Chatter instability in milling systems with flexible rotating spindles - Anew theoretical approach

The stability characteristics of a milling system are investigated in this paper. A model is developed that includes the gyroscopic effects of the rot ating spindle and on the basis of this model new insight into the physics o f chatter instability is obtained In the analysis the basic Fourier series method for solving a harmonically time-varying system without time lag is e xtended to obtain a finite-order characteristic equation for the milling sy stem in terms of the system matrices. The complex eigenvalues of the result ing characteristic equation can be efficiently predicted by using Muller's optimization algorithm with deflation, and the stability lobes can be predi cted by using a nonlinear optimization procedure at different rotating spee ds based on the Nyquist stability criterion. In this study it was found tha t including the gyroscopic effects of the rotating spindle increases the re al parts of the eigenvalues of the system. This reduces the critical axial depth of cut. Ii is also found that the milling forces primarily excite the backward-wave modes but stabilize the forward-wave modes of the rotating s pindle.