Chatter Instability in Milling Systems with Flexible Rotating Spindles—A New Theoretical Approach

Abstract

The stability characteristics of a milling system are investigated in this paper. A model is developed that includes the gyroscopic effects of the rotating spindle and on the basis of this model new insight into the physics of chatter instability is obtained. In the analysis the basic Fourier series method for solving a harmonically time-varying system without time lag is extended to obtain a finite-order characteristic equation for the milling system in terms of the system matrices. The complex eigenvalues of the resulting characteristic equation can be efficiently predicted by using Mu¨ller’s optimization algorithm with deflation, and the stability lobes can be predicted by using a nonlinear optimization procedure at different rotating speeds based on the Nyquist stability criterion. In this study it was found that including the gyroscopic effects of the rotating spindle increases the real parts of the eigenvalues of the system. This reduces the critical axial depth of cut. It is also found that the milling forces primarily excite the backward-wave modes but stabilize the forward-wave modes of the rotating spindle.