Micro frequency-shift based spectral refinement algorithm and its application in spectrum analysis during milling process

•A new spectral refinement algorithm named MFS-FFT was proposed.•MFS-FFT perform spectral refinement over the entire frequency axis.•When the refinement multiple is below six, the cost is smaller than that of CZT.•This algorithm has been verified by a spindle speed ramp-up milling experiment. The purpose of spectral refinement is to obtain a finer spectrum structure so as to realize a more accurate spectral measurement. In this paper, a micro frequency-shift based spectral refinement algorithm (MFS-FFT) is introduced. This algorithm can efficiently perform any multiple spectral refinement and achieve the refinement over the entire frequency axis without band selection. Two kinds of micro frequency shifters suitable for this algorithm are discussed. The influence of window functions on this algorithm is also analyzed. Compared with the Chirp Z-transform (CZT), the proposed algorithm can achieve the same accuracy as CZT. Our complexity analysis has shown that when the refinement multiple is less than six, the computational cost is always smaller than that of CZT. A spindle speed ramp-up milling experiment has been performed in order to verify the proposed algorithm. Experimental results show that the MFS-FFT algorithm can effectively improve the accuracy of spectral estimation.