Roughness model of an optical surface in ultrasonic assisted diamond turning

In this paper, the theoretical model is established to predict the optical surface roughness of difficult-to-cut material in ultrasonic assisted diamond turning (UADT). The effects of kinematics, material elastic recovery, and plastic side flow aiming at the characteristics of vibration cutting are considered. The convincing results predicted can be obtained when main machining parameters change, such as cutting speed, cutting depth, tool feed rate, tool frequency, and amplitude. Furthermore, the qualitative analysis of the model is demonstrated on the basis of comparing the trend variation by theoretical results and simulative results with the finite element method (FEM). The arithmetic average value of the vertical coordinates of the workpiece surface nodes is regarded as the surface roughness in the FEM. The minimum mesh size of workpiece is set as 5 nm in order to gain relatively exact results and avoid exceeded element distortions. Moreover, the accuracy of the predictive model is verified by cutting the MB5 magnesium alloy with UADT. The maximum error for surface roughness Ra is merely 10.26%, and average error is only about 6% after analyzing experiment and prediction results. The optimal surface roughness Ra of magnesium alloy reflector can be 3.388 nm with UADT so that the optical application level is realized only by UADT means without subsequent abrasive machining. Therefore, the predicting model is valuable for theory guidance and engineering application in the optical manufactory field of difficult-to-cut material with UADT.