弹性球状小磨头加工WolterⅠ型掠入射反射镜的去除函数

Removal function for fabrication of WolterⅠ grazing mirror by elastic ball tool

提出用弹性球状小磨头以旋进方式加工WolterⅠ型反射镜的柱面内表面,根据Preston方程、Hertz接触理论和掠入射反射镜特殊的柱面结构,推导出基于旋偏动模式的磨头去除函数理论模型。实验结果表明,理论去除函数曲线与实验曲线的均方根距离偏差σ为0.101 22μm,偏差比值κ为9.8%。分析验证了不同旋偏角对去除函数的影响并与理论模拟结果进行了比较。结果显示,随着旋偏角的增大,最大去除值位置逐渐向y轴正方向偏移。不同的旋偏角,最大理论去除深度与最大实际去除深度的均方根偏差为0.201μm;最大理论去除位置与最大实际去除位置的均方根偏差为0.255 mm。旋偏角越大,材料去除量就越多,去除函数也越显对称。实验结果很好地验证了去除函数理论模型的准确性,该模型可指导WolterⅠ型掠入射反射镜的加工,实现确定性材料去除。

A novel technology for fabricating WolterⅠgrazing mirrors by an elastic ball tool was described in this paper.According to the Hertz contacting theory and Preston equation,a removal function model for tool movement on a cylinder surface was established based on the precession motion.The comparison of the theoretica1 model and the experimental results shows that the RMS distance warp between the theoretica1 removal function curve and the experimental curve is 0.101 22 μm,and its deflection ratio is 9.8%.Furthermore,the effect of different precession angles on the removal function was validated,which points out that the larger the precession angle is,the more the material are removed and the max removal point moves to the centre of contact area closely.With different precession angles,the rms deviation of max removal depth is 0.201 μm and the rms position deviation of max removal depth is 0.255 mm.The experimental results verify the feasibility of the theoretica1 model of removel function.The model can direct the fabrication of WolterⅠgrazing mirrors and can realize the deterministic material removal.