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Research on the calculation method of the ultra-precision turning trajectory of large-vector high-convex cylinders
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摘要:
阵列微结构光学元件广泛用于各种光束匀化场合，而常规的加工方法难以满足大矢高凸柱面阵列的精度要求。本文采用超精密车削成型法，分析了影响金刚石车削的主要因素，设计了顺序搜索法和二分搜索法寻找车削轨迹，并对比了两种方法的优缺点，结合Matlab软件用二分搜索法成功找到车削轨迹及数控程序，并在超精密车床上进行了车削实验，得到了表面轮廓误差在135 nm的大矢高阵列微结构。证明了二分搜索法能够准确获得车削轨迹，并且此法可同时适用于球面轮廓和非球面轮廓，具有重要的工程应用价值。
Abstract:Array microstructure optical elements are widely used in various beam homogenization occasions, but conventional processing methods cannot meet the accuracy requirements of large-sagittal convex cylindrical arrays. In this paper, the ultra-precision turning forming method is used to analyze the main factors affecting diamond turning, the sequential search method and the binary search method are designed to find the turning track, and the advantages and disadvantages of the two methods are compared. Furthermore, the binary search method is successfully found by combining the Matlab software turning trajectory and the numerical control program. As proof-of-concept demonstrations, turning experiments are carried on an ultra-precision lathe, and a large-vector high-array microstructure with a surface profile error of 135 nm is obtained. It proves that the force binary search method can accurately obtain the turning trajectory, and this method can be applied to both spherical and aspherical contours, showing important engineering application value.
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Overview: Array microstructured optical elements are widely used in various beam homogenization occasions, with complex structures and extremely high surface shape accuracy requirements. The microstructures of large-sag high-convex cylindrical arrays have the characteristics of high sagittal height, large diameter, small seam, and high surface shape accuracy. It is often difficult for conventional processing methods to meet the accuracy requirements. As a ultra-precision turning forming method, the diamond tip has a micron-level structure, and the processing accuracy is not limited by the height of the microstructure, which is a very potential method for processing the microstructure of the large array of high convex cylindrical arrays.
How to ensure the machining accuracy is an important problem that needs to be solved in ultra-precision turning. This paper analyzes the main factors that affect diamond turning-turning trajectories. Increasing the turning trajectory accuracy can improve the turning surface accuracy and obtain a good machining surface shape. This article analyzes and compares two methods, namely sequential search method and binary search method, to find the best turning trajectory, and each method has its own advantages and disadvantages. The sequential search method can obtain a high-precision turning trajectory, but the calculation amount will gradually increase as the stepping distance decreases, which leads to lower efficiency. The binary search method can quickly obtain the turning trajectory, and the calculation amount is relatively small. So the calculation time is short, which greatly improves the turning efficiency. Combined with actual production applications, improving efficiency is one of the important issues that need to be considered. Therefore, this paper chooses the binary search method to find the turning contour trajectory.
The binary search method can be used to find the turning trajectories of both spherical and aspherical contours. Combined with laboratory conditions, the experiment took the spherical contour as an example, and the spherical turning trajectory was successfully generated through numerical control programs. Furthermore, turning experiments on ultra-precision turning machine tools were carried out, with the turning results being analyzed using the least square method. The original curve is compared with the fitted curve, and the difference curve is obtained. It is found that the contour error of the workpiece after processing is 135 nm, and the expected surface shape and good surface contour error are basically obtained. This article provides a theoretical basis for how to find the turning trajectory of the large-vector convex cylindrical array microstructure, and has important practical application value.
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图 1 大矢高凸柱面阵列微结构。(a) 大矢高凸柱面; (b) 柱面参数; (c) 柱面接缝
Figure 1. Arrayed microstructures with large-vector high-convex cylinders. (a) Large-vector high-convex cylinders; (b) Cylindrical parameters; (c) Cylindrical seams
图 3 二分法寻找车削轨迹。(a) 二分法原理图；(b) 二分法流程图
Figure 3. Dichotomy to find the turning trajectory. (a) Schematic diagram of the dichotomy; (b) Dichotomy flowchart
图 9 球面阵列结果分析。(a) 测量原始曲线；(b) 最小二乘法拟合曲线；(c) 球面轮廓误差
Figure 9. Analysis of spherical array results. (a) Measured original curve; (b) Fitting curve by least squares; (c) Deviation between the leveling curve and the fitting curve
表 1 实验车削参数
Table 1. Experimental turning parameters
实验参数 实验参数值 主轴转速/(r/mm) 500 进给速度/(mm/min) 3 刀具半径R/mm 0.5 曲线T1宽度/mm 0.534 接缝宽度T2/mm 0.02 切削周期数 10 
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