An Improved Tool Path Model Including Periodic Delay for Chatter Prediction in Milling

The efficiency of the high-speed milling process is often limited by the occurrence of 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 the 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 $π$ radians. An updated model for the milling process is presented which features a model of the undeformed chip thickness and a time-periodic delay. In combination with this tool path model, a nonlinear cutting force model is used, to include the dependency of the chatter boundary on the feed rate. The stability of the milling system, and hence the occurrence of chatter, is investigated using both the traditional and the trochoidal model by means of the semi-discretization method. Due to the combination of this updated tool path model with a nonlinear cutting force model, the periodic solution of this system, representing a chatter-free process, needs to be computed before the stability can be investigated. This periodic solution is computed using a finite difference method for delay-differential equations. 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. Also the use of the nonlinear cutting force model results in significant differences in the SLD compared to the linear cutting force model.