射镜的面板厚度和蜂窝尺寸之间彼此关联制约着,严重影响反射镜的轻量化设计。针对蜂窝夹芯结构的超轻ULE反射镜,提出了一种充气平衡式减小网格效应的加工方法,运用控制变量法,通过实验比对了正常加工和充气平衡式两种研抛状态下网格效应的变化。实验结果表明:当反射镜面形精度RMS达到1/10λ (λ=632.8 nm)以上时,正常加工的面形图存在明显的网格效应,而充气加工则没有,可见反射镜内部充气可有效平衡加工压力,使反射镜在加工过程中有筋区域和无筋区域的变形趋于一致,从而有效减小网格效应。Abstract: For the mirror with traditional honeycomb sandwich structure, due to the existence of grid effect in the processing, the thickness of the mirror panel and the honeycomb size are correlated with each other, which seriously affects the lightweight design of the mirror. Aiming at the ultra-light mirror with honeycomb sandwich structure, an inflatable balanced processing method to reduce the grid effect was proposed. By using the control variable method to design test, the changes of grid effect under normal processing and inflatable balanced processing were compared. The experimental results show that when the mirror surface precision RMS reached more than 1/10λ (λ=632.8 nm), there is an obvious grid effect in the normal processing without inflation, but not in the inflatable balanced processing. It could be seen that inflating the inside of the mirror could effectively balance the processing pressure and make the deformation of the reinforced area and the non-reinforced area tend to be the same during processing, so as to effectively reduce the grid effect.
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Key words:
- optical processing /
- grid effect /
- inflatable balanced /
- ultra-light mirror
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表 1 ULE主镜的力学性能参数表
Table 1. Mechanical property parameters of ULE primary mirror
Mechanical property parameters Value Modulus of elasticity/GPa 67 Density/t·mm−3 2.21×10−9 Poisson's ratio 0.17 表 2 支撑筋处面形PV值和RMS值分析
Table 2. Analysis of PV and RMS values of surface shape at support ribs
Surface A Surface B The reduction rate PV of area 1/nm 182.9 50.7 72.3% RMS of area 1/nm 41.3 13.2 68.5% PV of area 2/nm 133.9 59.3 55.7% RMS of area 2/nm 38.7 10.3 73.4% -
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