Modelling of surface roughness in elliptical vibration cutting of ductile materials

Elliptical vibration cutting (EVC) is a widely used ultra-precision machine technology. However, the surface roughness prediction of EVC is difficult for the complicated surface generation process. In this paper, the surface generation mechanism of EVC is elucidated. A new surface roughness model is proposed considering the roughness in the nominal cutting direction (NCD) and feed direction (FD). The roughness in the NCD is determined by kinematics, tool edge radius, tool flank face interference, and material spring back. For the first time, the influence of material spring back in previous cutting cycle on surface roughness generation is considered in EVC along the NCD. The roughness in the FD is determined by kinematics, tool nose radius, shift distance, tool interference, material spring back and material pile-up. The material spring back is determined by using a function of the plastic strain of workpiece material in the third deformation zone and the minimum undeformed chip thickness. For calculating the roughness component of material pile-up, a function related to tool edge radius, depth of cut, residual height caused by tool nose radius and feed rate is constructed. The experimental results show that the proposed model has a high prediction accuracy. According to the model, the influencing mechanism of various machining factors on the surface roughness variation is clarified and a high-efficiency machining method without deteriorating surface roughness is obtained.