Abstract
The stability properties of cutting processes are strongly limited by the so-called regenerative effect. This effect is originated in the presence of a time-delay in the dynamical system of the machine tool. This delay is inversely proportional to the cutting speed. Consequently, conventional cutting with a single-edge tool is modeled by an autonomous delay-differential equation (DDE). In case of milling, the varying number of cutting edges results in a kind of parametric excitation, and the corresponding mathematical model is a non-autonomous DDE. In case of low-immersion milling, this affects the stability boundaries in a substantial way. Cutting with varying spindle speed results non-autonomous DDEs where the time delay itself depends on the time periodically. A new semi-discretization method is proposed to handle the stability of these non-autonomous systems. The stability properties and corresponding bifurcations are compared in the above different cases of machining.
