Study on Machining Technology of Large Aspheric Aluminum Reflector with Three Axis Linkage
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摘要: 为解决单点金刚石车削技术（single-point diamond turning，SPDT）应用于大口径大弦高非球面铝反射镜加工中遇到的车床导轨行程、工作台回转容积受限和加工质量较低的问题，针对φ682 mm口径、弦高220 mm的凹非球面铝反射镜加工，首先，提出基于SPDT的三轴联动加工方法，在两轴加工基础上加入旋转B轴进行协同加工，使得导轨行程和工作台回转容积能够满足加工需求。然后，设计专用笼状夹具，并通过有限元法研究支撑杆数量、杆径、上下连接板厚度参数对夹具-工件形变特征的影响，通过极差和方差分析研究不同因素对夹具-工件最大变形量影响的显著性，得到一组最佳夹具设计参数组合，即夹具支撑杆数量为24，杆径为22 mm，上下连接板厚度为25 mm。最后，将铝反射镜固定在优化后的笼状夹具上，通过三轴联动加工实现了对φ682 mm口径非球面铝反射镜的加工。对调刀件的检测结果表明：调刀件面形精度Pv值为0.6 μm，表面粗糙度Ra约为10.1 nm，可认为φ682 mm口径非球面铝反射镜的面形精度和表面粗糙度均达到使用要求。本研究能够为同类大口径大弦高非球面反射镜的加工提供一定的理论基础和加工工艺技术参考。Abstract: To solve the problem of single point diamond turning(SPDT), technology was used for the processing of large diameter and chord height aspheric aluminum mirrors, which have the problems of limited lathe guide stroke, limited rotary volume of worktable, and low processing quality. To process a concave aspheric aluminum mirror with a diameter of φ682 mm and a chord height of 220 mm, first, a three-axis linkage processing method based on SPDT was proposed, which adds rotary b-axis on the basis of two-axis processing, such that the guide rail travel and table rotation volume can meet the processing requirements. Then, the special cage fixture was designed, and the influence of the number of supporting rods, the diameter of supporting rods, and the thickness of upper and lower connecting plates on the jig-work piece deformation characteristics were examined using the finite element method. The influence of different factors on the maximum deformation of jig and work piece was evaluated via range and variance analysis. A set of optimal jig design parameters was obtained, that is, the number of jig support rods was 24, the diameter of the rods was 22 mm, and the thickness of the upper and lower connecting plates was 25 mm. Finally, the aluminum mirror was fixed on the optimized cage clamp, and the processing of the φ682 mm aspheric aluminum mirror was realized through three-axis linkage processing. The test results show that the surface accuracy Pv of the tool adjusting part was 0.6 μm, and the surface roughness Ra was approximately 10.1 nm. It can be considered that the surface accuracy and surface roughness of the φ682 mm aspheric aluminum mirror can meet the requirements. This study can provide a theoretical basis and technological reference for the processing of the same type of large aperture and high chord aspheric mirror.
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图 7 最大变形量随各参数变化趋势
Figure 7. The variation trend of maximum deformation with various parameters
表 1 材料参数
Table 1 Material parameters
Material Density/(kg·m-3) Young modulus/(GPa) Poisson ratio Coefficient of thermal expansion Aluminum alloy 2770 71 0.33 23 Stainless steel 7750 193 0.31 17 
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表 2 坐标变换结果
Table 2 Coordinate transformation results
Coordinate point X-coordinate/mm Z-coordinate/mm Tool rotation angle-β/º A1 310 219.878377 A1' 308.75 220.71 56.54 A2 309.9 219.727043 A2' 308.65 220.55 56.53 A3 309.8 219.575771 A3' 308.55 220.40 56.52 A4 309.7 219.424562 A4' 308.45 220.25 56.51 A5 309.6 219.273416 A5' 308.35 220.10 56.50 … … …
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表 3 夹具参数
Table 3 Fixture parameters
Factors Code Level 1 2 3 Support rod number N A 12 18 24 Support rod diameter R/(mm) B 12 22 26 Plate thickness T/(mm) C 15 20 25 Spindle speed n/(r/min) 200
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表 4 正交实验方案及结果
Table 4 Orthogonal experimental scheme and results
NO. Support rod
numberSupport rod
diameterPlate
thicknessMax total
deformationN R/mm T/mm D/mm 1 12 12 15 0.49531 2 12 22 20 0.31924 3 12 26 25 0.28334 4 18 12 20 0.42477 5 18 22 25 0.30412 6 18 26 15 0.35454 7 24 12 25 0.39917 8 24 22 15 0.41238 9 24 26 20 0.36372
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表 5 表面粗糙度的方差分析
Table 5 Analysis of variance of surface roughness
Variation
sourceSS df MS F Contribution/% A 0.002 2 0.001 1.198 0.7 B 0.020 2 0.010 14.935 52.6 C 0.013 2 0.006 9.372 31.6 Error 0.001 2 0.001 15.1 Sum 0.036 8 0.018 100
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