Robust Chatter Stability Prediction of the Milling Process considering Uncertain Machining Positions

Milling stability is a function of the tool point frequency response functions (FRFs), which vary with the movements of the moving parts within the whole machine tool work volume. The position-dependent tool point FRFs result in uncertain prediction of the stability lobe diagram (SLD) for chatter-free machining parameter selection. Taking the variations of modal parameters to represent the variations of tool point FRFs, this paper introduces the edge theorem to predict the robust milling chatter stability. The application of the edge theorem requires the minimum and maximum modal parameters within the machining space defined by the machining position and machining allowance information. Then, radial basis function artificial neural networks (RBFANNs) are used to predict the position-dependent modal parameters in X and Y directions based on the sample information of machining positions and related modal parameters at the tool point. Moreover, sample machining spaces are determined based on the aforementioned sample positions, and the trained RBFANNs are used to obtain corresponding sample extreme modal parameters. On this basis, RBFANNs for predicting the position and machining allowance-dependent extreme modal parameters can also be trained, and they are combined with the edge theorem and zero exclusion condition to calculate robust pairs of the spindle speed (n) and limiting axial cutting depth (aplim) and then plot the robust SLD (RSLD). A case study was performed on a real three-axial vertical machining center, and the plotted RSLD considering position variations was compared with the traditional SLD. Results of the chatter tests show that the RSLD can provide more reliable (ap, n) pairs to guarantee the milling stability, validating the feasibility of the proposed robust milling chatter stability prediction method