# Identification of Impact Frequency for Down-the-Hole Drills Using Motor Current Signature Analysis
## 4 Discussion  
The analysis of the three proposed methods based on MCSA to identify the impact frequency in DTH drilling systems allows us to establish advantages and disadvantages between them. In some cases, the differences are derived from practical implications, while in other cases, they are related to mathematical limitations. The side bands approach has the most straightforward implementation of the evaluated approaches since it only requires direct FFT analysis of the motor current signal during the SP-stage and calculating the frequency offset difference between the side bands with the fundamental component. However, since additional side bands are expected to appear in the spectrum due to different dynamics, the user must know the rated operational range for the impact frequency of the drilling rig. Moreover, recent works show that, in the case of incipient motor faults, additional side bands can appear close to the frequency components associated with oscillating loads [35; 37], further complicating the separation of the frequency of interest. Compared with the side bands method, the waterfall approach requires the FFT-based algorithms to be performed twice to identify the impact frequency. The first execution is used to construct the waterfall plot (using STFT), and the second execution computes the frequency spectrum of the fundamental component of \(\text{I}_{m}\) extracted from the waterfall  
Figure 12: Frequency spectra of upper envelopes for motor current signal during SP-stage: (**a**) 530 samples for spline interpolation; (**b**) 970 samples for spline interpolation; (**c**) 1200 samples for spline interpolation. plot, from where the impact frequency can be identified. The method is sensitive to the time segment selected for the construction of the waterfall plot, which should be carefully chosen to properly capture the dynamic variations of the current amplitude due to hammer percussion. By capturing these variations, the frequency spectrum of the resulting data array I\({}_{m,fund}\) obtained from the waterfall plot will include frequency content related to the impact frequency. However, the maximum impact frequencies that can be captured by this method are inherently restricted to the Nyquist frequency of the sampling rate used to construct I\({}_{m,fund}\). As explained in Section 3.2, the maximum impact frequency that can be identified in practice will be around half the rated motor frequency. The last evaluated method corresponds to the envelope approach, which uses spline interpolation between local peaks of the motor current amplitude. In this approach, the modulation of the motor current due to the torsional impacts traduced in load torque dynamic variation is detected by applying the FFT to the envelope signals. The method requires the number of samples \(n\) for spline interpolation to be specified as an input parameter, which can be intuitively selected through a preliminary analysis of the current signal. A sensitivity analysis applied for the case study showed that this method is not very sensitive to the choice of \(n\), providing an ample range for the value of \(n\) without degrading the results. The envelope method overcomes the inherent limitations of the side bands and waterfall approaches, providing a simple and effective technique for identifying both the impact frequency and the related motor current amplitude. Future research in this topic will include extensive experimental evaluations using different hammer bits and rock samples within a wide range of compressive strengths to validate the proposed approaches in a wide range of operational conditions.