Strong non-linear dynamics of cutting processes

A strong non-linear dynamic model is developed to investigate the dynamic characteristics of cutting processes. First, the multiple scales method is applied to study the weak non-linear stability, and then the numerical method to solve the problems of strong non-linearity in cutting processes. The former shows that the subcritical bifurcation predicted by the weak non-linear theory is compatible with that predicted by the strong non-linear theory. The numerical study reveals that different cutting thicknesses result in qualitatively different behavior of the finite amplitude instability. Going from small cutting thicknesses to the large ones, the behavior of the finite amplitude instability can be divided into an unconditional stable region, a conditional stable region, a periodic region and a breakdown region. (C) 1997 Academic Press Limited.