Multi-frequency Chatter Analysis Using the Shift Theorem

During machining, the use of variable helix tools can potentially improve the system's stability to regenerative chatter. However, this configuration of tool has a distributed time delay, which makes the stability analysis more complex. The analysis is further exacerbated by the time-periodic coefficients that occur during milling. The present contribution demonstrates how the Fourier transform and harmonic transfer function approach can be used to analyse the system stability. This provides new insight into the stability of these tools, based on a mathematically elegant approach that makes extensive use of the shift theorem.