Study on the construction mechanism of stability lobes in milling process with multiple modes

The stability of milling process dominated by multiple modes was traditionally predicted in the time domain by only selecting the most flexible mode. This paper theoretically studies the construction mechanism of stability lobes by simultaneously considering all dominant modes and provides an efficient method to predict stability lobes of milling systems with multiple modes in the time domain. It is theoretically proved that the effective stability lobes of milling system with multiple modes is made up of the lowest envelop of the stability lobes achieved with each single mode; hence, lowest envelop method (LEM) is established to predict the ultimate stability lobe by taking the lowest envelop of a group of stability lobes, which are calculated by separately considering different dominant modes composing the overall dynamic compliance. Typical advantage of LEM lies in that the computation time and the memory usage required in stability prediction can be greatly reduced for time domain solution. Moreover, the accuracy of prediction can be increased, when the effects of multiple modes are taken into account instead of considering only the most flexible mode. Formulation of the dynamic milling process with multiple modes is derived in semi-discrete time domain by including the effects of multiple delays. A series of simulations and experiments demonstrate the high efficiency and validity of LEM.