Modeling of the effect of tool edge radius on surface generation in elliptical vibration cutting

Abstract

The elliptical vibration cutting (EVC) technique has been found to be a promising technique for ultraprecision machining of various materials. During the EVC process, two-dimension vibration movement of the cutting tool generates consecutively overlapping EVC cycles. In each cycle, the tool position relative to the workpiece gets continuously varied, and meanwhile, cusps are left along the nominal cutting direction. Such vibration marks, which have never been found in conventional cutting process, are considered to be a critical characteristic for the EVC technique. In order to analyze this unique characteristic, an analytical model based on geometrical relationships in the EVC process was developed to calculate the theoretical roughness, where the tool edge is assumed to be perfectly sharp. However, the effect of tool edge radius is probably significant, especially in the situation where the tool edge radius is comparable to the vibration amplitudes. Hence, in the present research, an analytical surface generation model for the EVC process is developed to better understand the surface generation process and predict the surface roughness. The tool edge radius is considered and investigated in detail in this new approach. Mathematical evaluation shows that the surface roughness value along the nominal cutting direction decreases with the increase of the edge radius. In order to validate the proposed model, a series of EVC grooving tests on soft and hard work materials were conducted using a polycrystalline diamond (PCD) tool by applying the ultrasonic EVC technique. The results show that the predicted roughness based on the proposed model correlates well with the experimental results measured by a white light interferometer, and the model considering the tool edge radius performs significantly better than the one without considering the edge radius in predicting the roughness along the nominal cutting direction.