Abstract
Abstract Unstable vibrations (Chatter) during machining operations is caused by the flexibility of various components of the machine tool or the workpiece, which can be stationary and symmetrical or rotating and non-symmetrical. Therefore, the structural dynamics of machining systems are best described by Linear Time Periodic (LTP) systems, but the existing solutions of chatter use Linear Time Invariant (LTI) descriptions of the machine tool dynamics. This paper presents an update to the widely used Multi-Frequency Solution of regenerative chatter by modelling the machine tool dynamics as a LTP system. The stability of the LTP system is then determined by utilizing the concept of Harmonic Transfer Functions (HTF) and Nyquist stability criterion. The presented method provides a unified solution to determine the stability of vibrations in both stationary and rotating coordinate frames, regardless of the stationary or rotating nature of the vibration modes. The accuracy of the presented approach is verified by comparing the predicted stability diagrams with the results of Multi-Frequency Solution, Semi-Discretization Method, and with experimental results.
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