Modelling of dynamic cutting force coefficients and chatter stability dependent on shear angle oscillation

Productivity of high-speed turning operations is limited by the onset of self-excited vibrations known as chatter. Unless avoided, chatter vibrations may cause large dynamic loads damaging the machine spindle, cutting tool or workpiece and leave a poor surface finish behind. Cutting force magnitude is proportional to the thickness of the chip removed from the workpiece. This paper presents a new procedure to determine dynamic cutting force coefficients (DCFC) required for process simulation by mechanistic modelling. In this study, a two degree of freedom complex dynamic model of turning with an orthogonal cutting system is considered. The complex dynamic system consists of a dynamic cutting system force model based on shear angle (φ) oscillations and penetration forces caused by the tool flank’s contact with the wavy surface. The dynamic cutting force coefficients are identified by operating a series of cutting tests at the desired frequency, while changing φ oscillations and penetration forces. It is shown that the process damping coefficient increases as the tool is worn, which increases the chatter stability limit in cutting. The chatter stability of a dynamic cutting process is solved using the Nyquist law and time domain simulation (TDS) techniques and compared favourably against experimental results at low cutting speeds. Finally, comparisons among the proposed mechanistic model and experimental results show a good agreement with the analytically established SLD and, thus, validate the effectiveness of the proposed model.