Despite recent advances and improvements in modeling and prediction of the dynamics of the machining process, an efficient machining process is limited due to chatter and instability of machining system. In fact, the machining system contains various kinds of joints, which cause difficulties in dynamics modeling, simulation and prediction. Moreover, the flexible support system results in large deformation and violent vibration of the workpiece when machining, and the thin-walled workpiece easily gives rise to the chatter of the machining system. Therefore, the dynamics of the flexible support system was considered to calculate stability lobe diagram in the modeling of milling process. The whole machining system was regarded as a closed loop composed by the machine tool structures, support, workpiece and machining process. In this paper, the receptance coupling (RC) method was introduced to predict the dynamics of the closed machining system. A milling process was taken for example to predict the chatter limitations using the dynamics of closed model. The mathematical model of the machining system (machine tool structures, spindle, holder and tool), together with the details of joint contacts, was given based on the RC method. The RC model was used to obtain the dynamics of the system, while receptance of the tool point was coupled. Based on the coupling model of the machining system, the depth limitations under different speeds were estimated for the technology parameter optimization in milling process. The response was considered to be the sum of the cutting point and the support system. The flexibility of the support system was considered to be the feedback of the cutting stiffness. By this means, the traditional model was modified to calculate the stability lobe diagram based on the dynamics of the spindle and support system. Furthermore, the milling experiment was carried out to verify the prediction results, and the dominant natural frequencies of receptance at tool point were obtained by modal testing to define the stability lobe diagram. It was found that the chatter results matched well with the stability lobes. It was concluded that the support system with poor stiffness might cause violent chatter especially when the workpiece was thin-walled. The cutting depth limitations of the flexible support system were lower than that of the rigid one. Moreover, this closed model of the machining system is appropriate for the chatter prediction of the flexible support system or thin-walled workpiece, so it is helpful for a better parameter optimization.

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