Transient Vibration Analysis Method for Predicting the Transient Behavior of Milling With Variable Spindle Speeds

Variable spindle speed (VSS) technique is widely adopted for its effective suppression of chatter. However, heavy transient vibrations occur in practical machining operations although the stable machining parameters are selected according to the asymptotic stability analysis methods. In this paper, this problem is addressed through establishing a transient vibration analysis method to predict the transient behavior of VSS milling. Firstly, the discrete dynamical map of VSS milling is constructed, and the response to initial conditions (RTICs) and the response to external forcing (RTEF) can fully describe the general milling dynamics. On this basis, two transient vibration growth phenomena are found and proved that strong transient vibrations are induced by the transient growth of RTIC or RTEF. To fully predict the transient vibration growth phenomenon, the proposed method adopts the transient stability and receptivity analyses to evaluate RTIC and RTEF, respectively. Other than the existing methods, it gives a stability criterion based on both eigenvalues and nonnormal eigenvectors and considers the transient behavior to external excitation. Besides simulations, a real milling test in an existing work and VSS milling experiments are adopted for verification. The results show good agreement with the prediction of the proposed method.