Regenerative Chatter is a mechanical vibration phenomenon that occurs in the unstable cutting process between the workpiece and cutting tools, it can produce poor surface quality and cause damage to the spindle system of the machine tool itself. This condition can be avoided by knowing the stability lobe diagram (combination of cutting depth with spindle speed) of the machining system. The stability lobe diagram (SLD) can be obtained by determining the frequency response function (FRF) at the cutting tools point. Basically, FRF measurements are carried out experimentally which are quite complicated and time-consuming, so that they are less efficient in the manufacturing process. Therefore, how to predict FRF analytically is very necessary for machining stability. In this study, we used the analytical method of receptance coupling sub-structure analysis (RCSA) to predict the FRF of the tool-holder assembly with the Timoshenko beam structural model at various lengths of cutting tools. The results show that the prediction accuracy is achieved well, so this method is effective and efficient in the manufacturing process.

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