ON THE SAMPLE STABILITY OF NONLINEAR CHATTER MACHINING

Abstract

This paper is concerned with the determination of sufficient conditions guaranteeing stability of nonlinear regenerative chatter machining subject to a stationary stochastic process of small intensity at a Hopf bifurcation point. The first step in the investigation is the identification of boundaries of linear stability and instability in the parametric plane of the machining model. Next, the conditions for nonlinear sample stability are derived using the mathematical framework of the classical Hopf bifurcation theorem, the center manifold theorem, the integral averaging method and the Lyapunov exponent. Sub- and supercritical bifurcations are established qualitatively. The investigations are analytical and they have been conducted without the assumption of small time delay between successive tool passes.