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 (a_plim) 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 (a_p, n) pairs to guarantee the milling stability, validating the feasibility of the proposed robust milling chatter stability prediction method.

中文翻译：

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考虑不确定加工位置的铣削过程稳健颤振稳定性预测

铣削稳定性是刀尖频率响应函数（FRF）的函数，它随整个机床工作空间内活动部件的运动而变化。位置相关的刀具点FRF会导致不确定凸角图（SLD）的不确定预测，以便选择无颤动的加工参数。以模态参数的变化来表示刀具点FRF的变化，本文介绍了边缘定理来预测鲁棒铣削颤振的稳定性。边缘定理的应用要求在由加工位置和加工余量信息定义的加工空间内的最小和最大模态参数。然后，使用径向基函数人工神经网络（RBFANNs）预测X中与位置有关的模态参数Y方向和Y方向基于加工位置的样本信息和刀具点上的相关模态参数。此外，根据上述样品位置确定样品加工空间，并使用经过训练的RBFANN获得相应的样品极限模态参数。在此基础上，还可以训练用于预测位置和取决于加工余量的极限模态参数的RBFANN，并将其与边缘定理和零排除条件相结合，以计算出可靠的主轴转速对（n）和极限轴向切削深度（一个_{p LIM}），然后绘制鲁棒SLD（RSLD）。在真实的三轴立式加工中心上进行了案例研究，并将考虑位置变化的RSLD与传统SLD进行了比较。颤振测试的结果表明，RSLD可以提供更可靠的（a _p，n）对，以保证铣削稳定性，从而验证了所提出的鲁棒铣削颤振稳定性预测方法的可行性。