The effect of torsional vibrations on metal cutting dynamics

The effect of torsional vibrations on the dynamics of metal cutting processes is studied. An extended dynamic process model is presented, where the spindle angle and the time delay are dynamic variables resulting in delay differential equations with state-dependent delay. Stability lobes are calculated based on the new extended process model and compared with results from the classical chatter theory with constant spindle speed and delay. For an ideal symmetric tool, stable cutting is characterized by a periodic spindle speed but still a constant delay. In this case, the main difference between the new extended and the classical model is a different periodic solution to periodic torsional tool displacements, which results only in slight modifications of the stability lobes. However, the new theory shows that it is important to consider tool asymmetries (e.g. runout), because this would result in periodically varying delays during stable cutting and larger stability changes due to torsional vibrations.