中文摘要：

分析了自行研制的磁流变抛光机床KDMRF-1000的拓扑结构以及坐标变换关系，对其进行了运动求解，建立了光学镜面的磁流变抛光后置处理算法模型。针对机床四轴联动的特点，对建立的磁流变抛光后置处理模型进行了近似处理。以球面镜的后置处理为例，推导了具有普适性的以光栅扫描方式加工光学镜面的后置处理算法，同时分析了这种近似处理引入的误差，仿真了其对不同口径和不同相对口径球面镜的影响，得到了这种近似处理算法对球面镜的加工范围。最后，对一块口径为200mm，相对口径为1：1．6的K9材料球面镜进行了磁流变抛光实验，在不考虑边缘效应的情况下其面形误差的PV值和RMS值分别达到了65nm和9nm以下，有效地验证了后置处理算法模型的准确性以及四轴联动近似处理的可行性。该算法对各类形状和大小的光学镜面加工均有参考意义。

英文摘要：

The topological structure and coordinate transformation of Magnetorheological Finishing （MRF） machine tool KDMRF-1000 were analyzed and its kinematics was calculated,then the post processing algorithm model of MRF for an optical lens was established. According to the characteristic of four-axis linkage machine tool, the model was treatmented approximately. By taking the post processing of a spherical lens as an example, a post processing algorithm that can be used for a raster tool path was deduced and the errors imported by this approximate treatment were analyzed. By simulating the effect of the algorithm on the spherical lenses with different apertures and relative apertures, the polishing range of this algorithm was achieved. Furthermore, a spherical part （K9, 200 mm in diameter, f=640 mm） was polished by MRF, experimental results show that obtained errors are less than 65 nm PV and 9 nm RMS in excluding the edge effect. This experiment proves the veracity of post processing algorithm and the feasibility of four-axis linkage approximate treatment. The work done in this paper has an important purpose for polishing the optical lenses with different apertures and shapes.