Abstract
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.
Highlights
Milling is one of the major machining processes that can obtain finished products with desired geometry, dimensions, and surface roughness by material removal
The most common self-induced vibration defined as regenerative chatter is a significant obstacle limiting improvements of the production efficiency and processing quality [1,2,3]. e regenerative chatter is caused by the forces generated during the dynamic cutting process and is not dependent on the external periodic forces. e disastrous nature of chatter vibration brings numerous negative effects including poor surface finish, aggravated tool wear, excessive noise, and damages to machine tool components [4, 5]
Altintas and Budak [13, 14] developed a two-degree-of-freedom (2DOF) dynamic model for the milling vibration system and proposed an analytical chatter prediction theory to obtain the stability lobe diagram (SLD) by introducing the Fourier approximation method. As this proposed method was proved to be efficient in obtaining the SLD, it lays a foundation in following milling stability predictions considering various affecting factors
Summary
Milling is one of the major machining processes that can obtain finished products with desired geometry, dimensions, and surface roughness by material removal. Robust milling stability predictions considering the tool point FRF uncertainties have been proposed, but few research studies focusing on the uncertainties caused by machining position variations were addressed [21]. Graham et al and Park and Qin [22, 23] have defined specific changes to modal parameters of the tool point FRFs considering effects of cutting force coefficients, high spindle speed, and so on and combined the edge theorem and zero exclusion condition method to obtain the robust SLD for machining parameter selection. En, at the optimal position, modal parameter variations within the machining space defined by threedirectional machining allowances were determined, and the edge theorem was used to predict the robust chatter-free machining parameters.
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