An analytical modelling of cutting forces in orthogonal elliptical vibration cutting

In the present work, an analytical model is proposed to predict the cutting forces in elliptical vibration cutting (EVC). In general, cutting force in metal cutting is a function of the shear angle (φ) and shear strength (τ) of the material. However, these parameters vary dynamically over a cutting cycle of EVC. In this work, the shear angle has been modelled based on the plasticity theory of maximum shear stress criteria. For transient shear strength prediction, the Johnson–Cook model is used. This model predicts shear strength for time-varying strain and strain rate in EVC. The obtained analytical results of cutting forces were compared with experimental results published in the literature and found to be in good agreement (within 12% error) with them. Based on the proposed model, the cutting forces can be modelled as a function of cutting process parameters (depth of cut, cutting velocity), tool parameter (rake angle), physical and thermo-mechanical properties for different materials, without any experimental inputs from EVC.