Feature extraction of the wear state of a deep hole drill tool based on the wavelet fractal dimension of the current signal

Given that wavelet transform and fractal theory reveal the self-similarity characteristics of objects from macro to micro levels, this study proposes a wavelet fractal dimension (WFD) to extract the fractal dimension feature of the wear state of a deep hole drill bit by using binary wavelet function as the scale. Weierstrass–Mandelbrot fractal functions with different theoretical fractal dimensions are introduced to evaluate the accuracy of WFD. Four methods for defining fractal dimensions are applied to estimate the fractal dimension of the current signal from the spindle motor in deep hole machining processing. Then, the variation law of the estimated value of the fractal dimensions with drill wear is investigated. Results show that the estimated value of WFD presents the smallest error compared with the theoretical value. Moreover, compared with other methods, the WFD of the current signal provides the strongest correlation with drill bit wear, which offers accurate characteristics for the monitoring of tool wear state.