Non-Normal Dynamic Analysis for Predicting Transient Milling Stability

Abstract

A transient milling stability analysis method is presented based on linear dynamics. Milling stability is usually analyzed based on asymptotic stability methods, such as the Floquet theory and the Nyquist stability criterion. These theories define stability that can return to equilibrium in an infinite time horizon under any initial condition. However, as a matter of fact, most dynamic processes in milling operations occur on a finite time scale. The transient vibration can be caused by some disturbance in practical milling process. Heavy transient vibrations were observed in existing works, though the machining parameters were selected in the stability zone determined by the asymptotic stability method. The strong transient vibrations will severely decrease the machining surface quality, especially for small workpieces in which the majority of machining process is executed in a short period of time. The analysis method of the transient milling stability is seldom studied, and only some experiments and conjectures can be found. Here the transient milling stability is defined as transient energy growth in a finite time horizon, and the prediction method of transient stability is proposed based on linear dynamics. The eigenvalues and non-normal eigenvectors of the Floquet transition matrix are all used to predict the transient milling stability, while only eigenvalues are employed in the traditional asymptotic stability analysis method. The transient stability is finally analyzed by taking the maximum vibration energy growth and the maximum duration time of transient energy growth in a finite time for optimal selection of processing parameters.