Updated tool path modelling with periodic delay for chatter prediction in milling.

The efficiency of the high speed milling process is often limited by chatter. In order to predict the occurrence of chatter, accurate models are necessary. In most models regarding milling, the cutter is assumed to follow a circular tooth path. However, the real tool path is trochoidal in an ideal case, i.e. without vibrations of the tool. Therefore, models using a circular tool path lead to errors, especially when the cutting angle is close to 0 or pi radians. An updated model for the milling process is presented which features an updated model of the undeformed chip thickness and a time-periodic delay. Furthermore, the stability of the milling system, and hence the occurrence of chatter, is investigated using the traditional and the new model by means of the semi-discretization method. Especially for low immersion cuts, the stability lobes diagram (SLD) using the updated model shows significant differences compared to the SLD using the traditional model.