Symmetry breaking in milling dynamics

Regenerative chatter vibrations arising during machining operations are a severe problem affecting the manufacturing production of high-precision mechanical components. A relatively deep understanding of this phenomenon when the cutting tool has equally spaced cutting teeth without runout has been achieved by now. However, real cutting tools are always affected by teeth runout in practical applications. Moreoever, they can be characterized by irregular geometries designed on purpose for enhancing their cutting performance. The most advanced dynamic milling models compute the effective tool-workpiece engagement conditions by taking into account the exact tool geometry and the nominal milling trochoidal kinematics. Nevertheless, they exclude the forced vibrations of the machining system from the stability analysis. In this work a more complete milling model is introduced, which takes into account the influence of forced vibrations on the effective tool-workpiece engagement conditions. By doing so, milling dynamics are linearized around the true steady state solution and a more correct stability analysis is carried out. The dynamic coupling between tool-workpiece engagement conditions and the steady state vibrations may arise even for small tool asymmetries and it gives rise to a kind of spontaneous symmetry breaking mechanism. This yet unexplained physical mechanism may have an important impact on the stability diagrams, as it will be demonstrated theoretically and experimentally in this work.