The stability of regenerative chatter in machining is studied, where the effect of structural vibrations into the cutting speed direction are not neglected. The inclusion of tangential or torsional vibrations in the chip thickness model lead to a delay differential equation (DDE) with state-dependent delay in the time domain. However, the system can be transformed into the angular domain, where the DDE has a constant delay but an additional nonlinear prefactor. The analysis of regenerative chatter vibrations in the angular domain is advantageous from a theoretical as well as from a numerical point of view compared to the conventional analysis in the time domain.
For generic turning, drilling and milling processes the analytical stability analysis in the frequency domain is shown. In this case, the effect of tangential or torsional vibrations on the stability of regenerative chatter is considered via an additional frequency response function in the structural model. The effect of vibrations into the cutting speed direction can stabilizing or de-stabilizing with respect to their negligence.