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A surface roughness model utilizing regression analysis method is developed for predicting roughness of ultraprecision machined surface with a single crystal diamond tool. The effects of the main variables,such as cutting speed,feed,and depth of cut on surface roughness are also analyzed in diamond ting aluminum alloy. In order to predict and control the surface roughness before ultraprecision machining,constrained variable metric method is used to select the optimum cutting conditions during process planning. A lot of experimental results show that the model can predict the surface roughness effectively under a certain cutting conditions .