Analytical modeling of chatter vibration in orthogonal cutting using a predictive force model

• An analytical chatter model is presented for chatter vibration analysis in orthogonal cutting.
• The present model uses a predicted force model to determine dynamic cutting forces theoretically.
• Dynamic cutting force coefficients are derived from geometric approximations.
• Stability analysis is investigated and SLD is obtained by the time domain semi-discrete method.

This work is motivated by the fact that the conventional chatter models cannot capture the thermo-mechanical properties of realistic cutting processes intuitively and the involved cutting force coefficients are generally constant identified through experimental methods less accurately. In this paper, a new analytical chatter model is presented for the simulation and analysis of chatter vibration in orthogonal cutting processes. This model is developed using a predicted force model, which can determine the dynamic cutting forces theoretically with the equivalent cutting parameters from the material properties, tool geometry and cutting conditions. Moreover, the dynamic cutting force coefficients are derived significantly from the geometric approximations over a given wide range of cutting parameters. Then, a single degree-of-freedom (SDOF) dynamic model of the machine tool system for chatter vibration in orthogonal cutting is considered and formulated as a time delay-differential equation. The stability analysis of the proposed model is investigated and the stability lobe diagram (SLD) is obtained further by the time domain semi-discrete method. Finally, Comparisons among the proposed model, the semi-analytical model, the existing chatter model and experimental results available in the literatures are provided. It is shown that the results agree well with the analytically established SLD and thus validate the effectiveness of the proposed model.