The concept of time-varying metal cutting chatter is developed in this paper and the AR and SETAR models based on the segmented time series are introduced to describe the time-variability, which is applied in analyzing the chatter in a type Mx-4 lathe. The emphasis of this work is placed on four aspects: the AR spectrum, the chatter modal damping ratio, the eigenvalues of a time-varying system and the limit cycle for a steady chatter. It is pointed out that, for time-varying chatter, its time interval is quite short compared with ordinary chatter and it will wither away owing to the time-varying parameters of the system. It is also shown that the machine cutting system under steady chatter is still stable and its damping is not equal to zero. The results can well explain the special phenomenon of chatter in Mx-4 lathe and is helpful to the study of time-varying metal cutting chatter.

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