考虑去除函数对数控小工具抛光光学元件精度的影响, 提出了如何根据需要加工的非球面参数以及抛光盘参数得到最优去除函数的方法。由于计算非球面上去除函数的核心是准确获得抛光盘与镜面间的动态压力分布, 本文提出利用有限元法仿真抛光盘与非球面间的压力分布, 并结合经典 Preston 方程与行星运动模型来得到非球面不同位置处的去除函数。 基于随动压力分布模型, 分析了沥青盘抛光非球面时在不同抛光位置处去除函数的变化。在曲率半径为1 000 mm的球面上进行了去除函数验证实验。结果表明: 基于本文理论得到的去除函线型更接近实际情况, 皮尔逊系数达到了 0.977。本文提出的方法可以方便地调整加工位置来得到相应的压力分布, 实现去除函数的优化, 对提高加工效率与精度有实际指导意义。

By taking the effect of Tool Influence Function(TIF) used in the NC program on the polishing accuracy for optical elements into account, the method how to obtain the optimized TIF based on the aspheric parameters to be polished and polishing pad parameters is proposed. As the key to calculate the TIF of aspheric elements is to obtain accurately the dynamic pressure distribution between polishing pad and mirror, this paper analyzes the pressure distribution between polishing pad and mirror by finite element method and obtains the TIFs in different positions on the aspheric surface by classic Preston equation and planet motion. The variation tendency of the pitch polishing pad in polishing an aspheric element is analyzed in different polishing positions based on the dynamic pressure distribution model. The TIF spot experiment is carried out on an aspheric element with a curvature of 1 000 mm. The result shows that the shape of TIF simulated by the theory introduced in the paper is more similar with that of the actual situation, and the Pearson correlation coefficient reaches 0.977. It concludes that the method can obtain the pressure distribution conveniently by changing the parameter of polishing position and can optimize the TIFs, which provides a theoretical basis for improving polishing efficiency and polishing accuracy.