On the global dynamics of chatter in the orthogonal cutting model

Zoltan Dombovari (1, 2) , David A.W. Barton (3) , R. Eddie Wilson (3) , Gabor Stepan (1)

1 Department of Applied Mechanics
2 Department of Mechanical Engineering
3 Department of Engineering Mathematics

The large-amplitude motions of a one degree-of-freedom model of orthogonal cutting are analysed. The model takes the form of a delay differential equation which is non-smooth at the instant at which the tool loses contact with the workpiece, and which is coupled to an algebraic equation that stores the profile of the cut surface whilst the tool is not in contact. This system is approximated by a smooth delay differential equation without algebraic effects which is analysed with numerical continuation software. The grazing bifurcation that defines the onset of chattering motion is thus analysed as are secondary (period-doubling etc.) bifurcations of chattering orbits, and convergence of the bifurcation diagrams is established in the vanishing limit of the smoothing parameters. The bifurcation diagrams of the smoothed system are then compared with initial value simulations of the full non-smooth delay differential algebraic equation. These simulations mostly validate the smoothing technique and show in detail how chaotic chattering dynamics emerge from the non-smooth bifurcations of periodic orbits.

Mots clés: Orthogonal cutting; Delay differential equation; Differential algebraic equation; Non-smooth; Chatter; Fly-over

Domaines: Mécanique des solides [physics.class-ph]; Mécanique des solides [physics.class-ph]

Zoltan Dombovari, David A.W. Barton, R. Eddie Wilson, Gabor Stepan. On the global dynamics of chatter in the orthogonal cutting model. International Journal of Non-Linear Mechanics, 2010, 46 (1), pp.330. ⟨10.1016/j.ijnonlinmec.2010.09.016⟩. ⟨hal-00701876⟩