Chatter stability of milling with speed-varying dynamics of spindles

The chatter stability of machine tool is dependent on the dynamic behavior of the spindle system, which is often expressed as the frequency response function (FRF) at the tool tip. The stability lobe diagram generated from stationary FRFs can lead to an inaccurate prediction in high and ultra high speed machining. This paper presents an alternative approach to predict the chatter stability lobes of high-speed milling with consideration of speed-varying spindle dynamics. With a dynamic model of a high-speed spindle system, the speed effects (i.e., gyroscopic moment and centrifugal forces) on both the spindle shaft and bearings are investigated systematically with simulations and experiments. The gyroscopic moment of the spindle shaft can increase the cross FRFs, but can hardly affect the direct FRFs at the tool tip due to the damping of the spindle system. The centrifugal forces on both the shaft and bearings lower the overall spindle system stiffness evidently as the speed increases. The speed-dependent FRFs at the tool tip are obtained from the dynamic spindle model and then integrated into the characteristic equation of the dynamic milling system. Nyquist stability criterion is used to generate the chatter stability lobe of high-speed milling operations. It is shown that the stability lobes with speed effects shift to the low speed range significantly. Finally, milling tests are performed to validate predicted the speed-dependent stability lobe. (C) 2011 Elsevier Ltd. All rights reserved.