A Scale Factor-Based Interpolated DFT for Chatter Frequency Estimation

In this paper, a scale factor-based interpolated discrete Fourier transform (IpDFT) algorithm is proposed to estimate the dominant chatter frequency. In practical measurement systems of machining processes, the number of acquired sine-wave cycles (NASCs) is small. Therefore, the significant spectral interference from the negative frequency leads to the degradation of conventional IpDFTs that neglect such interference. The proposed IpDFT algorithm overcomes this problem by completely removing the long-range leakage of the negative frequency of the investigated component. We establish statistical properties of the approach contaminated with white noise, including upper and lower bounds of the theoretical variance. The simulation results demonstrate that our IpDFT algorithm outperforms existing IpDFT algorithms, especially when the NASC approaches zero. The proposed IpDFT algorithm has better antinoise capability and computational efficiency than the optimization-based algorithm by Radil. Furthermore, it is illustrated that the simulation results agree well with upper and lower bounds of the theoretical variance. Cutting force signals are collected to evaluate the algorithm experimentally.