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中文摘要：
以永磁型磁流变抛光机为基础,提出了在光栅式加工轨迹下结合四轴联动机床（不含抛光轮转动轴）和变去除函数实现磁流变抛光技术确定性加工曲面的方法。讨论了曲面上光栅式加工轨迹等面积规划原则和基于矩阵乘积运算的驻留时间求解算法。分析了磁流变四轴联动机床的机械补偿方式,同时以变去除函数模型为基础从算法上实现了机械的剩余补偿。应用以氧化铈为抛光粉的水基磁流液对口径为80mm、曲率半径为800mm的BK7材料凸球面进行了修形验证实验,一次加工（5.5min）后显示：面形误差分布峰谷值（PV）和均方根值（RMS）从117.47nm和22.78nm分别收敛到60.80nm和6.28nm。实验结果表明：结合四轴联动的低自由度机床和变去除函数算法补偿的磁流变加工工艺能够有效地实现球面及低陡度非球面等曲面的高效确定性加工,为磁流变抛光在光学制造中的应用提供了有力的支持。
英文摘要：
On the basis of permanent magnet Magnetorheological Finishing（MRF）machine,a magnetorheological finishing method by combining a 4-axis machine with a variable removal function was developed to figure the sphere surface in a raster path.The principle of equal area observed on the raster path and the dwell time algorithm based on matrix multiplication computation were discussed.A mechanical compensating strategy based on the 4-axis machine was analyzed,including machine compensating and algorithm compensating of the variable removal function.By using water based magnetorheological fluid with the polishing powder of cerium oxide,apolishing experiment on a convex made of BK7 material with a diameter of 80 mm and curvature radius of 800 mm was carried out.The experiments show that error values（PV and RMS）have been converged from 117.47 nm and 22.78 nm to60.80 nm and 6.28 nm respectively with just one polishing cycle（5.5min）.The result demonstrates that strategy of variable removal function compensating based on the 4-axis machine can effectively figure the sphere and asphere surfaces determinately by the MRF,which reduces the cost of the MRF machine,and pushes its applications to the the usual optical shop.
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