“…Because the workpiece and toolholder are deformed, the relative position of the workpiece and the tool changes, resulting in vibration, causing machining errors and reducing the surface quality of the workpiece. The mathematical equation describing the vibration phenomenon of the turning process presented by M. Siddhpura and S. Katiyar as follows [4,5]: (1) where: m, k and c are the mass, stiffness and damping coefficient, respectively, and P(t) is the cutting force in feed (x) direction. P(t) = (2) where: Kf is the cutting coefficient in feed direction, b is the chip width (width of cut), T is the time delay between current time and previous time, and is the dynamic chip thickness due to the tool vibration.…”